2-CONNECTED k-REGULAR GRAPHS ON AT MOST 3k+3 VERTICES TO BE HAMILTONIAN (CONTINUED)

Let X~* and Y~* be generated by S(?){v_0},where G(S)is Hamiltonian connected and|X~*|=x~*,|Y~*|=Y~* and S_1~*,S_2~*,…,S_(x*)~* be the sets of vertices contained in the opensegments of C between vertices of X~*.Let S_1~*,x_1,S_2~*,x_2,…,S_(x*)~*,x_(?)~* be the segmentsand vertices of X~* in order around C.S_i~* is said to be an X~*(3)-interval if one ofx_(i-1)and x_i belongs to X_j~*—X_2~*.Let S=S_1~*,and S={a_1,c_1,c_2,…,c_1,b_1}.It is easy to see that the statement inLemma 2 can be modified as(?)({a_1,b_1},S_i~*)≤(?)     

考虑仓库容量扩张的多周期随机存贮模型——折扣准则

研究了仓库容量可以控制的、基于折扣准则的多周期随机存贮模型.利用马氏决策过程(MDP)的方法,建立了最小折现成本所满足的最优方程,在此基础上,得到了一个(Ut*,yt*(b))结构的最优策略:当仓库容量小于Ut*时将容量扩充到Ut*,并订货至Ut*;否则保持仓库容量不变,且当存贮量小于yt*(b)时订货到yt*(b),反之不订货.     

THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES

The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.     

C~*与L_p~*空间中的算子逼近

§1.引言 以2π为周期的连续函数类记作C~*,以2π为周期的p次幂可积的函数类记作L_p~*(1≤p<∞).我们统一用X~*表示C~*或L_p~*. 考虑算子     

Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.     

Nonlinear skew lie triple derivations between factors

Let A be a factor.For A,B∈A,define by [A,B]_*=AB-BA~* the skew Lie product of A and B.In this article,it is proved that a map Φ:A→A satisfies Φ([[A,B]_*,C]_*)=[[Φ(A),B]_*,C]_w+[[A,Φ(B)]_*,C]_*+[[A,B]_*,Φ(C)]_* for all A,B,C∈A if and only if Φ is an additive *-derivation.     

IDEAL STRUCTURE OF UNIFORM ROE ALGEBRAS OVER SIMPLE CORES

This paper characterizes ideal structure of the uniform Roe algebra B*(X) over simple cores X. A necessary and sufficient condition for a principal ideal of B*(X) to be spatial is given and an example of non-spatial ideal of B*(X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B*(X) are completely described by the corona of the Stone-Cech compactification of X.     

SP权对的分解

如权对(u,v)∈S_p(10,f~*(x)是 f 的 Hardy-Littlewood 极大函数。     

Homological Epimorphisms,Compactly Generated t-Structures and Gorenstein-Projective Modules

The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D~b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.     

RETRACTED ARTICLE: Some applications of BP-theorem in approximation theory

In this paper we apply Bishop-Phelps property to show that if X is a Banach space and G X is the maximal subspace so that G⊥ = {x* ∈ X*|x*(y) = 0; y∈ G} is an L-summand in X*, then L1(Ω,G) is contained in a maximal proximinal subspace of L1(Ω,X).     

CLIFFORD MARTINGALES Φ-EQUIVALENCE BETWEEN S（f） AND f^＊

ＣＬＩＦＦＯＲＤＭＡＲＴＩＮＧＡＬＥＳΦ－ＥＱＵＩＶＡＬＥＮＣＥＢＥＴＷＥＥＮＳ（ｆ）ＡＮＤｆ￥ＬＯＮＧＲＵＬＩＮ；ＱＩＡＮＴＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ．）...     

Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces

In this paper, we will obtain the weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{1,\kappa}(w)$ for $0<\kappa<1$ and $w\in A_1$.     

$C^*$-代数上可加Jordan左$*$-导子的刻画

设$\delta$是一个$*$-代数$\mathcal A$到其左$\mathcal A$-模$\mathcal M$的可加映射, 如果对任意$A\in\mathcal A$, 有$\delta(A^2)=A\delta(A)+A^*\delta(A)$, 则称$\delta$~是一个可加Jordan左$*$-导子. 在本文中, 我们证明了复的单位$C^*$- 代数到其Banach左模的每个可加Jordan左$*$-导子都恒等于零. 设$G\in\mathcal A$, 如果对任意$A,B\in \mathcal A$, 当$AB=G$时, 有$\delta(AB)=A\delta(B)+B^*\delta(A)$, 则称$\delta$在$G$处左$*$-可导. 我们证明了复的单位$C^*$-代数到其Banach左模的在单位点处左$*$-可导的连续可加映射恒等于零.     

