正则解析半群与正则Cosine函数

在本文中,我们的主要结果是：若Ａ是一个正则解析半群的生成元,则Ａ也一定是某正则Ｃｏｓｉｎｅ函数的生成元．     

Continuous extension of a densely parameterized semigroup

Let be a dense sub-semigroup of ℝ₊, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over can be extended to a weakly continuous semigroup over ℝ₊. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over ℝ₊. O.M. Shalit was partially supported by the Gutwirth Fellowship.     

非线性Lipschitz算子的Lipschitz对偶算子及其应用

在文山中我们对非线性Ｌｉｐｓｃｈｉｔｚ算子定义了其Ｌｉｐｓｃｈｉｔｚ对偶算子,并证明了任意非线性Ｌｉｐｓｃｈｉｔｚ算子的Ｌｉｐｓｃｈｉｔｚ对偶算子是一个定义在Ｌｉｐｓｃｈｉｔｚ对偶空间上的有界线性算子．本文还进一步证明：设Ｃ为 Ｂａｎａｃｈ空间 Ｘ的闭子集,Ｃ＊Ｌ为Ｃ的 Ｌｉｐｓｃｈｉｔｚ对偶空间,Ｕ为 Ｃ＊Ｌ上的有界线性算子,则当且仅当 Ｕ为 ｗ＊－ｗ＊连续的同态变换时,存在Ｌｉｐｓｃｈｉｔｚ连续算子Ｔ,使Ｕ为Ｔ的Ｌｉｐｓｃｈｉｔｚ对偶算子．这一结论的理论意义在于：它表明一个非线性Ｌｉｐｓｃｈｉｔｚ算子的可逆性问题可转化为有界线性算子的可逆性问题．作为应用,通过引入一个新概念──ＰＸ－对偶算子,在一般框架下给出了非线性算子半群的生成定理．     

非Lipschitz仿射映射的半拓扑半群的强遍历定理(英)

本文在Banach空间中给出了非Lipschitzian仿信射拓扑半群的强遍历定理。     

非线性Lipschitz算子半群的表示

本文通过引入若干Lipschitz对偶概念,将非线性Lipschitz算子半群对偶映射到Lipschitz对偶空间中,使其转化为线性算子半群。该线性算子半群被证明是一个C_0~*-半群,因而是某个C_0-半群的对偶半群。从而证明了,在等距意义下,一个非线性Lipschitz算子半群可以延拓为一个C_0-半群。基于这些结论,本文给出了一系列全新的非线性Lipschitz算子半群的表示公式。     

Semilinear evolution equations with nonlinear constraints and applications

This paper deals with a general class of evolution problems for semilinear equations coupled with nonlinear constraints. Those constraints may contain compositions of nonlinear operators and unbounded linear operators, and hence the associated operators are not necessarily formulated in the form of continuous perturbations of linear operators. Accordingly, a family of equivalent norms is introduced to discuss 'quasidissipativity' in a local sense of the operators and a generation theory for nonlinear semigroups is employed to construct solution operators on bounded sets. It is a feature of our treatment that the resultant solution operators are obtained as nonlinear semigroups on the whole space which are not 'quasicontractive' but locally equi-Lipschitz continuous.     

AN EXPONENTIAL STABILITY PROBLEM ON THE SMALL DELAY LINEAR SYSTEM

1IntroductionLetXbea'Banachspace,andB(X)betheBanachspaceofcontinuouslinearoperatorsfromXintoX.LetT(t)bea(CO)selltigroup,andletAbeitsinfinitesilllalgenerator.WedenotethedomainandtherangeofAbyD(A)andR(A).LetBbelongtoB(X).FOrthelinearsystem:andthedelaylinearsystem:wherer>0,((.)EC([--.,o],x)={fif:[--r,oj~X,fiscontinuous},r(t)EC[o,.)'05r(t)5r.Weconsidertileexponentialstabilityequivalencebetweellthesolutionof(1)and(2),whichllleans:ifthereexistM,a>0,sllththatIIS(f)II5Me--\"'(f20),whereS(…     

Continuity and generators of dynamical semigroups for infinite Bose systems

For a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations (CCR) we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von Neumann algebra associated with a representation of the CCR. Then the explicit form of the generators of the extended semigroups is calculated.     

