Mathematics doi: 10.3390/math14213864

Authors: Junping Li

This paper investigates cumulative reward functionals for birth–death processes with Poisson-driven total catastrophes. Using an auxiliary killed Markov process, we derive the integral equations for the distribution and expectation of the reward accumulated up to the first catastrophe, and establish the existence and uniqueness of bounded solutions. Explicit expressions are provided for constant birth–death rates. The asymptotic limits of the scaled expected reward are analyzed for vanishing and diverging catastrophe rates, with limiting behavior classified by the recurrence of the underlying catastrophe-free birth–death process.

Mathematics doi: 10.3390/math14213863

Authors: Najwa Mohammed Al-Asmari Rawan Bossly Mohd Danish Siddiqi

The study of hyperbolic Ricci solitons and hyperbolic Yamabe solitons on Riemannian concircular structure manifolds is the main focus of the current research. We derive the expression of the Ricci curvature and scalar curvature of Riemannian concircular structure manifolds admitting hyperbolic Ricci solitons. Also, we show that the rate of change of hyperbolic Ricci solitons on Riemannian concircular structure manifolds is shrinking. Moreover, we discuss the nature of hyperbolic Ricci solitons and critical value and singular point on Ricci pseudo-symmetric Riemannian concircular structure manifolds, concircular pseudo-symmetric Riemannian concircular structure manifolds, projective pseudo-symmetric Riemannian concircular structure manifolds and conharmonic pseudo-symmetric Riemannian concircular structure manifolds. Lastly, depending solely on the rate of these solitons, we investigate certain applications in terms of modified second hyperbolic Yamabe solitons and modified second hyperbolic Ricci solitons.

Mathematics doi: 10.3390/math14213862

Authors: Xiu Shu Xinming Zhang Di Yuan

Accurate medical image segmentation and the diagnostic decisions it supports are increasingly constrained by the cost of supervision: dense voxel-level annotation by expert clinicians remains slow, expensive, and difficult to scale, leaving many anatomies, pathologies, and modalities sparsely labeled. A large literature therefore relaxes the demand for full masks, yet existing surveys often catalog broad forms of limited supervision without directly comparing the practical trade-off between label granularity, annotation burden, and segmentation quality. This review focuses on weakly and coarsely labeled settings (image-level tags, points/clicks, bounding boxes, scribbles, and coarse masks, together with gaze or partial annotations as separate, protocol-dependent forms of supervision) and organizes them through an annotation-economics perspective that considers per-case annotation cost, required expertise, scalability, and the reported performance gap relative to full supervision. The evidence suggests that box and scribble supervision can provide favorable cost–performance trade-offs in several medical segmentation studies, although the reported metrics and datasets are heterogeneous and should not be interpreted as a unified quantitative frontier. We next examine the foundation-model turn, namely the Segment Anything Model and its medical derivatives, and argue that promptable models re-encode rather than eliminate human supervision, moving part of the effort from offline labeling to inference-time interaction. Finally, we extend the analysis beyond Dice to ask whether weakly produced masks support downstream clinical tasks: aggregate measurements may be relatively tolerant of moderate boundary error, whereas texture and high-order radiomic features can be substantially more sensitive. We close by identifying benchmark fragmentation, annotation variability, and the still-limited evidence connecting weak segmentation to clinical outcomes as open problems and propose a unified “weak label → task” benchmark for future evaluation.

Mathematics doi: 10.3390/math14213861

Authors: Zhengchang Jin Wei Wang Lin Zhang Wenjuan Guo

The release of Wolbachia-infected mosquitoes is an environmentally friendly and effective strategy for suppressing wild mosquito populations. This paper investigates the finite-time stability of a class of impulsive reaction–diffusion mosquito population suppression models. Taking into account impulse intensities, diffusion coefficients, and birth rates, we establish sufficient conditions for the finite-time stability of both delay-free and delayed systems and provide rigorous theoretical analyses. Numerical simulations validate the theoretical results and demonstrate the effectiveness of impulsive control in achieving finite-time stability for both systems.

Mathematics doi: 10.3390/math14213859

Authors: Zahra S. Hafed Ashraf M. Zenkour

The formulation of effective (true) static stress acting on a deformed surface is based on well-established principles of continuum mechanics. In this study, the solid is expected to be exposed to a uniform static uniaxial stress field. By accounting for second-order stress-strain interactions, a modified set of elastic motion equations is obtained, which incorporates the influence of static surface forces and body forces on elastic wave propagation in isotropic media. The thermal response is modelled using the generalized heat conduction equation within the modified Lord–Shulman magneto-thermoelastic framework, augmented by a higher-order time derivative of order N. The resulting coupled system of governing partial differential equations is explained by assuming harmonic wave forms and employing the method of separation of variables. This formulation enables a systematic examination of magnetothermoelastic wave propagation and the corresponding stress behaviour of the solid, with particular emphasis on the role of the operator order. A comprehensive numerical analysis is carried out to examine the spatial and temporal variations of temperature, displacements, dilatation, and stress components. The results demonstrate that operator order N has a pronounced influence on the thermoelastic response: larger values of N significantly reduce thermal oscillations and enhance the decay of thermal disturbances, while the limiting case N → ∞ produces the smoothest and most stable temperature distribution.

Mathematics doi: 10.3390/math14213860

Authors: Pooja Gokul Joshi Gopal Kumar Gupta Maria Luminita Scutaru Sorin Vlase

Bulk service queueing systems such as M/Mb/1/N and M/Mb/c/N, which are characterised by multiple servers c, fixed batch-size service b, and finite capacity N, indicate the performance measures that are numerically derivable but mathematically complex to evaluate across various parameter ranges. This study addresses that challenge by applying the Michaelis–Menten (M-M) regression model, originally formulated for enzyme kinetics, as an empirical substitute for these measures. The steady-state probabilities are obtained by forming the generator matrix Q, which is solved via LU decomposition process. This yields the exact expressions for average queue length Lq, average system length L, average waiting time Wq, effective arrival rate λeff, blocking probability pblock, and server utilisation. Identifying the inherently saturating, nonlinear relationship between these performance measures and the traffic intensity ρ, the M-M kinetics regression model, originally evolved for enzyme reaction rates, is utilised as an empirical substitute for capturing saturating behaviour. Levenberg–Marquardt, a non-linear least-squares regression algorithm, is used for estimating model parameters Vmax and Kmax. The fitted M-M model signifies excellent agreement with the exact solutions solved by using LU decomposition across a wide range of system configurations, with the coefficient of determination R² reaching as high as 99.5%. Beyond accuracy, the regression-based approach offers substantial computational efficiency over complex numerical evaluation, making it attractive for rapid system design and optimisation. Results establish Michaelis–Menten regression as a feasible non-linear regression approach for bulk queueing analysis, spanning classical queueing theory and modelling approaches. It offers practical applications for improving decision-making in the analysis of congestion, capacity optimisation, and dynamic resource allocation, which arise frequently in transportation networks, cloud computing job schedulers, and manufacturing assembly lines.

Mathematics doi: 10.3390/math14213858

Authors: Yue Zhang Zifei Liu Yujin Lv Guanghao Liu

This paper develops an identification-based implementation of zero-sum tracking control for a linear composite plant with an unmeasured shared disturbance. Weak-form regression estimates unknown coefficients from sampled states, the applied input, and a known reference, with an instrumental-variable projection compared against ordinary weak least squares. A common identified model supplies the regulator equations and a full-system game Riccati equation retaining both disturbance channels. A square-completion identity gives the exact-model saddle interpretation under explicit admissibility conditions. A separate uncertainty-dependent stability margin and tracking bound retain the effect of reference mismatch. Two simulation models are tested under five disturbance laws, recording noise, parameter changes and weak excitation. A deterministic tracking adaptation of a recent two-loop game-PI algorithm is additionally implemented, with its required extra disturbance record. It achieves more accurate noiseless gains, while IV-game passes 80/80 paired noisy-trial screens versus 35/80 for this comparator under the specified protocol. Warm, paired offline timings are also reported. The unequal sensor information, supplied initial policies and rejected candidates are explicitly documented. These results support the stated acquisition protocol, but not exact identification under arbitrary hidden disturbances, universal superiority, or hardware real-time guarantees.

Mathematics doi: 10.3390/math14213854

Authors: George Livadiotis

The paper develops the mathematical expressions of momentum and energy as functions of speed within the framework of relativity with synchronization-induced anisotropy, using the invariant contractions of the velocity and momentum four-vectors. This form of anisotropy arises from the freedom in choosing the synchronization convention for distant clocks. In that case, the one-way speeds of light in opposite directions need not be equal, although the measured round-trip speed remains invariant. Einstein’s special relativity appears as the symmetric limit of a broader relativistic framework based on asynchronous synchronization. In Einstein’s isotropic relativity, the dependence of momentum and energy on speed is governed by the Lorentz factor, which approaches unity in the low-speed limit, u << c. However, it is shown that these expressions are invariant with respect to the synchronization anisotropy parameter, namely the governing equations remain structurally invariant, regardless of the value of the anisotropy parameter. We then extend the analysis to a relativistic framework formulated with complex four-vectors and repeat the derivation for complex anisotropy. Remarkably, the same momentum and energy relations as functions of speed are recovered, exactly as in Einstein’s isotropic theory. Hence, the resulting expressions remain independent of the synchronization convention, even when the synchronization anisotropy parameter is allowed to take complex values.

Mathematics doi: 10.3390/math14213857

Authors: Young Eui Min Man-Je Kim

Model-based fault diagnosis narrows down fault candidates by checking the consistency between a mathematical model of the plant and the measurements. Depending on the sensor configuration and the system structure, however, different faults may share an identical residual signature. In such cases, the diagnosis keeps the true fault inside the candidate set but cannot single it out, and this structural indistinguishability is not resolved by tuning thresholds or post-processing the residuals. This paper proposes a method that reuses the diagnostic model on the candidates left by the existing diagnosis in order to rank them. Assuming each candidate to be the true fault and propagating the model forward yields predictions whose comparison with the actual measurements exposes temporal differences that the residual signature does not carry. A limited computational budget is distributed over several candidates so that the comparison is well defined, and the weight given to the two sources of information is adjusted according to how confident the existing diagnosis is. On a three-tank fault diagnosis benchmark, the probability assigned to the true fault at instants where the existing diagnosis selected a different candidate increased from 0.2547 to 0.6735; the isolation accuracy over the three faults sharing an identical residual signature improved from 31.5% to 52.7%; and the accuracy over all seven faults improved from 59.4% to 76.7%. On that benchmark, learning-based methods taking the same residuals as input did not exceed 0.30 on the indistinguishable set even with 512 samples per fault, whereas the proposed method uses no fault data at all. On a second benchmark, an electric motor, the same procedure raised that probability from 0.3523 to 0.7110. Across twelve combinations of fault magnitude and process noise, the method was never below the existing diagnosis, although the gain exceeded 0.34 only in the six where the fault magnitude was at least 12.5 times the process noise standard deviation.

Mathematics doi: 10.3390/math14213856

Authors: Bosen Yang Chao He

Investment capacity couples startup–investor recommendations, but independent scoring and ranking ignores this coupling, repeatedly recommending a few investors. We formulate quarterly matching as capacity-constrained entropic optimal transport and propose CapTHG. A relation-specific heterogeneous attention encoder processes causal quarterly snapshots of a temporal heterogeneous graph, and a differentiable Sinkhorn layer converts its scores into a capacity-feasible transport plan. A dustbin handles upper-bound capacities, training is end-to-end with a plan likelihood loss, and an activity-based proxy from a recent window estimates capacity. We characterize the capacity-feasible set with the dustbin score as a retention threshold, derive the linear programming limit and error bound as regularization vanishes, and prove linear convergence and a gradient equal to the plan. In a quarterly rolling evaluation on real financing rounds from a public Crunchbase snapshot, CapTHG attains the highest round-level recall and normalized discounted cumulative gain among all baselines. For every encoder, capacity-constrained Sinkhorn ranking lowers capacity overload and raises investor coverage versus score ranking. Accuracy also improves only under joint training with the plan. Capacity and plan likelihood loss contribute most in the ablation study; results are stable across capacity definitions and candidate sets. Controlled numerical experiments agree with the theory, supporting transport-based capacity-constrained matching.

Mathematics doi: 10.3390/math14213855

Authors: Juan Carlos González-Aguirre María Fernanda Jiménez Gamaliel Blé Rafael Martínez-García Carlos Alfonso Álvarez-González Alam Yair Hidalgo

In this work, Bayesian estimation is performed for the parameters of a mathematical model, formulated as a system of ordinary differential equations, that describes cannibalism dynamics in larval populations of Atractosteus tropicus reared in a pond. The model divides the population into three subclasses: vulnerable, cannibalistic, and non-vulnerable individuals. Parameter estimation is conducted under two scenarios: a fed population and an unfed population. Correlation matrices are calculated for both cases. For the fed population, the most influential parameters are food quality and the time devoted to managing cannibalistic individuals. In contrast, for the unfed population, the strongest correlation occurs between the mortality rate and the transition rate of cannibalistic individuals to the non-vulnerable class. Therefore, providing larvae with high-quality food substantially reduces cannibalism and the handling time required and, consequently, increases the survival of the species.

Mathematics doi: 10.3390/math14213853

Authors: Prabu Radhakrishnan Soumyendra Singh Dharminder Chaudhary Cheng-Chi Lee

This paper presents a Radial Basis Function Neural Network (RBFNN) that approximates the vector field of a four-dimensional prey–migration–predator–superpredator ecological model with prey refuge, considered in deterministic and stochastic formulations. The network is trained directly on the governing equations without the need for any simulated trajectories for training. The network learns the deterministic vector field, and hence analytical verification is carried out for the deterministic model, with a proof of global existence of the solution, a proof of the boundedness of the solution, a classification of five equilibria via the Jacobian matrix, and a proof of local exponential stability of the coexistence equilibrium via a Lyapunov function. The RBFNN is validated by comparing its trajectories to those of the RK45 solver, checking its long-term behavior, performing phase-space analysis, and computing the eigenvalues of the equilibrium and Jacobian of the learned field. For the stochastic formulation, the learned drift is added with explicit noise terms and is compared with the Euler–Maruyama and Milstein methods using a finer-step Milstein method as a reference. The numerical results presented here establish that the RBFNN can be used as an alternative to a deterministic vector field in standard numerical solvers, and that the framework can be used to compare the computational efficiency of the vector field evaluation in more complex dynamical systems where the field evaluation is more costly.

Mathematics doi: 10.3390/math14213851

Authors: Ya Li Gufeng Gong Mingfang He

Detection of abnormal campus behavior is challenging because abnormal targets often exhibit large scale variations, small spatial extensions, frequent occlusions, complex background interference, and strong dependencies on relative spatial relationships. To address these issues, this study proposes SCE-YOLO, a campus-based abnormal behavior detection framework built on YOLO11n. The framework is designed from three complementary computational perspectives: spatial-frequency representation enhancement, dynamic spatial relationship modeling, and efficient multi-scale feature reconstruction. First, a C3k2-SFEM module is introduced to jointly model local texture information, directional edge responses, and global frequency components, thereby improving the representation of fine-grained abnormal cues, low-contrast targets, and irregular structures. Second, a C2DPB module incorporates Dynamic Position Bias into the attention mechanism, enabling feature interactions to be jointly determined by semantic similarity and relative spatial geometry. This design strengthens the modeling of human poses, target interactions, and long-range contextual dependencies under crowded and occluded conditions. Third, an Efficient Up-Convolution Block (EUCB) is embedded in the neck to reconstruct high-resolution spatial information through lightweight upsampling, depthwise convolution, and channel interaction, reducing boundary blurring and detail degradation during multi-scale feature propagation. In addition, the Campus Abnormal Behavior Detection Dataset (CABDD) constructed contains five representative abnormal-event categories, covering diverse viewpoints, target scales, illumination conditions, and occlusion levels. Experimental results show that SCE-YOLO achieves a Precision of 85.6%, a Recall of 71.7%, an mAP50 of 77.0%, and an mAP50:95 of 55.6% on CABDD, representing improvements of 4.5, 4.7, 4.6, and 4.1 percentage points, respectively, over the YOLO11n baseline. These results demonstrate that jointly enhancing feature representation, spatial interaction modeling, and multi-scale reconstruction can effectively improve abnormal-target recognition and localization in complex campus surveillance scenes.

