Γ-等变分歧问题的有限决定性

本文研究了关于Γ-右等价和Γ-左-右等价的Γ-等变分歧问题,利用了奇点理论和紧群表示论,获得了判别这类问题的一些准则,并推广了文[3]的一些结果.     

一类极小问题解的存在性

在Luminita A.Vese文章中给出的一个重要泛函算法的基础上,讨论了此泛函的一些其它理论结论,即利用Γ-收敛的性质得到该泛函极小点存在问题,泛函的变量空间的弱＊列紧等性质.同时讨论了在图像处理中一个相关泛函的极小点存在问题.     

模糊数空间上Γ-收敛的保序性

证明在Γ收敛下,模糊数空间上的小于等于关系和近似小于等于关系保持不变.     

（r, s）-STABILITY OF UNFOLDING OFF-EQUIVARIANT BIFURCATION PROBLEM

In this paper,the F-equivariant (s,t)-equivalence relation and F-equivariant infinitesimally (r,s)-stability of F-equivariant bifurcation problem are defined. The criterion for F-equivariant infinitesimally (r, s)-stability is proven when F is a compact finite Lie group . Transversality condition is used to characterize the stability.     

gr－正则环和矩阵环的gr－正则性

本文主要证明了（１）当Ｇ是有限群时，Ｇ－型分次环Ｒ是ｇｒ－正则的当且仅当ＲＧ是正则的当且仅当Ｍ＿Ｇ（Ｒ）是ｇｒ－正则的当且仅当对每个和Ｇ的任意非空子集Ｈ和Ｆ，Ｍ＿（ＨＸＦ）（Ｒ）的每个矩阵都有１－逆。（２）当Ｇ是任意群，Ｇ－型分次环只是反ｇｒ－正则的当且仅当Ｆ是反正则的当且仅当对每个和Ｇ的任意作非空子集Ｈ和Ｋ，ＦＭ＿（Ｈ×Ｆ）（Ｒ）的每个矩阵有２－逆当且仅当ＦＭ＿Ｇ（Ｒ）是ｇｒ－反正则的。     

Characterizations of multivariate normality II. Through linear regressions

It is established that a vector (X′₁, X′₂, …, X′_k) has a multivariate normal distribution if (i) for each X_i the regression on the rest is linear, (ii) the conditional distribution of X₁ about the regression does not depend on the rest of the variables, and (iii) the conditional distribution of X₂ about the regression does not depend on the rest of the variables, provided that the regression coefficients satisfy some more conditions that those given by [4]J. Multivar. Anal. 6 81–94].     

ON DETERMINATION OF THE IMPULSIVESOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

1IntroductionInthispaper,wediscussthecompletesolutionoftheLinearNon-HomogeneousMatrixDifferentialEquations(LNHMDEs)describedbyA(p)PNH(t)=B(p)U(t),t2o,(1)wherepgd/dtthedifferentialoperator,A(p)=A,,Pq' A,,-1Pq1-' ' A1p AoERfa],",,rankR(.)A(p)=rlAieR",,i=O,1,2,',qi,qi>1,B(p)=Blpl BI-,P,-' -.' B1p BOeR[P],'",BjER'",j=o,1,2,...,l,l2o,PNH(t):[o, oc)-R'isthepseudostateoftheLNHMDE,u(f):[o, oo)-R"isanitimespiecewisecontinuouslydifferentiablefunctioncalledtheinputoftheLNHMDE…     

Homogenization of Random Fractional Obstacle Problems via Γ-Convergence

We show that solutions to the viscous conservation laws in several space dimensions converge to rarefactions as time tends to infinity, when the initial data belongs to some large global class of functions. The convergence takes place in, and in L^p(RxK), where K is compact in Rn–1, and we determine the asymptotic rate.     

Weighted energy-dissipation functionals for doubly nonlinear evolution

This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.