A GENERALIZED MODELING FOR CEMENT-BASED MATERIALS UNDER LARGE RANGE OF COMPRESSION STATE

The aim of this study is to describe the main behavior of cement-based materials under large compression state based on the recent experimental research. In this paper, the strainstress relations are firstly analyzed and confining pressure state is regarded as low/medium/high state. A generalized cup modeling is introduced by a coupled deviatoric shearing, pore collapse and damage mechanism within thermodynamic framework. A series of numerical simulations are performed for the considered cement paste and concrete. Comparisons between numerical predictions and experimental results show that the proposed model is able to describe the main features of mechanical behavior under large range of compression state.     

An Inequality for Tail Probabilities of Martingales with Bounded Differences

Let M _n =X₁+...+X_n be a martingale with bounded differences X_m=M_m-M_m-1 such that large8473.gif" alt="Popf" align="BASELINE" BORDER="0">{|X_m|large8804.gif" alt="le" align="MIDDLE" BORDER="0"> large963.gif" alt="sgr" align="BASELINE" BORDER="0"> _m}=1 with some nonnegative large963.gif" alt="sgr" align="BASELINE" BORDER="0">_m. Write large963.gif" alt="sgr" align="BASELINE" BORDER="0">²= large963.gif" alt="sgr" align="BASELINE" BORDER="0"> ₁ ² + ... +large963.gif" alt="sgr" align="BASELINE" BORDER="0"> _n ² . We prove the inequalities large8473.gif" alt="Popf" align="BASELINE" BORDER="0">{M _nlarge8805.gif" alt="ge" align="MIDDLE" BORDER="0">x}large8804.gif" alt="le" align="MIDDLE" BORDER="0">c(1-large934.gif" alt="PHgr" align="BASELINE" BORDER="0">(x/large963.gif" alt="sgr" align="BASELINE" BORDER="0">)), large8473.gif" alt="Popf" align="BASELINE" BORDER="0">{M _n large10878.gif" alt="ges" align="MIDDLE" BORDER="0"> x}large10877.gif" alt="les" align="MIDDLE" BORDER="0"> 1- c(1-large934.gif" alt="PHgr" align="BASELINE" BORDER="0"> (-x/large963.gif" alt="sgr" align="BASELINE" BORDER="0">)) with a constant . The result yields sharp inequalities in some models related to the measure concentration phenomena.     

A Large Deviations Principle Related to the Strong Arc-Sine Law

We show a large deviations principle for the family of random variables when tlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">+large8734.gif" alt="infin" align="MIDDLE" BORDER="0">, where B=(B _u ,ularge8805.gif" alt="ge" align="MIDDLE" BORDER="0">0) is a standard linear Brownian motion.     

Generalized One-Sided Laws for the Larger Observations of a Triangular Array

Consider independent and identically distributed random variables {X,X _nj , 1large8804.gif" alt="le" align="MIDDLE" BORDER="0">jlarge8804.gif" alt="le" align="MIDDLE" BORDER="0">n,nlarge8805.gif" alt="ge" align="MIDDLE" BORDER="0">1} with density f(x)=px ^–p–1 I(xlarge8805.gif" alt="ge" align="MIDDLE" BORDER="0">1), where p>0. We show that there exist unusual generalized Laws of the Iterated Logarithm involving the larger order statistics from our array.     

Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations

We consider the derivative nonlinear Schrödinger equations

where the coefficient satisfies the time growth condition

is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type

where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when

     

Very Large Cyclic Compounds

Very large ring systems, containing more than 50 ring members, are becoming increasingly important in different topics in natural sciences. These so-called large8216.gif" alt="lsquo" align="BASELINE" BORDER="0">gigantocycleslarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> differ from smaller macrocycles in physical properties, special structural features and chemical behaviour. This article is meant to be the first summary of such ring systems and a synopsis of the most remarkable examples with their fascinating nano-scaled structures and ingenious synthesis. To restrict the scope of the article, only isolated and completely characterized, monodisperse compounds are presented. Furthermore, attention is mainly directed at organic gigantocycles. Some large8216.gif" alt="lsquo" align="BASELINE" BORDER="0">ultracycleslarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> with more than 100 ring members, mainly occurring in polymer chemistry and nature, will also be described.     

广义KdV-Burgers方程长时间性态的谱方法

1．引言随着无限维动力系统研究的发展和深入,人们对非线性发展方程长时间性态的研究越来越重视[1－6］,而这种研究在很大程度上依赖于数值计算的结果,因此,计算结果是否可靠,计算格式先得是否合适都是值得探讨和深入研究的问题17－10．广义KdV－Burg6rs方程是一类重要的非线性发展方程,在实际问题中也有着广泛的应用,因此,对它的研究即有理论价值也有实际意义．本文讨论如下的广义KdV－Burgers方程的周期初值问题其中a,q是已知实常数,且a＞0八。）,g（。）,h00是已知实函数．文［10］对上述问题构造了半离散的Fourier谱逼近…     

关于多指标变量大数律尾概率级数的完全收敛性

本文对ｉｄ多指标随机变量序列｛Ｘｋ;ｋ∈Ｎｄ｝（ｄ≥２）的部分和Ｓｎ＝∑ｋ≤ｎＸｋ及Ｈ（ｔ）↑＋∞,（ｔ→＋∞）,提出并讨论了Порохоров的３个问题（ｄ≥２）,并讨论了多指标随机变量和的完全收敛性．     

A Strong Law for Mixing Random Variables

A sharp almost sure bound is derived for limit points of average sum of weakly dependent random variables, which ensures strong laws of large numbers for large981.gif" alt="phiv" align="MIDDLE" BORDER="0"> and large968.gif" alt="psgr" align="MIDDLE" BORDER="0">-mixing random variables, without assumptions on rate of tending to zero of large981.gif" alt="phiv" align="MIDDLE" BORDER="0"> and large968.gif" alt="psgr" align="MIDDLE" BORDER="0">-mixing parameters large981.gif" alt="phiv" align="MIDDLE" BORDER="0">_n and large968.gif" alt="psgr" align="MIDDLE" BORDER="0">_n.     

Two-dimensional asymptotic expansions for large deviations of spherically distributed random vectors if the dominating point degenerates asymptotically

A geometric approach to asymptotic expansions for large-deviation probabilities, developed for the Gaussian law by Breitung and Richter [J. Multivariate Anal.,58, 1–20 (1996)], will be extended in the present paper to the class of spherical measures by utilizing their common geometric properties. This approach consists of rewriting the probabilities under consideration as large parameter values of the Laplace transform of a suitably defined function, expanding this function in a power series, and then applying Watson’s lemma. A geometric representation of the Laplace transform allows one to combine the global and local properties of both the underlying measure and the large-deviation domain. A special new type of difficulty is to be dealt with because the so-called dominating points of the large-deviation domain degenerate asymptotically. As is shown in Richter and Schumacher (in print), the typical statistical applications of large-deviation theory lead to such situations. In the present paper, consideration is restricted to a certain two-dimensional domain of large-deviations having asymptotically degenerating dominating points. The key assumption is a parametrized expansion for the inverse $\bar g^{ - 1} $ of the negative logarithm of the density-generating function of the two-dimensional spherical law under consideration.