Mathematics doi: 10.3390/math14213852

Authors: Jeong Woo Seo Ho-Young Jung

Multimodal large language models (MLLMs) process an interleaved image–text sequence with a single autoregressive backbone under causal attention. Since the causal mask prevents image tokens from attending to the question that follows them, their representations are computed without access to the query, which has been identified as a source of visual hallucination. Modality-mutual attention (MMA) mitigates this issue by unlocking the image-to-question region of the causal mask, and dual-order training (DOT) mitigates it by additionally training on the reversed text-first order. However, MMA turns the global causal mask into a sample-dependent dense mask. Consequently, attention cannot be executed via FlashAttention, which is the most efficient attention path, and falls back to a slower implementation. Furthermore, the positional information in the unlocked region does not match that of the reversed input order that motivates the unlock, that is, the positional semantics are inconsistent. To address both problems, we propose FlashAttention-compatible MMA with virtual reordering (FMMA-VR), which repairs the positional information of the unlocked region as if the two modalities were reordered, without physically reordering the sequence. The proposed method is implemented as a Triton-based region-aware FlashAttention-style kernel. On identically pretrained models, it accelerates the attention path by up to 3.59× over conventional MMA for long sequences during supervised fine-tuning (SFT). In post-SFT evaluations, it stays on par with conventional MMA across ten benchmark metrics under full fine-tuning. Under low-budget LoRA adaptation, where the positional shift of conventional MMA is not absorbed, FMMA-VR additionally improves the hallucination-sensitive metrics by large margins.

Mathematics doi: 10.3390/math14213850

Authors: Garnik V. Abgaryan Yury V. Shestopalov

We analyze parameter dependence of the complex resonance frequency (RF) spectrum of the nonselfadjoint boundary-value problems associated with a mathematical model of the resonance scattering by an infinite dielectric cylinder. The notions of spectral mapping and spectral set are introduced and applied to solve the addressed problem. A particular focus is toward RF evolution with respect to the varying complex refraction index, visualization of spectral sets, and developing robust methods aimed at the RF calculation and determination of spectral sets.

Mathematics doi: 10.3390/math14213849

Authors: Haifei Yang Ganwei Cai Junjie Gong Yu Long

Emergency delivery by multiple unmanned aerial vehicles (UAVs) requires scheduling decisions that account for demand accumulation, payload-dependent energy consumption, and the feasibility of successive sorties. To address this coupled problem, this paper proposes an energy-aware discrete black-winged kite algorithm with local search and insertion screening (EDBKA-LS-I). The model minimizes cumulative unmet demand exposure subject to payload, battery, return energy, and mission time constraints. Payload-dependent energy is calibrated from public flight records, and a sufficient speed dominance condition supports preprocessing under no-wait landing delivery. Geometric and random screening select insertion candidates for complete evaluation, while bounded local search refines UAV assignments, the sortie order, and customer sequences. Nine synthetic and public layout-derived instances were tested with twenty seeds per method under matched evaluation budgets. Three instances were additionally tested with five seeds per method under a six-second search budget. Relative to adaptive large neighborhood search with identical screening, EDBKA-LS-I reduced the mean cumulative unmet demand exposure by 7.74% and 7.93% under the respective budgets. EDBKA-LS-I also obtained lower mean exposure than variable neighborhood search on seven of nine instances under the evaluation budget. EDBKA-LS-I achieved complete service in all main comparisons. The energy model attained a mean absolute prediction error of 0.993 Wh on forty held-out delivery flights.

Mathematics doi: 10.3390/math14213848

Authors: Shengjiang Xu Liwei Wang Long Tian Yinming Zhong Junshan Wang Wei Guo Haotian Zhang

Multi-view clustering has emerged as a powerful approach to geological facies characterization because it can integrate heterogeneous well-log sequences. However, real-world well-log data are susceptible to severe localized environmental disturbances, such as borehole collapse. Moreover, conventional pairwise graph methods fail to capture the inherent high-order semantic correlations in sequential petrophysical data, whereas standard tensor methods indiscriminately retain high-frequency structural noise. To address these limitations, we propose Smooth Tensor Multi-View Clustering on Well Logs via Hypergraph Topology and Concurrent Group Sparsity (HTCGS). First, HTCGS introduces a source-view hypergraph topology-injection mechanism that propagates high-order geological manifold structures across heterogeneous modalities, thereby enabling robust geometric prealignment. Second, it employs a cross-view concurrent joint-group-sparsity regularizer that uses an ℓ2,1-norm penalty to separate localized anomalies into an explicit cross-view error matrix, thereby preserving the latent subspace. Finally, HTCGS applies the Smooth Tensor Nuclear Norm (STNN) to the purified latent features, which acts as a low-pass tensor filter to extract global consensus information reflecting macroscopic geological continuity. The resulting unified objective is efficiently optimized using the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on five benchmark datasets, comprising four well-log datasets and one seismic-facies dataset, show that HTCGS outperforms six recent representative multi-view clustering baselines.

Mathematics doi: 10.3390/math14213847

Authors: Anthony Sofo

In the original publication [...]

Mathematics doi: 10.3390/math14213846

Authors: Ionuţ-Orlando Grigore-Atimuţ Călin-Adrian Popa

We propose JEPADepth, a self-supervised monocular depth estimation framework that augments photometric view synthesis with an auxiliary masked-prediction loss computed in the representation space of a pretrained DINOv3 Vision Transformer (ViT), following the Image Joint-Embedding Predictive Architecture (I-JEPA) principle. A predictor infers target-region embeddings from visible context-region embeddings under structured masking; the predictor and target encoder are discarded at inference, so the deployed 24 M-parameter model costs no more than the photometric-only baseline. On the KITTI Eigen split, adding the JEPA objective to an identical DINOv3 photometric baseline lowers absolute relative error from 0.105 to 0.101 and raises δ1 from 0.891 to 0.898, a gain roughly four times the run-to-run standard deviation measured over five random seeds. On the improved ground truth, it reaches 0.075 absolute relative error, matching the best transformer competitor while using 11% fewer inference parameters. Under zero-shot transfer without fine-tuning, it obtains the best absolute relative error on Make3D (0.275) and ties the best on Cityscapes (0.143) while leading on five of seven metrics. Training overhead is ∼16%; inference cost is unchanged.

Mathematics doi: 10.3390/math14203845

Authors: Xiyan Li Bo Liang Zhengjie Deng

Reversible data hiding (RDH) in structured images remains challenging: most deep-learning methods target natural images, where distortions can be spread across the entire picture. When the carrier contains functionally critical regions—the finder and alignment patterns of a QR code, for instance—a uniform allocation of distortion directly hurts machine readability and, as a result, reversibility. This paper presents AR-WeNet, a structure-aware reversible data hiding framework for images with rigid functional structures. It brings together two components: (1) a Regulatory Information Encryption Module (RIEM) that turns a structured regulatory record into an encrypted binary pattern through UTF-8 encoding, QR error-correction coding, and Arnold scrambling; and (2) a DWT-domain invertible neural network backbone enhanced by Multi-Scale Wavelet Subband Attention (MSWA). A region-adaptive embedding (RAE) strategy, steered by a predefined structural weight map, concentrates embedding distortions in redundant data modules while leaving functional modules intact. On the self-constructed E-Voucher-500 benchmark, AR-WeNet reaches 63.29 dB PSNR, 0.9999 SSIM, a 0.000% pre-correction bit error rate, and 100% exact QR decoding success—an 8.00 dB improvement over the uniform-weighting WeNet baseline. Robustness tests under JPEG compression, Gaussian noise, and cropping confirm resilience at both the bit level and the decoding level. On DIV2K, the INN backbone achieves 55.27 dB, surpassing HiNet by 10.41 dB, showing that the design extends beyond structured images to natural-image hiding.

Mathematics doi: 10.3390/math14203844

Authors: Domagoj Kovačević

We develop an explicit operator and coefficient calculus for admissible (g,K) modules of SU(2,2), where g=sl(4,C) and K=S(U(2)×U(2)). The K-types are indexed by triples (n,k,m). We introduce operators Aδ and Bδ associated with the noncompact roots, together with auxiliary operators Q and R, and establish their commutator relations, central coefficient relations, and, in the unitary setting, adjoint and norm identities. For multiplicity-one K-types, these results reduce part of the analysis to scalar coefficients arising from compositions such as AδBδ and BδAδ. We derive explicit coefficient relations and necessary sign restrictions and analyze families according to the minimal value N of n+m. For N=0, the coefficient system has a two-parameter structure and exhibits natural reducibility boundaries when certain coefficients vanish. For N>0, the method yields both larger K-type patterns and multiplicity-free ladder-type patterns. The resulting K-type patterns agree with those occurring in the known classification of the unitary dual of SU(2,2), although a complete comparison, including reducibility phenomena, is beyond the scope of the present paper. The coefficient calculus provides an explicit framework for studying unitary (g,K) modules through their K-type structure.

Mathematics doi: 10.3390/math14203842

Authors: Yue Su

We propose a latent Ornstein–Uhlenbeck (OU)-driven log-ARCH model in which a continuous-time stochastic factor governs the volatility level while a sparse lag structure captures volatility feedback. The OU process is discretized exactly, yielding a linear Gaussian state transition, while the log transformation produces a linear state-space representation with a non-Gaussian observation disturbance. We therefore employ a Gaussian quasi-likelihood based on the Kalman filter. A two-stage procedure is developed: an existence-based pilot screening rule first identifies the active lag set with probability approaching one under explicit pilot approximation and pseudo-true separation conditions, after which the finite-dimensional structural parameters are estimated by Gaussian quasi-maximum likelihood. Under a fixed sampling interval and long-span asymptotics, and under the stated identification, mixing, and score central limit conditions, we establish consistency and asymptotic normality of the structural estimator. For the latent state, we do not claim N−1/2 convergence; instead, the Gaussian quasi-smoother covariance converges to a non-degenerate steady-state limit. Monte Carlo experiments distinguish the theorem-aligned fixed-threshold screening rule from a practical sign-flip calibration device. An enlarged experiment with M=1000 replications documents substantial contraction of the median bias and interquartile range of the mean-reversion estimator as the sample size increases, although a residual upper tail remains at moderate sample sizes. The screening experiments show improving support recovery when the pseudo-true separation condition is favorable and deterioration in more difficult designs with weaker ARCH signals. Sensitivity analyses examine alternative maximal lag orders and kernels, and a standardized Student-t8 experiment is reported strictly as a misspecification diagnostic rather than as evidence for the Gaussian-theory statements.

Mathematics doi: 10.3390/math14203843

Authors: Fatimah Alghamdi Álvaro Antón-Sancho Samer R. Yaseen

First-type L-fuzzy rough approximation operators have so far been studied relative to a single L-fuzzy relation on a universe of discourse, an assumption at odds with the way multi-source, multi-sensor, and multi-granular information systems are actually modelled. This paper analyses their aggregation over an arbitrary indexed family of relations, combining the individual upper approximations by pointwise infimum and the individual lower approximations by pointwise supremum. We show that this meet/join rule is the unique aggregation mechanism compatible with a natural conservative axiom system, and we exhibit, on an explicit finite completely distributive lattice, a family of relations whose aggregated operators cannot be reproduced by any single relation. This is an existence result: a second example on the three-element chain shows that the phenomenon is not peculiar to one lattice, while on the two-element Boolean lattice every pair of relations on a two-point universe turns out to be representable, so our examples do not establish non-representability on every completely distributive lattice. This non-representability turns out to be an operator-level phenomenon: the associated fixed-point systems can coincide with those of a single, universal relation even when the operators themselves do not, so that representability at the level of operators and at the level of fixed points are logically independent properties. We further establish the monotonicity bounds satisfied by the aggregated operators under arbitrary unions and intersections of inputs, and show by a finite counterexample that complete distributivity of the underlying lattice does not strengthen these bounds into equalities. Building on these operator-level results, we identify explicit conditions under which the fixed-point system of an aggregated operator forms an Alexandrov fuzzy topology, exhibit a family whose fixed-point system is strictly richer than that of a specific single relation, and delimit the separation and connectedness properties that such fixed-point systems may or may not inherit from their constituent relations. Finally, we use the aggregated operators for three-way decisions and compare them with output averaging and relation-level fusion through a worked example, a sensitivity analysis and a simulation study. Among all rules that aggregate the outputs of the sources internally, the conservative rule defers the fewest objects, for the minimum and maximum it never commits against the object’s own evidence when the thresholds lie on either side of 1/2, and its price is that it inherits the errors of every source.

Mathematics doi: 10.3390/math14203841

Authors: Yifan Liu Xinxin Wang

Efficient subsidy allocation for heterogeneous community-based elderly care services requires identifying latent service demand and optimizing service providers’ responses under fiscal constraints. To address this problem, this study develops a data-driven Stackelberg game framework for demand-aware subsidy optimization. The framework transforms unstructured user-generated reviews into empirical demand-priority weights through Latent Dirichlet Allocation (LDA) topic modeling and incorporates these data-derived parameters into a budget-constrained Stackelberg game to optimize differentiated subsidy decisions. A total of 11,257 elderly care-related reviews from e-commerce platforms were collected and refined into 3907 valid samples. Six major service needs were identified: Daily Living Care, Meals and Nutrition, Smart Safety Monitoring, Medical Assistance, Professional Nursing, and Home Rehabilitation. These demand weights were incorporated into the optimization model to characterize heterogeneous service priorities and determine equilibrium subsidy decisions. The numerical experiments show that differentiated subsidies substantially improve demand-weighted service coverage compared with demand-unaware allocation under the same fiscal constraint. At a budget of RMB 300,000, the demand-aware model achieves a demand-weighted coverage of 0.8328, compared with 0.7309 for the demand-unaware model. Budget sensitivity analysis further shows diminishing marginal returns to fiscal expansion, with full potential demand reached at the model-based threshold of RMB 479,500. Robustness analysis indicates that the main allocation results remain stable under perturbations of the empirically derived demand-priority weights.

Mathematics doi: 10.3390/math14203840

Authors: Haoyun Zhang Haibo Zhang

Efficiently extracting and integrating multi-scale global and local information remains a main challenge in remote-sensing semantic-segmentation tasks. Current convolutional neural networks (CNNs) can only capture fine-grained details but cannot model long-range dependencies. In contrast, sequence models, such as Transformer-based and Mamba-based models, have the ability to capture broad context. However, they have limitations in preserving local details. Recent hybrid architectures combine both to balance these strengths, but it is still difficult to fuse multi-scale global and local features in a unified and efficient manner. In this work, we propose ViL-UNet, a dual-branch encoder–decoder network, which addresses this challenge by combining a Vision-LSTM (ViL) global encoder with a CNN-based local encoder. The global encoder captures long-range dependencies across multiple scales. Furthermore, the local encoder preserves fine spatial details. We also design a novel Multi-Scale Fusing Module to integrate these complementary representations by resizing the global and local features to a common spatial grid, concatenating them, and generating a unified feature representation that captures broad contextual cues and fine-grained local information. The decoder applies Efficient Global–Local Attention and Squeeze-and-Excitation. In addition, the skip connections bring the fused multi-scale features back to higher resolutions. To demonstrate ViL-UNet’s effectiveness, we compared it against state-of-the-art methods on the ISPRS Vaihingen and LoveDA Urban benchmarks. Across both datasets, ViL-UNet consistently delivers more accurate semantic segmentation by efficiently capturing multi-scale global and local context in large-scale remote-sensing scenes.

