Article
Mathematics, Applied
Yimin Sun, Xin Zhong, Ling Zhou
Summary: We investigate a simplified compressible isentropic nematic liquid crystal flow in 1183. We show the existence and uniqueness of global solutions belonging to a new class of functions provided that the initial energy is properly small. Our result may be regarded as a generalization of Li-Xu-Zhang's work (Li et al., 2018) in the sense that the lower regularities of initial data are required.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
P. C. da Silva Junior, O. P. Ferreira, L. D. Secchin, G. N. Silva
Summary: This paper discusses a new version of a secant-type method for solving constrained mixed generalized equations. The method combines the secant method with the conditional gradient method to achieve convergence of the solution. By assuming Lipschitz condition on the gradient and the metric regularity property, and using the contraction mapping principle, it is shown that the sequence generated by the proposed algorithm is well-defined and locally convergent with a linear or superlinear rate for the solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Clain, J. Figueiredo
Summary: This study proposes a detailed construction of a very high-order polynomial representation and introduces a functional to assess the quality of the reconstruction. Several optimization techniques are implemented and their advantages in terms of accuracy and stability are demonstrated.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gengen Zhang, Jingyu Li, Qiong-Ao Huang
Summary: In this paper, a novel class of unconditionally energy stable schemes are constructed for solving gradient flow models by combining the relaxed scalar auxiliary variable (SAV) approach with the linear multistep technique. The proposed schemes achieve second-order temporal accuracy and strictly unconditional energy stability.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Mathematics, Applied
Fernando Montaner, Irene Paniello
Summary: In this study, we examine Jordan 3-graded Lie algebras satisfying 3-graded polynomial identities. By utilizing the Tits-Kantor-Koecher construction, we interpret the PI condition in terms of their associated Jordan pairs, thereby formulating an analogue of the Posner-Rowen Theorem for strongly prime PI Jordan 3-graded Lie algebras. Furthermore, we describe arbitrary PI Jordan 3-graded Lie algebras by introducing the Kostrikin radical of the Lie algebras.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Pawel Przybylowicz, Verena Schwarz, Michaela Szoelgyenyi
Summary: This paper investigates the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. A complete error analysis is provided under substantially weaker assumptions compared to existing literature. Optimality of the randomized Milstein algorithm is proved in case the jump-commutativity condition is satisfied through establishing matching lower bounds. Additionally, some insight into the multidimensional case is given by investigating the optimal convergence rate for the approximation of jump-diffusion type Levys' areas. Finally, numerical experiments are reported to support the theoretical findings.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Jian He, Jinlin Li, Zhenrong Lu, Bangzhong Zhang
Summary: This paper studies a multi-block separable convex optimization problem where the objective function is the sum of individual convex functions without overlapping variables. The linearized version of the generalized alternating direction method of multipliers (L-GADMM) has been proven to be efficient for two-block separable convex programming problems, and its convergence has been analyzed. However, the analysis and applications of the extended L-GADMM (m >= 3) are still in their early stages. In this paper, the algorithm is extended to the general case, and global convergence and convergence rates are theoretically established. The efficiency of the method is demonstrated through numerical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ippei Nagamachi, Teppei Takamatsu
Summary: In this paper, we study the invariants and related phenomena of regular varieties and rings over imperfect fields. We give a criterion for geometric normality of such rings, study the Picard schemes of curves, and define new invariants relating to δ-invariants, genus changes, conductors, and Jacobian numbers. As an application, we refine Tate's genus change theorem and show that the Jacobian number of a curve is 2p/(p - 1) times the genus change.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
E. Aourir, N. Izem, H. Laeli Dastjerdi
Summary: This paper presents a meshless collocation method based on radial basis functions for solving third kind VIEs. The method utilizes radial basis functions as basis functions and does not require meshing. The formulation of the suggested equations and error analysis of the approach are described. Illustrative examples demonstrate the reliability and effectiveness of the new approach, comparing it to other methods and showing its accuracy.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Young-Pil Choi, Jinwook Jung
