Banach空间积分双半群的生成条件

研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.     

标准算子代数上满足某些等式的广义导子的刻画(英文)

令H为复数域C上的Hilbert空间,A为H上的标准算子代数.设δ:A→B(H)是线性映射.本文证明了,如果对任意A∈A成立δ(AA~*A)=δ(A)A~*A-Aδ(A~*)A+AA~*δ(A),则存在λ∈C及算子S,T∈B(H)满足S+T=λI,使得对所有的A∈A都有δ(A)=SA-AT.     

代数的张量积的同调满同态的构造

利用已知的代数的同调满同态来构造其张量积代数的同调满同态.设A,B,C,D是域k上的有限维代数,如果环同态f:A→C和g:B→D是环的同调满同态,则fg:AB→CD也是环的同调满同态.     

余Frame范畴中余积的构造

首先,在并半格中引入了上覆盖关系的概念,并以此为基础引入强并半格以及强并半格中上覆盖和C-滤子的概念,证明了强并半格S中全体C-滤子之族C Fil(S)是余Frame,讨论了简单上集值映射u:S→C Fil(S)的相关并半格同态性质;其次,证明了由一族余Frame{A_λ|λ∈Γ}的直积Π_(λ∈Γ)A_λ中只有有限个坐标非零的元素构成的子集A是强并半格,还证明了A是余Frame族{A_λ|λ∈Γ}在并半格范畴中的余积对象;最后,通过各个坐标集中的上覆盖关系在A中定义了上覆盖C~*,再结合简单上集值映射u:A→C~*Fil(A)和标准入射qλ:Aλ→Π_(λ∈Γ)A_λ(λ∈Γ),证明了强并半格A中由上覆盖C~*诱导的余Frame C~*Fil(A)是余Frame族{A_λ|λ∈Γ}在余Frame范畴中的余积对象.     

von Neumann代数中套子代数上的Lie导子

本文对因子von Neumann代数中套子代数上的线性映射L:alg_Mβ→M满足L(AB—BA)=L(A)B-BL(A)+AL(B)-L(B)A( A,B∈alg_Mβ)进行了刻划,证明了存在线性函数h:alg_Mβ→C;且对任意A,B∈alg_Mβ,有h(AB—BA)=0和算子T∈M,使得对任意X∈alg_Mβ,都有L(X)=XT-TX+h(X)I.     

半张量积下矩阵方程组AX=B,XC=D的最小二乘解

本文研究了半张量积下矩阵方程组AX=B,XC=D在不同情况下的最小二乘解X*∈R~(p×q),其中矩阵A∈R~(m×n),B∈R~(h×k),C∈R~(a×b),D∈R~(l×d)给定.根据半张量积的定义将其转变为普通乘积下的矩阵方程组,再结合矩阵奇异值分解及矩阵微分给出该方程组在不同情况下最小二乘解的解析表达式,并用数值算例加以验证.     

关于完备随机内积模中的Lax-Milgram定理的注记

设(S,X)为数域K上以σ-有限测度空间(Ω,A,μ)为基的完备的RIP-模,而且α:S×S→L(μ,K)满足如下条件:(A)存在ξ∈L (μ),使得a(p,q)ξ·X~p·X~q,p,q∈S;(B)a是coercive(即,存在η∈L (μ),使得a(p,p)η·X~p2,p∈S且μ({ωη(ω)=0})=0);(C)对每个q∈S,a(·,q):S→L(μ,K)是模同态,且对每个p∈S,a(p,ξq1 ηq2)=ξ-a(p,q1) η-a(p,q2),q1,q2∈S及ξ,η∈L(μ,K).则存在唯一的连续模同态A:S→S使A-1存在且μ-a.s.有界,还满足:(1)a(p,q)=XA(p),q,p,q∈S;(2)X~A-1(p)1ηX~p,p∈S.     

不定酉不变线性映射的刻戈及相关结果

Let A and B be unital C*-algebras, and let J ∈ A, L ∈ B be Hermitian invertible elements. For every T ∈ A and S ∈ B,define TJ(?)=J-1T*J and SL(?) =L-1S*L. Then in such a way we endow the C*-algebras A and B with indefinite structures. We characterize firstly the Jordan (J, L)-(?)-homomorphisms on C*-algebras. As applications, we further classify the bounded linear maps ?:A→B preserving (J, L)-unitary elements. When A = B(H) and B = B(K), where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T →UVTV-1((?)T ∈ B(H)) or T→UVT(?)V-1 ((?)T ∈ B(H)), where U ∈ B(K) is indefinite unitary and, V : H→K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.     

上三角算子矩阵的单值延拓性质的摄动

设H为无限维可分的复Hilbert空间,B(H)为H上的有界线性算子全体.算子T∈B(H)称为具有单值延拓性质,若对任意一个开集U(?)C,满足方程(T-λI)f(λ)=0(任给λ∈U)的唯一的解析函数f:U→H为零函数;T∈B(H)称为满足单值延拓性质的稳定性,若对任意一个紧算子K∈B(H),T+K都满足单值延拓性质.本文给出了2×2上三角算子矩阵在紧摄动下满足单值延拓性质的稳定性的特征.     