Mathematics doi: 10.3390/math14203839

Authors: Levent Kula

In this paper, we investigate three classes of f-weighted direction curves, namely tangent, principal, and binormal direction curves, obtained by integrating positive smooth multiples of the corresponding Frenet vector fields of a generating Frenet curve in Euclidean three-space. We derive curvature and torsion relations for these associated curves and investigate their connections with general helices, slant helices, clad helices, and g-clad helices. In particular, the weighted tangent direction construction preserves certain helix invariants of the generating curve, while suitable choices of the weight function modify its curvature and torsion. We establish conditions on the weight functions under which the resulting curves satisfy the characterizations of rectifying, Mannheim, and Bertrand curves. We also investigate conditions for constructing spherical weighted direction curves and introduce g-weighted normal, rectifying, and osculating direction curves associated with them. Explicit examples illustrate successive weighted constructions, including the generation of a rectifying clad helix and a Salkowski curve. The main contribution is a common construction framework in which the choice of a Frenet direction field and a positive weight function allows several classes of special space curves to be investigated through their geometric characterizations, subject to the required regularity and nonvanishing conditions.

Mathematics doi: 10.3390/math14203838

Authors: Qin Li Geng Yang Bob Zhang Ming Yang

Anchor graphs are widely recognized for their capability to reduce the computational complexity of clustering. When regression techniques are applied to anchor graphs, existing regression-based methods mainly focus on directly learning sample labels, while the label distribution induced on anchors through sample–anchor relationships remains insufficiently explored. We propose Efficient Discrete Multi-View Clustering with Tensorized Label Learning (EDMVC_TLL) to address this limitation. Specifically, we fully leverage the probabilistic properties of anchor graphs to establish the relationship between sample labels and anchor labels, utilizing anchor labels to guide the learning of sample labels. Furthermore, we introduce an innovative regularization term to balance anchor labels, avoiding trivial solutions and enhancing sample labels’ quality. The tensor Schatten p-norm explores complementary information embedded in different views. Additionally, we adopt an adaptive anchor graph, integrating it into the subsequent optimization process to improve the quality of the anchor graph. An efficient optimization algorithm is developed, and extensive experiments on six benchmark datasets demonstrate that EDMVC_TLL consistently achieves the best performance in terms of ACC, NMI, and Purity among the compared methods.

Mathematics doi: 10.3390/math14203837

Authors: Chao Li Ilia Derevitskii Sergey Kovalchuk

This paper presents a partial differential equation (PDE)-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through nonlocal perception kernels and external potential fields. Extending classical transport equations, the framework represents opinion popularity as a continuous distribution, enabling direct interactions without Bayesian guessing of beliefs. Using azithromycin and prednisolone as illustrative treatment features from a real-world coronavirus disease 2019 (COVID-19) dataset, the numerical experiments exhibit reduced local perception-to-target discrepancy under target-based updating, redistribution and the formation of a new unimodal density under fact-informed updates with potential guidance, and persistent multiple peaks without target-based fitting or an external potential field. Quantitative evaluation uses population-weighted local perception-to-target Wasserstein distance estimates for the selected treatment dimensions.

Mathematics doi: 10.3390/math14203836

Authors: Yanzhe Dong Binwei Xu Yujia Liu Liang Wu

This study extends an existing single-period mixed-integer linear programming (MILP) formulation to a multi-period index-tracking problem. The proposed model allows the tracking portfolio to be rebalanced at predetermined times while limiting the associated transaction costs. Two benchmark strategies are considered: a fixed portfolio with no rebalancing and a portfolio reselected under a large transaction-cost limit intended to approximate unrestricted rebalancing. The models are evaluated using constituent data for the SSE 50 and CSI 100 indices. Tracking performance is measured in-sample and out-of-sample for different portfolio cardinalities, sample lengths, and transaction-cost limits. Among the parameter values examined, at least one multi-period specification produces a lower out-of-sample root-mean-square error (RMSE) than both benchmarks in seven of the eight reported configurations. However, the optimal transaction-cost limit varies across configurations, indicating that tracking performance is sensitive to the permitted degree of rebalancing.

Mathematics doi: 10.3390/math14203835

Authors: Jinjia Chen Yulun Chen Kun Yang Xingyu Zhou Yingchao Wang Feng Xue Tianfu Li

Regulatory instruments alter institutional payoffs, but they do not choose which equilibrium a decentralized financial system will realize. A policy that appears safe at one computed response can therefore coexist with an unobserved fire-sale or funding-run outcome. We pose policy construction as a set-containment requirement: every approximate Nash equilibrium of the regulated game must remain inside a buffered stability target. EquiImplement enforces this requirement with state-dependent mixtures of admissible unilateral deviations over the target complement. When policy features enter payoffs affinely, holding this proof object fixed gives affine inequalities in the regulatory vector and a concave minimum margin, producing a convex semi-infinite policy subproblem. A rigorous regional separator locates the weakest-covered state, and the same verified counterexample drives both the next policy solve and certificate revision. A preset outer-iteration budget gives finite execution and one of three outputs: globally certified containment, budget infeasibility within the prescribed incentive–certificate family, or an unresolved status. The evaluation covers 330 fire-sale and rollover/run games. At the default budget, EquiImplement attains full-stability rates of 95.0%, 85.6%, and 92.5%, while reducing the worst-equilibrium violation from 0.037 for the strongest non-oracle baseline to 0.016. The mean regulatory cost over returned budget-feasible evaluation policies decreases from 0.119 to 0.113. Further analyses relate certification difficulty to stability-target tightness, leverage, market depth, liquidity buffers, and coordination strength. The results show that a deviation-based proof object can serve directly as an optimization interface for financial regulation under equilibrium multiplicity.

Mathematics doi: 10.3390/math14203833

Authors: Nicholas Tenkorang Xiangya Wang George Ekow Quaye Xiaogang Su

The end-cut preference (ECP), the tendency of greedy tree algorithms to select split points near the extremes of a predictor’s range, can produce unstable and highly imbalanced partitions. For survival trees based on the maximized log-rank statistic, we prove that, under the null and an expanding admissible cutpoint range, every maximizing cutpoint leaves any fixed interior quantile interval with probability tending to one. The proof compares the tight interior maximum of a studentized empirical bridge with its diverging maximum over cutpoints approaching an endpoint. An exact variance decomposition of a quadratic Taylor polynomial also identifies a non-negative hard-split term with boundary scale (1−2c)2Λn/{nc(1−c)}. For the smooth sigmoid surrogate (SSS), the corresponding Cox-score term is uniformly Op(a/n), where a is the sigmoid shape parameter. This bound has no endpoint factor. Numerical experiments across censoring levels, signal strengths, split restrictions, and recursive splitting show that SSS generally selects fewer end cuts and yields lower cutpoint RMSE under the alternatives studied, with the clearest gains for weak signals, while retaining the interpretation of ordinary hard splits.

Mathematics doi: 10.3390/math14203834

Authors: Ümit Sarp

Star polygon motifs (m-grams), widely observed across historical architecture and combinatorial game theory, lie at the intersection of geometry and algebraic graph theory. In this study, we construct a formal graph family, denoted by Starm(n), by analyzing the topological structure of these motifs via the conceptual union of centered polygonal numbers (CPm) and triangular numbers (Tn). Its interior faces form an internally triangulated planar grid topology. After establishing the vertex and edge capacities via Euler’s planar formula, we obtain the exact edge partition space and the closed-form M-polynomial of the network. Applying the Deutsch–Klavžar differential operators to this polynomial, we derive closed and asymptotic expressions for key degree-based invariants: the First and Second Zagreb, Randić, Harmonic, Forgotten, Inverse Degree, and Sombor indices. All analytical derivations are validated computationally using breadth-first search (BFS) algorithms in linear time O(|V|+|E|). Finally, we introduce four geometric transformations—Annular Projection, Logarithmic Spiral Twisting, Girih Rosette Folding, and Kaleidoscopic Quotient Graphs—to classify the underlying generative mechanics of these cultural patterns.

Mathematics doi: 10.3390/math14203832

Authors: Wahiba Bouabsa Fatimah Alshahrani

We study scalar nonparametric regression with a probability-measure-valued predictor observed along a dependent time series. A Nadaraya–Watson smoother localizes directly in the quadratic Wasserstein metric. The revised theory separates generic functional-kernel arguments from contributions generated by Wasserstein predictor geometry and local recurrence. We introduce an aggregate local-recurrence condition that is weaker than pairwise anti-clustering and is compatible with strongly overlapping empirical-distribution windows. For one-dimensional Gaussian location–scale predictors, we obtain an exact Euclidean small-ball expansion; we then extend the geometry to nonsingular multivariate Gaussian predictors through the Bures–Wasserstein Riemannian metric, obtaining an explicit local dimension and small-ball exponent. Under geometric strong mixing, local Hölder smoothness, and small-ball regularity, we establish strong consistency, an almost-sure rate, a variance expansion, and a triangular-array central limit theorem. We further derive a local long-run-variance CLT, a finite-dimensional joint CLT for several Wasserstein targets, and simultaneous confidence intervals. Feasible inference uses a direct Bartlett–HAC estimator whose consistency is now justified by an explicit fourth-order local cumulant condition rather than by geometric mixing alone. For tuning, we introduce an empirical small-ball admissibility screen and allow selection from a possibly growing grid on a separated chronological block. A truncation extension handles locally unbounded responses. Simulations satisfy the stated bounded-response assumptions and stress-test overlapping windows. The Mauna Loa CO2 illustration adds interpolation, window/horizon, and deterministic-overlap sensitivity, stationarity diagnostics, coefficient intervals, and a stronger AIC-selected autoregressive comparator. The latter can outperform the Wasserstein smoother, so the application is interpreted as an empirical illustration rather than evidence of universal predictive superiority.

Mathematics doi: 10.3390/math14203831

Authors: Xiangxian Dou Li Wan Jinlong Xie Qianhui Liu Yuzhen Yu

Accurate stress integration at large strain increments requires control of both trajectory error and yield-surface drift. This study presents RK-RM, a hybrid strategy combining explicit Runge–Kutta integration with cutting-plane return mapping. A forward–backward calculation constructs complementary internal variables, which are combined with the forward stress to initialize the correction. The method is examined with the Modified Cam-Clay and Unified Hardening (UH) models in material-point tests, triaxial simulations, and a foundation loading example. The UH triaxial comparisons show smaller deviatoric-stress errors than the tested closest point projection (CPPM) implementation, while additional undrained material-point comparisons show lower local constitutive cost. Accuracy depends on the loading path, step size, and correction strategy. The results support RK-RM as a practical stress-integration option for the constitutive models and loading conditions considered.

Mathematics doi: 10.3390/math14203830

Authors: Bolai Jin Haotian Zheng Yangjian Yang

To address the limitations of the standard Escape Algorithm (ESC), including its tendency to become trapped in local optima and its slow convergence speed in complex optimization scenarios, this paper proposes an Improved Escape Algorithm (IESC) for global optimization and robot path planning. First, a reinforcement learning–based decision-making mechanism using Q-learning is introduced to replace the fixed rule–driven population update strategy in ESC. By constructing a closed-loop framework of “individual–action–reward,” the proposed method enables adaptive strategy selection and effectively balances exploration and exploitation during different stages of the optimization process. Second, to enhance information interaction among individuals, a thermal conduction–enhanced search strategy is developed. Inspired by heat transfer principles, this strategy leverages global population information through the combined guidance of the population means and the global best solution, thereby improving local search directionality and convergence stability. Third, an elite-guided Lévy flight and quadratic interpolation fusion strategy is incorporated to strengthen global exploration and fine-grained local exploitation. Elite individuals guide long-range Lévy flights to avoid premature convergence, while quadratic interpolation refines solutions around high-quality regions to improve optimization precision. The performance of the proposed IESC is comprehensively evaluated on the CEC2017 benchmark suite, covering unimodal, multimodal, hybrid, and composite functions with multiple dimensional settings. Experimental results demonstrate that IESC consistently outperforms several state-of-the-art metaheuristic algorithms in terms of optimization accuracy, convergence speed, and robustness. Furthermore, IESC is applied to robot path planning, where a multi-objective model considering path length, smoothness, and feasibility is constructed under collision-avoidance constraints. Simulation results show that the paths generated by IESC are shorter, smoother, and more stable than those produced by comparative algorithms. These findings indicate that the proposed IESC provides an effective and reliable optimization framework for robot path planning and other complex optimization problems.

Mathematics doi: 10.3390/math14203829

Authors: JangHo Seo Joonwoo Lee

Existing elevator-dispatch research uses quadratic waiting-cost models and restricts reassignment near pickup to preserve service decisions. Although fixing a hall-call assignment removes it from the decision variables, its service remains on the route, so omitting its interactions changes the objective for the remaining calls. This study examines the resulting omission loss and the computation of the retained interactions. Conditioning on fixed assignments yields a unary correction. Its omission loss is bounded, and reachable three-floor states approach the bound even for arbitrarily short reassignment thresholds. Under explicit service assumptions, floor-ordered pair-cost formulas include the merged-turnaround boundary and permit linear arithmetic for supported fixed-call interaction sums after unary evaluation. Across 30 paired seeds and 75 synthetic interfloor settings, adding the correction to move-and-swap search reduced mean waiting time by 0.50 s (95% interval 0.40–0.59 s). Separately, structured coefficient assembly reduced the equal-cell mean of complete dispatch time from 46.039 to 36.945 microseconds on identical inputs, a 19.8% reduction. The omission bound and interaction formulas provide an analytical basis for retaining fixed-call service costs, with measured service and computational benefits in the tested interfloor regime.

Mathematics doi: 10.3390/math14203828

Authors: Alberto d’Onofrio Solafa Fadlallah

We extend the classical Ross–Macdonald model for describing the spread of vector-borne diseases. First, we include spontaneous behavioral changes driven by the current and past information on the disease incidence. Second, we include seasonality in the infective potential of mosquito bites. This results in a hereditary model with distributed delay. We analytically investigate the general properties of both the disease-free equilibrium and the endemic equilibrium, in particular their local stability, and, for the DFE, we also show its global stability, even in the periodically forced model. We focused on two key scenarios: (i) a near-critical regime and (ii) a regime with a large basic reproduction number due to a large abundance of mosquitoes with respect to the human population. In the case of special memory kernels allowing a finite-dimensional reduction of the model, such as the Erlang kernels of orders 2 and 3, as well as the acquisition–fading kernel, we analytically and numerically investigate (i) the occurrence of oscillations of Yakubovich type in the autonomous model and (ii) the interplay between seasonality and behavior in the periodically forced model, and we show that this interplay can trigger nonlinear resonances and chaos.

Mathematics doi: 10.3390/math14203827

Authors: Reem K. Alhefthi Silvestru Sever Dragomir

The Berezin number and Berezin norm have become indispensable tools for analyzing the structure of operators on reproducing kernel Hilbert spaces, yet the gap between these quantities and the operator norm is still far from fully understood. In this paper, we narrow that gap by establishing several new reverse-type inequalities for ber(V) and ∥V∥ber˜ under natural disc-localization and accretivity conditions. Combining a refinement of the Schwarz inequality due to Dragomir with Buzano’s inequality, we further derive sharp bounds for ber(A*TA) and for products TA, together with their power-type extensions. Applying the polar decomposition, we also obtain companion inequalities for |T|α and the Aluthge transform. Finally, for operators with closed range, we use the Moore–Penrose inverse to derive new reverse-type Berezin inequalities that refine and complement the results obtained via the polar decomposition, and we illustrate the sharpness of these bounds with an explicit example.

