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学者姓名：徐文青
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Abstract ：
We devote this paper to a theoretic analysis of deep neural networks from a gametheoretical perspective. We consider a general deep neural network D with linear activation functions f (x) = x + b. We show that the deep neural network can be transformed into a non-atomic congestion game, regardless whether it is fully connected or locally connected. Moreover, we show that learning the weight and bias vectors of D for a training set H is equivalent to computing an optimal solution of the corresponding non-atomic congestion game. In particular, when D is a deep neural network for a classification task, then the learning is equivalent to computing a Wardrop equilibrium of the corresponding non-atomic congestion game. (c) 2022 Elsevier B.V. All rights reserved.
Keyword ：
Wardrop equilibria Wardrop equilibria Local minima Local minima Deep neural networks Deep neural networks Non -atomic congestion game Non -atomic congestion game
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| GB/T 7714 | Ren, Chunying , Wu, Zijun , Xu, Dachuan et al. A game-theoretic perspective of deep neural networks [J]. | THEORETICAL COMPUTER SCIENCE , 2023 , 939 : 48-62 . |
| MLA | Ren, Chunying et al. "A game-theoretic perspective of deep neural networks" . | THEORETICAL COMPUTER SCIENCE 939 (2023) : 48-62 . |
| APA | Ren, Chunying , Wu, Zijun , Xu, Dachuan , Xu, Wenqing . A game-theoretic perspective of deep neural networks . | THEORETICAL COMPUTER SCIENCE , 2023 , 939 , 48-62 . |
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Abstract ：
In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system by imposing natural boundary conditions and regularity assumptions on the initial data, without any compatibility condition.
Keyword ：
2D magneto-micropolar equations 2D magneto-micropolar equations Initial-boundary value problem Initial-boundary value problem Zero angular viscosity Zero angular viscosity
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| GB/T 7714 | Wang, Shasha , Xu, Wen-Qing , Liu, Jitao . Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity [J]. | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2021 , 72 (3) . |
| MLA | Wang, Shasha et al. "Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity" . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 72 . 3 (2021) . |
| APA | Wang, Shasha , Xu, Wen-Qing , Liu, Jitao . Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2021 , 72 (3) . |
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Abstract ：
This article concerns the initial-boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with ill-prepared initial data. We consider a non-slip boundary condition for the velocity field and inhomogeneous Dirichlet boundary condition for the temperature. By means of multi-scale analysis and matched asymptotic expansion methods, we establish an accurate approximating solution for the viscous and diffusive Boussinesq system. We also study the convergence of the infinite Prandtl number limit.
Keyword ：
Rayleigh-Benard convection Rayleigh-Benard convection initial-boundary layer initial-boundary layer infinite Prandtl number limit infinite Prandtl number limit Boussinesq system Boussinesq system asymptotic expansion asymptotic expansion
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| GB/T 7714 | Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing . INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION [J]. | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 2020 . |
| MLA | Fan, Xiaoting et al. "INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION" . | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (2020) . |
| APA | Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing . INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION . | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 2020 . |
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Abstract ：
We study the boundary layer problem of a Keller-Segel model in a domain of two space dimensions with vanishing chemical diffusion coefficient. By using the method of matched asymptotic expansions of singular perturbation theory, we construct an accurate approximate solution which incorporates the effects of boundary layers and then use the classical energy estimates to prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero.
Keyword ：
energy estimates energy estimates boundary layer phenomenon boundary layer phenomenon Keller-Segel model Keller-Segel model matched asymptotic expansions matched asymptotic expansions
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| GB/T 7714 | Meng, Linlin , Xu, Wen-Qing , Wang, Shu . Boundary layer analysis for a 2-D Keller-Segel model [J]. | OPEN MATHEMATICS , 2020 , 18 : 1895-1914 . |
| MLA | Meng, Linlin et al. "Boundary layer analysis for a 2-D Keller-Segel model" . | OPEN MATHEMATICS 18 (2020) : 1895-1914 . |
| APA | Meng, Linlin , Xu, Wen-Qing , Wang, Shu . Boundary layer analysis for a 2-D Keller-Segel model . | OPEN MATHEMATICS , 2020 , 18 , 1895-1914 . |
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Abstract ：
We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the asymptotic expansion methods of singular perturbation theory, we construct an exact approximating solution for the viscous and diffusive Boussinesq system with well-prepared initial data. In addition, we obtain the convergence result of the vanishing diffusivity limit.
Keyword ：
vanishing diffusivity limit vanishing diffusivity limit boundary layers boundary layers Rayleigh-Benard convection Rayleigh-Benard convection Boussinesq system Boussinesq system asymptotic expansion asymptotic expansion Ming Mei Ming Mei
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| GB/T 7714 | Fan, Xiaoting , Xu, Wen-Qing , Wang, Shu et al. Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection [J]. | APPLICABLE ANALYSIS , 2020 , 99 (12) : 2026-2044 . |
| MLA | Fan, Xiaoting et al. "Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection" . | APPLICABLE ANALYSIS 99 . 12 (2020) : 2026-2044 . |
| APA | Fan, Xiaoting , Xu, Wen-Qing , Wang, Shu , Wang, Wei . Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection . | APPLICABLE ANALYSIS , 2020 , 99 (12) , 2026-2044 . |
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Abstract ：
In this paper, we study the approximation of pi through the semiperimeter or area of a random n-sided polygon inscribed in a unit circle in R-2. We show that, with probability 1, the approximation error goes to 0 as n -> infinity, and is roughly sextupled when compared with the classical Archimedean approach of using a regular n-sided polygon. By combining both the semiperimeter and area of these random inscribed polygons, we also construct extrapolation improvements that can significantly speed up the convergence of these approximations.
