关于Fujita型反应扩散方程组的Cauchy问题

本文研究Ｆｕｊｉｔａ型反应扩散方程组ｕｔ－Δｕ＝α１｜ｕ｜ｑ１－１ｕ＋β１｜ｖ｜ｐ１－１ｖ，（ｘ∈ＲＮ，ｔ＞０），ｖｔ－Δｖ＝α２｜ｕ｜ｑ２－１ｕ＋β２｜ｖ｜ｐ２－１ｖ，ｕ（ｘ，０）＝ｕ０（ｘ）０，ｖ（ｘ，０）＝ｖ０（ｘ）０，（ｘ∈ＲＮ）Ｌｐ解的整体存在性和有限时间Ｂｌｏｗ ｕｐ问题．这里ｑｉ＞１，ｐｉ＞１（ｉ＝１，２），α１０，α２＞０，β１＞０，β２０，１ｐ＋∞．     

一个带非线性边界条件的强耦合抛物方程组的整体存在性与爆破

本文处理带非线性边界条件 u n=uα, v n=vβ ,(x ,t) ∈ Ω× (0 ,T)的抛物方程组ut =vpΔu ,vt=uqΔv ,(x ,t) ∈Ω× (0 ,T) ,其中Ω RN 为一个有界区域 ,p ,q>0和α ,β≥ 0为常数 .研究了上述问题正解的整体存在性和爆破 ,建立了整体存在和爆破的新标准 .证明了当max{p+β,q+α}≤ 1时正解 (u ,v)整体存在 ,当min{p+β ,q+α}>1且max{α ,β}<1时正解 (u ,v)在有限时刻爆破     

Multiplicity of Weak Solutions for a $(p(x), q(x))$-Kirchhoff Equation with Neumann Boundary Conditions

The aim of this study is to investigate the existence of infinitely many weak solutions for the $(p(x), q(x))$-Kirchhoff Neumann problem described by the following equation : \begin{equation*} \left\{\begin{array}{ll} -\left(a_{1}+a_{2}\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx\right)\Delta_{p(\cdot)}u-\left(b_{1}+b_{2}\int_{\Omega}\frac{1}{q(x)}|\nabla u|^{q(x)}dx\right)\Delta_{q(\cdot)}u\+\lambda(x)\Big(|u|^{p(x)-2} u+|u|^{q(x)-2} u\Big)= f_1(x,u)+f_2(x,u) &\mbox{ in } \Omega, \\frac{\partial u}{\partial \nu} =0 \quad &\mbox{on} \quad \partial\Omega.\end{array}\right. \end{equation*} By employing a critical point theorem proposed by B. Ricceri, which stems from a more comprehensive variational principle, we have successfully established the existence of infinitely many weak solutions for the aforementioned problem.     

一类拟线性二阶微分方程解的振动与非振动的判定

本文讨论了拟线性微分方程（ｐ（ｘ＇））＇＋ｑ（ｔ）ｐ（ｘ）＝０,ｔ≥ｔ０,ｑ（ｔ）≥０（这里 ｐ（ｕ）＝｜ｕ｜ｐ－１ｕ,ｐ＞０是常数）的解的振动与非振动条件,并改进了文献［２］的结果．     

On the conjugacy classes in maximal unipotent subgroups of simple algebraic groups

Let G be a simple algebraic group over the algebraically closed field k of characteristic p ≥ 0. Assume p is zero or good for G. Let B be a Borel subgroup of G; we write U for the unipotent radical of B and u for the Lie algebra of U. Using relative Springer isomorphisms} we analyze the adjoint orbits of U in u. In particular, we show that an adjoint orbit of U in u contains a unique so-called minimal representative. In case p > 0, assume G is defined and split over the finite field of p elements F_p. Let q be a power of p and let G(q) be the finite group of F_q-rational points of G. Let F be the Frobenius morphism such that G(q) = G^F. Assume B is F-stable, so that U is also F-stable and U(q) is a Sylow p-subgroup of G(q). We show that the conjugacy classes of U(q) are in correspondence with the F-stable adjoint orbits of U in u. This allows us to deduce results about the conjugacy classes of U(q).     