Mathematics doi: 10.3390/math14203826

Authors: Osama Abdulaziz Alamri Basim S. O. Alsaedi Javid Gani Dar

Extropy, the complementary dual of Shannon entropy, has Rényi and Tsallis generalizations. For finite discrete distributions, a general asymptotic theory for plug-in estimators of functionals F(p)=∑iϕ(pi) is available in an arXiv preprint. Independently, the Mathai–Haubold entropy is a power-kernel, one-parameter generalization of Shannon’s differential entropy that recovers Shannon and Tsallis entropies as special or limiting cases. Its cumulative version, based on the distribution and survival functions rather than the density, has been studied through series representations involving moments of extreme order statistics. In this paper, We apply the Mathai–Haubold power kernel, so far used for cumulative entropies of continuous lifetimes, to the complementary probabilities 1−pi and study the resulting Mathai–Haubold extropy JαMH(p). We show that JαMH is an exact affine transform of the power sum S2−α(p)=∑i(1−pi)2−α that also defines the Tsallis extropy. It is therefore a reparameterization of the Tsallis extropy at the complementary order 2−α, not an independent measure. We also study the associated divergence DαMH(p∥q). It is not a new class of divergence: it equals (r−1) times a Cressie–Read (Csiszár f-) divergence between the normalized complementary probability vectors. Hence, it is nonnegative and jointly convex, and it satisfies a data-processing inequality for Markov processing of those normalized vectors; we show by an explicit counterexample that this does not extend to arbitrary coarsening of the original categorical variable. We prove asymptotic normality of its plug-in estimator for a fixed reference distribution q. A Monte Carlo study confirms n-consistency and O(n−1) bias, and adequate normal approximation of the extropy estimator from n≳200. An application to observed categorical data (cut grades of 53,940 diamonds) illustrates the inference; a warranty-claim example is hypothetical and serves only as an illustration.

Mathematics doi: 10.3390/math14203825

Authors: Anna Ovsyannikova Evgenia Kirillova Anna Kovalenko Anastasiia Lelekova Alexandra Ovsyannikova Makhamet Urtenov

Membrane profiling and near-membrane spacers modify concentration polarization by altering fluid flow and the membrane–solution interface. This study examines their combined influence using a two-dimensional Nernst–Planck–Poisson–Navier–Stokes model with a voltage ramp of 5 mV/s. The geometries comprise a smooth membrane without spacers, a profiled membrane without spacers, and six wing arrangements adjacent to a profiled membrane. The feed concentration is 0.01 mol/m3, the protrusion radius is 0.5 mm, and the center-to-center pitch is 1.5 mm. Current data from five identifiable model files are compared over a common interval up to 1.2 V using a dimensionless domain-integrated current. Wing placement affects the current response, while profiling increases the geometric membrane contour by 28.54%. An analytical reference limiting current is calculated using the Levêque equation. The comparison with published three-dimensional results provides qualitative support for the transport mechanism. Systematic numerical uncertainty assessment, quantitative three-dimensional validation, geometry optimization, and energy comparisons at equal salt removal are identified as further research beyond the scope of the present study.

Mathematics doi: 10.3390/math14203824

Authors: Francis Mora-Ferreras Manuel Montero Victor Ramírez

We study logarithmic Hardy operators and their commutators on the half-line Morrey spaces defined using all bounded intervals. For 1≤p<∞, 0<λ<1, and γ>−1, the positive dilation principle gives the exact norm Γ(γ+1)[p/(p+λ−1)]γ+1, attained by a power function. We obtain exact norms for Hardy iterates and a reverse inequality for nonnegative nonincreasing functions. For the fractional operator, we prove a mapping theorem between distinct Morrey spaces, establish the necessary scaling relation, and give explicit upper bounds throughout a logarithmic range that is optimal for finiteness at every point. We distinguish this pointwise threshold from the almost-everywhere mapping endpoint. For the one-sided point-value symbol class, we prove embeddings into ordinary and central mean-oscillation spaces and identify its relation to the symmetric point-value class through even extension. This symbol condition yields explicit logarithmic and fractional commutator estimates. The symbol b(x)=logx raises the logarithmic order by one and gives an exact commutator norm with which the general upper bound can be compared.

Mathematics doi: 10.3390/math14203823

Authors: Ismail Alabbadi Wieslaw Krawcewicz

We study the global bifurcation of nonstationary periodic solutions for a class of delayed nonlinear parabolic systems on the unit disk with Neumann boundary conditions and an additional finite symmetry group Γ. After normalizing the unknown period, the problem is formulated as a two-parameter equivariant bifurcation problem with symmetry group G=S1×O(2)×Γ, where S1 represents time translations, O(2) describes the spatial symmetries of the disk, and Γ acts on the internal state space. Using the twisted G-equivariant degree, we construct a local bifurcation invariant at isolated critical points and obtain global bifurcation results for nonstationary periodic solutions with prescribed spatio-temporal symmetries. The abstract theory is applied to a coupled nonlinear optical system with diffractive feedback and octahedral symmetry Γ=S4. By decomposing the corresponding S4-representation into its isotypic components, we determine the critical Hopf bifurcation parameters (αo,βo) associated with the nontrivial components and compute the corresponding maximal twisted orbit types. The resulting equivariant bifurcation invariants detect several distinct spatio-temporal symmetry types associated with the bifurcating periodic solutions. In particular, the analysis provides a mechanism for detecting rotating, standing, and other spatio-temporally symmetric periodic patterns. These results provide a symmetry-sensitive global bifurcation framework for delayed nonlinear parabolic systems with combined spatial and internal symmetries.

Mathematics doi: 10.3390/math14203822

Authors: Ke Yan Shaobo Chen Qi Zhang

With the rapid development of live-streaming e-commerce and artificial intelligence, human and AI live-streaming have become two product information disclosure formats in online retail. From the perspective of product information disclosure, we develop a game-theoretic model of a live-streaming e-commerce supply chain comprising a brand owner and an e-commerce platform. We derive Stackelberg equilibria under the resale mode through backward induction, obtain the optimal retail price and information disclosure level under the agency mode through joint optimization, and then compare disclosure-format and sales-mode preferences. The results show that (1) AI live-streaming does not always achieve a higher information disclosure level. It leads to a higher disclosure level only when consumer trust in AI live-streaming disclosure is high, or when trust is moderate and sensitivity to the information disclosure level is low; otherwise, human live-streaming disclosure achieves a higher disclosure level. (2) Under the resale mode, the brand owner and the e-commerce platform have consistent preferences regarding disclosure formats. Both prefer AI live-streaming when consumer trust in AI disclosure is high, or when trust is low but sensitivity is also low, whereas both prefer human live-streaming when trust is low and sensitivity is high. Under the agency mode, their preferences diverge when consumer trust is low and sensitivity is moderate. (3) Regarding sales modes, the brand owner prefers the agency mode only when the commission rate and consumer sensitivity to information disclosure are both low; otherwise, it prefers the resale mode. These findings provide theoretical and managerial implications for disclosure-format selection and sales-mode decisions in live-streaming e-commerce.

Mathematics doi: 10.3390/math14203821

Authors: Mikail Mohammed Salim Farheen Naaz

Edge–cloud task scheduling reserves uplink capacity before the wireless service state is known. The reserve depends on both the probability law over a prescribed service-state library and the geometry representing that library. This study separates and quantifies these two effects in a fixed-workload finite-state model. We eliminate post-state bandwidth–CPU recourse exactly, derive a quadratic capacity representation in inverse-square-root spectral efficiencies, and compare empirical (EMP), Wasserstein, hard-support (HARD), and rectangular (BOX) uncertainty models under schedule reoptimization. The analysis yields an exact support-rectangularization premium, a resource-weighted joint-extreme deficit with a relative-cost factor below two, a sandwich bound on the optimized premium, and a finite hardening radius for chance-constrained capacity. Across 60 instances, mean savings from retaining joint support are 6.45–9.32% relative to rectangular protection. Across 20 instances, mean relative increases are 7.39–10.82% for EMP-to-HARD, 8.80–9.26% for support rectangularization, and 16.98–20.89% for EMP-to-BOX; all are deterministic optimization bounds. Positive lower bounds persist for both changed-target workloads, all nine nested-support cases, and both probability-side variations, while intermediate Wasserstein capacity changes under the alternative transport metric. Probability protection and support geometry impose distinct, quantifiable capacity costs.

Mathematics doi: 10.3390/math14203820

Authors: Gustavo Álvarez Igor Kondrashuk

Integral transformations are useful mathematical tool to work out signals and wave packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory—particularly from quantum chromodynamics, in which the optic theorem and the renormalization group equation can be solved by a unique contour integral written in two different “dual” ways related between themselves by a complex map in the complex plane of the Mellin variable. The inverse integral transformation should be modified to be applied for these contour integral solutions. These modified inverse transformations may be used in security protocols for quantum computers. Here, we present a brief review of the basic integral transforms and propose their modification for the extended domains.

Mathematics doi: 10.3390/math14203819

Authors: Ahlam Almulhim

For a graph G=(V,E), a function f:V⟶{0,1,2} is a vertex–edge Roman {2}-dominating function (veR2DF) if for every edge xy∈E, either f(x)+f(y)≥1 or ∑z∈N(x)∪N(y)f(z)≥2. The sum ∑v∈Vf(v) is the weight of the function f. The vertex–edge Roman {2}-domination number of G, denoted by γveR2(G), is the minimum weight of a veR2DF of G. In this paper, we prove that for any connected graph G of order n≥4, then γveR2(G)≤n2, and this result is sharp. We also prove Nordhaus–Gaddum inequalities for γveR2(G). In addition, we characterize trees with equal vertex–edge Roman {2}-domination, vertex–edge domination, and domination numbers.

Mathematics doi: 10.3390/math14203818

Authors: Edwin Barrios-Rivera Daiver Cardona-Salgado Ilya Dikariev Carmen A. Ramirez-Bernate Olga Vasilieva Mikhail Svinin

This study presents a mathematical modeling framework to analyze the impact of integrating sterilizing treatment into tuberculosis (TB) control strategies, particularly in resource-limited settings. The numerical analysis of the proposed mathematical framework indicates that while sterilizing treatment alone is highly effective in reducing TB incidence and mortality, its widespread implementation requires significant financial investment. The optimal control approach demonstrates that a mixed strategy, combining sterilizing and non-sterilizing treatments, can achieve comparable public health benefits at a lower cost, especially in medium-term planning. From a long-term perspective, however, our results suggest that exclusively sterilizing treatment ultimately leads to greater reductions in TB incidence, prevalence, and mortality, justifying its higher initial cost. This is primarily due to the ability of sterilizing drugs to eliminate latent TB infections, prevent future active infections and disease-induced deaths, and avoid a considerable number of treatments. Additionally, under scenarios where the cost of sterilizing drugs decreases over time, a swift transition to a solely sterilizing treatment could result in both epidemiological and economic advantages for healthcare systems.

Mathematics doi: 10.3390/math14203815

Authors: Kexin Zhang Shubin Liu Xinyuan Zhang Jun Zhang

Collaborative Attention Ant Colony Optimization (CAACO) integrates a deterministic coordinate-based attention prior with subpath decomposition, memetic MAX–MIN Ant System search, and double-bridge perturbation for the symmetric Euclidean Traveling Salesman Problem. The attention prior combines coordinate-direction compatibility and distance information to guide candidate selection without model training. Random-offset slicing organizes endpoint-constrained subpath search, while local improvement and perturbation refine and diversify the tour. An exploratory comparison of Full CAACO and CAACO-KNN uses 30 recorded runs per configuration on each of eight EUC_2D benchmark instances. Average instance-level mean GAP values are 2.945% and 3.222%, respectively, with a lower mean for Full CAACO on six instances. A two-sided exact Wilcoxon signed-rank test over the eight instance means gives p=0.0391; four per-instance comparisons remain significant after Holm correction. The results characterize configuration-level performance on the selected benchmarks and motivate further controlled evaluation of attention-guided search.

Mathematics doi: 10.3390/math14203816

Authors: Yonit Barron Guy Pery

This paper develops a continuous-review inventory framework that integrates stochastic demand, stochastic returns, perishability, stochastic lead times, and lost sales. Unlike most inventory studies, which treat returns primarily as a reverse logistics phenomenon, product returns are modeled as an endogenous stochastic replenishment source that directly influences replenishment planning and procurement decisions. The inventory process is formulated as a continuous-time Markov chain, enabling the derivation of exact steady-state performance measures and long-term cost expressions. This paper further examines fixed-quantity replenishment policies under practical ordering constraints. The results show that return flows substantially reduce procurement requirements, inventory levels, and total system costs. The analysis accommodates both classical (r<Q) and non-classical (r>Q) operating regimes and reveals that the latter may emerge naturally when replenishment quantities are exogenously fixed. The model is subsequently extended to a new (Q,r,ψ) policy that allows outstanding replenishment orders to be canceled when inventory is recovered by returning during the lead time. Numerical experiments indicate that cancellation flexibility can generate substantial cost savings, particularly in return-intensive environments with high inventory carrying costs. Overall, the findings demonstrate that returns constitute a strategic replenishment resource and should be explicitly incorporated into inventory planning and control.

Mathematics doi: 10.3390/math14203817

Authors: Mustafa Ghaleb Zaafir Riaz Radhwan A. Saleh Zead Saleh Ibrahim Althamary Sajjad Ahmad Khan Kerem Küçük Hamdi Altaheri

Cooperative unmanned aerial vehicle (UAV) swarms require secure transaction-level admission decisions when tasks, relay roles, control privileges, or mission assets are transferred between aircraft. Existing authentication and intrusion-detection mechanisms address complementary aspects of security and motivate integrating a mandatory protocol check with post-authentication behavioral and corroborative assessment. This paper introduces TriTrust, a risk-aware three-factor trust-fusion architecture that enforces a mandatory protocol-admission gate, followed by logistic fusion of traffic-behavior and competence-weighted witness scores for gate-passing candidates. The framework further incorporates validation-fitted score mapping and robust federated maintenance of the witness classifier. Evaluation on a constructed proxy-handover benchmark derived from public UAV cyber-physical records using cyber-condition-derived labels, sampled gate outcomes, and simulated witness views demonstrates that the modeled gate provides the dominant control over false acceptance: removing it increases mean seed-level raw-score false-acceptance rate (FAR) from 0.43% to 9.62%. Across five prespecified resamplings of the same source corpus, the isotonic-mapped full pipeline attains a mean seed-level area under the receiver operating characteristic curve (AUC) of 0.9926, a mean FAR of 0.83%, and a mean false-rejection rate (FRR) of 1.75%. Under 20% scaled sign-reversal poisoning, coordinatewise median aggregation maintains mean witness-classifier accuracy of 0.8552, compared with 0.2920 for sample-size-weighted averaging. Feature-space stress tests further show that false acceptance under learned-input manipulation remains limited by the modeled gate, whereas gate bypass combined with learned-factor compromise produces high false-acceptance rates. These results characterize the contributions and failure boundary of protocol gating, post-gate trust fusion, score mapping, and robust federated maintenance within the constructed benchmark.