Keyword ：
random polygon random polygon random division random division Borel-Cantelli lemma Borel-Cantelli lemma extrapolation extrapolation Archimedean polygon Archimedean polygon
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| GB/T 7714 | Xu, Wen-Qing , Meng, Linlin , Li, Yong . Random Polygons and Estimations of pi [J]. | OPEN MATHEMATICS , 2019 , 17 : 575-581 . |
| MLA | Xu, Wen-Qing et al. "Random Polygons and Estimations of pi" . | OPEN MATHEMATICS 17 (2019) : 575-581 . |
| APA | Xu, Wen-Qing , Meng, Linlin , Li, Yong . Random Polygons and Estimations of pi . | OPEN MATHEMATICS , 2019 , 17 , 575-581 . |
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Abstract ：
In this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response alpha and the viscosity nu vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of nu, alpha and the radius of the family of spatial domains. (C) 2019 Elsevier Ltd. All rights reserved.
Keyword ：
Expanding domain Expanding domain Vanishing viscosity limits Vanishing viscosity limits Vanishing alpha limits Vanishing alpha limits Second grade fluid equations Second grade fluid equations
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| GB/T 7714 | Liu, Jitao , Xu, Wen-Qing . Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane [J]. | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2019 , 49 : 355-367 . |
| MLA | Liu, Jitao et al. "Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane" . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 49 (2019) : 355-367 . |
| APA | Liu, Jitao , Xu, Wen-Qing . Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2019 , 49 , 355-367 . |
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Abstract ：
In this paper, we consider the vanishing viscosity limit problem for a system arising from the Keller-Segel equations in three space dimensions. First, we construct an accurate approximate solution that incorporates the effects of boundary layers. Then, we prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero. Our approach is based on the method of matched asymptotic expansions of singular perturbation theory and the classical energy estimates.
Keyword ：
matched asymptotic expansions matched asymptotic expansions energy estimates energy estimates boundary layer phenomenon boundary layer phenomenon chemotaxis chemotaxis Keller-Segel model Keller-Segel model
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| GB/T 7714 | Meng, Linlin , Xu, Wen-Qing , Wang, Shu . On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2019 , 43 (2) : 920-938 . |
| MLA | Meng, Linlin et al. "On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 43 . 2 (2019) : 920-938 . |
| APA | Meng, Linlin , Xu, Wen-Qing , Wang, Shu . On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2019 , 43 (2) , 920-938 . |
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Abstract ：
The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Benard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates O (epsilon(3/2)) and O(epsilon(2)).
Keyword ：
Rayleigh-Benard convection Rayleigh-Benard convection Asymptotic expansion Asymptotic expansion Infinite Prandtl number limit Infinite Prandtl number limit Boussinesq system Boussinesq system Initial layers Initial layers Two-time-scale approach Two-time-scale approach
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| GB/T 7714 | Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing et al. Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit [J]. | OPEN MATHEMATICS , 2018 , 16 : 1145-1160 . |
| MLA | Fan, Xiaoting et al. "Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit" . | OPEN MATHEMATICS 16 (2018) : 1145-1160 . |
| APA | Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing , Liu, Mingshuo . Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit . | OPEN MATHEMATICS , 2018 , 16 , 1145-1160 . |
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Abstract ：
In this paper, we study the global regularity to a three-dimensional logarithmic sub-dissipative Navier-Stokes model. This system takes the form of partial derivative(t)u + (D(-1/2)u) . del u + del p = -A(2)u, where D and A are Fourier multipliers defined by D = vertical bar del vertical bar and A = vertical bar del vertical bar ln(-1/4)(e + lambda ln(e + vertical bar del vertical bar)) with lambda >= 0. The symbols of the D and A are m(xi) = vertical bar xi vertical bar and h(xi) = vertical bar xi vertical bar/g(xi) respectively, where g(xi) = ln(1/4) (e + lambda ln(e + vertical bar xi vertical bar lambda >= 0. It is clear that for the Navier-Stokes equations, global regularity is true under the assumption that h(xi) = vertical bar xi vertical bar(alpha) for alpha >= 5/4. Here by changing the advection term we greatly weaken the dissipation to h(xi) = vertical bar xi vertical bar/g(xi). We prove the global well-posedness for any smooth initial data in H-s(R-3), s >= 3 by using the energy method.
Keyword ：
energy estimates energy estimates global regularity global regularity Navier-Stokes equations Navier-Stokes equations sub-dissipation sub-dissipation
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| GB/T 7714 | Shao, Shuguang , Wang, Shu , Xu, Wen-Qing . GLOBAL REGULARITY FOR A MODEL OF NAVIER-STOKES EQUATIONS WITH LOGARITHMIC SUB-DISSIPATION [J]. | KINETIC AND RELATED MODELS , 2018 , 11 (1) : 179-190 . |
| MLA | Shao, Shuguang et al. "GLOBAL REGULARITY FOR A MODEL OF NAVIER-STOKES EQUATIONS WITH LOGARITHMIC SUB-DISSIPATION" . | KINETIC AND RELATED MODELS 11 . 1 (2018) : 179-190 . |
| APA | Shao, Shuguang , Wang, Shu , Xu, Wen-Qing . GLOBAL REGULARITY FOR A MODEL OF NAVIER-STOKES EQUATIONS WITH LOGARITHMIC SUB-DISSIPATION . | KINETIC AND RELATED MODELS , 2018 , 11 (1) , 179-190 . |
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