Symmetry and regularity of solutions to a system with three-component integral equations

Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < n,n is a positive constant,p,q and r satisfy some suitable conditions.It is shown that every positive regular solution(u(x),v(x),w(x)) is radially symmetric and monotonic about some point by developing the moving plane method in an integral form.In addition,the regularity of the solutions is also proved by the contraction mapping principle.The conformal invariant property of the system is also investigated.     

A Finite—dimensional Integrable System with Time Parameter

ＡＦｉｎｉｔｅ－ｄｉｍｅｎｓｉｏｎａｌＩｎｔｅｇｒａｂｌｅＳｙｓｔｅｍｗｉｔｈＴｉｍｅＰａｒａｍｅｔｅｒＺｈａｎｇＪｉｎｓｈｕｎ（张金顺）；ＷａｎｇＨｏｎｇｙｅ（王鸿业）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒ...     

On Weighted Estimates of Solutions for Nonlinear Higher Order Elliptic Problems

In the domain D = z m F it is considered a degenerate nonlinear higher order elliptic equation such that the corresponding energetic space is W 1, q (D, w q ) 7 W m , p ( D , w p ), mp < q < n , and w q , w p are weighted functions from some Muckenhoupt classes. A behavior of a solution u ( x ) is studied for the equation under consideration with the boundary value condition , where and f ( x ) = 1 for x ] F . The pointwise estimate for u ( x ) is proved in terms of the weighted higher order capacity of the set F and the distance from the point x to the set F .     

Symmetric exclusion on random sets and a related problem for random walks in random environment

Summary We study symmetric exclusion on a random set, where the underlying kernelp(x, y) is strictly positive. The random set is generated by Bernoulli experiments with success probabilityq.We prove that for certain values of the involved parameters the transport of particles through the system is drastically different from the classical situation on . In dimension one and the transport of particles occurs on a nonclassical scale and is (on a macroscopic scale)not governed by the heat equation as in the case:r<|log(1-q)| on a random set, or in the classical situation on .The reason for this behaviour is, that a random walk with jump ratesp(x, y) restricted to the random set, converges to Brownian motion in the usual scaling ifr<|log(1-q)| but yields nontrivial limit behaviour only in the scalingxu _-1 x,tu _1+a t(>) if + >r > |log(1-q)|. We calculate and study the limiting processes for the various scalings for fixed random sets. We shortly discuss the caser=+, here in general a great variety of scales yields nontrivial limits.Finally we discuss the case of a stationary random set.     

关于二阶完全非线性抛物组的差分格式

则称二阶完全非线性组(1)是一致抛物的.我们在矩形域Q_T={0≤x≤l,0≤t≤T}(l>0,T>0)上研究方程组(1)满足边界条件     

Parallel Composition of Graph Grammars

The specification of complex systems is usually done by the divide and conquer idea: the system is divided into smaller, less complex components that are developed separately and then merged in some way to form the specification of the whole system. The main aim of this paper is to provide an approach to the parallel composition of graph grammars, formalizing the intuitive idea of divide and conquer described above. This parallel composition of graph grammars provides a suitable formalism for the specification of concurrent systems based on the specifications of their components. Dividing is formalized by special graph grammar morphisms, called specialization morphisms. These morphisms also describe structural and behavioural compatibilities between graph grammars. As a main result, we characterize the parallel composition as the pullback in the category of graph grammars.     

分数阶Schrodinger—Kirchhoff方程无穷多高能量解的存在性

本文研究如下带有变号势函数的分数阶Schrodinger Kirchhoff方程(a+b∫∫R^N|u(x)-u(y)|^p/|x-y|^N+p^sdxdy)^p-1(-△)p^su+λV(x)|u|^p-2u=f(x,u)-μg(x)|u|^q-2u,x∈R^N.其中s∈(0,1),p∈[2,∞),q∈(l,p),a,b>0,λ,μ>0均为正常数,在V,f,g等函数合适的条件下,运用喷泉定理获得该系统无穷多高能量解的存在性.     