Mathematics doi: 10.3390/math14203814

Authors: Ivo Petráš

The internal temperature of a lithium-ion cell governs aging and safety, but commercial cells cannot be measured without invasive sensors. We survey direct and indirect (thermoelectric-model, PDE-observer, impedance-based) estimation methods and find that fractional-order operators appear in battery electrical models but have not been used in thermal state equations for internal-temperature estimation. In this paper, we generalize the classical two-state lumped thermal model by Caputo derivatives of orders α1,α2∈(0,1] and give a Caputo-consistent Grünwald–Letnikov discretization, verified against Mittag-Leffler and L1 reference solutions. In a numerical study with drive-cycle-like excitation, we compare the fractional plant and two independent integer-order plants (one with unmodeled entropic heat) with integer chains of the same parameter count. Identification from surface temperature alone is ill-conditioned for all models; a better surface fit does not guarantee a better core estimate, and the fractional model is advantageous only when the plant dynamics are indeed fractional. When calibrated with an internal sensor, the core temperature is estimated from the surface within 0.01–1.1∘C. The results are simulation-based; experimental validation is the next step.

Mathematics doi: 10.3390/math14203813

Authors: Muntasir Suhail Osman Abdalla Adam Osman Mohammed Rabih

We study generalized derivations of complex multiplicative α2-weighted Ω-Hom-Lie superalgebras. The chosen structural identity is shown to be stable under Yau twisting, and every regular algebra in this class untwists canonically to an Ω-Lie superalgebra. To retain the auxiliary operators that occur in generalized derivation identities, we work with generalized derivation triples and quasiderivation pairs. In this framework, these derivation-type maps are treated as mathematical operators encoding infinitesimal symmetries of the underlying graded algebraic structure. The triple space is a Lie superalgebra, and quasiderivation pairs fit into a short exact sequence of Lie superalgebras whose kernel measures precisely the ambiguity of the auxiliary map. We prove GDerα(L)=QDerα(L)+QCentα(L), and establish the corresponding Ω-compatible decomposition for balanced generalized derivations. We then construct a three-layer envelope for generalized derivation triples and a two-layer envelope for quasiderivation pairs, obtaining injective Lie-superalgebra embeddings into α-commuting derivation algebras. A structural obstruction shows that, when α2≠0, the original nonzero Ω cannot simply be copied to the active layers of these two-step envelopes as their structural form. For centerless algebras, the full derivation superalgebra of the two-layer envelope is determined as an explicit semidirect product. Finally, a structure-constant criterion reduces the pair and triple spaces to homogeneous linear systems. For the regular family Hτ, τ∈C×∖{1}, we obtain dimDerατ=1 and dimQDerατ=dimGDerατ=4, while the Ω-compatible first-component space has dimension 3.

Mathematics doi: 10.3390/math14203812

Authors: Radu-Anton Moldovan Marian Pompiliu Cristescu

Investment risk modeling remains challenging due to uncertainty, structural change, and market dynamics. This study develops an integrated empirical framework linking adaptive Bayesian forecasting, predictive-uncertainty evaluation, and risk-sensitive portfolio decision-making in a five-asset system comprising Microsoft, NVIDIA, Tesla, IBM, and Boeing. The TVP-VAR is employed as an established adaptive forecasting component and evaluated against expanding-mean and fixed-parameter VAR benchmarks using point-forecast accuracy, probabilistic calibration, regime-specific performance, and investment outcomes. Results show that the TVP-VAR does not systematically outperform simpler benchmarks in one-step-ahead point forecasting. However, it produces higher mean log scores and 95% predictive-interval coverage closer to nominal levels across all five assets, although these improvements generally require wider intervals and do not yield superior CRPS values. Sensitivity analysis shows that the strongest model-based portfolio performance occurs at λ = 1, where forgetting-factor-driven coefficient variation is eliminated while adaptive covariance updating remains active. Nevertheless, the equal-weight portfolio delivers the strongest overall risk-adjusted performance. Comparison with static covariance indicates that the economic advantage of adaptive covariance estimation is modest and criterion-dependent. Greater parameter adaptivity does not imply universal statistical or economic superiority; its value is more evident in predictive-uncertainty representation and calibration than in consistently improved point forecasts or portfolio outcomes.

Mathematics doi: 10.3390/math14203810

Authors: Kanyarat Thitiwatthanakan Nuttaphat Sukchitt Manad Khamkong

This study examines two weighted (variance-standardized) versions of classical nonparametric single change-point tests, the weighted Pettitt (W-Pet-CP) and weighted Cramér–von Mises (W-CvM-CP) tests, in which the change-point process is divided by w(τ)=(τ/n)(1−τ/n) to reduce the loss of detection ability for changes near the ends of a series. We derive their limiting null distributions and their behavior under fixed and local location and scale alternatives, and compare them, using Monte Carlo simulation, with the Pettitt, Cramér–von Mises, Mood and Lepage change-point tests. Both weighted tests kept the nominal type I error and markedly improved the ability to locate changes near the boundaries, and W-CvM-CP and Lepage-CP were the only procedures that were effective for both location and scale shifts. In a second stage, the tests were applied to annual maximum (Tmax) and minimum (Tmin) temperatures and their difference (D=Tmax−Tmin) at eight stations in upper northern Thailand (1957–2025 at six stations and 1981–2025 at two), with false-discovery-rate control and field-significance testing, and copula models were fitted to the joint behavior of Tmax and Tmin. After multiplicity adjustment, upward shifts in Tmin of 1.6–3.1 °C were detected at all eight stations, mostly around 1987 and 1999, whereas Tmax shifted significantly only at Mae Hong Son (1982) and Lampang (1978). Decreases in D, clustered around 1999, were regionally significant under the independence assumption but less robust to serial correlation. The dependence between Tmax and Tmin was weak (Kendall’s |τK|≤0.21) and vanished after the detected shifts were removed, so copula-based joint return periods are reported with bootstrap confidence intervals and interpreted with caution.

Mathematics doi: 10.3390/math14203811

Authors: Ebrahem Elkady Ahmed Salem Hyun-Soo Kang Jae-Won Suh

Light field angular super-resolution (LFASR) seeks to recover missing viewpoints from sparsely captured angular samples, while preserving the underlying scene structure across views. This task is complicated by disparity-induced variations, incomplete visibility near occlusion boundaries, and view-dependent appearance changes caused by reflective surfaces. In this work, we propose a cross-domain EPI–spatial–angular (X-ESA) framework that combines EPI-based geometric modeling with complementary spatial and angular feature extraction. A CSWin-based EPI transformer captures long-range, slope-aligned dependencies, while dedicated convolutional branches refine spatial details and cross-view relationships. These features are integrated through a mesh–progressive fusion strategy, followed by channel attention and spatial residual refinement. Experiments on real-world and synthetic datasets under the 2×2→7×7 setting result in average performances of 41.29 dB/0.989 SSIM and 40.98 dB/0.989 SSIM, respectively. The proposed model contains 2.84M trainable parameters and provides competitive reconstruction quality relative to existing LFASR methods.

Mathematics doi: 10.3390/math14203808

Authors: Sunghwan Yoo Seokkyeong Boo Yong Ju Jung

Real-world motion blur exhibits complex, spatially varying characteristics that challenge existing deblurring methods. While multi-stage architectures offer progressive refinement, simple inter-stage interactions often limit effective information transfer. To address this, we propose CPINet, a Cross-stage Patch Interaction Network for coarse-guided image deblurring. CPINet employs a two-stage coarse-to-fine framework: the first stage uses an Uncertain Flow-based Prior Network (UFPNet) for coarse restoration, followed by a second stage for fine-grained patch-level refinement. The second stage utilizes a Coarse-guided Patch Encoding (CPE) block with a Patch-wise Cross-Channel Attention Gating (PCAG) mechanism to integrate first-stage features. Furthermore, a Patch-based Multi-Kernel Dual-Branch (P-MKDB) block is incorporated into the decoder to effectively handle diverse local blur patterns. Experiments on GoPro, HIDE, and RealBlur show competitive deblurring performance, while ablation studies support the contribution of the proposed cross-stage patch interaction and patch-wise refinement. Notably, CPINet improves the mean PSNR from 36.98 dB to 37.61 dB and the mean SSIM from 0.954 to 0.961 relative to UFPNet, with both metrics averaged across RealBlur-J and RealBlur-R. These improvements demonstrate its effectiveness in challenging real-world scenarios.

Mathematics doi: 10.3390/math14203809

Authors: Mudassir Shams Bruno Carpentieri

We study high-order predictor–corrector schemes for the simultaneous computation of polynomial roots with known multiplicities. The proposed method, BKM*, combines a fourth-order two-step modified Newton approximation, a coupled Ehrlich-type predictor of order six for multiple roots, and a final Gargantini–Farmer–Loizou correction. A local convergence analysis establishes a vector Q-order of at least eighteen, together with explicit leading error terms. The analysis is extended to a multiplicative correction factor applied to the final corrector: if the factor differs from one by O(εk), the local order is at least min(18,6+k). For a correction factor derived from a fifth-order scalar method, k=2, so the resulting weighted variant has an order of at least eight, and the weight reduces rather than increases the order. To isolate the role of the predictor, we also examine the composition of one PKM* step with the same corrector, which also has a local order of at least eighteen and requires fewer function evaluations per iteration. Experiments in 6000-digit arithmetic on polynomials of degrees 12, 20 and 21 confirm observed orders close to 18 and 8, and show that neither order-eighteen composition is uniformly faster: the composition with fewer function evaluations per iteration requires less computing time when both need the same number of iterations, whereas BKM* benefits from a more favourable pre-asymptotic phase from the more distant starting configurations.

Mathematics doi: 10.3390/math14203807

Authors: Volodymyr Tverdomed Natalia Kokriatska Leonid Tymchenko Yurii Didenko Mykhailo Braikovskyi Mariia Demchenko Vaidas Lukoševičius Ramūnas Skvireckas Rolandas Makaras

Signal processing systems operating in noisy or dynamically changing environments require computational architectures capable of multilevel parallel information processing. Biological sensory systems have naturally evolved such architectures through hierarchical organization, providing inspiration for efficient computational models. This paper presents a mathematical model of the direct parallel–hierarchical transformation (PHT), its FPGA implementation, and an application to laser-beam spot processing. The original experiment yielded an average coordinate-determination error of 0.47%, a maximum error of 1.6%, and a standard deviation of 0.36%. The 269-frame tr0_269 dataset constitutes one sequentially acquired frame sequence; its 70/199 division is therefore treated as an internal functional division within that sequence rather than as a separation of independent laser tracks. For the subsequent 199-frame segment, the complete modified PHT chain gave a mean coordinate-determination error of 0.567 pixels; the repeated calculation gave 0.569 pixels, supporting reproducibility within this frame sequence. For an additional check, separate completed frame sequences were used without overlap: TRASSA00 and FRAME02-FRAME05 were used for implementation checks and parameter definition, whereas FRAME06-FRAME11 were not used for parameter selection and were used only for subsequent evaluation of the method. The FMT headers show that FRAME02-FRAME11 are separate completed acquisition sequences with individual start and end times; the gaps between successive sequences substantially exceed the 40 ms inter-frame period, excluding their interpretation as contiguous fragments of one continuously stored FMT file. No sequence and no frame contributed to both groups. The 38-section method produced a lower mean coordinate-determination error than the six-section method in all six evaluation sequences, with means across the six sequences of 0.815 and 1.321 pixels, respectively (Wilcoxon statistic 0; one-sided p-value 0.015625; 95% confidence interval from whole-sequence resampling, −1.178 to −0.152 pixels). In an additional evaluation of the complete PHT on FRAME06-FRAME11, the shape-coefficient limits were determined only from TRASSA00 and FRAME02-FRAME05 as the central 95% empirical interval [0.637, 0.862] and then applied unchanged to FRAME06-FRAME11. On the same evaluation frames, the mean same-frame error of the complete PHT was 0.961 pixels versus 0.822 pixels for the direct 38-section stage. The complete method produced a larger same-frame error in all six sequences because its acceptance logic can retain the preceding accepted coordinate. The FPGA implementation reached 7 ms/frame with register memory and 25 ms/frame with serial memory.

Mathematics doi: 10.3390/math14203806

Authors: Mohammed Alliheedi Saad Alqithami

Open-set intrusion detection must distinguish known traffic classes, reject previously unobserved attacks, and respect the available communication between a traffic monitor and a coordinator. We study X-MAG-COS, a compact evidence-message architecture that separates known-class prediction from rejection using predictive uncertainty, local anomaly evidence, and a message-prototype residual. Beyond structural properties, we derive bounds that propagate packet-scalar quantization through a normalized one-versus-rest classifier, possible predicted-class prototype changes, the composite score, and the calibrated rejection decision. The primary evaluation uses eight leave-one-attack-family-out tasks and five seeds on 5G-NIDD with training-only feature screening, packet-decoded inference, and disjoint normalization and calibration subsets. The ownership map contains two highly imbalanced metadata partitions, not eight active physical monitors. A matched extension evaluates six algorithmic replacements and four controls at identical realized false-positive counts within each task. At the all-known FPRs targeted at 0.1%,1%, and 5%, the 16-byte reference attains mean unknown recalls of 0.0934, 0.5484, and 0.7242; centralized random forest attains 0.6781, 0.7557, and 0.7942. Replacing the local forest with extra trees raises near-5% recall to 0.8062 but lowers stringent-level recall, while mean fusion has the opposite operating-point tradeoff. These substitutions do not establish a uniformly superior configuration. Fixed-model precision diagnostics satisfy the derived score and decision bounds within a stated 10−8 numerical tolerance without constituting a machine-verified proof. The 12-byte detection-only record remains a competitive alternative; the 16-byte record additionally contains an optional attribution proxy whose analyst-facing value is unmeasured. UDPFlood, the largest attack family and 37.6% of the corpus, retains below-chance mean ranking with AUROC 0.4818 ± 0.0190. Controlled peer-context experiments and separately retrained CICIoT2023 results further delimit the approach. The findings establish a characterized communication–detection tradeoff, not universal detection superiority, validated explainability, or deployment readiness.

Mathematics doi: 10.3390/math14203805

Authors: Ali Nabavi Rabih Ghostine

Given a fixed non-adjacent pair of vertices, suppose we know how many induced subgraphs make the pair look like false twins, allowing up to a prescribed number of disagreements. Can this local witness count recover how strongly the two vertices agree in the full graph? We study this inverse question. In the main deterministic setting, the graph size, the induced-subgraph size, the allowed number of disagreements and the exhaustive witness count are treated as known, while the global adjacency-agreement count is unknown. We first prove an exact counting formula and use it to determine when the unknown agreement count can be recovered uniquely and when saturation causes information to be lost. We then study the regime in which the subgraph size and the allowed number of disagreements grow proportionally with the graph. A method-of-types argument gives the exponential growth rate up to an O(logN) error. The resulting rate develops a plateau before the exact finite count itself becomes constant. Thus there is a range in which different global agreement levels are still distinguishable at finite size but are no longer distinguishable at exponential scale. In the exact-witness case we also obtain sharp asymptotic and finite-size stability estimates. Numerical calculations illustrate the finite-size behavior, and strongly regular graphs and the dense stochastic block model are discussed as examples.

Mathematics doi: 10.3390/math14203802

Authors: Yiqin Lin Wenbo Li Liping Zhou

We extend the factored Newton iteration originally developed by Benner et al. for algebraic Riccati equations with a negative quadratic term—to the positive-real case. Unlike the negative-sign setting, the positive sign introduces two well-posedness issues: each intermediate matrix Ak must remain nonsingular, and the DC-gain condition must be preserved to ensure the validity of the factored inversion formula. We prove rigorously that both properties are invariant under the Newton update. The resulting structure-exploiting solver, GENPF, reduces the per-iteration cost from 16n3 to approximately 2n3 floating-point operations when the input matrices are tall and skinny. Numerical experiments confirm that GENPF preserves the quadratic convergence and accuracy of the conventional Newton iteration, requires significantly less computational time, and maintains the DC-gain condition throughout the iteration.