Some polynomials associated with up-down permutations

Up-down permutations, introduced many years ago by André under the name alternating permutations, were studied by Carlitz and coauthors in a series of papers in the 1970s. We return to this class of permutations and discuss several sets of polynomials associated with them. These polynomials allow us to divide up-down permutations into various subclasses, with the aid of the exponential formula. We find explicit, albeit complicated, expressions for the coefficients, and we explain how one set of polynomials counts up-down permutations of even length when evaluated at x=1, and of odd length when evaluated at x=2. We also introduce a new kind of sequence that is equinumerous with the up-down permutations, and we give a bijection.     

An Application of Exponential Sum Estimates

Let p be an odd prime and let δ be a fixed real number with 0<δ<2. For an integer a with 0<a<p, denote by ā the unique integer between 0 and p satisfying a ā≡1 (mod p). Further, let {x} denote the fractional part of x. We derive an asymptotic formula for the number of pairs of integers (a, b with . This work is supported by N. S. F. of P. R. China (10271093)     

Algebraic aspects of an ordered band arising in nonlinear signal processing

For any positive integers M and N we define a selfdually ordered band ℬ(M,N) of cardinality and ask whether or not it is lattice-ordered. The origin of ℬ(M,N) in nonlinear signal processing is outlined.     

Formal adjoint operators and asymptotic formula for solutions of autonomous linear integral equations

For autonomous linear integral equations, we establish an explicit asymptotic representation formula of solutions, developing the spectral analysis for the generator of the solution semigroup as well as the one for the formal adjoint operator associated with the generator.     

关于余弦算子函数的一个结果

设Ａ是Ｂａｎａｃｈ空间Ｘ中的闭线性算子,对凡　是单射。文中定义了Ｂａｎａｃｈ空间　范数　强于Ｘ的范数。我们证明了算子Ａ在空间Ｚ中的部分ＡＺ生成Ｚ中的一个余弦算子函数,空间Ｚ具有某种意义上的极大性。     

Banach空间中非Lipschitzian交换非线性拓扑半群的遍历理论

本文在满足opial条件或存在Frechet可微范数的一致凸Banach空间中,给出了非Lipschitzian交换拓扑半群的遍历收敛定理及弱收敛定理.     

Well-posedness for a variable-coefficient wave equation with nonlinear damped acoustic boundary conditions

We consider a variable-coefficient wave equation with nonlinear damped acoustic boundary conditions. Well-posedness in the Hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups.     

Semilinear equations with exponential nonlinearity and measure data

We study the existence and non-existence of solutions of the problem

(0.1)

where Ω is a bounded domain in , N3, and μ is a Radon measure. We prove that if , then (0.1) has a unique solution. We also show that the constant 4π in this condition cannot be improved.     

Accurate dense output formula for exponential integrators using the scaling and squaring method

This paper proposes an accurate dense output formula for exponential integrators. The computation of matrix exponential function is a vital step in implementing exponential integrators. By scrutinizing the computational process of matrix exponentials using the scaling and squaring method, valuable intermediate results in this process are identified and then used to establish a dense output formula. Efficient computation of dense outputs by the proposed formula enables time integration methods to set their simulation step sizes more flexibly. The efficacy of the proposed formula is verified through numerical examples from the power engineering field.     

Weak and strong solutions of a nonlinear subsonic flow-structure interaction: Semigroup approach

We consider a non-rotational, subsonic flow-structure interaction describing the flow of gas above a flexible plate. A perturbed wave equation describes the flow, and a second-order nonlinear plate equation describes the plate’s displacement. It is shown that the linearization of the model generates a strongly continuous semigroup with respect to the topology generated by “finite energy” considerations. An interesting feature of the problem is that linear perturbed flow-structure interaction is not monotone with respect to the standard norm describing the finite energy space. The main tool used in overcoming this difficulty is the construction of a suitable inner product on the finite energy space which allows the application of ω-maximal monotone operator theory. The obtained result allows us to employ suitable perturbation theory in order to discuss well-posedness of weak and strong solutions corresponding to several classes of nonlinear dynamics including the full flow-structure interaction with von Karman, Berger’s and other semilinear plate equations.     

GEOMETRY OF EXPONENTIAL TYPE REGRESSION MODELS AND ITS ASYMPTOTIC INFERENCE

In this paper,exponential type regression modeis are considered from geometric point of view.The stochastic expansions relsting to the estimate are derived and are used to study several asymptotic inference problems.The biases and the covariances relating to the estimate may be calculated based on the expansions.The information loss of the estimate and a limit theorem connected with the observed and expected Fisher informations are obtained in terms of the curvatures.