非线性Neumann问题正解的存在性

研究非线性Neumann问题(p(t)u′)′+q(t)u=f(t,u),t∈(0,1),u′(0)=u′(1)=0正解的存在性,其中p,q∈C[0,1]满足p(t)>0,0*,t∈[0,1],b*,t∈[0,1],b^*为线性问题(p(t)u′)′+bu=0,u′(0)=0,u(1)=0的第一特征值.运用拓扑度理论及Rabinowitz全局分歧定理为上述问题建立了正解的存在性结果.     

一类三阶拟线性微分方程非振动解的渐近性

主要讨论的是一类三阶拟线性微分方程(p(t)|u″|~(α-1)u″)′+q(t)|u|~(β-1)u=0其中α0,β0,p(t)和q(t)是定义在区间[a,∞)上的连续函数,且满足当t≥a时p(t)0,q(t)0.当t→∞时此方程满足∫_a~∞1/((p(t))~(1/α))dt=∞的特殊非振动解存在的充分必要条件.     

一类新的魔术染色

借鉴于Kotzig和Rosa在1970年定义的边魔术全标号,我们给具有p个顶点和q条边的图G定义了一个新的染色标号,叫作k-魔术染色f,其中f是一一映射V（G）∪E（G）→{1,2,…,p＋q},使得任何边uv∈E（G）满足f（u）＋f（v）=k＋f（uv）,并得到超级k-魔术染色的概念.我们得到了一些具有k-魔术染色或超级k-魔术染色图的性质以及构造这些图的方法.最后,我们猜测所有的树具有一个超级k-魔术染色.     

Difference Schemes of Fully Nonlinear Parabolic Systems of Second Order

The general difference schemes for the first boundary problem of the fully nonlinear parabolic systems of second order f(x, t, u, u_x, u_{xx}, u_t) = 0 are considered in the rectangular domain Q_T = {0 ≤ x ≤ l, 0 ≤ t ≤ T}, where u(x, t) and f(x, t, u, p, r, q) are two m-dimensional vector functions with m ≥ 1 for (x, t) ∈ Q_T and u, p, r, q ∈ R^m. The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a priori estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear parabolic systems are also obtained.     

THE INEFFICIENCY OF LEASTSQUARES IN GAUSS-MARKOV ANDVARIANCE COMPONENT MODELS

1.IntroductionThispaperwillusethefollowingnotations.ForanymatrixA,A andW(A)denotetheMoors-PenroseinverseandthecolumnspaceofA,respectively.ForanysquarematrixA,IAImeansthedeterminantofA,A20(A>0)meansAisnonnegative(positive)definite.ConsidertheGauss-MarkovmodelY=Xo e,E(e)=0,Coy(e)~a'E,(1.1)whereYisann-dimensionalobservablerandomvector,XisannxpknownmatrixwithcolUInn-fUllrank,Tisapdimensionalparametervector,eisann-dimensionalunobserVablerandomvector,aZisanunknownpositiveparameter,Z20.I…     

On Complete Arcs Arising from Plane Curves

We point out an interplay between -Frobenius non-classical plane curves and complete -arcs in . A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete -arcs with parameters and being a power of the characteristic. In addition, for q a square, new complete -arcs with either and or and are constructed by using certain reducible plane curves.     

三维磁微极流体方程弱解的正则性

本文给出了磁微极流体方程弱解的一个新的正则性准则:如果u满足uz ∈Lq(0,T;Lp(R3)),其中p≥3且满足3/p+2/q≤1,那么弱解(u,ω,b)在(0,T)是光滑解.     

W2,ploc(\Omega)\cap C1,α(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations

In this paper we study fully nonlinear elliptic equations F(D²u, x) = 0 in Ω ⊂ R^n with Neumann boundary conditions \frac{∂u}{∂v} = a(x)u under the rather mild structure conditions and without the concavity condition. We establish the global C^{1,Ω} estimates and the interior W^{2,p} estimates for W^{2,q}(Ω) solutions (q > 2n) by introducing new independent variables, and moreover prove the existence of W^{2,p}_{loc}(Ω)∩ C^{1,α}(\bar \Omega} viscosity solutions by using the accretive operator methods, where p E (0, 2), α ∈ (0, 1}.