Mathematics doi: 10.3390/math14203804

Authors: Ayşe Metin Karakaş Fatma Bulut Murat Karakaş Sinan Çalık

This study introduces the Topp–Leone Juchez (TLJ) distribution, a flexible two-parameter lifetime model constructed from the one-parameter Juchez distribution through the Topp–Leone transformation. The proposed model provides additional shape and hazard-rate flexibility while remaining parsimonious. Several distributional and reliability properties are derived, including the survival and hazard functions, quantile function, moments, entropy measures, and stress–strength reliability. Classical and Bayesian estimation procedures are investigated, and their finite-sample performance is examined through Monte Carlo simulations. Two real-data applications involving accelerated life-test and aircraft window-glass strength data are also considered. The results show that the TLJ model provides competitive fits relative to several established lifetime distributions. For the aircraft window-glass data, the TLJ and Gamma models provide very similar empirical support, with an AIC difference of only 0.0858. Importantly, the TLJ model is not a nested extension of the Juchez distribution, since setting α=1 does not recover the original Juchez model. Overall, the results demonstrate the usefulness of the TLJ construction as a flexible alternative for lifetime-data analysis.

Mathematics doi: 10.3390/math14203803

Authors: Gregory A. Chechkin Rustem R. Gadyl’shin Andrey L. Piatnitski

This paper studies the vibration of a body with a hole (trap), which is caused by a plane acoustic wave. We assume that the body contains a periodic microstructure of small inclusions, which can partially reflect acoustic waves, and consider the scattering problem for the acoustic waves, which is modeled by an appropriate boundary value problem for the Helmholtz equation. Our goal is to describe the asymptotic behavior of the spectrum of this boundary value problem as the period of the microstructure and the diameter of the hole tend to zero. The scattering frequencies are characterized by the poles of the analytic continuation of the resolvent of the corresponding boundary value problem.

Mathematics doi: 10.3390/math14203801

Authors: Gary F. Dargush

In recent years, convolved action principles have provided attractive variational formulations for a variety of linear problems in engineering science, including those with dissipative elements. The inclusion of a temporal convolution circumvents the main issues of Hamilton’s principle relating to an inconsistent set of end point conditions in time and its inability to address dissipative processes. The present theory paper introduces the concept of virtual convolved action to extend the applicability of convolved action principles to quite general nonlinear problems. This can also be viewed as an extension of the principle of virtual work to produce novel weak forms of the governing equations over space and time for dynamical phenomena. Initially, this idea is used to develop the principle of virtual convolved action for the dynamics of continuum solids. Afterwards, the same concept of virtual convolved action is applied to Maxwell’s theory of electromagnetism with promising theoretical results for both linear and nonlinear media. With that established, a new principle of stationary convolved action is derived for the linear case, including definition of the action, the weak form and the corresponding Euler–Lagrange equations that recover the original statement of the initial/boundary value problem of electromagnetics.

Mathematics doi: 10.3390/math14203800

Authors: Omar Hernández-González

This paper proposes a saturated high-gain observer for a class of state-affine nonlinear systems with coupled structures under sampled-output measurements. The study is motivated by state estimation for quadrotor trajectory tracking, where output measurements are available only at large sampling intervals and are corrupted by noise. Although continuous-discrete high-gain observers are effective for reconstructing unmeasured states, large correction gains may induce the peaking phenomenon during transient stages, producing aggressive estimated signals that can affect the closed-loop response. To address this issue, the proposed observer introduces saturated correction terms that explicitly bound the transient injection signals while preserving the convergence properties of the high-gain framework. This strategy enables aggressive observer gain selection to accelerate convergence dynamics while completely suppressing transient peaking in the estimated states. The proposed observer is applied to a quadrotor trajectory-tracking problem, and numerical simulations are conducted under large sampling periods and measurement noise.

Mathematics doi: 10.3390/math14203799

Authors: Leon Cohen

We define the characteristic function operator eiθA+iτB, where A and B are explicit functions of the operators x and D. Operators of this form arise in a wide range of applications, including quantum mechanics, evolution equations, and time–frequency analysis. We briefly review the historical development of the characteristic function operator and present a general method for evaluating its action on functions in both the spatial and Fourier domains. The method relies on solving the eigenvalue problem for θA+τB. A number of examples are presented. The method is then applied to the solution of evolution equations.

Mathematics doi: 10.3390/math14203798

Authors: Kunmeng Li Jintao Li Yuanhui Li Yongjiang Wang Jiaqi Zhang

A mechanics-based mathematical model is developed for the support-parameter design of a pre-stressed expandable prop group in horizontal and gently inclined thin-vein stopes. First, pressure-arch theory and equivalent-beam theory are combined to derive analytical expressions for the nonuniform roof-load distribution and roof deflection. The force method and deformation-compatibility conditions are then used to characterize the roof–support interaction and to compare the mechanical responses of retained rock pillars, conventional concrete pillars, and pre-stressed expandable props. The analysis indicates that pre-stressed expandable props establish roof contact earlier than conventional concrete pillars and require a lower reaction force than high-stiffness retained rock pillars while permitting controlled roof convergence. Subsequently, a coupled roof–prop group model is formulated using deformation-compatibility equations to determine the required support force at each prop location and to coordinate prop-group spacing with the number of steel pipes in each prop. The proposed model is applied to a field test at a gold mine in Dandong, China, and its predictions are evaluated against monitored support loads. For a 20 m stope span, the preferred center-to-center spacing is determined to be 5.0 m. The stabilized loads of the three monitored props are approximately 922, 1060, and 778 kN, compared with theoretical values of 841, 964, and 841 kN, corresponding to relative deviations of 8.8%, 9.1%, and 8.1%, respectively. All measured loads remain below the designed ultimate bearing capacities. The results demonstrate that the proposed model captures the nonuniform load-sharing characteristics of the prop-group system, particularly the higher support demand in the central part of the stope, and provides a mechanics-based basis for rational support-parameter design.

Mathematics doi: 10.3390/math14203797

Authors: Ke Wang Wanjie Tao Yuchen Yuan Zhang-Hua Fu Xin Cai Yanyan Zheng Quan Lu Ning Jiang Yuanyuan Liu

Large-scale telemarketing recommendation is crucial for personalized customer outreach in various industries like banking and telecommunications. However, traditional individual-level recommendation approaches suffer from high computational overhead in large-scale scenarios, making group-level recommendation a promising alternative. Nevertheless, existing group-level recommendation methods rely on distance-based similarity metrics that overlook long-tail density variations and decouple clustering from resource allocation, leading to suboptimal allocation decisions. To address these challenges, we propose a novel Group Behavior-guided Multi-density Graph Clustering (GBMGC) framework, which integrates multi-density behavior-aware graph clustering with constrained resource allocation optimization for efficient and scalable telemarketing recommendation. The framework adopts a two-stage design consisting of Density-aware Graph Clustering (DGC) and Group-guided Optimization Recommendation (GOR), with Tree-structured Parzen Estimator (TPE)-based hyperparameter selection. Specifically, to overcome the limitation of conventional distance-based similarity grouping in capturing long-tail behavioral density patterns, DGC constructs a weighted behavioral graph using heuristic weights derived from statistical tests on historical response distributions and applies adaptive density thresholds to identify groups with different population densities. In the second stage, based on the resulting group structure, GOR formulates the scheduling process as a constrained integer programming problem to maximize expected answer rates under practical constraints. Finally, TPE selects the key hyperparameters of DGC and GOR using validation-set performance as feedback, reducing manual hyperparameter search. Evaluated on a financial telemarketing test dataset with more than 3 M records and the MovieLens-1 M test dataset with approximately 0.2 M records, GBMGC achieves higher answer rate (AR) point estimates than the compared methods on the historically matched observations under the adopted offline evaluation protocol, while maintaining favorable computational efficiency. The results on MovieLens-1 M provide additional evidence of its applicability beyond the telemarketing recommendation setting.

Mathematics doi: 10.3390/math14203796

Authors: Maja Nedović Srđan Milićević Dunja Arsić Jelena Čolić Oravec

The spectrum of a matrix contains information essential for understanding the dynamics of the real system behind the matrix. Knowledge of eigenvalues and generalized eigenvalues is of great importance in stability analysis. In this paper, we present a new technique for obtaining spectrum localizations of any given square complex matrix with respect to any chosen partition of the index set. The construction of the localization set is tightly related to special H-matrices introduced in this paper by the name Partitioned Pupkov matrices. The new matrix class is applied in order to obtain an estimate of the spectral radius of graphs and matrices. Results on spectral radius for a weighted digraph with matrix weights are widely applicable in modeling multidimensional dynamics, analysis of system stability and connectivity strengths of corresponding networks. We present further possibilities for application to localization of generalized eigenvalues of matrix pencils. We obtain a norm estimate of the inverse for matrices in the new class. The relationships between the new criteria and well-known matrix classes are analyzed, and numerical examples illustrate how the proposed estimates and localization sets compare to existing bounds.

Mathematics doi: 10.3390/math14203795

Authors: Samuel Montañez-Jacquez Ernesto Moya-Albor

We develop Bayesian Mechanics Portfolio Theory (BMPT), which represents an investor as an agent that infers hidden market states, encodes preferences, evaluates policies by expected free energy, and acts. We first prove a boundary theorem showing that if actions change neither the admissible observation channel nor the transition law of the latent state, expected information gain is policy invariant, so policy rankings are determined by pragmatic value, implementation terms, and any nonuniform policy prior. Under a mean–variance-compatible pragmatic cost, BMPT recovers the subjective tangency portfolio at this boundary. We instantiate BMPT as Causal Hierarchical Active Inference (CHAI), a hierarchy of coupled generative-model layers around a hierarchical risk parity base. A prospectively registered walk-forward exercise on twelve exchange-traded funds serves as an implementation demonstration, not as a test of trading-strategy outperformance. CHAI is classified as a tie against its matched base; the Sharpe ratio difference is −0.023 (90% interval [−0.037,−0.009]), with the interval inside the prespecified equivalence margin. A constructed action-gated environment restores policy-specific epistemic value. BMPT therefore provides a broader, explicit, auditable, and causally disciplined model of adaptive portfolio choice; the paper does not claim superior realized returns.

Mathematics doi: 10.3390/math14203794

Authors: Khadija Mabrouk Maryam Gharamah Alshehri Mohamed Rossafi

We study multipliers Mm,f,g of continuous K-frames over a σ-finite measure space. We give criteria for invertibility on Ran(K) governed by ∥m−1∥∞, and show that previously published criteria stated in terms of ∥m∥∞ have hypotheses that no admissible data can satisfy, so that they are vacuous rather than false. A Douglas-type characterization replaces the known one: Mm,f,g is invertible on Ran(K) exactly when Ran(K)⊆Ran(πRan(K)Mm¯,g,f). We then characterize the existence of continuous K-right and K-left inverses by range inclusions, identify those of minimal norm, and represent one-sided inverses as multipliers of continuous K-duals; a two-dimensional example shows that a representation formula for K-left inverses previously stated in the discrete setting is not correct as stated. Finally, we prove that pointwise biorthogonality is ineffective when μ has no atoms, and replace it by a μ-weighted biorthogonality along a partition of Ω into blocks, which we then extend to families that are not constant on the blocks.

Mathematics doi: 10.3390/math14203793

Authors: Gaofeng Che Jinchun Deng

This paper develops an adaptive model predictive control (AMPC) scheme for uncertain nonaffine nonlinear systems by integrating deep Koopman operator theory into a fully data-driven modeling framework. Complex nonlinear systems typically feature prominent nonaffine dynamics and are vulnerable to external disturbances, posing substantial difficulties for controller synthesis. Conventional Koopman-based methods depend on manually designed lifting functions, which suffer from limited modeling accuracy and heavy reliance on prior system knowledge. To address these deficiencies, this work adopts a deep neural network to autonomously learn optimal lifting dictionaries and construct a high-dimensional linear embedding of original nonlinear dynamics. This achieves global system linearization without parametric prior information and converts intractable nonaffine dynamics into a bilinear form amenable to linear control design. On this basis, model predictive control (MPC) is deployed as the core feedback module to guarantee closed-loop stability and satisfy system constraints via real-time receding horizon optimization. Furthermore, an iterative learning control (ILC) strategy is integrated to compensate for system uncertainties and external disturbances. The resulting composite control framework combines the real-time stabilizing merit of MPC and the iterative feedforward refinement capability of ILC across repeated operation trials. Rigorous convergence analysis based on the composite energy function theory verifies the asymptotic zero convergence of tracking errors for repetitive uncertainty components, while bounded residual error exists for non-repetitive disturbances. Comparative simulation results demonstrate that the proposed method effectively reduces modeling and tracking errors while preserving stable closed-loop performance. Quantitative evaluations further validate its superior precision and robustness over existing benchmark approaches, illustrating great applicability to complex nonlinear uncertain systems.

Mathematics doi: 10.3390/math14203792

Authors: Peng Ren Fuchu Dai Sanhong Chen

It is essential to explore dynamic response of a deep V-shaped slope for incident SH waves, meeting the challenges of extreme disasters including earthquakes. A novel analytical solution is proposed to effectively evaluate dynamic response of deep V-shaped slopes for incident SH waves. A validation of this solution is confirmed through comparisons with boundary integral equations and another analytical approach. More importantly, it can provide the exact analytical expressions of unknown coefficients of wave functions and present a new idea solving relative problems. The new numerical results show that displacement amplitudes and phases change apparently with the dimensionless distance. Moreover, effects of incident angles, angles of slopes and the dimensionless frequencies to the dynamic response of deep V-shaped slopes are significantly discussed in a wide range of frequencies. Regular patterns of displacement amplitudes are symmetric for vertical incidence. The oscillation numbers of displacement amplitudes on a facing wave surface and its left are often more than these on a shadow surface and its right for oblique and horizontal incidence. However, the regular patterns of displacement phases versus the dimensionless distance are similar. This study would enhance theoretical and practical significance for an analytical approach, wave motion and site effects.

Mathematics doi: 10.3390/math14203791

Authors: Zihan Xu Shuaishuai Fu Aijun Yang Ligang Shi

Smallholder farmers often lack the capacity to adopt green technologies, and their risk aversion further limits green production. Outsourcing green technology to specialized service providers is a promising solution, but it remains unclear how power structure affects farmers’ adoption of such outsourcing, how supply chain members rank different power structures, and whether outsourcing always improves social welfare. To address these questions, this paper develops an equilibrium model of an agricultural supply chain consisting of a risk-averse farmer, a retailer, and a green technology service provider. The farmer may either continue traditional production or outsource green technology. Farmer risk aversion is captured by conditional value-at-risk (CVaR). We derive equilibrium decisions under three power structures: service-provider-led, retailer-led, and vertical Nash. We characterize the adoption threshold for green technology outsourcing, compare equilibrium planting acreage, green technology input, prices, and member payoffs, and evaluate social welfare. The results show that outsourcing becomes preferable when farmers are less risk averse, and the outsourcing threshold is lowest under service provider leadership. The farmer prefers vertical Nash when consumers’ green preference is low and service-provider leadership when it is high. Service providers benefit from leadership, while retailers do not always do so. Social welfare can improve under service-provider-led outsourcing but may decrease under retailer-led and vertical Nash regimes. An extension with exogenous service pricing is also analyzed. These findings provide equilibrium-based implications for sustainable agricultural outsourcing policy.

