Search Results (921)

The primary objective of this paper is to introduce and investigate several novel subclasses of bi-univalent functions associated with the $q-$ calculus framework. Using appropriate analytical techniques, we derive coefficient bounds for the initial coefficients of the functions belonging to these newly defined classes. In particular, we provide explicit estimates for the second-order Hankel determinant and address the classical Fekete–Szegö functional problem within the context of these classes under suitable conditions. It is important to note that the findings presented in this work not only contribute to the ongoing development of $q-$analogs in geometric function theory, but also serve as a unifying generalization of many previously known results, which are obtained as special cases of our main findings. Full article

Solanum rostratum is a globally regulated invasive species, known for its detrimental impacts on local biodiversity, human and livestock health, and agricultural productivity. This study employed the Biomod2 ensemble modeling framework to analyze the geographic distribution of S. rostratum in China, identify key environmental factors limiting its spread, and provide a scientific basis for its management and control. By integrating species distribution data with multiple environmental variables, we predicted the potential geographic distribution of this species. Pearson correlation analysis and variance inflation factor (VIF) testing were applied to identify significant environmental variables constraining its spread, including precipitation seasonality (bio15), mean temperature of the wettest quarter (bio8), precipitation of the warmest quarter (bio18), isothermality (bio3), precipitation of the driest month (bio14), and human footprint. Three Biomod2-based ensemble models (EMmean, EMca and EMwmean) were based on the receiver operating characteristic curve (ROC), true skill statistic (TSS), and Kappa coefficient. Of these, EMca demonstrated the highest predictive accuracy. The model identified highly suitable habitats for S. rostratum primarily in semi-arid and semi-humid regions with high human activity, including the Northeast Plain, bounded by the Greater Khingan, Lesser Khingan, and Changbai Mountains; the northern North China Plain extending to the Shandong Hills and Yellow River basin; and the Junggar Basin extending to the Altai Mountains. These regions should be prioritized for future monitoring and control efforts. This study provides both empirical data and theoretical insights to accurately delineate potential invasion zones of S. rostratum, enhancing surveillance and guiding effective prevention and control strategies. Full article

We consider two steady-state heat conduction systems called, S and $S_{\alpha }$, in a multidimensional bounded domain D for the Poisson equation with source energy g. In one system, we impose mixed boundary conditions (temperature b on the boundary ${\mathsf{\Gamma }}_1$, heat flux q on ${\mathsf{\Gamma }}_2$ and an adiabatic condition on ${\mathsf{\Gamma }}_3$). In the other system, the condition on ${\mathsf{\Gamma }}_1$ is replaced by a convective heat flux condition with coefficient $\alpha$. For each of these systems, we consider three associated optimization problems $\left(P_i\right)$ and $\left(P_{i\alpha }\right)$, $i=1,2,3$, where the variable is the source energy g, the heat flux q and the environmental temperature b, respectively. In the particular case where D is a rectangle, the explicit continuous optimization variables and the corresponding state of the systems are known. In the present work, by using a finite difference scheme, we obtain the discrete systems $\left(S^h\right)$ and $\left(S_{\alpha }^h\right)$ and discrete optimization problems $\left(P_i^h\right)$ and $\left(P_{i\alpha }^h\right)$, $i=1,2,3$, where h is the space step in the discretization. Explicit discrete solutions are found, and convergence and estimation errors results are proved when h goes to zero and when $\alpha$ goes to infinity. Moreover, some numerical simulations are provided in order to test theoretical results. Finally, we note that the use of a three-point finite-difference approximation for the Neumann or Robin boundary condition at the boundary improves the global order of convergence from $O\left(h\right)$ to $O\left(h^2\right)$. Full article

In recent times, countries have made it a point of duty to promote economic activities that will foster a sustainable environment following the Sustainable Development Goals (SDGs). One of the measures employed to achieve these goals, especially SDGs 7 and 13, is the adoption of renewable energy consumption. As a result, this research investigates the effect of financial globalization (FGLO) and technological innovation (TECH) on renewable energy consumption (RENC) in Nigeria from 1990 to 2020 using the Autoregressive Distributed Lag (ARDL) model. In addition, this research contributes to the existing literature by employing the Frequency Domain Causality Approach to capture long- and short-run causal relationships. Also, control variables such as financial development (FIND) and economic growth (GDP) were employed. The ARDL result is as follows: (1) The bounds test confirms a long-run association between the variables. (2) In the long-run, TECH and FIND spur RENC, while GDP reduces RENC. In addition, FGLO has a positive long-run coefficient, but the evidence is not strong enough to claim a clear long-run effect. (3) In the short-run, FGLO and FIND increase RENC, while GDP reduces RENC. Furthermore, the Frequency Domain Causality results confirm that TECH Granger causes RENC in the medium and long term, FIND Granger causes RENC in the medium and long term, while GDP Granger causes RENC in the short, medium, and long term. Based on these results, policies are recommended. Full article

