Search Results (4,692)

In the analysis and design of multi-agent systems, the representation and communication of knowledge is a critical challenge. The traditional methods of the past, such as dynamic epistemic logic, often lack a process algebraic perspective for modeling concurrent belief-driven interactions. This paper proposes the Calculus of Epistemic Systems (CES), a process calculus that formalizes agents’ communication behaviors within an epistemic environment and captures how epistemic interactions dynamically update agents’ belief bases. We establish key epistemic properties of CES and investigate strong bisimilarity, weak bisimilarity, and observational congruence, proving their substitutivity under all combinators. A persuasion scenario between a companion agent and an elderly user demonstrates the framework’s applicability. Additionally, we show how CES can embed process terms as modal operators in a dynamic epistemic logic. This may unify two major lines of research. Full article

Baseflow cannot be measured directly, so many separation methods exist, and they disagree. We review 16 methods spanning digital filters, graphical partitioning, recession analysis, and conductivity mass balance (CMB). We show that most recursive filters are special cases of a generalized three-parameter equation, which separates linear reservoir from signal processing families and identifies the Boughton and Eckhardt filters as algebraically equivalent. All 16 are implemented in baseflowx, an open-source Python (version 3.9 or later) package, with eight of them validated against independently published results. The methods rank the 398 reference catchments similarly but differ in level: pairs correlating above 0.93 diverge by up to 0.22 in mean absolute baseflow index (BFI). We compared 15 streamflow-only methods with a CMB reference at 31 screened catchments, with 24 more as a robustness check. All estimated larger baseflows than CMB on average, reflecting the quantities separated: hydrograph-based methods count bank storage return, slow interflow, and other delayed water as baseflow, whereas CMB partitions by conductance. CMB-derived ${\mathrm{BFI}}_{\max }$ values were below the conventional 0.80 Eckhardt default at all 55 catchments. Parameter choice also produced most of the variation attributed to method choice. Streamflow-only methods can support relative comparisons and trends but cannot constrain an absolute baseflow fraction without an external reference. Full article

In this paper, we introduce and systematically investigate several classes of localized Baer-type rings associated with a fixed idempotent element e, namely e-Baer, e-quasi-Baer, e-$p.q.$-Baer, e-PP, and e-APP rings. We develop a unified structural framework relating these localized annihilator classes to weak localized zero-product conditions, including weak e-symmetric, weak e-reversible, weak e-reflexive, and weak e-semicommutative properties. We establish the principal implication relations among these classes and, under suitable hypotheses, obtain equivalence results connecting several localized and global conditions. Examples and counterexamples are provided to distinguish the classes and to demonstrate the failure of converse implications in general. We further study the behavior of localized annihilator conditions under various algebraic constructions and infinite operations. In particular, we establish permanence and transfer results for left e-APP rings under matrix, polynomial, Laurent polynomial, monoid, skew monoid, and skew polynomial extensions, as well as under Morita equivalence. For formal power series extensions, where the left $\mathrm{APP}$ property is not preserved in general, we obtain two sufficient conditions on the corner ring $eRe$ that ensure preservation of the left e-APP property. We also establish structural equivalences between left e-APP and left e-$p.q.$-Baer rings under suitable finiteness assumptions. These results provide a systematic connection between classical annihilator theory and its localized counterpart and extend the study of localized regularity and Baer-type properties in ring theory. Full article

This article presents a two-way convolution of the Mittag-Leffler function with Sheffer polynomials via the umbral algebraic method, thereby introducing the Mittag-Leffler–Sheffer polynomials (MLSPs) and the Sheffer–Mittag-Leffler function (SMLF). We establish their generating functions, series definitions, quasi-monomial properties, and differential equations. Using Wronskian and Pascal functional matrices, we derive recursive formulas and differential recursive identities for these hybrid polynomials. Various special cases including Mittag-Leffler–Appell, Mittag-Leffler–Hermite, and Mittag-Leffler–Miller–Lee polynomials are examined. Additionally, a graphical investigation of the zero distributions of selected members of these polynomial families is presented using computational tools. Full article

