关于逐步回归分析的一个注记

逐步回归是多元回归分析筛选自变量的一种重要思想方法。利用矩阵消去变换的知识,证明了逐步回归第一步引入变量,第二步引入变量,第三步不可能剔除变量。最后对经典Hald数据利用SAS统计软件,编程实现逐步回归分析.     

幂理想消去的置换环

引进了一类新的部分幂消去的置换环, 得到了置换环幂理想消去的等价刻画, 推广了幂消去的相关结果.     

正则环上的幂问题

本文研究了正则环上模的幂消去，得到了幂消去的内直和刻划．建立了正则环上的幂比较结构，从而给出了正则环上幂消去、幂的弱消去以及ｕ－正则性之间的关系     

关于(g,f)-2-消去图

一个图G称为一个(g,f)-2-消去图,如果G的任何两条边不属于它的一个(g,f)-因子.本文给出了当g＜f时一个图是(g,f)-2-消去图的一个充要条件.     

可量词消去的带根节点的树理论

讨论了带根节点r的有向树、无向树理论的量词消去性质,找到决定理论量词消去的三类特殊公式,并给出了在语言■_0={E,r}(E为有向边或无向边)及添加二元距离关系D_(n,n)w所得膨胀语言下,可量词消去的这两类理论的完全分类.     

素数阶群理论的量词消去算法及其上界

在以前的一些工作中,作者已经证明语言(?)={+,0,e)上素数阶群的理论T有量词消去性质并研究了它的判定问题的复杂性.本文在此基础上将利用T的判定问题的复杂性结果给出理论T的量词消去的一个算法,同时给出该算法的复杂性上界.     

模的弱消去问题和Exchange环的弱稳定条件

本文研究模的弱消去问题和exchange环的弱稳定条件,给出了wsrl条件的新刻划,证明了对具有有限exchange性质的模,外弱消去等价于内弱消去并等价于自同态环满足wsrl条件.     

推广的韩-刘-张反常消去公式

在[Anomaly cancellation and modularity, Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics,2014:87-104,World Sci.Publ.,Hackensack,NJ]中,韩-刘-张给出了一个反常消去公式,推广了GreenSchwarz公式和Schwartz-Witten公式.本文研究了两个推广的韩-刘-张公式和一个奇数维的韩-刘-张公式.通过研究一些示性式的模性质,给出了奇数维新的反常消去公式.     

可量词消去的树形偏序理论的分类

提出了偏序的全序片段、序模式的概念以刻画树形偏序的结构特征,以此为基础,讨论了有最小元0的树形偏序理论的量词消去性质,给出了在语言(?)_0={,0}及其膨胀语言下可以量词消去的这类理论的完全分类。     

关于分数可消去图的若干结果

令G=(V(G),E(G))是一个图,并令9和f是两个定义在V(G)上的整数值函数且对所有的x∈V(G)有g(x)≤f(z)成立．若对G的每一条边e都存在G的一个分数(g,f)-因子G_h使得h(e)=0,其中h是G_h的示性函数,则称G是一个分数(g,f)-消去图,若在G中删去E′■E(G),|E′|=k后,所得图有分数完美匹配,则称G是分数k-边-可消去的。本文给出了图是1-可消去,2-可消去和k-边-可消去的与韧度和孤立韧度相关的充分条件。证明了这些结果在一定意义上是最好可能的．     

Certain Characterizations of Normal Distribution via Transformations

It is well known that i.i.d. (independent and identically distributed) normal random variables are transformed into i.i.d. normal random variables by any orthogonal transformation. Less well known are nonlinear transformations with the above-mentioned property. In this work we present nonlinear transformations preserving normality, which are more general than the existing ones in the literature.     

A Hodograph Transformation Applicable to a Large Class of PDEs

We present a hodograph transformation providing solutions for a wide family of multidimensional nonlinear partial differential equations and discuss several applications to concrete examples.     

正交变换在重积分中某些应用

正交变换是代数学的基本内容 ,其用途十分广泛 .重积分的计算往往存在技术性的困难 ,若利用“正交变换”的有关理论去解决某些重积分的计算问题是颇有功效的 .本文将以“正交变换”为工具 ,简洁的处理重积分的某些问题     

Sums of commuting square-zero transformations

We show that a linear transformation on a vector space is a sum of two commuting square-zero transformations if and only if it is a nilpotent transformation with index of nilpotency at most 3 and the codimension of in kerT is greater than or equal to the dimension of the space . We also characterize products of two commuting unipotent transformations with index 2.     

Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane

We present a new vorticity-raising transformation for the second integrable complexification of the sine-Gordon equation on the plane. The new transformation is a product of four Schlesinger maps of the Painleve-V equation to itself and allows constructing the n-vortex solution more efficiently than the previously reported transformation comprising a product of 2n maps. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 405–409, August, 2005.     

Measurable linear transformations on abstract Wiener spaces

Measurable linear transformations from an abstract Wiener space to a Hilbert space are characterized. It is shown that the measure on any infinite dimensional abstract Wiener space can be transformed to that on any other by a measurable linear transformation.     

Integrability properties of a generalized reduction of the KdV6 equation

We consider the integrability properties of a generalized version of a similarity reduction of the so-called KdV6 equation, an equation that has recently generated much interest. We give a linear problem for this generalized reduction and show that it satisfies the requirements of the Ablowitz-Ramani-Segur algorithm. In addition we give a Bäcklund transformation to a related equation, giving also an auto-Bäcklund transformation for this last. Our results mirror those for the Korteweg-de Vries equation itself, which has a similarity reduction to an ordinary differential equation which is related by a Bäcklund transformation to the second Painlevé equation, this last having an auto-Bäcklund transformation.     

Remark to transformations of linear differential and functional-differential equations

For linear differential and functional-differential equations of the n-th order criteria of equivalence with respect to the pointwise transformation are derived.     

Rational Landen transformations on

The Landen transformation preserves the value of an elliptic integral, and its iteration produces the classical arithmetic-geometric mean AGM. We present analogous transformations for rational functions integrated over the whole real line.

     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].