Evaluating the vertical bearing capacity of offshore wind turbine pile-ring composite foundations under complex marine environmental loads is critical for ensuring engineering safety. This study employs the rigorously validated T-EMSD upper-bound method to conduct a three-dimensional numerical analysis of the vertical bearing capacity of pile-ring composite foundations in saturated clay. It systematically investigates the influence of soil homogeneity ($\eta$, diameter ratio (D/B), embedment ratio (L/B), and external shaft friction coefficient ($\alpha$) on the bearing capacity factor $N_c$, and reveals the associated failure mechanism through velocity field analysis. The results indicate that the bearing capacity factor $N_c$ increases significantly with the diameter ratio D/B. The system exhibits optimal bearing performance when the pile shaft friction is fully mobilized ($\alpha$ = 1) in homogeneous soil ($\eta =1$). Moreover, as the embedment ratio L/B increases, the plastic zone extends downward along the pile shaft, enhancing the deep foundation effect. Based on parametric analysis, a predictive formula for the net bearing capacity factor of the pile-ring composite foundation under homogeneous conditions is established. Verified against existing numerical methods and experimental data, the formula demonstrates an error margin within ±5%, indicating its good suitability for engineering applications. Furthermore, by establishing a ratio relationship, the net bearing capacity factor under heterogeneous conditions is correlated with that under homogeneous conditions. This enables a more in-depth analysis of the influences of soil strength heterogeneity and external shaft friction coefficient on the vertical bearing capacity of the pile-ring composite foundation. The work presented in this paper provides a theoretical basis for the design and bearing capacity assessment of this type of composite foundation. Full article

This article presents a novel framework for encrypting color images to enhance digital data security using deep learning and artificial intelligence techniques. The system employs a two-model neural architecture: the first, a Convolutional Neural Network (CNN), verifies sender authenticity during user authentication, while the second extracts unique fingerprint features. These features are converted into high-entropy encryption keys using Particle Swarm Optimization (PSO), minimizing key similarity and ensuring that no key is reused or transmitted. Keys are generated in real time simultaneously at both the sender and receiver ends, preventing interception or leakage and providing maximum confidentiality. Encrypted images are secured using the Advanced Encryption Standard (AES-256) with keys uniquely bound to each user’s biometric identity, ensuring personalized privacy. Evaluation using security and encryption metrics yielded strong results: entropy of 7.9991, correlation coefficient below 0.00001, NPCR of 99.66%, UACI of 33.9069%, and key space of 2²⁵⁶. Although the final encryption employs an AES-256 key (key space of 2²⁵⁶), this key is derived from a much larger deep-key space of 2⁸¹⁹² generated by multi-layer neural feature extraction and optimized via PSO, thereby significantly enhancing the overall cryptographic strength. The system also demonstrated robustness against common attacks, including noise and cropping, while maintaining recoverable original content. Furthermore, the neural models achieved classification accuracy exceeding 99.83% with an error rate below 0.05%, confirming the framework’s reliability and practical applicability. This approach provides a secure, dynamic, and efficient image encryption paradigm, combining biometric authentication and AI-based feature extraction for advanced cybersecurity applications. Full article

The present work is focused on a predator–prey model with the Holling type II interaction function, which is influenced by diffusion, advection and nonlinear reaction effects. Firstly, we show that the solutions of this dynamical model are bounded and unique. Secondly we use the Lyapunov function and then show that the equilibrium points are globally stable. Thirdly, we obtain the solution profile when the diffusion coefficient is small. For this purpose we introduce self-similar structures to convert the nonlinear partial differential equations into nonlinear ordinary differential equations and then use the singular perturbation technique to solve these equations. Fourthly, we use the Hamiltonian and Lighthill’s technique to obtain upper stationary solutions for a small coefficient of the advection term. Lastly, we consider a large diffusion coefficient and obtain the asymptotic profiles of nonstationary solutions with the help of nonlinear point scaling. Full article