Multi-parametric industrial time-series forecasting is important for predictive monitoring, soft sensing, and decision support in complex process industries. This study proposes a process-informed hybrid ARX-residual deep sequence architecture for short-horizon multi-output forecasting of fluid catalytic cracking unit (FCCU) product yields. The model combines a frozen linear ARX branch with causal temporal convolution, a three-layer GRU, causal self-attention, additive attention pooling, residual gating, and a consistency-regularized multi-output objective. Experiments were performed on an open simulated FCCU benchmark containing 20,160 one-minute observations from seven normal and disturbed operating scenarios. The leakage-controlled pipeline uses scenario-wise chronological splitting, train-only median imputation and standardization, exclusion of fault-timing metadata and direct algebraic target components, and 30 min causal windows for five-minute-ahead forecasting. Across ten prespecified random seeds, the proposed model achieved a historical-test RMSE of 0.022809 $\pm$ 0.000116, compared with 0.022751 for ARX-like Ridge. Dependence-aware statistical analyses did not establish a consistent statistical advantage for either model across the evaluated runs. Rolling-origin evaluation likewise showed similar point accuracy, while leave-one-scenario-out evaluation revealed severe extrapolation failure for the unseen pressure-drop scenario. The results support the reproducibility of the proposed architecture and the importance of the ARX-based dynamic structure, but they do not establish the statistical superiority of the full deep residual architecture. Independent industrial data or newly prespecified simulation trajectories are required for confirmatory external validation. Full article

Soft set theory provides useful mathematical tools for handling uncertainties. However, to address simultaneous multi-parameter constraints, a more dynamic intersectional approach is necessary. In this study, we introduce the concept of a soft intersectional module (soft int-module) and utilize level sets to characterize its underlying algebraic structure. Also, by defining soft int-submodules, we investigate whether they are closed under addition and multiplication operations with a soft int-ideal, and their behavior under module homomorphisms. Finally, using soft int-modules, a logistics-based mathematical model is presented to show how it solves simultaneous conditions in a supply chain network. Full article

We study resonances and time decay in a quantum waveguide with two semitransparent barriers. The model is first analyzed as a one-dimensional Schrödinger operator with two delta interactions and then extended to a two-dimensional strip, where transverse Dirichlet modes reduce the problem, channel by channel, to the one-dimensional setting. We derive explicit scattering amplitudes and characterize resonance poles by analytic continuation. In the strong-barrier regime $\rho ={\alpha }^{-1}\to 0^{+}$, the real parts of the resonances approach the eigenvalues of the decoupled cavity, while the imaginary parts are negative and of order ${\alpha }^{-2}$, so the lifetimes grow like ${\alpha }^2$. We also study the time evolution on short, intermediate, and long time scales: the survival probability is quadratic at short times, in accordance with the quantum Zeno effect; the intermediate regime is resonance-dominated and approximately exponential; and the long-time behavior is governed by the low-energy threshold and becomes algebraic. Numerical simulations complement the analysis by confirming these regimes and by showing the breakdown of exponential decay. They also provide an empirical fit for the breakdown time $t_{\mathrm{br}}$ in terms of the barrier strength $\alpha$ and the distance $d_1$ between the barriers. Full article

The description of the internal spaces of fermion and boson fields with “basis vectors”, which are the superpositions of odd and even products of the operators ${\gamma }^a$, with the index a running in internal and external space-time, suggests in $d=2(2n+1)$-dimensions in internal space, such as $d=(13+1)$, and $d=(3+1)$ in external space-time, a unified picture of all so far observed fermions and bosons. Quarks, leptons, antiquarks, and antileptons appear in families - each family contains fermions and antifermions. Bosons—gravitons, photons, weak bosons, gluons, and scalars, which carry the spatial index $\alpha$ (for tensors and vectors $\alpha =n=$$(0,1,2,3)$ and for scalars $\alpha \ge 5$)—appear in two orthogonal groups. All fields are assumed to have non-zero momenta and angular momenta only in the $d=(3+1)$, $SO(3,1)$, of ordinary space-time. In any $d=2(2n+1)$-dimensional space, the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of bosons. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates “basis vectors” and their properties in $d=(13+1)$ and $d=(5+1)$. The article presents new results and discusses open problems with this theory. Full article