A General Stochastic Calculus Approach to Insider Trading

The purpose of this paper is to present a general stochastic calculus approach to insider trading. We consider a market driven by a standard Brownian motion $B(t)$ on a filtered probability space $\displaystyle (\Omega,\F,\left\{\F\right\}_{t\geq 0},P)$ where the coefficients are adapted to a filtration ${\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$, with $\F_t\subset\G_t$ for all $t\in [0,T]$, $T>0$ being a fixed terminal time. By an {\it insider} in this market we mean a person who has access to a filtration (information) $\displaystyle{\Bbb H}=\left\{\H_t\right\}_{0\leq t\leq T}$ which is strictly bigger than the filtration $\displaystyle{\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$. In this context an insider strategy is represented by an $\H_t$-adapted process $\phi(t)$ and we interpret all anticipating integrals as the forward integral defined in [23] and [25]. We consider an optimal portfolio problem with general utility for an insider with access to a general information $\H_t \supset\G_t$ and show that if an optimal insider portfolio $\pi^*(t)$ of this problem exists, then $B(t)$ is an $\H_t$-semimartingale, i.e. the enlargement of filtration property holds. This is a converse of previously known results in this field. Moreover, if $\pi^*$ exists we obtain an explicit expression in terms of $\pi^*$ for the semimartingale decomposition of $B(t)$ with respect to $\H_t$. This is a generalization of results in [16], [20] and [2].     

On differentiability properties of typical continuous functions and Haar null sets

Let () be the set of all continuous functions on which have a derivative ( , respectively) at least at one point . B. R. Hunt (1994) proved that is Haar null (in Christensen's sense) in .

In the present article it is proved that neither nor its complement is Haar null in . Moreover, the same assertion holds if we consider the approximate derivative (or the ``strong' preponderant derivative) instead of the ordinary derivative; these results are proved using a new result on typical (in the sense of category) continuous functions, which is of interest in its own right.

     

Cesăro summability of the character system of the p-series field in the Kaczmarz rearrangement

Let $G_p$ be the $p$-series field. In this paper we prove the a.e. convergence $\sigma_n f\to f$ $(n\to \infty)$ for an integrable function $f\in L^1(G_p)$, where $\sigma_nf$ is the $n$th $(C,1)$ mean of $f$ with respect to the character system in the Kaczmarz rearrangement. We define the maximal operator $\sigma^* $ by $\sigma^*f := \sup_n|\sigma_nf|$. We prove that $\sigma^*$ is of type $(q,q)$ for all $1相似文献   

因子上非线性混合三重积保持映射

设$\mathcal{A}$, $\mathcal{B}$是两个因子且$\dim\mathcal{A}>4$.本文证明了双射$\phi:\mathcal{A}\rightarrow\mathcal{B}$ 满足对所有的$A,B,C\in\mathcal A$有$\phi([A,B]\bullet C)=[\phi(A),\phi(B)]\bullet\phi(C)$当且仅当$\phi$是线性*-同构, 共轭线性*- 同构,负的线性*-同构, 负的共轭线性*-同构.     

关于正态分布的次序统计量的随机序

设$X_1,X_2,\cdots,X_n$和$X^*_1,X^*_2,\cdots,X^*_n$分别服从正态分布$N(\mu_i,\sigma^2)$和$N(\mu^*_i,\sigma^2)$,以$X_{(1)}$,$X^*_{(1)}$分别表示$X_1,\cdots,X_n$和$X^*_1,\cdots,X^*_n$的极小次序统计量,以$X_{(n)}$, $X^*_{(n)}$分别表示$X_1,\cdots,X_n$和$X^*_1,\cdots$,$X^*_n$的极大次序统计量. 我们得到了如下结果:(i)\,如果存在严格单调函数$f$使得$(f(\mu_{1}),\cdots,f(\mu_{n}))\succeq_{\text{m}}$ $(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,且$f'(x)f'(x)\!\geq\!0$, 则$X_{(1)}\!\leq_{\text{st}}\!X^*_{(1)}$;(ii)\,如果存在严格单调函数$f$使得$(f(\mu_{1})$,$\cdots,f(\mu_{n}))\succeq_{\text{m}}(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,且$f'(x)f'(x)\leq 0$, 则$X_{(n)}\geq_{\text{st}}X^*_{(n)}$.(iii)\,设$X_{1},X_{2},\cdots,X_{n}$和\, $X^*_{1},X^*_{2},\cdots,X^*_{n}$分别服从正态分布$N(\mu,\sigma_i^2)$和$N(\mu,\sigma_i^{*2})$,若$({1}/{\sigma_{1}},\cdots,{1}/{\sigma_{n}})\succeq_{\text{m}}({1}/{\sigma^{*}_{1}},\cdots,{1}/{\sigma^{*}_{n}})$,则有$X_{(1)}\leq_{\text{st}}X^*_{(1)}$和$X_{(n)}\geq_{\text{st}}X^*_{(n)}$同时成立.     

具有对合运算的$n$-clean环

A *-ring is called *-clean if every element of the ring can be written as the sum of a projection and a unit. For an integer n ≥ 1, we call a *-ring R n-*-clean if for any a ∈ R,a = p + u1 + ··· + unwhere p is a projection and ui are units for all i. Basic properties of n-*-clean rings are considered, and a number of illustrative examples of 2-*-clean rings which are not *-clean are provided. In addition, extension properties of n-*-clean rings are discussed.     

Approximate Lie $\ast$-Derivations on $\rho$-complete Convex Modular algebras

In this paper, we obtain generalized Hyers--Ulam stability results of a $(m,n)$-Cauchy-Jensen functional equation associated with approximate Lie $*$-derivations on $\rho$-complete convex modular $*$-algebras $\chi_\rho$ with $\Delta_\mu$-condition on the convex modular $\rho$.