This paper introduces coefficient functionals for a new subclass (${\mathcal{S}}_{tanh}^{*})$ of starlike functions associated with the tangent hyperbolic function, including the first four sharp coefficient bounds, the Fekete-Szegő problem, Zalcman inequalities, and Hankel determinants. For this class, logarithmic and inverse problems are also studied. Furthermore, we define families of functions that are related to the functions $1+sin\mu ,$${\left(1+\alpha \mu \right)}^2,1+{\displaystyle \frac{\mu }{1-\beta {\mu }^2}}$, represented by ${\mathcal{Y}}_{sin},{\mathcal{Y}}_{\alpha }$ and ${\mathcal{Y}}_{\beta }$, respectively. Using the Schwarz-Pick lemma and the theory of subordination, involving the function $1+{\displaystyle \frac{1}{2}}tanh\mu$, we find the majorization radii and construct majorization results of the form $\left|g^{\prime }\left(\mu \right)\right|\le \left|h^{\prime }\left(\mu \right)\right|$ for functions g majorized by h. Through graphical analysis, we also demonstrate that our defined class ${\mathcal{S}}_{tanh}^{*}$ is non-empty, which validates our study in this article. Full article

No-reference image quality assessment (NR-IQA) models achieve high correlation with human mean opinion scores (MOS) on clean benchmarks, yet recent work shows they can be highly vulnerable to small adversarial perturbations that severely degrade ranking consistency, including in black-box settings. We introduce the Spectral Robustness Mixer (SRM), a lightweight neck inserted between an NR-IQA backbone and regression head, designed to reduce adversarial sensitivity without changing the dataset, label format, or target metric. SRM couples (i) deep-to-shallow cross-scale fusion via a Nyström low-rank attention surrogate, (ii) ridge-conditioned landmark kernels with ridge regularization, solved via numerically stable small-matrix factorization (SVD/LU) to improve conditioning, and (iii) variance-aware entropy-regularized fusion gates with a bounded gain cap to limit gradient amplification. We evaluate SRM on TID2013 and KonIQ-10k under a white-box ${\mathcal{l}}_{\infty }/{\mathcal{l}}_2$ attack ensemble that includes per-image regression objectives and a correlation-aware pairwise inversion objective (a ranking-inspired surrogate for correlation inversion), with expectation-over-transformation (EOT) and anti-gradient masking checks. At $ϵ=4/255$ (${\mathcal{l}}_{\infty }$), SRM improves worst-case robust Spearman’s rank-order correlation coefficient (SROCC; defined as the minimum over our fixed attack ensemble) by an absolute $0.06$–$0.08$ SROCC points (i.e., correlation-coefficient units, not percentage gain) across datasets/backbones, while keeping clean SROCC within $0.00$–$0.01$ of the baseline. We observe similar trends for Pearson linear correlation coefficient (PLCC). Full article

One major challenge faced by deep learning-based methods that detect target objects in the form of bounding boxes is object occlusion. High degrees of occlusion significantly diminish the accuracy of instance segmentation. Nonetheless, complex-valued Fourier descriptors can robustly represent object boundaries using minimal information. In this study, the impact of integrating Fourier descriptors—renowned for their strong representational capacity—with deep network models (UNet) that exhibit high generalization performance on instance segmentation accuracy was investigated. Within the scope of the research, nine network models were designed based on different strategies for utilizing frequency components. These variants fall into four strategy families: (i) UNet-style spectrum regression on fixed low-frequency windows (FUNet), (ii) magnitude-guided frequency selection/ROI construction (FUNet–Thr, FUNet–BBox), (iii) sequence models over tokenized FFT coefficients (BiLSTM Patch/Sorted), and (iv) encoder-only spectrum predictors with different depth/capacity (EncoderFFT1/2). To fairly evaluate the models’ performance in segmenting objects subjected to disruptive factors (e.g., occlusion, blurring, noise), a specialized synthetic dataset was prepared. The task is formulated as single-target (single-instance), single-class segmentation. This dataset, automatically generated according to initial parameter values, contains images of objects moving at various speeds within a single frame. Among these models, the one termed FUNet, which relies on partial matching of central frequency components, achieved the highest segmentation accuracy despite the disruptive effects. Under the challenging Dataset 8 setting, the proposed FUNet achieved the highest overlap-based performance (Dice = 0.9329, IoU = 0.8842) among Attention U-Net, U-Net, and FourierNet, with statistically significant gains confirmed by paired per-image tests. Full article

