Article
Engineering, Multidisciplinary
Pouria Behnoudfar, Quanling Deng, Victor M. Calo
Summary: This study introduces a variational splitting technique for the generalized-alpha method to solve hyperbolic partial differential equations. By using tensor-product meshes and conducting spectral analysis, the method's stability and efficiency are optimized.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Lazhar Bougo, Smail Bougou, Ammar Khanfer
Summary: The existence and uniqueness of the generalized boundary value problem of the Thomas-Fermi equation is proven, where y''+f(x,y)=0, 0<infinity, y(0)=1, y(infinity)=0, p(y)f(x,y)=-yp+1, p>0, 0<x<infinity. Additionally, highly accurate approximate solutions for this new boundary value problem in the study of many-electron systems are obtained.
Article
Mathematics, Applied
Chun Li
Summary: Utilizing a generalized version of the Weierstrass theorem and a novel space decomposition approach, we have shown the existence of two minimal periodic solutions for a class of subquadratic even Hamiltonian systems. This represents the first proof of multiple minimal periodic solutions for Hamiltonian systems with subquadratic potentials.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Rende Zhao, Shangqian Wu, Cun Wang, Hailiang Xu, Xianqiang Jiang, Yansong Wang
Summary: The study focused on the implementation of MSOGI in the discrete-time domain for extracting signals with multiple harmonics. It was found that the discretization method greatly impacts the performance, and a novel method was proposed to enhance both the phase and the quadrature characteristic performance. The new method shows promising results both theoretically and experimentally.
IEEE TRANSACTIONS ON POWER ELECTRONICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Julee Shahni, Randhir Singh
Summary: An efficient numerical algorithm based on Laguerre wavelets collocation technique is presented for solving a class of Thomas-Fermi boundary value problems, providing better approximation compared to existing methods.
ENGINEERING WITH COMPUTERS
(2022)
Article
Automation & Control Systems
Jixing Lv, Xiaozhe Ju, Liang Jing, Changhong Wang
Summary: This article studies the predefined-time observation problem of generalized strict-feedback second-order systems and proposes an adaptive predefined-time observer that achieves complete reconstruction with small observation errors and a predefinable upper bound on settling time.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Mathematics, Interdisciplinary Applications
Surendra Kumar, Paras Sharma
Summary: This paper studies impulsive second-order stochastic differential systems in a separable Hilbert space X. By using projection operators, the given problem is restricted to a finite-dimensional subspace. The existence and convergence of estimated solutions are investigated using the theories of cosine family and fractional powers of a closed linear operator. The existence and convergence of Faedo-Galerkin approximate solutions are also examined. Finally, examples are constructed to demonstrate the effectiveness of the obtained results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Automation & Control Systems
Gengjin Shi, Zhiqiang Gao, YangQuan Chen, Donghai Li, Yanjun Ding
Summary: This paper discusses the control of high-order unstable systems and proposes the generalized desired dynamic equational (G-DDE) PID controller as a viable solution. The G-DDE PID controller not only guarantees closed-loop stability but also has a simple structure and tuning procedure. Simulations and experimental results demonstrate the advantages of G-DDE PID in reference tracking, disturbance rejection, and robustness, making it a convenient and effective control strategy for high-order unstable systems that can be readily implemented on common industrial platforms.
Article
Operations Research & Management Science
V. D. Thinh, T. D. Chuong, N. L. H. Anh
Summary: This paper studies an uncertain inequality system and deals with it using a deterministic approach in robust optimization. By computing the tangent sets and the epi-subderivative of the indicator function of the robust system's solution set, the graphical derivative for the normal cone mapping can be calculated. The paper establishes second order necessary and sufficient optimality conditions and derives necessary and sufficient conditions for stability properties in optimization problems involving uncertain constraints.
JOURNAL OF GLOBAL OPTIMIZATION
(2023)
Article
Mathematics, Applied
Hao Chen, Yeru Yang
Summary: This study investigates the convergence and efficient implementation of generalized Stormer-Cowell methods (GSCMs) when applied to large-scale second-order stiff semilinear systems. Theoretical analysis proves the uniqueness and convergence order of the GSCMs under certain conditions. Practical computation involves a linear iterative scheme for solving discretized nonlinear algebraic equations and a block triangular preconditioning strategy for solving linear systems. Numerical tests demonstrate the effectiveness of the proposed methods.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Tengjin Zhao, Zhiyue Zhang, Tongke Wang
Summary: A new efficient method combining the Puiseux series asymptotic technique with an augmented compact finite volume method is proposed to develop a numerical approximate solution for the Thomas-Fermi equation on semi-infinity domain. The method not only obtains high precision numerical solution, but also precise initial slope, which is crucial for measuring the quality of the algorithm.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Guangwang Su, Guangming Xue
Summary: This paper deals with abstract second order nonlinear evolution differential equations subject to generalized mixed variational inequalities. By applying Ky Fan inequality theorem, it is proven that the solution set of variational inequalities is bounded, closed and convex, without the rigid restriction of monotonicity. Additionally, the existence of solutions for a class of nonlinear differential equations is discussed.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2021)
Article
Optics
Khalid Hossain, Subhadeep Gupta, Michael McNeil Forbes
Summary: In this experiment, a ring geometry is used to directly detect the entrainment effect in a mixture of bosonic and fermionic superfluids. The choice of ring geometry eliminates variations in the mean-field interaction strength, enhancing the detection of entrainment-induced phase gradient.
Article
Computer Science, Artificial Intelligence
Huayan Zhang, Zhishuai He, Xiaochao Wang
Summary: The paper introduces a relaxed second-order total generalized variation model on triangulated surfaces and an iterative two-stage mesh denoising method based on this model. The proposed method shows good performance in terms of computational efficiency and high-quality denoising results.
SIAM JOURNAL ON IMAGING SCIENCES
(2022)
Article
Mathematics, Applied
Zijun Hao, Zhongping Wan, Xiaoni Chi, Zheng-Fen Jin
Summary: The generalized lower-order penalty algorithm is proposed for solving the second-order cone mixed complementarity problems (SOCMCPs), with the proof of convergence under certain assumptions. Numerical results are reported to examine the efficiency of the algorithm.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
