三维MANDELBROT渗流下临界形状

本文研究了三雏andelbrot渗流下临界形态，证明了渗流函数θ（p）在pc点是不连续的，同时得到当p＜pc时，三维Mandelbrot渗流A的最大连通分支是点，即A是“尘状”的．     

二维渗流最低水平开穿透的宽度

在二维渗流中,设rn是矩形[O,n]2的最低水平开穿透,令ξn=max｛y：（xy）∈rn｝．本文证明了在临界状态p＝pc时,存在常数0＜C1＜C2＜1,当n充分大时有存在,而在上临界状态p＞pc时,有存在］＝0.     

随机无穷点集上欧几里德最小扩张树的自包含性

本文证明好的欧氏空间无穷点集上最小扩张树的自包含性．应用上述性质,以及AlexanderK．S．[1]中有关二维Poisson连续渗流的结果,我们给出二维情形AldousD．和SteeleJ．M．[2]之猜想的一个新证明,区别于AlexanderK．S．[3]对上述猜想的排除法证明,我们直接证明它,显然,我们的证明更简单．对Poisson连续渗流,得到其二维临界值相对于Poisson最小扩张树的一个刻画;最后我们给出上述临界值相对于点渗流临界值的一个上下界估计。     

三维MANDELBROT渗流下临界形态

本文研究了三维andelbrot渗流下临界形态,证明了渗流函数θ(p)在pc点是不连续的,同时得到当p相似文献   

一类带有扩散和时滞的捕食与被捕食模型的渐近性质

本文中，我们考虑一类带有扩散和时滞的捕食与被捕食系统．我们分析了系统的非负不变性，边界平衡点性质，全局渐近稳定性及永久持续生存性．在这一系统中，当时滞由0变到ro时，系统在平衡点附近发生Hopf分支．即当r增加通过临界值ro时，从正平衡点分支出周期解．     

Sierpinski Gasket格点图上的渗流模型

本文研究了Ｓｉｅｒｐｉｎｓｋｉ ｇａｓｋｅｔ上的边渗流模型。首先证明了该模型没有临界现象,进一步给出了其一个指数衰减律,进而证明了临界值的唯一性。     

具有自由边界的二维渗流问题

渗流的自由边界问题是工程上很受关注的问题．现有的数值分析方法需事先估计边界形态，逐次逼近．本文采用“变分不等式”的模式，结合有限元方法研究有自由边界的渗流问题，在整个结构区域内作有限元剖分，避免了传统的有限元分析中估计自由边界、反复修正计算区域的迭代过程．本文方法为简单而快速地分析渗流自由边界问题提供了一条有效的途径．     

X~2分布中一些临界值的近似计算方法

数理统计中常常需要查Ｘ２分布表，以确定临界值ｘ２ａ。但由于分布表只可能就固定的自由度ｎ，关于一些特殊的置信度或显著性水平ａ而确定所对应的临界值，一般ａ所对应的临界值表中查不到并且计算比较困难．本文借助原有分布数表，通过代数方法给出关于一般ａ而确定Ｘ２分布临界值的几个近似分式及部分公式的误差估计式。     

应用积分经验过程检验多元分布函数的相等性

本文引进投影积分经验过程用于检验两个或K个多元分布函数的相等性，自助法用于确定临界值的逼近，数论方法有效地计算自动法确定的临界值，且进行了一些模拟试验．     

饱和粘土非线性渗流规律与径向固结

以多孔介质等效渗流概念得出粘土平均孔隙微尺度数量级范围在0.01 μm至0.1μm,与测试结果一致．实验结果表明饱和粘土微尺度孔隙渗流为非线性流．理论推导表明固液界面作用与渗透率平方根或孔隙半径成反比,固液界面相互作用是导致饱和粘土非线性渗流的重要原因．提出了精确描述饱和粘土微尺度孔隙非线性渗流基本规律的数学模型,其参数量纲明确,物理意义清楚．建立了饱和粘土非线性渗流新定律,统一描述了从较低到较高水力梯度全过程渗流曲线特征,达西定律是其特例．基于新定律,建立了饱和粘土非线性渗流定流量径向固结数学模型．以粘性边界层思想与稳态依序替换法及积分方程法,导出了粘土非线性渗流平均质量守恒方程及活动边界运动方程,给出了饱和粘土非线性渗流超孔隙水压力分布公式与平均固结度计算公式,获得了粘土层压力分布规律和平均固结度随时间变化规律．结果表明:饱和粘土非线性渗流使活动边界运动速度减小．研究结果为粘土地质工程与岩土工程应用提供了新的科学依据．达西渗流径向固结计算是新的非线性渗流固结计算的特例．     

