拟线性双曲组的经典解的奇性形成

This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C1 solution to Cauchy problem.     

ON THE RELIABILITY OF MEDIUM LOGIC(ML)

Medium logic (ML) is set up for the common theoritical foundation of the classical mathematics and fuzzy mathematics. It has been formalized as a new theory of logic. See note (1) and note (2). As mathematical logic the ML's construct reches the study of the informal deductive inference by means of studying the formal inference in it, and it demands the formal inference of ML reliable reflected the deductive inference. For this reason, this paper deals with its reliability. The result shows that the formal inference of M L consists with deductive inference, and that ML reliably reflects the deductive inference.     

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.     

THE FUNDAMENTAL THEOREM OF ULTRAPRODUCT IN PAVELKA'S LOGIC

In [This Zeitschrift 25 (1979), 45-52, 119-134, 447-464], Pavelka systematically discussed propositional calculi with values in enriched residuated lattices and developed a general framework for approximate reasoning. In the first part of this paper we introduce the concept of generalized quantifiers into Pavelka's logic and establish the fundamental theorem of ultraproduct in first order Pavelka's logic with generalized quantifiers. In the second part of this paper we show that the fundamental theorem of ultraproduct in first order Pavelka's logic is preserved under some direct product of lattices of truth values.     

GLOBAL CLASSICAL SOLUTIONS OF THE BOLTZMANN EQUATION NEAR MAXWELLIANS

Global classical solutions near Maxwellians are constructed for the Bolt.zma.nn equation in a periodic box with angular soft cutoff, that is, -3<γ< 0. The construction of global solution is based on an energy method used in [9].     

环上的典型的线性李代数的理想

设Ｒ是有１的交换环，本文证明了：当ｎ〉２时，ｓｌｎ（Ｒ）的理想都是标准的。当２∈Ｒ＾＊，ｎ〉３时，ｓｐｎ（Ｒ）与ｓｏｎ（Ｒ）的理想也都是标准的。     

基于巴斯卡数据成败型元件串联系统可靠性经典精确置信限

设Ａ为由Ｋ个相互独立的成败型元件组成的串联系统，第ｉ个元件的可靠性ｐｉ，ｐｉ未知，ｉ＝１，２，…，Ｋ．设对第ｉ个元件，对于给定的ｍｉ，有ｎｉ个巴斯卡试验数据：Ｘｉ１，Ｘｉ２，…，Ｘｉｎｉ，其中Ｘｉｊ表示对第ｉ个元件进行试验，试验进行到ｍｉ次成功时所需要的试验次数ｊ＝１，２，…，ｎｉ，ｉ＝１，２，…，Ｋ．记Ｔｉ＝Ｘｉ１＋Ｘｉ２＋…＋Ｘｉｎｉ，ｉ＝１，２，…，ｋ．本文研究基于统计量（Ｔ１，Ｔ２，…，Ｔｋ）求串联系统Ａ的可靠性经典精确最优置信下限．     

G(o)del逻辑和L*逻辑中公式的真度分布

研究了G\"{o}del逻辑系统和$L^\ast$逻辑系统中公式的真度的分布情况. 结果表明在G\"{o}del逻辑系统和$L^\ast$逻辑系统中含有$n$个原子命题的公式($n$元公式)的真度集分别为$\{\frac{i}{(n+ 1)!}\vert 0 \le i \le (n + 1)! ,i \in N\}$和$\{\frac{i}{(n + 1)!}\vert 0\le i \le 2^n(n + 1)!,i \in N\}.$ 进而得到了G\"{o}del逻辑系统和$L^\ast$逻辑系统中公式的真度集均为[0,1]上的有理数集. 最后,还给出了两系统中公式的相似度,伪距离的分布情况.     

MAXIMAL ATTRACTORS OF CLASSICAL SOLUTIONS FOR REACTION DIFFUSION EQUATIONS WITH DISPERSION

The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region.Finally, a few examples of application are given.     

