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	1. Isometric immersions of a complete and connected Riemannian manifold
	DUAN Jiu-Shun,ZHOU Heng-Yu,ZHOU Heng-Yu
	Mathematics 17 January 2023
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	Abstract:In this paper, some basic concepts and theorems of Riemannian manifolds are introduced briefly, and then the concept of isometric immersion is introduced in oeder to introduce the basic cconcept of submanifolds. After introducing Hideki Omori's maximum principle on Riemannian manifolds, a basic theorem of isometric immersion of Riemannian manifolds is proved by using this theorem with modern mathematical language. By replacing $R^n$in the theorem with a more general space and adding additional conditions, the generalized theorem is obtained, and the proof is given in a similar way.
	TO cite this article:DUAN Jiu-Shun,ZHOU Heng-Yu,ZHOU Heng-Yu. Isometric immersions of a complete and connected Riemannian manifold[OL].[17 January 2023] http://en.paper.edu.cn/en_releasepaper/content/4758897


	2. Solitons, breathers and lumps for a generalized (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation in a fluid
	BAI Fan,BAI Fan, JIANG Yan, JIANG Yan,TIAN Bo,TIAN Bo,LIU Tian-Zhi,LIU Tian-Zhi
	Mathematics 08 January 2023
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	Abstract:Fluids are studied in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a generalized (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation in a fluid. Via the Hirota method, bilinear forms, soliton, breather and lump solutions of that equation are obtained. At the same time, solitons, breathers and lumps are depicted. We find that the amplitude and shape of the one soliton keep unchanged during the propagation and the interaction between the two solitons is elastic. We observe that the shapes and amplitudes of the breather and lump remain unchanged during the propagation. We present the one solitons, two solitons, breathers and lumps with the influence of the coefficients in the equation.
	TO cite this article:BAI Fan,BAI Fan, JIANG Yan, et al. Solitons, breathers and lumps for a generalized (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation in a fluid[OL].[ 8 January 2023] http://en.paper.edu.cn/en_releasepaper/content/4758823

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	3. A Brief Survey of Nonlinear Conjugate Gradient Methods for Vector Optimization
	HE Qing-Rui,CHEN Chun-Rong
	Mathematics 22 December 2022
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	Abstract:Conjugate gradient methods are important first-order algorithms, which are characterized by low memory requirements and strong convergence properties. Conjugate gradient methods were first proposed for solving symmetric and positive-definite linear systems, and then developed into a class of major approaches for solving nonlinear unconstrained minimization problems. In recent years, conjugate gradient methods have been also applied to vector optimization problems. In this paper, we mainly introduce the research status and convergence results of nonlinear conjugate gradient methods for vector optimization, and give an instance to illustrate their practicability.
	TO cite this article:HE Qing-Rui,CHEN Chun-Rong. A Brief Survey of Nonlinear Conjugate Gradient Methods for Vector Optimization[OL].[22 December 2022] http://en.paper.edu.cn/en_releasepaper/content/4758680


	4. Nonnegative LAD-LASSO and Application in index tracking
	LIANG Rong-Mei
	Mathematics 31 October 2022
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	Abstract:In this paper,we combine LAD-LASSO estimation and nonnegative constraint estimation,to propose a robust estimation which can do parameter estimation and variable selection in non negative problem.Compared with LAD-LASSO, he can better handle some non negative problems in economy. And compared with non negative estimation,it can do variable selection.With easily estimated tuning parameters,the non negative enjoys oracle property.Furthermore,we propose a non negative coordinate descent algorithm and do some data simulation. We also applied the model to stock index tracking and compared with non negative LASSO.
	TO cite this article:LIANG Rong-Mei. Nonnegative LAD-LASSO and Application in index tracking[OL].[31 October 2022] http://en.paper.edu.cn/en_releasepaper/content/4758259


	5. Trajectory tracking of manipulator with full state constraints based on observer
	ZHANG Su-Su,CUI Ming-Yue
	Mathematics 17 May 2022
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	Abstract:This paper studies the trajectory tracking of manipulator under disturbances and full state constraints. Firstly, for time-varying disturbances of manipulator, under reasonable assumptions, a disturbance observer is designed to estimate time-varying disturbances. Then, by making full use of the properties of the system, skillfully constructs a barrier Lyapunov function, and designs a vector state feedback tracking controller based on disturbance observer, so that the tracking error can be sufficiently small by adjusting the parameters while keeping the state limited. Finally, the effectiveness of the control strategy is verified by a two degree of freedom manipulator system.
	TO cite this article:ZHANG Su-Su,CUI Ming-Yue. Trajectory tracking of manipulator with full state constraints based on observer[OL].[17 May 2022] http://en.paper.edu.cn/en_releasepaper/content/4757772


