Article
Computer Science, Theory & Methods
Marc Haerkoenen, Lisa Nicklasson, Bogdan Raita
Summary: We study linear PDE with constant coefficients and investigate the connection between the constant rank condition and primary decomposition. We also make progress in the study of weak lower semicontinuity of integral functionals defined on sequences of PDE constrained fields when the PDEs do not have constant rank.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Computer Science, Theory & Methods
Lynn Pickering, Tereso del Rio Almajano, Matthew England, Kelly Cohen
Summary: In recent years, there has been an increase in the use of machine learning techniques in mathematics, specifically in symbolic computation for optimizing and selecting algorithms. This paper explores the potential of using explainable AI techniques on these ML models to provide new insights for symbolic computation and inspire new implementations within computer algebra systems.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Computer Science, Theory & Methods
Ke-Ming Chang, Kuo-Chang Chen
Summary: In this paper, we develop symbolic computation algorithms to investigate the finiteness of central configurations for the planar n-body problem. We introduce matrix algebra to determine possible diagrams and asymptotic orders, devise criteria to reduce computational complexity, and determine possible zw-diagrams by automated deductions. For the planar six-body problem, we show that there are at most 86 zw-diagrams.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Mathematics, Applied
Meng Zhao
Summary: In this paper, a reaction-diffusion waterborne pathogen model with free boundary is studied. The existence of a unique global solution is proved, and the longtime behavior is analyzed through a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are obtained, which differs from the previous results by Zhou et al. (2018) stating that the epidemic will spread when the basic reproduction number is larger than 1.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Gulsemay Yigit, Wakil Sarfaraz, Raquel Barreira, Anotida Madzvamuse
Summary: This study presents theoretical considerations and analysis of the effects of circular geometry on the stability of reaction-diffusion systems with linear cross-diffusion on circular domains. The highlights include deriving necessary and sufficient conditions for cross-diffusion driven instability and computing parameter spaces for pattern formation. Finite element simulations are also conducted to support the theoretical findings. The study suggests that linear cross-diffusion coupled with reaction-diffusion theory is a promising mechanism for pattern formation.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Xuan Ma, Yating Wang
Summary: In this paper, the dynamics of a rarefied gas in a finite channel is studied, specifically focusing on the phenomenon of Couette flow. The authors demonstrate that the unsteady Couette flow for the Boltzmann equation converges to a 1D steady state and derive the exponential time decay rate. The analysis holds for all hard potentials.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Torsten Lindstrom
Summary: This paper aims to analyze the mechanism for the interplay of deterministic and stochastic models in contagious diseases. Deterministic models usually predict global stability, while stochastic models exhibit oscillatory patterns. The study found that evolution maximizes the infectiousness of diseases and discussed the relationship between herd immunity concept and vaccination programs.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Dong Deng, Hongxun Wei
Summary: This paper investigates the existence and nonexistence of time-periodic traveling waves for a diffusive influenza model with treatment and seasonality. By utilizing the next generation operator theory and Schauder's fixed point theorem, the conditions for the existence of time-periodic traveling wave solutions are obtained, along with the proof of nonexistence in certain cases and exponential decay for waves with critical speed.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Sudeep Singh Sanga, Khushbu S. Antala
Summary: State-dependent queues accurately capture the dynamic behavior of systems and enable realistic modeling of real-world scenarios. This investigation proposes a state-dependent single unreliable server finite queueing model with admission control F-policy to address the congestion problem. Chapman-Kolmogorov equations are used to establish a mathematical model, and suitable values for state-dependent parameters are set to deduce specific models. Various queueing indices are established to predict the validity of state-dependent queues. The cost function is optimized using a genetic algorithm and quasi-Newton method, allowing businesses to optimize resource allocation and achieve cost-efficient service delivery.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Alexis Goujon, Arian Etemadi, Michael Unser
