Mathematics

This study presents a comparative machine-learning investigation for predicting the optical absorption coefficient of truncated pyramidal GaN/AlxGa1−xN quantum dots. The physical dataset is generated by solving the three-dimensional Schrödinger equation using a coordinate-transformation method combined with the finite-difference method (FDM). The coordinate transformation maps the sloping boundar…

Resolvent Monte Carlo estimates eigenvalues of large matrices by sampling Markov chains and reading the target value off a truncated resolvent quotient, trading exact arithmetic for a stochastic error that the almost-optimal sampling scheme is designed to suppress. This paper studies when that error vanishes outright. An exact closed-form identity is derived for the variance of the moment estimat…

We compare the specific dissipation Q−1ω for the Becker, Lomnitz, and Lambert models in linear viscoelasticity. Graphically, the specific dissipation of these models behaves similarly as ω→0+ and ω→+∞. Furthermore, we obtain analytic formulas for the asymptotic behavior of Q−1ω in the Becker and Lomnitz models as ω→0+ and ω→+∞, where the latter limit coincides with the specific dissipation of the…

Modeling choice is key to modal analysis of rib-reinforced vibration test fixtures; however, systematic criteria for selecting shell or solid finite element (FE) models remain limited. This study proposes a decision framework that translates comparisons between shell and solid models into selection criteria. Five headlamp vibration test fixtures were modeled using shell and solid elements under i…

This work constructs high-order numerical methods for a class of nonlinear fractional differential equations featuring the Caputo fractional derivative with respect to another function. Through variable transformation of the fractional differential operator, the original governing problem is converted into a weakly singular Volterra integral equation. After conducting the variable substitution x=…

The economic scheduling of grid-connected microgrids requires the coordinated dispatch of renewable energy sources, controllable distributed generators, battery energy storage systems, and power exchange with the utility grid while satisfying various operational constraints. Owing to the time-varying nature of renewable generation and load demand, this problem often exhibits strong nonlinearity, …

Predicting compressive–shear fracture in rock masses containing complex flaw distributions remains a major challenge in rock engineering. We propose an improved non-ordinary state-based peridynamics (NOSB-PD) model to simulate rock fracture behavior in this work. A stabilized NOSB-PD formulation is developed by incorporating a bond-level deformation gradient strategy to effectively suppress the z…

A mixed redundancy, in which some components of a subsystem operate under active redundancy while the others wait in cold standby, has recently been shown to achieve a higher system reliability than the traditional active and standby strategies within equivalent resources. Existing reliability models for the strategy, however, either provide only a lower bound of the subsystem reliability or rest…

This study investigates the collaborative green vehicle routing problem with time-dependent travel speeds (CGVRP-TD), which integrates horizontal collaboration among multiple depots with time-dependent traffic conditions. The problem jointly optimizes customer allocation, vehicle routing, and departure-time decisions to minimize transportation-related carbon emissions subject to vehicle capacity …

We study the maximum possible number of edges in certain classes of hypergraphs with a given number of vertices. Our approach uses a generalized notion of a path, which need not consist solely of a sequence of vertices and may terminate in an edge. Certain hypergraphs, known as Greechie diagrams, are used to model events in quantum experiments described by orthoalgebras, orthomodular posets, and …

This paper presents a method for determining weight coefficients in multi-objective UAV task assignment under a competitive data-collection setting, where two UAV companies independently visit each other’s sensor nodes. In this setting, each company expresses operational intent through weights for data value, distance utility, and flight safety. Our own weights are prescribed by higher-level plan…

We introduce a robust nonparametric regression framework for functional covariates that combines functional principal component analysis (FPCA), marginal copula-scale normalization, bounded-score M-estimation, and multivariate Bernstein smoothing. The proposed procedure reduces the infinite-dimensional functional predictor to a low-dimensional score representation, transforms the retained scores …

This paper presents an analytical investigation of a class of two-dimensional nonlinear discrete systems governed by bilinear difference equations. By leveraging the explicit representation theory for first-order bilinear recursions, we derive closed-form representations for the solution sequences under general assumptions on system parameters. Special attention is given to parameter configuratio…

Portfolio optimization remains a challenging problem due to the dynamic, nonlinear, and uncertain characteristics of financial markets. Traditional portfolio construction approaches, including mean variance optimization and conventional Black–Litterman models, often suffer from inaccurate estimation of expected returns and unstable allocation caused by parameter uncertainty. These limitations bec…

This paper investigates inverse spectral problems for a class of discrete Sturm–Liouville operators with multiple transmission interfaces. The presence of several interfaces generates a coupled spectral structure in which the reconstruction of the operator coefficients is determined by a common generalized spectral function. A generalized spectral framework adapted to the multi-interface setting …

Gallai’s theorem states that if the Euclidean plane is colored with finitely many colors then every finite configuration of points admits a monochromatic homothetic copy. This paper presents a detailed exposition of a proof originally published by Ernst Witt in 1952 and subsequently expanded by Alexander Soifer. Additional intermediate steps are supplied throughout, yielding a self-contained and …

Domination is among the most popular topics in graph theory, both due to its combinatorial appeal and a number of practical applications. Cylindrical graphs are Cartesian products of a path and a cycle. Usually, for some special subfamilies, natural constructions exist that give exact solutions. On the other hand, in general, exact values of invariants on cylindrical graphs are hard to compute. I…

Learning behavior plays an important role in the day-to-day route choice process, which is essentially a repeated decision-making process. This paper proposes two learning models for the day-to-day route choice process, one for the full-information (FI) condition and one for the partial-information (PI) condition. Both models are developed based on attraction-based reinforcement learning theory b…

Classical MANOVA procedures are not directly applicable in high-dimensional settings where the number of variables is comparable to, or exceeds, the sample size, and many existing high-dimensional MANOVA tests remain sensitive to outlying observations. This study proposes a weighted minimum regularized covariance determinant (MRCD)-based robust Wilks’ Lambda test for one-way high-dimensional MANO…

The accuracy of the numerical simulation of unsteady cloud cavitation around a hydrofoil depends on the combination of the cavitation model, the Reynolds-Averaged Navier–Stokes (RANS) turbulence model and the exponential coefficient n of the Reboud’s correction. To assess the influence of such choices, three turbulence models, three cavitation models and two values of n have been combined to pred…