	6. Resistance distance and the Kirchhoff index-based graph invariants of hexagonalization of graphs
	XU Can , YANG Yu-Jun
	Mathematics 15 April 2022
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	Abstract:Let $G$ be a connected graph. we consider the resistance distance and Kirchhoff index of the hexagonalization graph $H(G)$ of a graph $G$. The haxagonalization graph $H(G)$ is the graph obtained from $G$ by replacing each edge of $G$ by two disjoint paths of length 3 with the end vertices of the edge as their end vertices. Let $H^{k}(G)$ denote the the graph obtained from $G$ by $k$-iterated hexagonalizations. Using algebraic and combinatorial methods, explict formulae for resistance distances and Kirchhoff indices of $H(G)$ and $H^{k}(G)$ are obtained. It turns out that resistance distances and Kirchhoff indices of $H(G)$ and $H^{k}(G)$ could be expressed in terms of resistance distances and related structural graph invariants of $G$.
	TO cite this article:XU Can , YANG Yu-Jun. Resistance distance and the Kirchhoff index-based graph invariants of hexagonalization of graphs[OL].[15 April 2022] http://en.paper.edu.cn/en_releasepaper/content/4757250


	7. Coupled rearrangement inequalities and their application for general pseudo-relativistic Schr\"odinger Hartree equations
	Pei Miaomiao,Wu Dan
	Mathematics 02 April 2022
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	Abstract:In this paper, we consider nonlinear pseudo-relativistic Schr\"odinger equations with Hartree type nonlinearities.We study their standing waves based on a variational framework.Instead of using a scaling argument, we employ coupled rearrangement inequalities to exclude the lack of compactness in the constrained minimizing problems,due to the inhomogeneous and nonlocal terms in the equations.To overcome these difficulties,we establish two new coupled rearrangement inequalities according to fully nonlinear pseudo-relativisticoperators and Hartree type nonlinearities.As a consequence, the existence of standing wavesis obtained via applying the concentration-compactness principle in subcritical case.Moreover, we also derive symmetric results and other properties of the minimizers.
	TO cite this article:Pei Miaomiao,Wu Dan. Coupled rearrangement inequalities and their application for general pseudo-relativistic Schr\"odinger Hartree equations[OL].[ 2 April 2022] http://en.paper.edu.cn/en_releasepaper/content/4757241


	8. Existence and asymptotic behavior of sign-changing solutions for the Schr\"{o}dinger-Bopp-Podolsky system with concave-convex nonlinearities
	Yi-Xin Hu, Xing-Ping Wu, Chun-Lei Tang
	Mathematics 28 March 2022
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	Abstract:In this paper, we study the Schr\"{o}dinger-Bopp-Podolsky system with con-cave-convex nonlinearities. If $0< \lambda < \lambda^{*}$, the system has a sign-changing solution by variational methods. Besides, we argument the asymptotic behavior of the solution as $a\rightarrow 0$.
	TO cite this article:Yi-Xin Hu, Xing-Ping Wu, Chun-Lei Tang. Existence and asymptotic behavior of sign-changing solutions for the Schr\"{o}dinger-Bopp-Podolsky system with concave-convex nonlinearities[OL].[28 March 2022] http://en.paper.edu.cn/en_releasepaper/content/4757256


	9. Existence of least-energy sign-changing solutions for the Schr\"{o}dinger-Bopp-Podolsky system with critical growth
	HU Yi-Xin,HU Yi-Xin,WU Xing-Ping,TANG Chun-Lei
	Mathematics 28 March 2022
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	Abstract:In this paper, we study the Schr\"{o}dinger-Bopp-Podolsky system\begin{equation}\begin{cases} -\Delta u+V(x)u+\phi u=\mu f(u)+u^{5} &\text{ in } \ \mathbb{R}^{3},\\ -\Delta \phi +a^{2}\Delta^{2}\phi =4\pi u^{2} &\text{ in } \ \mathbb{R}^{3}, \end{cases}\end{equation}thereinto, we request that $a,\ \mu >0$, the function $V(x)$ and $f(u)$ satisfies some specified conditions. By using constraint variational method and quantitative deformation lemma, we derive two results. If $\mu$ is large enough, the system has a least-energy sign-changing solution $u_{\mu}$. And the energy of the solution is twice as large as that of the ground state solution.
	TO cite this article:HU Yi-Xin,HU Yi-Xin,WU Xing-Ping, et al. Existence of least-energy sign-changing solutions for the Schr\"{o}dinger-Bopp-Podolsky system with critical growth[OL].[28 March 2022] http://en.paper.edu.cn/en_releasepaper/content/4756852


	10. Optimal Sampling Algorithms for Block Matrix Multiplication
	NIU Cheng-Mei, LI Han-Yu
	Mathematics 25 March 2022
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	Abstract:In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Specifically, based on the A-optimal design criterion, we obtain the optimal sampling probabilities and sampling block sizes. To improve the practicability of the block sizes, two modified ones with less computation cost are provided. With respect to the second one, we devise a two step algorithm. Extensive numerical results show that our methods outperform the state-of-the-art ones given in the literature.
	TO cite this article:NIU Cheng-Mei, LI Han-Yu. Optimal Sampling Algorithms for Block Matrix Multiplication[OL].[25 March 2022] http://en.paper.edu.cn/en_releasepaper/content/4757220

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