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BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS

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Journal of Computational mathematics 2002年第4期20卷 349-362页

作者： Xiao-yuan Qian (department of applied mathematics, dalian university of technology,{2., China) department of applied mathematics Dalian University of Technology Dalian 116024

Non-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced. The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.

关键词： fractal bivariate functions interpolation

Mitophagy and cGAS-STING crosstalk in neuroinflammation

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Acta Pharmaceutica Sinica B 2024年第8期14卷 3327-3361页

作者： Xiaogang Zhou Jing Wang Lu Yu Gan Qiao dalian Qin Betty Yuen-Kwan Law Fang Ren Jianming Wu Anguo Wu Sichuan Key Medical Laboratory of New Drug Discovery and Drugability Evaluation Luzhou Key Laboratory of Activity Screening and Druggability Evaluation for Chinese Materia MedicaKey Laboratory of Medical Electrophysiology of Ministry of EducationSchool of PharmacySouthwest Medical UniversityLuzhou 646000China State Key Laboratory of Quality Research in Chinese Medicine Macao University of Science and TechnologyMacao SAR 999078China Chongqing Key Laboratory of Sichuan-Chongqing Co-construction for Diagnosis and Treatment of Infectious Diseases Integrated Traditional Chinese and Western Medicine Chongqing Traditional Chinese Medicine HospitalChongqing 400021China

Mitophagy,essential for mitochondrial health,selectively degrades damaged *** is intricately linked to the cGAS-STING pathway,which is crucial for innate *** pathway responds to mitochondrial DNA and is associated with cellular stress *** review explores the molecular details and regulatory mechanisms of mitophagy and the cGAS-STING *** critically evaluate the literature demonstrating how dysfunctional mitophagy leads to neuroinflammatory conditions,primarily through the accumulation of damaged mitochondria,which activates the cGAS-STING *** activation prompts the production of pro-inflammatory cytokines,exacerbating *** review emphasizes the interaction between mitophagy and the cGAS-STING *** mitophagy may suppress the cGAS-STING pathway,offering protection against ***,impaired mitophagy may activate the cGAS-STING pathway,leading to chronic ***,we explored how this interaction influences neurodegenerative disorders,suggesting a common mechanism underlying these *** conclusion,there is a need for additional targeted research to unravel the complexities of mitophagy-cGAS-STING interactions and their role in *** review highlights potential therapies targeting these pathways,potentially leading to new treatments for neuroinflammatory and neurodegenerative *** synthesis enhances our understanding of the cellular and molecular foundations of neuroinflammation and opens new therapeutic avenues for neurodegenerative disease research.

关键词： Neuroinflammation Mitophagy cGAS-STING Innate immunity Mitochondrial DNA Crosstalk Therapeutic avenues Neurodegenerative diseases

Solvability of Elliptic Boundary Value Problems without Standard Landesman-Lazer Condition

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Acta Mathematica Sinica,English Series 2000年第2期16卷 349-359页

作者： Zhiqing Han department of applied mathematics.dalian {2. of technology,dalian 11602.,P.R.China department of applied mathematics Dalian University of Technology Dalian 116024 P. R. China

In this paper we prove a very general result concerning solvability of the resonant problem: Δu+λku+g（x, u）=h（x）;u=0, xΩ, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem when λk=λ1. in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.

关键词： Elliptic boundary value problems Leray-Schauder degree continuation method Landesman-Lazer condition Semi-Landesman-Lazer conditions Sign condition

Nonsingularity in second-order cone programming via the smoothing metric projector

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Science China mathematics 2010年第4期53卷 1025-1038页

作者： WANG Yun 1,& ZHANG LiWei 2.1 College of Information Sciences and Engineering,Shandong Agricultural university,Tai’an 2.1018,China 2.department of applied mathematics,{2. university of technology,{2. 11602.,China College of Information Sciences and Engineering Shandong Agricultural University Tai’an China department of applied mathematics Dalian University of Technology Dalian China

Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker ***,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker ***,the analysis does not need the strict complementarity condition.

关键词： second-order cone programming problem smoothing metric projector B-subdifferential Clarke’s generalized Jacobian smoothing Newton method

New Complexiton Solutions of (2.1)-Dimensional Nizhnik-Novikov-Veselov Equations

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Communications in Theoretical Physics 2006年第9期46卷 407-414页

作者： ZHANG Yuan-Yuan,~+ ZHENG Ying, ZHANG Hong-Qing department of applied mathematics, dalian university of technology,{2., China department of applied mathematics Dalian University of Technology Dalian 116024 China

In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2.1)-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.

关键词： rational expansion method (2.1)-dimensional Nizhnik Novikov-Veselov equations complexiton solutions

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

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Acta Mathematica Scientia 2005年第1期25卷 170-178页

作者：孙清滢 department of applied mathematics university of Petroleum Dongying 257061 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

关键词： Non-linear programming three term memory gradient method convergence non-monotone line search technique numerical experiment

IMPROVING EIGENVECTORS IN ARNOLDI'S METHOD

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Journal of Computational mathematics 2000年第3期18卷 265-276页

作者： Zhong-xiao Jia (department of applied mathematics, dalian university of technology,{2., China) Ludwig Elsner (Fakultat fur Mathematik, university Bielefeld, Postfach 100131, 33501 Bielefeld,Germany) 大连理工大学辽宁大连 116024 Universitt Bielefeld 德国 Bielefeld 33501

The Ritz vectors obtained by Arnoldi's method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the efficiency of Arnoldi type algorithms, we propose a strategy that uses Ritz values obtained from an m-dimensional Krylov subspace but chooses modified approximate eigenvectors in an (m + 1)-dimensional Krylov subspace. Residual norm of each new approximate eigenpair is minimal over the span of the Ritz vector and the (m+1)th basis vector, which is available when the m-step Arnoldi process is run. The resulting modi- fied m-step Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m + 1)-step one. Based on this strategy, we present a modified m-step restarted Arnoldi algorithm. Numerical examples show that the modified m-step restarted algorithm and its version with Chebyshev acceleration are often considerably more efficient than the standard (m+ 1)-step restarted ones.

关键词： Large unsymmetric The m-step Arnoldi process The m-step Arnoldi method Eigenvalue Ritz value Eigenvector Ritz vector Modified

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science China mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua KONG~(1+) Ming-xin WANG~(2.3) 1 department of applied mathematics,dalian {2. of technology,dalian 11602.,China 2.department of mathematics,Southeast {2.,Nanjing 2.0018,China 3 department of mathematics,Xuzhou Normal {2.,Xuzhou 2.1116,China department of applied mathematics Dalian University of Technology Dalian China department of mathematics Southeast University Nanjing China department of mathematics Xuzhou Normal University Xuzhou China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35K65

The Structure of Clarke's Generalized Gradient andComputing Some of Its Element for the SmoothComposition of Max-Type Functions

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运筹学学报 1997年第2期1卷 12-19页

作者： YAN GAO(department of applied mathematics, dalian university of technology,{2. 11602., China) 大连理工大学应用数学系辽宁大连

Clarke’s generalized gradient of the smooth composition of max-type functions isconsidered. Clarke’s generalized gradient of this class of functions is a convex hull of afinite number of points. Several elements of Clarke’s generalized gradient is *** elements of Clarke’s generalized gradient for this class of functions, at apoint, is transformed into computing gradients of a smooth function, at a point, bydetermining the compatibility of systems of linear inequalities.

关键词： Clarke’s generalized gradient Max-type function Lipschitzian function quasidifferentiable function nonsmooth optimization