Summary: This study investigates the global-in-time well-posedness of the pressureless Euler-alignment system with singular communication weights. A global-in-time bounded solution is constructed using the method of characteristics, and uniqueness is obtained via optimal transport techniques.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Yuan Tian, Huanmeng Li, Kaibiao Sun
Summary: This study proposes a fishery model with dual effects of fear and cooperative hunting based on the cooperative hunting behaviors of predators and the fear response of prey in natural ecosystems. The impact of fear level and cooperative hunting intensity on the dynamics of the model is investigated. Additionally, a state-feedback intermittent fishing strategy is adopted for rational exploitation of fishery resources.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Wanai Li
Summary: This paper proposes a new framework that combines quadrature-based and quadrature-free discontinuous Galerkin methods and applies them to triangular and tetrahedral grids. Four different DG schemes are derived by choosing specific test functions and collocation points, improving computational efficiency and ease of code implementation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiyuan Chen, Qiubao Wang
Summary: This paper introduces a technique that combines dynamical mechanisms and machine learning to reduce dimensionality in high-dimensional complex systems. The method utilizes Hopf bifurcation theory to establish a model paradigm and utilizes machine learning to train location parameters. The effectiveness and robustness of the proposed method are tested and validated through experiments and simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Mathematics, Applied
Zhong Tan, Saiguo Xu
Summary: This paper investigates the Rayleigh-Taylor instability of three-dimensional inhomogeneous incompressible Euler equations with damping in a horizontal slab. It is shown that the Euler system with damping is nonlinearly unstable around the given steady state if the steady density profile is non-monotonous along the height. A new variational structure is developed to construct the growing mode solution, and the difficulty in proving the sharp exponential growth rate is overcome by exploiting the structures in linearized Euler equations. Combined with error estimates and a standard bootstrapping argument, the nonlinear instability is established.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Vivek Mohan Mallick, Kartik Roy
Summary: This paper explores the relation between Perling's toric Proj of a multigraded ring A and Brenner and Schroer's homogeneous spectrum ProjMH A of the same ring. It shows that there is always a canonical open embedding and studies a criterion for them to be isomorphic.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Hongxing Zhao
Summary: This paper investigates the flow of fluid through a thin corrugated domain saturated with porous medium, governed by the Navier-Stokes model. Asymptotic models are derived by comparing the relation between a and the size of the periodic cylinders. The homogenization technique based on the generalized Poincare inequality is used to prove the main results.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Christoffer Soderberg
Summary: This article studies the properties of preprojective algebras of representation finite species. It focuses on understanding the structure of preprojective algebras through their Nakayama automorphism and the existence of almost Koszul complexes. It also introduces a higher dimensional analogue of representation finite algebras and provides a complete description of the almost Koszul complex for the preprojective algebra of a tensor product of two species.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Shiqi Xing
Summary: According to the theorem cited above, a finitely presented torsion-free module is SG-projective if and only if it is projective. In this paper, we prove that the w-conductor m[Y] of D is SG-projective but not projective, and all maximal w-ideals other than m[Y] are w-invertible. This implies that a finitely presented torsion-free SG-projective module does not necessarily need to be projective.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Andrew Buchanan, Ivan Dimitrov, Olivia Grace, Charles Paquette, David Wehlau, Tianyuan Xu
Summary: This paper applies quiver representation theory and stable representations to study the representations of free products, obtaining criteria for simple modules and proving their sufficiency in general position. It also establishes the semi-simplicity of modules in general position and derives a closed formula for parameters describing simple modules using quiver moduli spaces.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Miaoqing Tian, Lili Han, Xiao He, Sining Zheng
Summary: This paper studies the attraction-repulsion chemotaxis system of two-species with two chemical substances. The behavior of solutions is determined by the interactions among diffusion, attraction, repulsion, logistic sources, and nonlinear productions in the system. The paper provides conditions for the global boundedness of solutions.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
