88 Result(s)
within
**-Wei Sun
Mathematics
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Article
On some determinants involving the tangent function
Let p be an odd prime and let \(a,b\in {\mathbb {Z}}\) a , ...
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Article
Sixth-order quasi-compact difference scheme for the time-dependent diffusion equation
This paper focuses on develo** a numerical method with high-order accuracy for solving the time-dependent diffusion equation. We discrete time first, which results in a modified Helmholtz equation at each ti...
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Article
On Certain Determinants and Related Legendre Symbols
Let p be an odd prime. For \(b,c\in {\mathbb {Z}}\) b , ...
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Article
Asymptotical stability of the exact solutions and the numerical solutions for impulsive neutral differential equations
In this paper, we not only study asymptotical stability of a class of linear impulsive neutral delay differential equations(INDDEs), but also study stability and asymptotical stability of nonlinear INDDEs. Asy...
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Article
An efficient red–black skewed extrapolation cascadic multigrid method for two-dimensional Poisson equation
We present a red–black skewed extrapolation cascadic multigrid (SkECMG) method to solve the Poisson equation in two dimensions based on the modified standard and skewed five-point finite difference discretizat...
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Article
Efficient finite difference scheme for a hidden-memory variable-order time-fractional diffusion equation
In this paper, a fast and memory-saving numerical scheme is presented for solving hidden-memory variable-order time-fractional diffusion equations based on the L1 method. Due to the nonlocality of fractional o...
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Article
Optimal Error Estimates of SAV Crank–Nicolson Finite Element Method for the Coupled Nonlinear Schrödinger Equation
In this paper, we reformulate the coupled nonlinear Schrödinger (CNLS) equation by using the scalar auxiliary variable (SAV) approach and solve the resulting system by using Crank-Nicolson finite element metho...
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Article
The tangent function and power residues modulo primes
Let p be an odd prime, and let a be an integer not divisible by p. When m is a positive integer with p ≡ 1 (mod 2m) and 2 is an mth power residue modulo p, we determine the value of the product
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Article
Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs
The main aim of this work is to study the asymptotic behavior for multi-scale McKean–Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e. the deviation between the slow co...
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Article
BS Invariance Pressures for Control Systems
Three types of BS inner invariance pressures for control systems, as well as three versions of measure-theoretic BS inner invariance pressures, are introduced in this paper. We show that those BS inner invaria...
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Article
Some parametric congruences involving generalized central trinomial coefficients
For \(n=0,1,2,\ldots \) n = 0 ...
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Article
Preconditioning Technique Based on Sine Transformation for Nonlocal Helmholtz Equations with Fractional Laplacian
We propose two preconditioners based on the fast sine transformation for solving linear systems with ill-conditioned multilevel Toeplitz structure. These matrices are generated by discretizing the two-dimensio...
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Article
Representing \({\varvec{n}}\) as \({\varvec{n=x+y+z}}\) with \({\varvec{x^2+y^2+z^2}}\) a square
In this paper, we mainly confirm the following conjecture of Sun posed in 2013: Each positive integer n can be written as \(n=x+y+z\) ...
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Article
On 4-Sachs Optimal Graphs
Let G be a graph with order n and adjacency matrix \({\textbf{A}}(G)\) A ...
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Article
A Mini-Batch Proximal Stochastic Recursive Gradient Algorithm with Diagonal Barzilai–Borwein Stepsize
Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term. Proximal stochastic gradient methods are popular for solving such composite optimizati...
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Article
Legendre Symbols Related to Certain Determinants
Let p be an odd prime. For \(b,c\in {\mathbb {Z}}\) b , ...
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Article
Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations
In this paper, a numerical method to solve the multi-dimensional spatial fractional Allen–Cahn equations has been investigated. After semi-discretizating the equations, a system of nonlinear ordinary different...
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Article
On Sums and Products in a Field
We study sums and products in a field. Let F be a field with ch(F) ≠ 2, where ch(F) is the characteristic of F. For any integer k ⩾ 4, we show that any x ∈ F can be written as a1 + … + ak with a1, …, ak ∈ F and a
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Article
Adaptive Asymptotic Tracking Control for Stochastic Nonlinear Systems with Unknown Backlash-Like Hysteresis
In this study, an adaptive asymptotic tracking control problem is considered for stochastic nonlinear systems with unknown backlash-like hysteresis. By utilizing backstep** technology and bound estimation ap...
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Article
A Sixth-Order Quasi-Compact Difference Scheme for Multidimensional Poisson Equations Without Derivatives of Source Term
Sixth-order compact difference schemes for Poisson equations have been widely investigated in the literature. Nevertheless, those methods are all constructed based on knowing the exact values of the derivative...
