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	1. Existence and concentration of semi-classical ground state solutions for Chern-Simons-Schr\"{o}dinger system
	Wang Linjing,Li Guidong,Tang Chun-Lei
	Mathematics 05 January 2021
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (173K B)

	Abstract:In this paper, we study the equation\begin{equation} -\varepsilon^{2}\Delta u+ V(x)u+\left(A_{0}(u)+A_{1}^{2}(u)+A_{2}^{2}(u)\right)u=f(u) \ \ \ \ \mathrm{in} ~ H^{1}(\mathbb{R}^{2}),\end{equation}where $\varepsilon$ is a small parameter, $V$ is the external potential,$A_i(i=0,1,2)$ is the gauge field and $f\in C(\mathbb{R}, \mathbb{R})$ is 5-superlinear growth.By using variational methods and analytic technique, we prove that this system possesses a ground state solution $u_\varepsilon$.Moreover, our results show that, as $\varepsilon\to 0$, the global maximum point $x_\varepsilon$ of $u_\varepsilon$ must concentrate at the global minimum point $x_0$ of $V$.
	TO cite this article:Wang Linjing,Li Guidong,Tang Chun-Lei. Existence and concentration of semi-classical ground state solutions for Chern-Simons-Schr\"{o}dinger system[OL].[ 5 January 2021] http://en.paper.edu.cn/en_releasepaper/content/4753373


	2. Optimizes a convex function on a multi-objective efficient set
	Wang Ting,Yao Bin
	Mathematics 03 December 2020
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (147K B)

	Abstract:The optimization problem of convex function on effective set of multi-objective optimizationhas many useful applications in multi-criteria decision making. In mathematics, problem (P) can be classified as a global optimization problem.This type of problem is more difficult to solve than convex programming problems.In this paper, penalty function method and parameter method for global optimal solution are proposed, and the cases with equality constraint are discussed.
	TO cite this article:Wang Ting,Yao Bin. Optimizes a convex function on a multi-objective efficient set[OL].[ 3 December 2020] http://en.paper.edu.cn/en_releasepaper/content/4753148


	3. Theory of scissor products and applications
	ZHU Yong-Wen
	Mathematics 18 November 2020
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (152K B)

	Abstract:In this paper, the concept of scissor products is introduced and its fundamental properties are discussed. Combining with the smaller-than-smaller carry method, scissor products can be used in the numerical calculation to form a new and systematic rapid calculation method for the multiplication of integers, which is parallel to but superior to the well-known rapid calculation method of Shi Fengshou. The advantages of the new theory lie in the following two aspects: (1) the scissor products can be understood and remembered very easily with the help of the ordinary $9\times 9$ multiplication table; (2) the smaller-than-smaller carry method makes carrying very easy. Our theory of scissor products can be applied to the rapid multiplication in two ways, in which we use or do not use the virtual carry method respectively.
	TO cite this article:ZHU Yong-Wen. Theory of scissor products and applications[OL].[18 November 2020] http://en.paper.edu.cn/en_releasepaper/content/4753020


	4. Penalized and constrained LAD estimation in fixed and high dimension
	Wu Xiao-Fe,Liang Rong-Mei,Ming Hao,Yang Hu
	Mathematics 19 July 2020
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (687K B)

	Abstract:In this paper, we proposed a $L_1$ penalized LAD estimation with some linear constraints. Different from constrained lasso, our estimation can perform well when heavy-tailed errors or outliers are found in the response. When the dimension of the estimation coefficient $p$ is fixed, the estimation enjoys the Oracle property with adjusted normal variance. When $p$ is greater than $n$, the error bound of estimation is sharper than $\sqrt{k\log(p)/n}$. It is worth noting the result is true for a wide range of noise distribution, even for the Cauchy distribution. Simulation and application to real data also confirm this.
	TO cite this article:Wu Xiao-Fe,Liang Rong-Mei,Ming Hao, et al. Penalized and constrained LAD estimation in fixed and high dimension[OL].[19 July 2020] http://en.paper.edu.cn/en_releasepaper/content/4752557


	5. Homogenization of a class of $p$-Laplace parabolic equation
	ZENG Xingyun,ZHAO Leina
	Mathematics 07 April 2020
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (626K B)

	Abstract:In this paper, we study the homogenization of a class of $p$-Laplacian parabolic equation defined on a $n$-dimensional cylinder which finally converges to a one-dimensional line segment. The problem is the parabolic equation with $p$-Laplacian operator, and the coefficient of this equation is a monotone, uniformly $p$-coercive, uniform $p$-growth Carathéodory function. Finally we obtain the solution and its limit of problem by L. Tartar theory, and the limit and asymptotic properties of the coefficients $A_\varepsilon$ of the equation are obtained.
	TO cite this article:ZENG Xingyun,ZHAO Leina. Homogenization of a class of $p$-Laplace parabolic equation[OL].[ 7 April 2020] http://en.paper.edu.cn/en_releasepaper/content/4751436


	6. Infinitely many high energy radial solutions for Chern-Simons-Schr\"{o}dinger systems
	YuYanyan,Tang Chunlei
	Mathematics 03 April 2020
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (469K B)

	Abstract:In this paper, we investigate the following Chern-Simons-Schr\"{o}dinger system\begin{equation*}\label{css}\begin{cases} -\Delta u+ u+A_{0}u+A_{1}^{2}u+A_{2}^{2}u=f(u), \&#

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