一个素变数丢番图不等式

本文证明了如果１＜ｃ＜２３７／２１４，则对于充分大的Ｎ和ε≥Ｎ－１／５（２３７／２１４－ｃ）＋ｖ（ｖ＞０）表达式Ｄ（Ｎ）：＝Σ｜ｐｃ１＋ｐｃ２＋ｐｃ３－Ｎ｜＜－εｌｏｇｐ１ｌｏｇｐ２ｌｏｇｐ３ 关于素变数ｐ１，ｐ２，ｐ３有渐近公式，改进了文献［１］的结果１＜Ｃ＜１．１．     

Linear Discrepancy of Totally Unimodular Matrices*†

  We show that the linear discrepancy of a totally unimodular m×n matrix A is at most

An extension of Willard’s Finite Basis Theorem: Congruence meet-semidistributive varieties of finite critical depth

Ross Willard proved that every congruence meet-semidistributive variety of algebras that has a finite residual bound and a finite signature can be axiomatized by some finite set of equations. We offer here a simplification of Willards proof, avoiding its use of Ramseys Theorem. This simplification also extends Willards theorem by replacing the finite residual bound with a weaker condition.In Celebration of the Sixtieth Birthday of Ralph N. McKenzieReceived February 26, 2004; accepted in final form August 2, 2004.     

平移不变的随机串测度

利用围道估计的方法，刻划在相变点处的平移不变随机串测度，证明了：对二维以上情况，当口充分大时，在临界点处，平移不变随机串测度有且只有两个极点，也即任一平移不变随机串测度都是这两个极点的凸组合．     

一个二元丢番图不等式

本文证明了如果1相似文献   

A plethora of three-dimensional periodic travelling gravity-capillary water waves with multipulse transverse profiles

This article presents a rigorous existence theory for three-dimensional gravity-capillary water waves which are uniformly translating and periodic in one spatial direction x and have the profile of a uni- or multipulse solitary wave in the other z. The waves are detected using a combination of Hamiltonian spatial dynamics and homoclinic Lyapunov-Schmidt theory. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which z is the timelike variable, and a family of points P_k,k+1, k = 1,2,... in its two-dimensional parameter space is identified at which a Hamiltonian 0²0² resonance takes place (the zero eigenspace and generalised eigenspace are respectively two and four dimensional). The point P_k,k+1 is precisely that at which a pair of two-dimensional periodic linear travelling waves with frequency ratio k:k+1 simultaneously exist (Wilton ripples). A reduction principle is applied to demonstrate that the problem is locally equivalent to a four-dimensional Hamiltonian system near P_k,k+1. It is shown that a Hamiltonian real semisimple 1:1 resonance, where two geometrically double real eigenvalues exist, arises along a critical curve R_k,k+1 emanating from P_k,k+1. Unipulse transverse homoclinic solutions to the reduced Hamiltonian system at points of R_k,k+1 near P_k,k+1 are found by a scaling and perturbation argument, and the homoclinic Lyapunov-Schmidt method is applied to construct an infinite family of multipulse homoclinic solutions which resemble multiple copies of the unipulse solutions.     

有关殆素数的二元丢番图不等式

Pr表示最多r个素因子的正整数.作者证明了,对于任一足够大的实数N和1＜c＜c0,不等式|pc+Pcr-N|＜N9/10(1-c0/c)对素数p和Pr是可解的.特别地,当1＜c＜c0=1.03074432…,有r=6.这个结果改进了翟文广和曹晓东的结果.     

On the continuity points of left-continuous t-norms

Left-continuous t-norms are much more complicated than the continuous ones, and obtaining a complete classification of them seems to be a very hard task. In this paper we investigate some aspects of left-continuous t-norms, with emphasis on their continuity points. In particular, we are interested in left-continuous t-norms which are isomorphic to t-norms which are continuous in the rationals. We characterize such a class, and we prove that it contains the class of all weakly cancellative left-continuous t-norms. S. Jenei was supported by the National Scientific Research Fund Hungary (OTKA F/032782) Mathematics Subject Classification (2000):20M14, 06F05