随机Solow经济增长模型及其解的性质

１９８７年诺贝尔（Ｎｏｂｅｌ）经济学奖获得者Ｓｏｌｏｗ教授，建立了确定性的经济增长模型（１９５６年）．它比较真实地描述了现实世界申的确定性的经济增长状况，然而对不确定性的现象，往往误差较大，甚至失效．本文把Ｓｏｌｏｗ模型扩展到随机情形，扩展了Ｂａｎａｃｈ压缩映像原理和不动点定理，获得了随机Ｓｏｌｏｗ模型主要方程和随机解的一些性质．     

巴氏空间中随机元的极限理论及其应用

本文综述了巴拿赫空间中随机元的极限理论及其应用的一些结果，主要内容为：极限理论的某些新结果；等周方法的优化技巧；巴氏空间几何的概率方法；在经验过程研究中的应用。重点是近十年来有关问题研究的一些进展。     

关于增正全连续凹算子不动点指数

In this paper, we have proved that fixed point index of completely continuous positively concave increasing operator on bounded domain Ω which contains zero point is only O or 1.     

An iterative method for solving nonlinear functional equations

An iterative method for solving nonlinear functional equations, viz. nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equation, nonlinear algebraic equations and fractional differential equations has been discussed.     

Extensions and isomorphisms for the generalized Fourier algebras of a locally compact group

It is shown that for amenable groups, all finite-dimensional extensions of A_p(G) algebras split strongly. Furthermore, each extension of A_p(G) which splits algebraically also splits strongly. We also show that if G is an almost connected locally compact group, or a subgroup of GL_n(V) (V being a finite-dimensional vector space), and if for a fixed p∈(1,∞), all finite-dimensional singular extensions of A_p(G) split strongly, then G is amenable. Continuous order isomorphisms for the pointwise order of A_p(G) algebras, are characterized as weighted composition maps. Similarly, order isomorphisms for the pointwise order of B_p(G) algebras, are characterized as ∗-algebra isomorphisms followed by multiplication by an invertible positive multiplier. In addition, it is shown that for amenable groups, an order isomorphism for the pointwise order between A_p(G) algebras that preserve cozero sets is necessarily continuous, and hence induces an algebra isomorphism.     

Convergence of weighted sums of tight random elements

Convergence of weighted sums of tight random elements {V_n} (in a separable Banach space) which have zero expected values and uniformly bounded rth moments (r > 1) is obtained. In particular, if {a_nk} is a Toeplitz sequence of real numbers, then | Σ_k=1^∞a_nkf(V_k)| → 0 in probability for each continuous linear functional f if and only if 6Σ_k=1^∞a_nkV_k 6→ 0 in probability. When the random elements are independent and max_{1≤k≤n | ank | = $\text{O}$(n^?8)} for some $\text{0 <}\text{1}\text{s}\text{< r ? 1}$, then |Σ_k=1^∞a_nkV_k 6→ 0 with probability 1. These results yield laws of large numbers without assuming geometric conditions on the Banach space. Finally, these results can be extended to random elements in certain Fréchet spaces.     

Jensen's inequality for a convex vector-valued function on an infinite-dimensional space

Jensen's inequality f(EX) ≤ Ef(X) for the expectation of a convex function of a random variable is extended to a generalized class of convex functions f whose domain and range are subsets of (possibly) infinite-dimensional linear topological spaces. Convexity of f is defined with respect to closed cone partial orderings, or more general binary relations, on the range of f. Two different methods of proof are given, one based on geometric properties of convex sets and the other based on the Strong Law of Large Numbers. Various conditions under which Jensen's inequality becomes strict are studied. The relation between Jensen's inequality and Fatou's Lemma is examined.     

关于Lipschitz映射空间的可余子空间

该文研究Lipschitz映射空间作为一个Banach空间的结构性质，主要研究了它的闭子空间有界线性算子空间（赋予算子范数）在其中的可余性．     

On the Solvability of x∈Ax＋λBx in a General Cone with A and B Multivalued k－set－contractive

ＯｎｔｈｅＳｏｌｖａｂｉｌｉｔｙｏｆｘ∈Ａｘ＋λＢｘｉｎａＧｅｎｅｒａｌＣｏｎｅ　ｗｉｔｈＡａｎｄＢＭｕｌｔｉｖａｌｕｅｄ　ｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｉｖｅＺｈａｎｇＱｉｎｇｙｏｎｇ（张庆雍）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｉｃ...