Some Properties of Solutions for Viscous Cahn-Hilliard Equation

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔｈｅｖｉｓｃｏｕｓＣａｈｎ－Ｈｉｌｉａｒｄｅｑｕａｔｉｏｎｕｔ＋γΔ２ｕ－ｋΔｕｔ＝Δφ（ｕ），（１．１）ｗｈｉｃｈａｒｉｓｅｓｆｒｏｍｍｏｄｅｌｉｎｇｔｈｅｄｙｎａｍｉｃ...     

Some Properties of M-Matrices

Recently, Markham has proved the following property of M-matrices. Theorem A Suppose A is an M-matrix with the property that for some positive integer p, A~p=L, where L is a lower-triangular matrix. Then A is a lower-triangular matrix. Clearly Theorem A is also true for an upper-triangular matrix. The purpose of this note is to generalize Theorem A to a block upper triangular matrix. If A is a real square matrix with nonpositive off-diagonal elements, each of the following is a necessary and sufficient condition for A to be an M-matrix.     

Some Optimal Block-Factorial Designs

The theory of optimal design plays a fundamental role in experimental design. Some of the results have been widely applied to the realistic world. In[1], Kiefer proved the optimality of some block designs. In this paper some block-factorial designs are discussed. When a block design d_2(v_2,b,k) is superimposed on other block design d_1(v_1,b,k), the resulting structure is called a block-factorial design and is abbreviated as d_1*d_2. The collection of all such designs is denoted by π(v_1,v_2, bk) or Ω. If d_1,d_2 are uniform and they are orthogonal to each other, the structure can be considered as an orthogonal design with three factors. In[2] Cheng pointed out that     

Some Main Properties of Homeomorphism

ＳｏｍｅＭａｉｎＰｒｏｐｅｒｔｉｅｓｏｆＨｏｍｅｏｍｏｒｐｈｉｓｍＦａｎｇＡｉｎｏｎｇ（方爱农）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖ，Ｓｈａｎｇｈａｉ，２０００３０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｅｎｇＭｉｎｄＲｅｃ...     

Some Properties of Bent Functions

First, this paper discusses and sums up some properties of a pair of functions p（x）, q（x） that makes （y ＋ 1）p（x） ＋ yq（x） into a bent function. Then it discusses the properties of bent functions. Also, the upper and lower bounds of the number of bent functions on GF（2）2k are discussed.     

Some Properties of Solutions for Some Types of Q-Difference Equations Originated from Q-Difference Painlevé Equation

In this paper, we mainly investigate some properties of meromorphic solutions for several q-difference equations, which can be seen as the q-difference analogues of Painlevé equations. Some results about the existence and the estimates of growth of meromorphic solution f for q-difference equations are obtained, especially for some estimates for the exponent of convergence of poles of ?_qf(z) := f(qz)-f(z), which extends some previous results by Qi and Yang.     

Some Properties of Two Kinds of Multifunctions

Let X and Y be metrizable topological linear spaces.In this paper,the following results are proved:(1)If X and Y are complete,F;X→Y is a point closed u.s.c.,and symmetric process with ——↑F(X)=Y,then either F(X) is meager in Y,or else F is an open multifunction with F(X)=Y.(2)If X is complete,and F:X→Y is a process with a subclosed graph,then F is l.s.c..We also discuss topological multi-homomorphisms between topological linear spaces.     

Connection Among Some Optimal Criteria for Symmetrical Fractional Factorial Designs

A fundamental and practical question for fractional factorial designs is the issue of optimal factor assignment. Recently, some new criteria, such as generalized minimum aberration, WV-criterion, NB-criterion and uniformity criterion are proposed for comparing and selecting fractions. In this paper, we indicate that these criteria agree quite well for symmetrical fraction factorial designs.     

Some Convergence Properties for ψ-Mixing Sequences

In this paper,we extend the Kolmogorov-type inequality to the case of ψ-mixing sequences.Moreover,we study the strong limit theorems for partial sums of ψ-mixing random variables.As a result,we extend the Khintchine-Kolmogorov-type convergence theorem,the three series theorem,Marcinkiewicz strong law of large number to the case of ψ-mixing sequences.     

Extensions of Some Sufficient Conditions for Starlikeness and Convexity of Order β

The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operators ε_(α,λ)~γ and H_m~l(α_1) related to the generalized Mittag-Leffler function E_(α,λ)~γ and the generalized hypergeometric function,defined in the unit disk,respectively.The results presented here make connections to some of the earlier known developments.     

Some Properties of Two Subclasses of Analytic Functions

This paper discusses some properties of two classes Vk[α,β] and Rk[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.     