Summary: This study generalizes the concept of upper and lower bounds to estimate the number of linear regions in neural networks with arbitrary and possibly multivariate CPWL activation functions. It introduces a stochastic framework to estimate the average number of linear regions and reveals the role of depth in exponential growth of the number of regions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Jin Zhao, Wen-An Yong
Summary: In this paper, a vectorial finite-difference-based lattice Boltzmann method (FDLBM) is proposed to solve the incompressible Navier-Stokes equations. The consistency, stability, and accuracy of the numerical schemes are analyzed, and a new boundary scheme is developed. Numerical experiments validate the feasibility of the proposed method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
J. L. E. da Silva
Summary: This work uses the Lambert-Tsallis function W-q(x) to provide geometric characteristics in classical and quantum information theory. It explores the function's applications in parameter estimation, Fisher distance, Kulback-Leibler divergence, purity measurement, and quantum disentanglement. It also connects the Lambert-Tsallis function to quantum fidelity, quantum affinity, and the quantum speed limit theory.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Anna Rettieva
Summary: This study considers a dynamic game model where players share a resource and aim to optimize different criteria. The study uses bargaining solutions to construct multicriteria Nash equilibrium and multicriteria cooperative equilibrium. Two approaches, cooperative incentive equilibrium and time-consistent payoff distribution procedure, are considered to maintain cooperative behavior.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
A. L. Balandin
Summary: The paper focuses on the electromagnetic inverse scattering problem for dielectric anisotropic and magnetically isotropic media. It introduces the tensor Fourier diffraction theorem as a useful tool for studying tensor fields in inverse electromagnetic scattering problems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhifeng Weng, Shuying Zhai, Weizhong Dai, Yanfang Yang, Yuchang Mo
Summary: The nonlocal model, which describes material heterogeneities and defects, has gained significant attention in materials science. This study focuses on a nonlocal ternary conservative Allen-Cahn model and proposes a linear energy stable scheme using a spatial convolution term. Rigorous analysis and numerical experiments validate the efficiency and stability of the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
M. Alizadeh, A. Asgharzadeh, E. Basiri
Summary: This paper discusses the problem of missing middle lifetimes in reliability studies and proposes a method for reconstructing the unobserved lifetimes. By finding balanced reconstruction regions and using constrained minimization problem, the reconstruction regions are obtained. A simulation study and two numerical examples are presented for illustrative and comparative purposes.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Prerna, Vikas Sharma
Summary: This paper presents a novel method for optimizing a quadratic function over the efficient set of a multi-objective integer linear programming problem. The method obtains a globally optimal solution by ranking and efficiency testing, and demonstrates high computational efficiency.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Silvia Falletta, Matteo Ferrari, Letizia Scuderi
Summary: In this paper, a numerical method for solving 2D Dirichlet timeharmonic elastic wave equations is proposed and analyzed. The method decouples the elastic vector field into scalar Pressure (P-) and Shear (S-) waves through a suitable Helmholtz-Hodge decomposition. The scalar potentials are approximated using a virtual element method with different mesh sizes and degrees of accuracy. The method's stability and convergence error estimate are provided for the displacement field, with the error contributions associated with the P- and S- waves separated. The proposed approach allows for tracking the two different wave numbers and using a high-order method for approximating the wave associated with the higher wave number.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Shuaibin Gao, Qian Guo, Junhao Hu, Chenggui Yuan
Summary: This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) and provides results on convergence rate and error. The tamed Euler-Maruyama scheme for the particle system reveals the propagation of chaos in LP sense.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Woula Themistoclakis, Marc Van Barel
Summary: In this paper, the authors generalize the interpolating rational functions introduced by Floater and Hormann, resulting in a new family of rational functions depending on an additional parameter gamma. The new rational functions share many properties with the original ones when gamma > 1. They have no real poles, interpolate the given data, preserve polynomials up to a certain degree, and have a barycentric-type representation. The associated Lebesgue constants are estimated in terms of the minimum and maximum distance between consecutive nodes. It is shown that for equidistant and quasi-equidistant nodes configurations, the new interpolants have uniformly bounded Lebesgue constants for all gamma > 1.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