Mathematics doi: 10.3390/math14203790

Authors: Luis Gustavo Alvarez Ascencio Celia Avalos-Ramos Enrique Alfonso Sánchez Pérez

In this paper, we consider a vector-valued operator T taking values in a quasi-Banach space X, assuming T is comonotonically additive on the positive cone. In this setting, we establish an optimal domain theorem through vector-valued Choquet integration. More precisely, given a σ-order continuous λ-quasi-Banach function space X with S(Σ)⊂X, an order continuous Banach lattice Y, and an operator T:X→Y that is comonotonically additive on the positive cone, we identify natural structural assumptions under which T can be represented as integration with respect to a vector capacity. In particular, assuming that T is Jordan decomposable, monotone, submodular, and lower semi-continuous, we construct a vector capacity ΛT such that T factors through the Choquet-type space Lqv1(ΛT) via the corresponding integration operator. Under suitable assumptions on the null sets of the underlying capacity, we prove an analogue of the classical Optimal Domain Theorem by showing that Lqv1(ΛT) is the largest σ-order continuous quasi-Banach function space to which T admits a continuous extension preserving the assumed structural properties. Consequently, Lqv1(ΛT) is the optimal domain of T, extending the classical Optimal Domain Theorem from continuous linear operators to comonotonically additive operators on the positive cone in the setting of Choquet integration.

Mathematics doi: 10.3390/math14203789

Authors: Jie Zhang Xiaojuan Xie Shungen Xiao Yuqin Wu Chuntong Dong

As electric buses become increasingly integrated into urban public transport systems, research on their role in transfer networks remains limited. Passengers often encounter extended waiting times during transfers, raising equity concerns. This study formulates a multi-objective mixed-integer quadratic programming (MIQP) model to optimise electric-bus transfer-station planning, considering station-level transfer equity, the surrounding built environment, multimodal transfers involving metro services and taxis, and the operational characteristics of electric buses. The model aims to (1) minimise passenger transfer-time burden, (2) reduce system operating costs, and (3) improve station-level horizontal transfer equity. Sensitivity analyses are conducted for time cost and preference parameters. The Harbin case study shows that, compared with the original scheme, the optimised scheme reduces total transfer time by 11.25%, decreases the variance-based equity indicator by 25.52%, reduces the maximum transfer utility by 14.99%, and lowers annual operating costs by 206,700 CNY. This study provides crucial insights for optimising electric-bus deployment in the broader context of public transport electrification.

Mathematics doi: 10.3390/math14203788

Authors: Ayesha Ahmad Adnan Khan

The financial world and the field of quantitative finance face the challenge of accurate and rapid valuation of American-style options, particularly in high-frequency trading and market-making environments. In this study, we propose a deep-learning-based framework for pricing American options using Parameterized Physics-Informed Neural Networks (PPINNs). The proposed approach extends standard PINNs by incorporating key model parameters (strike price, volatility, and interest rate) as network inputs, along with the standard practice of using stock price and time to maturity as PINN inputs. The modified structure is called Parameterized-PINNs. It retains the physics-informed formulation of PINNs by incorporating the governing partial differential equation into the learning process while enabling a single trained network to generalize across a broad range of option configurations without requiring retraining. Numerical experiments demonstrate that the proposed model achieves high average pricing accuracy, with an L2 relative error of approximately 0.20% for call options and 0.09% for put options, over the full evaluation domain. However, local relative errors in deep out-of-the-money regions under extreme parameter combinations can be substantially higher, primarily due to near-zero option values rather than large absolute mispricings. Once trained with a one-time offline cost of approximately 65 min for call options or 71 min for put options, PPINN inference takes almost 1.5 ms per option, approximately 1000 times faster than the Monte Carlo benchmark in the reported single-option evaluation, making it well suited to applications requiring repeated revaluation across a stable parameter regime. The framework is further evaluated using 1500 observed American option prices for two actively traded U.S. equities (Tesla and Amazon). The market-data experiment provides an additional empirical assessment of practical applicability. Overall, the numerical experiments demonstrate that PPINNs can provide accurate and low-latency approximations to the specified Black–Scholes American option pricing problem, with potential applicability to repeated valuation under stable model assumptions.

Mathematics doi: 10.3390/math14203787

Authors: Suares Clovis Oukouomi Noutchie

We establish a compactness theorem for three-dimensional incompressible Navier–Stokes approximations with varying regularization mechanisms. Equation residuals are measured in a negative space compatible with the velocity, pressure, and convection, whereas errors in the local energy balance are represented by separate vanishing functionals. This separation covers residual stresses converging only in L3/2 and avoids an unjustified force–energy pairing. Uniform energy, normalized-pressure, and equation residual bounds yield a translation modulus whose constants are independent of the regulator and strong local convergence in every space-time Lebesgue class below 10/3, including the cubic class needed for the nonlinear energy flux. We prove stability of suitability and an exact identity relating the limiting local energy defect, the weak limit of approximate defects, and dissipation concentration. For a transport-mollified Friedrichs scheme on the three-torus, every admissibility condition is verified without invoking the abstract compactness theorem. Finally, classical one-scale epsilon regularity gives a fixed-scale lower bound for approximants converging to a singular suitable limit. This last conclusion is a consequence of the framework rather than a new epsilon regularity theorem. No interchange of regulator and shrinking-scale limits is asserted.

Mathematics doi: 10.3390/math14203786

Authors: Bowen Duan Qingmin Zhang Peibo Hao

Single-cell differential expression analysis combines a gene-level statistic with a false discovery rate (FDR) procedure. We examine how these two choices affect error control and power by pairing four statistics with BH, e-BH, data-splitting mirror, and target–decoy procedures. The benchmark uses zero-inflated negative-binomial simulations and a donor-level model fitted to Kang18 control data, with known signal genes in both designs. We vary dropout, signal type, gene number, and cross-gene dependence. Higher dropout reduces power across all 16 combinations in the mean-shift experiment, whereas null FDR depends on the statistic and its tail calibration. Distribution-sensitive statistics detect equal-mean dispersion changes that mean-based statistics largely miss. The apparent power gain of data splitting and target–decoy at a larger gene count is not reproduced when the number of signals is held fixed. The working e-value is sensitive to null-score calibration, and donor dependence affects some procedures without a common monotone pattern. These results show why benchmark comparisons should separate the signal being tested, the calibration of the input evidence, and the multiple-testing rule.

Mathematics doi: 10.3390/math14203785

Authors: Ergül Türkmen Engin Kaynar Yıldız Aydın

In this paper, we introduce the concept of ps-injective modules, which plays a key role in our approach. We develop the various properties of these modules. In particular, we prove that for a ring R, every projective semisimple R-module is injective if and only if every R-module is ps-injective. Furthermore, we show that every ps-injective R-module is injective if and only if R is a left semiartinian and left SI-ring. In addition, using the projective socle of the ring R, we investigate in detail the structure of modules whose socle is singular.

Mathematics doi: 10.3390/math14203784

Authors: Sebastiano Ettore Spoto

Inference from a finite observation window in fractional dynamics depends on what is known about the forcing. We study whether fractional orders can be distinguished under uncertain excitation and whether calibrated interventions can exclude a competing model family. For passive observations, the known-forcing case provides a conditional reference. Covariance-weighted projection quantifies the order information that remains when the forcing and physical coefficients are uncertain. With 33 forcing coefficients and memory-only observations, the retained fraction of the squared order-sensitivity norm decreases from 2.01×10−3 after forcing elimination to 9.40×10−7 after two physical coefficients are also profiled. Different optimizers attain matching objective values even though the fully profiled order remains poorly constrained. In the active cascade, causal convolution contrasts eliminate a common unmeasured input. A positive annihilator removes unknown decay and ordinary dynamics, and a quartic deterministic error certificate tests the single-order family. Assuming zero common history, bounded gains, repeatable inputs, and the stated waveform regularity, the fine-resolution acquisition excludes that family for both blocks throughout the prescribed continuous order interval. The coarse-resolution acquisition remains inconclusive. These diagnostics inform forcing restrictions, the choice of complementary measurements and acquisition precision; they do not establish global recovery or field validation.

Mathematics doi: 10.3390/math14203783

Authors: Wenxin Zhang Rufei Zhang Qian Zhu

This paper employs the established time-varying parameter vector autoregressive connectedness framework (TVP-VAR-DY) based on generalized forecast error variance decomposition (GFEVD) to characterize the nonlinear, time-dependent risk spillover network linking carbon and multi-sector energy financial assets. Our core empirical contribution is to integrate three distinct categories of uncertainty risks with a 10-dimensional carbon-energy financial system in a unified analytical framework. We construct a 10-dimensional stochastic financial system comprising EUA carbon futures, fossil energy commodity futures (crude oil, natural gas, coal), and clean energy equity indices (wind, solar, hydropower). By utilizing monthly logarithmic return stationary time series spanning 2011–2025, we perform numerical estimations of static connectedness matrices, dynamic total spillover indices, directional pairwise spillover networks, and net risk transmission metrics under three distinct multidimensional uncertainty risk factors: geopolitical risk (GPR), economic policy uncertainty (EPU), and climate policy uncertainty (CPU). The empirical results show three key findings. First, spillover effects of multidimensional uncertainty risks exhibit heterogeneous patterns: climate policy uncertainty acts as the primary risk transmitter, followed by geopolitical risk, while economic policy uncertainty exerts weaker and mostly indirect transmission. External uncertainties (climate policy and geopolitical risks) are associated with spillover effects between carbon and energy markets far more strongly than endogenous uncertainties, and extreme events coincide with structural surges in total spillover magnitude. Second, carbon markets function as an intermediary bridge in risk transmission: they absorb upstream uncertainty spillovers and propagate volatility to all energy subsectors, gradually evolving from net risk receivers to neutral market participants alongside improved climate governance frameworks. Third, different shock types generate distinct spillover patterns: sudden emergencies are linked to rapid, large-magnitude yet short-lived spillovers, whereas policy-driven shocks exert stable, persistent impacts; policy factors play a pivotal guiding role in market volatility and the energy transition. This study integrates three categories of uncertainty into a unified analytical framework, clarifies differentiated risk response logics across energy segments via quantitative network analysis, and provides empirical evidence and quantitative references for global climate governance and cross-market risk supervision.

Mathematics doi: 10.3390/math14203781

Authors: Yuqing Jiao Siok Yee Tan Fadilla ’Atyka Nor Rashid Huifen Xing Yong Zhang

Small objects in underwater and traffic-sign images often have weak boundaries and low contrast. Downsampling and multi-scale fusion can further weaken the features needed to detect them. We propose ContextFlow-YOLO, a YOLOv8n-based detector designed to preserve context during feature extraction and reuse it across scales. Its context-preserving backbone combines local features with surrounding and global information during downsampling. The global-guided scale-sequence neck distributes this context to features at different levels. A nonlinear context-attention fusion unit then refines the responses used for prediction. ContextFlow-YOLO obtains mAP@0.5 scores of 0.855, 0.838, and 0.826 on URPC2019, URPC2020, and TT100K, respectively. On TT100K, the model uses 6.11 M parameters and runs at 134 FPS. Heatmap and receptive-field visualizations show more concentrated target responses and broader feature coverage than YOLOv8n.

Mathematics doi: 10.3390/math14203782

Authors: Hsien-Chung Wu

This paper establishes an embedding theorem for solving multiobjective linear set optimization problems. By introducing a partial order through this embedding framework, we formally define three solution concepts, which are optimal solution, Pareto optimal solution, and ideally optimal solution. We derive distinct optimality conditions for each solution type. Furthermore, by specifying an appropriate convex cone, we demonstrate that these solutions can be practically computed by solving equivalent conventional linear programming problems using the simplex method.

Mathematics doi: 10.3390/math14203780

Authors: Ehmet Kasim Rena Eskar Taiyong Wang

This paper investigates the well-posedness (WP) and asymptotic stability of a standby repairable system with partial failure and priority, wherein components in a partial failure state remain unrepaired during system operation. The governing integro-differential equations are reformulated as an abstract Cauchy problem (ACP) on an appropriately chosen Banach space via the introduction of a linear operator. Using C0− semigroup theory together with spectral analysis, we prove that the system operator generates a positive contraction C0− semigroup, thereby guaranteeing the existence of unique time-dependent solution (TDS). Moreover, through a detailed examination of the spectral distribution of the generator on the imaginary axis, we establish the strong convergence of the TDS to its steady-state solution (SSS) as time tends to infinity. Complementing these analytical results, a Monte Carlo simulation (MCS) is performed to track the transient evolution of reliability indices, providing numerical validation of the theoretical predictions. These results offer a theoretical basis for evaluating system reliability and inform maintenance strategies in continuous-production environments.

Mathematics doi: 10.3390/math14203779

Authors: Fu Hong Jianjun Jiao Linkun Wang Shiyu Wang

We study the asymptotic integration of second-order impulsive differential equations whose impulse conditions are of the general linear type Δx(θi)+aix(θi)=0,Δp(t)x′(θi)+bix(θi)+cix′(θi)=0, so that the state and the quasi-derivative are coupled simultaneously at the impulse moments. Our main contributions are as follows. First, we show that a first-order derivative term h(t)x′ in the differential operator can be absorbed into a renormalized quasi-derivative P(t)x′=p(t)exp∫h/px′; this transformation leaves the dimensionless pair ci/p(θi),bi/p(θi) and hence the monodromy factor (1−ai)1−ci/p(θi) unchanged, so the monodromy data alone carry no information on bi: within the present framework bi is a free parameter, and it is the simultaneous nonvanishing of bi and ci that places the equation outside the two impulse classes treated in the literature. Second, for the associated homogeneous linear impulsive equation we establish a generalized Wronskian (Abel) identity and prove the existence of positive principal and nonprincipal solutions, characterized by the divergence and convergence of the weighted integral ∫∞γ(t,t0)/(p(t)u2(t))dt, where γ(t,t0) is the product of the monodromy factors, together with the ordering of the quasi-logarithmic derivatives pu′/u<pv′/v. Third, using these solutions and the Schauder fixed point theorem, we prove that the associated nonlinear impulsive equations admit solutions with prescribed asymptotic behavior x(t)=av(t)+bu(t)+o(u(t)) and x(t)=av(t)+bu(t)+o(v(t)); in the second representation the coefficient a is determined by the leading term, while b is not identifiable since bu=o(v), and this is stated precisely in Theorem 4. The separated and mixed impulse cases are recovered as particular limits of our framework. Examples with explicit principal and nonprincipal solutions and numerical simulations, for which the integration scheme and its tolerances are specified, illustrate the results.

Mathematics doi: 10.3390/math14203778

Authors: Tianyu Huang Ke Tang Youyou Li

Short-horizon emergency re-optimization of airport apron ground-support operations works when its objective carries timing stability, and backfires when it does not. Using a new benchmark—89 days of Amsterdam and Chicago ADS-B ground traces including transponder-equipped ramp service vehicles, with semi-synthetic task and fault layers: 3540 counterfactual-controlled fault episodes and 740 test reschedule instances with CP-SAT references (85% proved optimal)—we score every recovery over the 30–120 min emergency horizon using a full-day shadow replay against a matched no-fault counterfactual, with date-level paired inference. CP-SAT with a start-time stability term, or with a lexicographic rule that returns the most plan-preserving plan attaining the first-stage window objective value, matches plan-preserving repair on realized disruption on vehicle-removal faults (median 1.6–2.4 vs. 2.7 ks) and lowers absolute realized tardiness on 19/19 test dates. The same model minimizing only in-window weighted tardiness is worse end-to-end than greedy earliest-due-date dispatch on 19/19 dates (exact p=3.8×10−6). For instances certified as optimal at every churn budget, the unconstrained solve reaches the window optimum of the minimal-churn solve yet realizes 2.6 times more disruption; learned re-optimizers trained on the same objective are worse still, and rolling-horizon repetition amplifies the harm. The harm travels through re-timing and re-sequencing rather than reassignment, so an assignment-only churn penalty does not help. The typical instance has no in-window headroom over greedy dispatch (median learning space 0). The ordering holds across ten generator settings and service-time noise. The benchmark will be made publicly available.