Some Properties of Sums of Independent Random Sets

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＳｕｍｓｏｆＩｎｄｅｐｅｎｄｅｎｔＲａｎｄｏｍＳｅｔｓ＊）ＷａｎｇＲｏｎｇｍｉｎｇ（汪荣明）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２０００...     

Some Spectral Properties of Metapositive Definite Matrice

ＳｏｍｅＳｐｅｃｔｒａｌＰｒｏｐｅｒｔｉｅｓｏｆＭｅｔａｐｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｔｒｉｃｅｓＬｉＺｈｕｘｉａｎｇ（李竹香）ＬｕＨｏｎｇｂｉｎ（吕洪斌）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｅｇ...     

Some Properties of Gromov–Hausdorff Distances

The Gromov?CHausdorff distance between metric spaces appears to be a useful tool for modeling some object matching procedures. Since its conception it has been mainly used by pure mathematicians who are interested in the topology generated by this distance, and quantitative consequences of the definition are not very common. As a result, only few lower bounds for the distance are known, and the stability of many metric invariants is not understood. This paper aims at clarifying some of these points by proving several results dealing with explicit lower bounds for the Gromov?CHausdorff distance which involve different standard metric invariants. We also study a modified version of the Gromov?CHausdorff distance which is motivated by practical applications and both prove a structural theorem for it and study its topological equivalence to the usual notion. This structural theorem provides a decomposition of the modified Gromov?CHausdorff distance as the supremum over a family of pseudo-metrics, each of which involves the comparison of certain discrete analogues of curvature. This modified version relates the standard Gromov?CHausdorff distance to the work of Boutin and Kemper, and Olver.     

Some Properties of the Metahomomorpisms on Groups

Ｔｈｅｃｏｎｃｅｐｔｏｆｍｅｔａｈｏｍｏｍｏｒｐｈｉｓｍｓｏｎｇｒｏｕｐｓｗａｓｇｉｖｅｎｂｙｔｈｅａｕｔｈｏｒｉｎ［１］．Ｉｔｓｍｏｔｉｖａｔｉｏｎｃｏｍｅｓｆｒｏｍ“ｔｈｅｐｒｏｂｌｅｍｏｆｓｅｔｔｈｅｏｒｅｔｉｃａｌｓｏｌｕｔｉｏｎｓｔｏｔ...     

Some Properties of Artin-Rees Modules and Rings

The class of Artin-Rees modules is large.It contains modules satisfying (accr).In this paper, we investigate such modules and show that some properties of modules satisfying (accr) can be generalized to modules of this class.     

Some Properties of Solutions for a Nonlinear Difusion System(II)

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＮｏｎｌｉｎｅａｒＤｉｆｕｓｉｏｎＳｙｓｔｅｍ（Ｉ）＊）ＷｕＺｈｕｏｑｕｎ（伍卓群）ａｎｄＹｉｎＪｉｎｇｘｕｅ（尹景学）（ＤｅｐａｒｔｍｅｍｔｏｆＭａｔｈｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓ...     

Some Properties of an Annulus Sum of 3-manifolds

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆａｎＡｎｎｕｌｕｓＳｕｍｏｆ３－ｍａｎｉｆｏｌｄｓＬｅｉＦｅｎｇｃｈｕｎ（雷逢春）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ１３００２３）Ａｂｓｔｒａｃｔ：Ｌｅｔ...     

Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

The relationship between the linear errors-in-variables model and the corresponding ordinary linear model in statistical inference is studied. It is shown that normality of the distribution of covariate is a necessary and sufficient condition for the equivalence. Therefore, testing for lack-of-fit in linear errors-in-variables model can be converted into testing for it in the corresponding ordinary linear model under normality assumption. A test of score type is constructed and the limiting chi-squared distribution is derived under the null hypothesis.Furthermore, we discuss the power of the test and the choice of the weight function involved in the test statistic.     

Some Properties of Divisible and Pure Fuzzy Subgroups

In [3] F. I. Sidky & M. Atif Mishref introduce the concepts of divisible and pure fuzzy subgroups and prove some of their properties. In this paper we further prove following results: Let f: G→G' be an isomorphism of groups and A' be a divisible (pure) fuzzy subgroup of G' under Min, then f~(-1) (A') is a divisible (pure) fuzzy subgroup of G; Let B be a divisible fuzzy subgroup of divisible subgroup H of group G, G=H(?)H', then there exists a fuzzy subgroup B' of H' such that B+B'=A is a fuzzy subgroup of G; If G is a divisible cyclic group, then G is finite group; If A is a fuzzy subgroup of divisible cyclic group, then A is trivial; suppose group G=G_1×G_2×…×G_m, G_i is a divisible cyclic subgroup of G, i=1, 2, …, m, A is a divsiible (pure) fuzzy subgroup of G under Min, then A is trivial.