This paper studies global asymptotic stability of Cohen–Grossberg neural networks involving discrete time delays in the neuron states and neutral delays in the time derivatives of the neuron states. An appropriate Lyapunov functional, which is defined by the linear combination of three Lyapunov functionals of the quadratic forms, is constructed to determine new criteria for global asymptotic stability of neutral-type neural networks with discrete delay parameters. The proposed stability conditions are established through a set of algebraic inequalities that utilize key matrix properties and parameters of system functions. These criteria are proved to be independent of delay components, and they can be tested by checking some algebraic inequalities. A numerical example is studied to illustrate the efficiency aspects of the derived stability conditions. Full article

Coefficient operators provide a natural way to reshape an analytic function before testing its geometry. This paper develops a two-parameter algebraically damped Hadamard-product operator and investigates the functions whose transformed images satisfy a disk-starlikeness condition. The construction retains a visible contribution from the first coefficients while allowing the higher-order tail to be attenuated at an adjustable algebraic rate. The geometric conclusion concerns the transformed function; it does not automatically imply that the original function is starlike or univalent. Sharp initial-coefficient estimates, a corrected Fekete–Szegö inequality, and corresponding extremal functions are obtained. The multiplier is compared quantitatively with several established coefficient operators, and the effects of its parameters on damping and coefficient flexibility are examined. A weighted-coefficient criterion yields transparent perturbation and convex-combination consequences, while explicit examples illustrate both membership and failure of the criterion. The practical profiles included in the paper are conceptual visualizations rather than empirically validated models. Full article

In this paper, we address the fast computation of highly oscillatory Bessel transforms involving algebraic-type singularities and Cauchy principal value integrals. By modifying the numerical steepest-descent method, we propose a new efficient quadrature rule. We first divide the considered integrals into two parts $I_{\omega }^1[f,s]$ and $I_{\omega }^2[f,s]$, which can be transformed into the infinite integrals on $[0,\infty )$ by the Cauchy residue theorem. Based on the asymptotic properties of the kernel function, we construct suitable Gaussian quadrature rules to enable efficient evaluation of the resulting infinite integrals. We next develop two new quadrature rules for this transform, applicable regardless of whether the endpoint a is zero or nonzero. Error bounds are established for both methods, and their effectiveness is validated through several numerical experiments. Full article

Rapid prediction of vehicle lift coefficient is an important issue in aerodynamic design. Traditional CFD/DSMC methods have high computational costs. Although commonly used machine-learning surrogate models offer high prediction efficiency, they struggle to provide explicit mathematical expressions. To balance prediction accuracy and model interpretability, this paper introduces the symbolic regression method and establishes an explicit modeling process for the lift coefficient. Using Mach number, angle of attack, and related flow parameters as inputs, validation is conducted on two-dimensional blunt body DSMC data and three-dimensional missile aerodynamic data, with comparisons against linear regression, quadratic polynomial regression, Kriging, random forest, XGBoost, and multilayer perceptron. The results show that symbolic regression can obtain high-precision explicit expressions on the two-dimensional blunt body data and can also build analytical models with certain predictive capability on the three-dimensional missile data with limited samples. Compared with traditional explicit regression methods, symbolic regression does not require a pre-specified fixed functional form; compared with black-box models, its advantage lies in providing interpretable and editable algebraic expressions. The findings indicate that symbolic regression has application potential in rapid explicit modeling of the lift coefficient. Full article

