This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem...
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This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.
The paper is concerned with a class of elliptic equation with critical exponent and Dipole *** precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of n...
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The paper is concerned with a class of elliptic equation with critical exponent and Dipole *** precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.
This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpola...
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This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.
Nowadays, when biometric identification is widely used, privacy protection in identification has become a very important issue. In recent years, many scholars have contributed to the biometric authentication with cryp...
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As the use of web browsers continues to grow, the potential for cybercrime and web-related criminal activities also increases. Digital forensic investigators must understand how different browsers function and the cri...
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The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary *** this paper,the hydrodynamic limit from the Bo...
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The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary *** this paper,the hydrodynamic limit from the Boltzmann equation with the specular reflection boundary condition to the incompressible Euler equations in a channel is *** on the multi-scaled Hilbert expansion,the equations with boundary conditions and compatibility conditions for interior solutions,and viscous and Knudsen boundary layers are derived under different scaling,***,some uniform estimates for the interior solutions,and viscous and Knudsen boundary layers are *** the help of the L^(2)-L^(∞) framework and the uniform estimates obtained above,the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales,and hence the hydrodynamic limit in the incompressible Euler level is justified.
Integrating Knowledge Graphs(KGs)into recommendation systems as supplementary information has become a prevalent *** leveraging the semantic relationships between entities in KGs,recommendation systems can better comp...
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Integrating Knowledge Graphs(KGs)into recommendation systems as supplementary information has become a prevalent *** leveraging the semantic relationships between entities in KGs,recommendation systems can better comprehend user *** to the unique structure of KGs,methods based on Graph Neural Networks(GNNs)have emerged as the current technical ***,existing GNN-based methods struggle to(1)filter out noisy information in real-world KGs,and(2)differentiate the item representations obtained from the knowledge graph and bipartite *** this paper,we introduce a novel model called Attention-enhanced and Knowledge-fused Dual item representations Network for recommendation(namely AKDN)that employs attention and gated mechanisms to guide aggregation on both knowledge graphs and bipartite *** particular,we firstly design an attention mechanism to determine the weight of each edge in the information aggregation on KGs,which reduces the influence of noisy information on the items and enables us to obtain more accurate and robust representations of the ***,we exploit a gated aggregation mechanism to differentiate collaborative signals and knowledge information,and leverage dual item representations to fuse them together for better capturing user behavior *** conduct extensive experiments on two public datasets which demonstrate the superior performance of our AKDN over state-of-the-art methods,like Knowledge Graph Attention Network(KGAT)and Knowledge Graph-based Intent Network(KGIN).
We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary...
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We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary variable(SAV)*** only needs to solve three linear equations at each time step,where each unknown variable can be solved *** is shown that the semi-discrete scheme has second-order accuracy in the temporal *** convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different *** examples are presented to further confirm the validity of the methods.
We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as th...
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We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.
In this paper, we propose a highly accurate scheme for two KdV systems of the Boussinesq type under periodic boundary conditions. The proposed scheme combines the Fourier-Galerkin method for spatial discretization wit...
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