Continuous plantar-pressure monitoring is important for objective gait analysis and early detection of abnormal loading; however, many existing solutions remain laboratory-bound (force plates and instrumented walkways) or rely on costly in-shoe multilayer sensor arrays. Here, we developed and optimized a fully screen-printed pressure-sensing insole based on carbon–polymer nanocomposite layers, with an emphasis on manufacturability and process control to bridge the gap between proof-of-concept force-sensitive resistor (FSR)-based insoles and scalable printed-electronics manufacturing workflows. Composite pastes containing carbon fillers (graphene nanoplatelets, carbon black, and graphite) were formulated to improve sensor repeatability and sensitivity. Sensors were characterized under compression loads from 100 N to 1300 N, showing a sensitivity of 10.5 ± 2.8 Ω per 100 N and a sheet-to-sheet coefficient of variation of 22.1% in resistance response. The effects of paste composition, screen mesh density, electrode layout, and lamination on sensitivity and repeatability were systematically evaluated. In addition, correlation analysis of resistance values from integrated quality-control meanders proved useful for monitoring screen-printing process stability. The final insole integrates printed carbon sensing pads and contacts, a dielectric spacer, and an adhesive layer in a thin, flexible format suitable for integration with wearable electronics. In practical static-load tests, repeated manual placement of weights yielded coefficients of variation as low as 4% at 500 g and a detection limit of ~0.1 N, comparable to a very light finger touch. These results demonstrate that low-cost screen-printed electronics can provide robust pressure sensing for wearable plantar-pressure monitoring. Full article

This study introduces a high-order numerical scheme for solving 1D second-order hyperbolic telegraph equations (HTEs) with variable coefficients. We employ a generalized temporal discretization (TD) of order p via the Rothe approach, combined with a spatial spectral collocation (SCM) method using generalized shifted Jacobi polynomials (GSJPs). By utilizing a Galerkin-type basis that structurally satisfies homogeneous boundary conditions (HBCs)—including Dirichlet or Neumann types—we achieve a global error bound of $\mathcal{O}({(\Delta \tau )}^p+N^{-s})$, where $\Delta \tau$ denotes the temporal step size and s represents the spatial regularity of the exact solution (ExaS). The proposed algorithm, Rothe-GSJP, allows for an optimal balance between the temporal and spatial parameters, minimizing computational effort for high-precision engineering applications such as Phase-Locked Loop (PLL) modeling. Numerical experiments performed on an i9-10850 workstation show that the scheme always reaches the machine precision floor of ${10}^{-16}$. While the framework supports temporal orders up to $p=6$, the results indicate that $p\in \{2,3,4\}$ provides an optimal balance between high-order precision and absolute stability. The Rothe-GSJP method proves to be a robust, efficient, and highly accurate alternative to traditional solvers for hyperbolic systems. Full article

In this paper, we introduce and investigate a new class of analytic functions generated by Euler polynomials through a suitable normalization. Using classical tools from geometric function theory, including coefficient monotonicity, Fejér-type inequalities, MacGregor’s criteria, and Ozaki’s close-to-convexity condition, we establish sufficient conditions for the univalence, starlikeness, convexity, and close-to-convexity of the proposed Euler-polynomial-based normalized function. Sharp radius results for starlikeness, convexity, and close-to-convexity in the disk ${\mathbb{D}}_{1/2}$ are derived by exploiting refined coefficient bounds involving higher-order Euler polynomial terms. Several illustrative examples and graphical demonstrations are provided to verify the theoretical findings. The results obtained extend the known geometric properties of special function-based analytic classes and offer a new perspective on the geometric behavior of Euler polynomials in the unit disk. Full article

In mine ventilation network calibration, sparse and inconsistent airflow measurements often lead to infeasibility in traditional optimization models. To overcome this challenge, this paper proposes a nonlinear programming calibration model incorporating slack variables. The model treats aerodynamic resistance corrections, airflow adjustments, unknown airflows, and resistance lower-bound slack variables as decision variables. The objective function is formulated to minimize the weighted sum of squares of resistance corrections, while penalty terms account for airflow adjustments and slack variables. Constraints integrate Kirchhoff’s laws with relaxed inequality constraints for resistance lower bounds. A calibration tool integrated via the ObjectARX interface was developed using C++, utilizing the Sequential Quadratic Programming (SQP) algorithm for the solution. The method was validated via a case study of a network comprising 39 branches and 16 measured airflows, optimized under five distinct initial conditions. Results demonstrate that the inclusion of slack variables mathematically guarantees the existence of feasible solutions. With a resistance correction weight of 10⁻² and a penalty coefficient of 10⁵, the model applies only minimal necessary corrections to handle overly tight constraints or data conflicts. The SQP algorithm exhibits superior global convergence, consistently iterating to optimal solutions that satisfy network balance laws regardless of initial values. This approach effectively resolves the infeasibility and data conflict issues inherent in traditional methods, demonstrating significant robustness and practical engineering utility. Full article

The q-calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q-derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via the q-derivative in combination with generalized bivariate Fibonacci polynomials, which have recently gained significant attention in mathematical research. For functions in this class, we establish bounds on the initial coefficients and provide estimates for the corresponding Fekete–Szegö functional. By appropriate specialization of parameters, our results recover several known findings and, importantly, produce bounds for new subclasses of bi-univalent functions not previously studied. This framework unifies earlier developments while extending the theory to novel, analytically meaningful classes. Full article