Mathematics doi: 10.3390/math14203776

Authors: Ayşegül Keten Keten Çopur

This paper investigates several equivalent formulations of the unconditionally p-approximation property. Inspired by these formulations, we introduce a new approximation property, called the weak unconditionally p-approximation property, and develop a number of equivalent characterizations for it. We also examine its relationship with the corresponding duality problem and obtain a partial answer. In addition, the weak bounded approximation property is reinterpreted within the framework of unconditionally p-compact sets, leading to new characterizations. Finally, we establish a three-space result for the weak unconditionally p-approximation property by showing that this property is preserved under suitable assumptions on a complemented subspace and the corresponding quotient space.

Mathematics doi: 10.3390/math14203777

Authors: Lorentz Jäntschi

The discrimination of structural isomers remains a central challenge in mathematical chemistry and molecular graph theory. In this work, twenty topological polynomials are evaluated on benzenoid (polyhex) systems containing between four and seven fused hexagons. Computational analysis of all non-isomorphic benzenoid graphs in this range shows that nine descriptors, including the Theta, Matching, Padmakar–Ivan, Vertex–Szeged, Adjacency Characteristic, Laplacian Characteristic, Signless Laplacian Characteristic, Distance Characteristic, and Harary Matrix Characteristic polynomials, exhibit zero degeneracy and uniquely distinguish all 333 benzenoid isomers with seven hexagons. The structural origin of this behavior is investigated through spectral and distance-based graph properties, and a theoretical framework is proposed distinguishing between (i) computationally verified discrimination on finite sets, (ii) exact algebraic properties and finite-domain completeness for catacondensed benzenoids, and (iii) a composite descriptor completeness conjecture. In contrast, Omega, Sadhana, and Zhang–Zhang polynomials display substantial degeneracy, reflecting information loss associated with quasi-orthogonal cut representations. The obtained results identify a class of topological descriptors with exceptional discriminatory capability and potential applicability in QSAR/QSPR modeling, molecular similarity analysis, and the characterization of extended benzenoid systems.

Mathematics doi: 10.3390/math14203775

Authors: Karla Avila Javier Lasso-Saldaña Jorge Gálvez David Bocanegra Omar Avalos

Physical exercise knowledge is usually distributed in flat catalogs, where muscles, equipment and training attributes are stored as independent columns and the dependencies that organize the domain are never made explicit. This work presents a heterogeneous multi-relational Fitness Knowledge Graph built from a public-domain exercise dataset and refined through expert-guided curation: 922 entities and 8598 typed assertions across nine semantic relations, each validated against an explicit domain and range schema before the graph is written. Its organization was assessed through relational representation learning, comparing seven models over thirty independent runs under the same protocol: free node embeddings, DistMult, TransE, ComplEx, a homogeneous Graph Convolutional Network, the same encoder combined with a relation-aware decoder, and a Relational Graph Convolutional Network. Models without propagation reconstruct observed edges more accurately, while propagation yields a markedly larger separation between exercise types, improving similarity scores from 0.652 for DistMult to between 0.810 and 0.968, significant under a paired Wilcoxon test with Holm correction. The advantage does not extend to every criterion: a translational decoder without propagation reaches a Silhouette score indistinguishable from that of the Relational Graph Convolutional Network with less than a third of its parameters. A control experiment removing the two relations derived from the source category field shows that this organization is carried by them, since every type-based metric collapses and the Silhouette score becomes negative for all seven models. The information does not leave the graph, as a parameter-free similarity over the seven remaining relations still recovers exercise type at 0.828 against 0.479 for random neighborhoods, placing the limitation in the training objective rather than in the relational design. Edge reconstruction and semantic organization therefore measure different properties of a representation, and the relational composition of the graph determines which property the representation space reflects.

Mathematics doi: 10.3390/math14203774

Authors: Muhammad Waqas Arshad David Q. Liu Syed Rizwan Hassan

Conjunction assessment needs risk screening that is early, scalable and interpretable. We ask whether projected quantum feature maps add predictive value to this task when compared with strong classical learners under strict leakage control. From 149,044 real SOCRATES conjunction events (119,568 object pairs), split pair-disjointly, we predict the base-ten logarithm of the maximum collision probability. We prove that the pair-disjoint held-out loss is unbiased for the risk on unseen pairs, that the logarithmic target preserves risk ranking, that the local six-qubit feature map is exactly a classical additive model, and when a validation-fitted ensemble assigns a member zero weight. In the configuration fixed a priori (encoding bandwidth π, linear outer kernel), the projected models trail gradient boosting (RMSE0.668 and 0.762 against 0.602), and the local map is no better than a linear ridge on the raw inputs. Matched experiments on identical training sets show that this shortfall comes from two design choices rather than from the representation: the bandwidth folds the dominant descriptors, and the linear outer kernel discards nonlinear structure. With a validated bandwidth and a Gaussian outer kernel, the local projected model outperforms a tuned classical Gaussian kernel on 1200-event subsets in all five draws (0.641±0.003) and has the lowest point estimate at full scale (0.589), where it is statistically tied with that kernel. It takes the largest weight in an ensemble that lowers RMSE from 0.599 to 0.579. This is not a quantum advantage: the local model is classically computable in closed form, and the interaction pattern of the entangled variant never improves accuracy. In 200 randomly seeded configurations at B=π and B=π/4, it reduces it, and at the validated bandwidth the difference is not significant at full scale.

Mathematics doi: 10.3390/math14203770

Authors: Wenjing Dou Sen Li Huiyan Shao Yiting Lin

As a classical signal processing tool based on second-order statistics (SOS), the ambiguity function (AF) can be formulated as a time-frequency correlation (TFC) function or a quadratic time-frequency distribution (QTFD). However, AF-based methods suffer performance degradation in impulsive noise with non-Gaussian characteristics. Recent studies have incorporated impulsive noise suppression techniques to improve robustness, yet achieving both strong robustness and low computational complexity remains challenging. Drawing inspiration from corrversoria entropy as a similarity measure, two new AFs, termed corrversoria entropy-based ambiguity distribution (CoVEAD) and corrversoria entropy-based ambiguity correlation (CoVEAC), are proposed. The former serves as a robust QTFD for characterizing the time-frequency features of nonstationary signals in impulsive noise, while the latter acts as a generalized TFC that mitigates the effects of impulsive noise on signal amplitude and phase. The important properties and computational costs of the two methods are discussed. Then, based on the proposed AFs, a direction-of-arrival (DOA) estimation algorithm for narrowband linear frequency modulated (LFM) signals and a joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation algorithm are developed. Simulation results demonstrate the superior performance of the proposed algorithms over existing methods in computational complexity and robustness, particularly in scenarios with strong impulsive noise.

Mathematics doi: 10.3390/math14203767

Authors: George Dassios George Fragoyiannis

In the present work we propose an analytic method that leads to ellipsoidal waves in closed form. This is achieved by reducing 4D ellipsoidal harmonics to 3D ellipsoidal waves via appropriately replacing one of the 4D ellipsoidal coordinates with the time variable. The method is demonstrated in the case of a low-degree harmonic.

Mathematics doi: 10.3390/math14203772

Authors: Xiaomin Li Mingfa Zheng Aoyu Zheng Haitao Zhong

This study addresses multistage task assignment and recovery for heterogeneous unmanned aerial vehicle (UAV) teams under progressively revealed disruptions and epistemic parameter uncertainty. A finite scenario tree is used to represent the sequential revelation of service demand and persistent UAV unavailability. Assignment and routing decisions are indexed by information nodes and linked through nonanticipativity, allowing a policy to adapt after new information becomes available without using future observations. Unit-distance fuel consumption is represented by normal uncertain variables, whereas service effectiveness is driven by node-specific lognormal uncertain factors. The resulting formulation incorporates heterogeneous capabilities, task completion, cross-stage collaboration, route continuity, flight-range limits, and consumable-payload capacities. A K–β risk model is developed to minimize the fuel-consumption and weighted service-deficit thresholds at prescribed belief levels. Inverse and generalized inverse uncertainty distributions yield a deterministic multiobjective reformulation while preserving the efficient policy set. A branch-risk-aware multiobjective evolutionary algorithm based on decomposition (BRA–MOEA/D) is designed as a structure-compatible solution method for the resulting combinatorial problem. On the tested medium and large benchmark instances, computational experiments produce feasible nondominated policies with distinct fuel–service tradeoffs; these results are evidence at the investigated scales rather than a general claim of algorithmic superiority or scalability. Mechanism comparisons show that adaptive branching and event-triggered recovery materially change the attainable risk-threshold front, while a sensitivity analysis confirms that the two belief levels separately regulate fuel-risk and service-risk conservatism. The model thereby links sequential adaptation and recovery decisions with belief-based risk control in heterogeneous UAV service operations.

Mathematics doi: 10.3390/math14203773

Authors: Ping Sun Chen Xu

A cell (i,j) of a Young diagram is called an inner cell if all four of its neighbours (i±1,j) and (i,j±1) also belong to the diagram. A standard Young tableau (SYT) of a hollow shape is one whose Young diagram contains no inner cells. In this paper, we establish a correspondence between hollow SYTs and {(1,0),(0,1)}-lattice paths with boundary restrictions. Using this correspondence, we derive enumeration formulas for two families of hollow SYTs: hollow rectangles truncated by the shifted staircase shape δk, and hollow shifted strips of constant width. Conversely, we obtain new enumerative identities for lattice paths with rectangular, trapezoidal, and periodic diagonal stair-step boundaries via the bijection with hollow SYTs.

Mathematics doi: 10.3390/math14203768

Authors: Hui Li Xiao Ren Jian Zhou Yixuan Shen Zhen Li

Nonmonotone transformations of fuzzy numbers arise in loss functions, dispersion measures, and higher-order risk criteria, but inverse-credibility laws apply directly only to monotone maps. Existing methods typically either compute transformed alpha-cuts without a credibilistic scalar functional or use endpoint formulas whose validity depends on monotonicity. We develop a calculus that preserves interior extrema before integration. For any continuous transformation of a fuzzy number whose transformed output is integrable, the expected value admits an extrema-based alpha-cut representation that requires neither regularity nor an inverse credibility distribution. For continuous nondecreasing radial losses, we derive the exact risk, prove a sharp factor-two bound for the conservative endpoint proxy, characterize both equality regimes, and localize the proxy excess to center-containing cuts. We also establish Lipschitz perturbation and certified midpoint-quadrature bounds. At the decision level, proxy constraints are conservative and proxy minimization has a factor-two guarantee. A reproducible experiment further shows that endpoint substitution can reverse the optimizer and contract the feasible set. The framework is further specialized to higher-order credibilistic moments: for regular fuzzy numbers, signed odd moments retain inverse-distribution formulas, whereas absolute and even moments are obtained from the extrema-based formulation without requiring regularity. Triangular and Gaussian closed forms, standardized coefficients, a scale-free bias function, and deterministic audits demonstrate the resulting error, stability, computation, and decision guarantees.

Mathematics doi: 10.3390/math14203771

Authors: Özge Öztekin

In this paper, we introduce and establish the concept of a central test set for free nilpotent Lie algebras. We prove that the central test rank of a free nilpotent Lie algebra Lc,2 of rank 2 and nilpotency class c = 3 equals 3. Furthermore, we show that a minimal central test set of L3,2 belongs to the lower-degree bracket structures and is explicitly given by the set 𝒯 = {[x,y], [[x,y],x], [x,y],y}. We also analyze higher nilpotency classes c ≥ 4 and delineate the degree conditions under which elements effectively eliminate non-central derivations.

Mathematics doi: 10.3390/math14203769

Authors: Jordan K. Kralev Tsonyo N. Slavov Asparuh Markovski Vladislav Slavov

Effective control of prosthetic legs is essential for restoring natural mobility and enhancing the quality of life for amputees. This paper presents a Direct Neural Dynamic Programming (DNDP) algorithm that leverages coupled action and critic neural networks to solve the optimal control problem for prosthetic gait trajectory tracking. By continuously learning and adapting to individual gait patterns, the DNDP action networks generate the control for the knee and ankle joints to reduce the gait tracking error. The proposed approach enables real-time optimization of control strategies without relying on precise system models, offering adaptability to subject-specific dynamics and varying conditions.

Mathematics doi: 10.3390/math14203766

Authors: Khalil Jouili Monia Charfeddine Mongi Ben Moussa

This paper presents a hierarchical safe control approach for DC microgrids, combining learning-based energy management with rigorous constraint enforcement. The main novelty is a covariance-aware coupling mechanism that simultaneously informs CBF constraint tightening, sliding-mode gain scheduling, and DRL state augmentation. A continuous Soft Actor-Critic agent generates smooth current references and a flexible load-shedding ratio. A predictive CBF quadratic program acts as a safety filter, using online confidence intervals from a recursive least-squares predictor. The filter ensures a sampled-data safety property with an inter-sample margin, applying to the actual uncertain microgrid via a robust-CBF term, provided the QP is feasible with zero slack and the true voltage stays within the confidence interval. The same covariance information serves as an online uncertainty metric for adaptive gain and weight scheduling. A composite Lyapunov–CBF theorem proves uniform ultimate boundedness and constraint satisfaction. Simulations under severe conditions show high-probability constraint satisfaction with negligible slack, while improving transient recovery and reducing battery stress. Comparisons with fuzzy logic, discrete DQL, and plain SAC isolate the CBF contribution, and ablation studies assess individual components. While robust MPC can also enforce constraints, the proposed method achieves comparable satisfaction with lower complexity. A clear distinction is maintained between theoretical guarantees and simulation observations.

Mathematics doi: 10.3390/math14203765

Authors: Zhadra Zhaxylykova Nurlana Alimbekova Farida Amenova Nurlan Temirbekov

Moving-boundary problems for incompressible flows often require repeated mesh generation when body-fitted finite element methods are used. This may become costly for flows with moving rigid obstacles, since the numerical solution from the previous time level also has to be transferred to the new finite element space. In this paper, we study a fictitious-domain finite element method for the two-dimensional incompressible Navier–Stokes equations with rigid obstacles. The aim is to analyze a penalized formulation on a fixed background domain and to compare it with a classical body-fitted finite element approach. The flow problem is extended to a larger fixed domain, and the effect of the solid domain is imposed by a nonlinear penalty term depending on the parameters ε and β. A fully discrete finite element scheme is constructed, and stability and convergence estimates are obtained for the fixed-obstacle auxiliary penalized problem. The moving obstacle case is examined numerically. Several numerical tests are presented. A manufactured auxiliary problem is used to check the spatial convergence of the method, the influence of the penalty parameter, and the behavior of the solution inside the fictitious domain. We also consider two moving obstacle examples: a rotating disk moving near a no-slip wall and two rotating disks moving along symmetric trajectories. The fictitious-domain solutions are compared with body-fitted finite element solutions, and the main flow patterns are reproduced without remeshing. The results indicate that the fictitious-domain finite element method is a practical alternative for moving obstacle flow problems. It is not universally faster than body-fitted methods, but it becomes advantageous when the geometry changes in time, since the fixed background mesh avoids repeated remeshing and the transfer of the previous solution between nonmatching meshes.