LOCAL CHARACTERISTIC OF HOLOMORPHIC AUTOMORPHISM ON CLASSICAL DOMAIMS

§1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　　ＬｅｔＭｂｅａｃｏｍｐｌｅｘｍａｎｉｆｏｌｄ.Ｆｏｒａｎｙｐ∈ＭａｎｄａｎｙＸ∈Ｔ1,0ｐ(Ｍ),ｔｈｅＫｏｂａｙａｓｈｉｉｎｆｉｎｉｔｅｓｉｍａｌｐｓｅｕｄｏｍｅｔｒｉｃ[1]ｏｆＸｉｓＦ(Ｘ):=ｉｎｆ｜ａ｜∈Ｃ,ｆ:ＤＭｓ.ｔ.ｆ(0)=ｐａｎｄｆ(ａｚ)=Ｘ,ｗｈｅｒｅＤｉｓｔｈｅｕｎｉｔｄｉｓｋａｎｄｆ∈Ｈｏｌ(Ｄ,Ｍ)ｉｓｔｈｅｈｏｌｏｍｏｒｐｈｉｃｍａｐｆｒｏｍＤｔｏＭ,ａｎｄｔｈｅＣａｒａｔｈｅｏｄｏｒｙｉｎｆｉｎｉｔｅｓｉｍａｌｐｅｕｓｄｏｍｅｔｒｉｃｏｆＸｉｓＥ(Ｘ):=ｓｕｐ…     

UNIFORM CONVERGENCE AND SEQUENCE OF MAPS ON A COMPACT METRIC SPACE WITH SOME CHAOTIC PROPERTIES

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.     

有相依关系的成败型元件串联系统可靠性经典精确最优置信下限

设有由Ｋ个成败型元件Ａ１，Ａ２，…，ＡＫ组成的串联系统，设Ａ１，Ａ２，…，ＡＫ之间有相依关系，要Ａ１成功的条件下Ａ２才可以试验，在Ａ１，Ａ２，都成功的条件下Ａ３才可以试验，…在Ａ１，Ａ２，…ＡＫ－１都成功的条件下Ａｋ才可以试验，设条件概率Ｐ（Ａｉ│Ａ１Ａ２…Ａｉ－１）ｐｉ，ｐｉ未知，ｉ＝１，２，…，Ｋ。设有样本（Ｘ１，Ｘ２，…，ＸＫ）（Ｘ≥Ｘ２≥…≥ＸＫ），本文用样本点排序法求此串联系统可靠性之经     

关于代数体函数微分多项式的某些结果

本文应用代数体函数及其微分多项式的有关理论,将仪洪勋关于亚纯函数微分多项式的几个结果推广到代数体函数物微分多项式。     

齐型空间上的一类积分算子

在齐型空间上讨论由分数次积分算子、奇异积分算子及ＢＭＯ函数所构成的几类Ｔｏｅｐｌｉｔｚ型算子的有界性．     

SOME LIMINF RESULTS ON INCREMENTS OF THE PRIMITIVES OF BROWNIAN MOTION

§ 1　Introduction and ResultsLet{W(t) ;t≥ 0 }be a standard Brownian motion.For a positive integer m,define aGaussian processXm(t) =1m!∫t0 (t-s) md W(s) ,(1 .1 )which was firstmentioned by[1 ] .This class of processes arises in several domains of ap-plied mathematics.For instance,the process X1 (· ) ,which has been studied at length,isthe solution of the Langevin's equation under certain physical conditions.Wahba[2 ,3] usedXm(· ) to derive a correspondence between smoothing by splines …     

A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM

This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.     

球面上连续映射的一些新结果

本文研究了从球面到欧氏空间连续映射的性质.利用Brouwer映射度理论和微分拓扑的基本方法,获得了Borsuk-Ulam型定理,推广了Borsuk-Ulam定理.     

GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM

In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations.     

几类高阶微分方程解的复振荡

本文研究了几类高阶线性微分方程解的增长性,零点,以及构成基础解的一组线形无关解的乘积的增长性.得到了5个定理,推广了陈宗煊,S.Bank和J.Langley给出的结果.