C~* -代数上完全正映射的刻画

本文给出C* -代数之间完全正映射的刻画,证明:如果A,B是有单位元的C*-代数,则映射Φ:A→B为完全正映射当且仅当存在保单位*-同态πA:A→B(K)、等距* -同态πB:B→B(H)及有界线性算子V:H→K,使得πB(Φ(1))=V*V 且■a∈A,都有πB(Φ(a))=V*π(a)V.作为推论,得到著名的Stinespring膨胀定理.     

Invariant Measures for a Stochastic Kuramoto–Sivashinsky Equation

Abstract

For the one-dimensional Kuramoto–Sivashinsky equation with random forcing term, existence and uniqueness of solutions is proved. Then, the Markovian semigroup is well defined; its properties are analyzed in order to provide sufficient conditions for existence and uniqueness of invariant measures for this stochastic equation. Finally, regularity results are presented.     

Momentum estimates and ergodicity for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise

In this paper, we consider the ergodicity of invariant measures for the stochastic Ginzburg-Landau equation with degenerate random forcing. First, we show the existence and pathwise uniqueness of strong solutions with H¹-initial data, and then the existence of an invariant measure for the Feller semigroup by the Krylov-Bogoliubov method. Then in the case of degenerate additive noise, using the notion of asymptotically strong Feller property, we prove the uniqueness of invariant measures for the transition semigroup.     

Existence,uniqueness, and stability of nonlinear evolution equations

In this paper we study existence, uniqueness, and stability of nonlinear evolution equations. We develop a new type of perturbation result for a C₀ semigroup in Banach space, where the nonlinear operators are not necessarily m-accretive or everywhere defined. Assuming that the semigroup has a smoothing property we obtain local existence, uniqueness and regularity results. We then establish a Liapunov theory which enables us to examine stability. To illustrate our theory several simple examples are presented.     

一类具有非线性kirchhoff-sine-Gordon广义方程的整体吸引子的存在性

主要目的是利用Galerkin逼近法和先验估计来证明一类具有非线性阻尼和外源项的耗散型sine-Gordon-kirchhoff方程的整体吸引子的存在性,首先通过先验估计证明系统存在唯一的整体解,再证明系统存在有界吸收集和算子半群光滑性质,最后得到系统存在整体吸引子.     

关于半环半群

This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.     

On Wiener-Poisson type multivalued stochastic differential equations with non-Lipschitz coefficients

In this paper, we prove local uniqueness for multivalued stochastic differential equations with Poisson jumps. Then existence and uniqueness of global solutions is obtained under the conditions that the coefficients satisfy locally Lipschitz continuity and one-sided linear growth of b. Moreover, we also prove the Markov property of the solution and the existence of invariant measures for the corresponding transition semigroup.     

On the existence of coproducts in the category of noncommutative algebras

The weakly multiplicative bilinear maps among R-algebras are introduced and the corresponding to them category of pointed algebras is defined. By the resolution of the respective universal problem, a new tensor product of two R-algebras is realized and its connection with the usual one is pointed out. Furthermore, after establishing the existence of an infinite (new) tensor product algebra, as a special colimit, it is shown that coproducts there always exist in the category Al of noncommutative (associative, unitary) R-algebras. Certain canonical decompositions of a given algebra in some particular cases are also investigated.     

中立型脉冲发展方程解的存在性和唯一性

本文研究了一类非线性中立型脉冲发展方程解的存在性和唯一性的问题.利用迭代分析方法结合半群理论的知识,得到了其解的表达式,并构造解的迭代序列,同时证明了其解的存在性和唯一性.通过研究发现其解的存在性和唯一性与脉冲时滞条件密不可分,利用迭代分析法求解此类问题具有一定的优越性.     

A theory of tensor products for module categories for a vertex operator algebra, III

This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a “vertex tensor category” structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a “complex analogue” of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. In this paper, we focus on a particular element P(z) of a certain moduli space of three-punctured Riemann spheres; in general, every element of this moduli space will give rise to a notion of tensor product, and one must consider all these notions in order to construct a vertex tensor category. Here we present the fundamental properties of the P(z)-tensor product of two modules for a vertex operator algebra. We give two constructions of a P(z)-tensor product, using the results, established in Parts I and II of this series, for a certain other element of the moduli space. The definitions and results in Parts I and II are recalled.     

一类非线性色散型发展方程反问题的整体解

将一类非线性色散型发展方程反问题转化为抽象空间非线性发展方程Cauchy问题。利用半群方法和赋等价范数技巧,建立了该类抽象发展方程整体解的存在唯一性定理,并应用于所论反问题,得到了该类非线性色散型发展方程反问题整体解的存在唯一性定理,本质地改进了袁忠信得出的解的局部存在唯一性结果。