To address the degradation of low-probability-of-intercept (LPI) radar waveform recognition caused by noise dispersion and the masking of modulation-dependent structures in low-SNR Choi–Williams distribution (CWD) images, this paper proposes RepNRS-LPI-Net, an integrated framework for robust recognition and lightweight deployment. CWD converts each received waveform into a two-dimensional time–frequency image that characterizes temporal evolution, frequency variation, and localized energy distribution. The proposed RepDW block integrates 3 × 3, 1 × 3, and 3 × 1 depthwise branches with an identity branch during training to capture joint time–frequency, temporal-direction, and frequency-direction responses while preserving informative features. These branches are then algebraically fused for efficient deployment. In addition, NRS-ECA combines channel recalibration with channel-dependent soft shrinkage to attenuate weakly supported noise-like activations without assuming that all weak responses are noise. Focal modulation and label smoothing are conservatively adopted as auxiliary training strategies to address difficulty imbalance and confidence regularization. Experimental results show that RepNRS-LPI-Net achieves 79.553350% overall accuracy and 49.137529% low-SNR accuracy, while the deployment form reduces the parameter count to 37,142 and the learned-layer computation to 15,722,496 MACs. These results indicate that RepNRS-LPI-Net improves measured recognition performance while substantially reducing deployment complexity under the modeled multipath, Rayleigh-fading, Doppler, and AWGN conditions. Full article

Multi-energy virtual power plants (VPPs) aggregate electricity, heating, and natural gas resources to provide flexible regulation services to the external power grid. Their operational flexibility, however, cannot be accurately characterized using equipment capacities or single-period energy balances alone, because district heating and natural gas networks introduce heat transport delays, pipeline thermal storage, pressure dynamics, and linepack effects. This paper proposes an operational flexibility boundary assessment method for electricity–heating–gas VPPs based on a dynamic energy circuit model (ECM). The frequency-domain ECM converts heating-network temperature dynamics and gas-network pressure dynamics into algebraic constraints, which are integrated with electric-network and multi-energy coupling-device constraints. The net exchange power at the point of common coupling (PCC) is used as the external flexibility interface, and the period-wise upper and lower boundaries are determined subject to network and device constraints, terminal-state recovery requirements, and an economic feasibility limit. Case studies on an electricity–heating–gas VPP demonstrate that the dynamic ECM captures the intertemporal regulation capability provided by pipeline thermal storage and gas-network linepack. Compared with the static model, the dynamic ECM exhibits consistently greater downward flexibility and comparable or lower upward flexibility in several periods, thereby correcting the underestimation of electrical absorption capability and the optimistic estimation of power-export capability caused by the static approximation. The economic feasibility constraint further excludes high-cost boundary schedules, yielding a technically feasible and economically acceptable flexibility range. Full article

The fine-structure constant is an empirical boundary datum of quantum electrodynamics (QED), not a value derived by the Standard Model. We give a conditional structural derivation in which its inverse is matched to the response capacity of a neutral codimension-two holonomy defect. The Indefinite Reconstruction Stability Principle and the topology of a punctured transverse space select codimension two and an integer winding group $\mathbb{Z}$. Phase and spin read-outs are represented by native norm-one groups $\mathrm{U}\left(1\right)$ and $\mathrm{SU}\left(2\right)$. Preserving their algebraic identities and multiplicative norms fixes the measures $2\pi$ and $2{\pi }^2$. Their three nonempty exposures have total capacity $\Omega =4{\pi }^3+{\pi }^2+\pi$. Four first-interface roles and one protected identity select $\mathbb{Z}/5\mathbb{Z}$; its 24 nonzero outgoing–returning state pairs form one symmetry orbit, fixing the first correction. At later resolutions, a separately declared asymmetric complete-source/exposed-target transfer rule—not the Chinese remainder theorem used only for common refinement—fixes the coefficients by unit counting without assuming composite-level transitivity. With a declared paired-interface grading rule, they yield an absolutely convergent odd-power tower with an exact logarithmic sum. A separate low-energy QED matching postulate identifies the structural response with the renormalized zero-momentum Maxwell coefficient, giving $\alpha {\left(0\right)}^{-1}=137.035999176142$, $0.041$ standard deviations below the 2022 CODATA value. No numerical coefficient is adjusted once the declared read-out, counting, transfer, grading, and matching assumptions are fixed. The construction does not derive QED dynamics or the running coupling. Full article