到欧氏空间的调和Morphisms的分类

本文使用了流形几何的方法，分类了从IR^m中开子集U到IR^n的水平相似的调和morphisms,作为推论，给出了Gudmundsson与Sigurdsson关于复欧氏空间的连通开子集之间的全纯调和morphisms的完全分类定理[8]的一个简单证明。

Linear Functional Equations and Twisted Polynomials

A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.

Poisson Morphisms and Reduced Affine Poisson Group Actions

We,establish the concept of a quotient affine Poisson group,and study the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson G-variety V.The Poisson morphisms(including equivariant cases)between Poisson affine varieties are also discussed.

Some Properties of Morphisms in Effect Algebras

In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.

Harmonic polynomial morphisms between Euclidean spaces

Two non-existence theorems on harmonic polynomial morphisms between Euclidean spaces have been

Bernstein theorem for harmonic morphisms from (N + 1)-sphere to N- manifold

morphism. Harmonic morphisms may be characterized as harmonic mappings which are horizontally weakly conformal. In recent years a substantial progress has been made in the field of harmonic morphism, for example, refs. [ 3—7]. In ref. [4], Baird and Wood proved the following: (ⅰ) Any non-constant harmonic morphism from (S^3, g_(can)) to a Riemann

Frobenius morphisms and stable module categories of repetitive algebras

Let k be the algebraic closure of a finite field F_q and A be a finite dimensional k-algebra with a Frobenius morphism F.In the present paper we establish a relation between the stable module category of the repetitive algebra of A and that of the repetitive algebra of the fixed-point algebra A^F.As an application,it is shown that the derived category of A^F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.

Two Notes on Auto morphisms of Modules over a PID

Let Z>be a principal ideal domain(PID)and M be a module over D.We prove the following two dual results:(i)If M is finitely generated and rr,y are two elements in M such that M/Dx≌M/Dy,then there exists an auto morphism a of M such that a(x)=y.(ii)If M satisfies the minimal cond计ion on submodules and X,Y are two locally cyclic submodules of M such that M/X≌M/Y and X≌Y,then there exists an automorphism a of M such that α(X)=Y.

Finite morphisms of projective and K■hler manifolds

In this paper we study finite morphisms of projective and compact K■hler manifolds, in particular,positivity properties of the associated vector bundle,deformation theory and ramified endomorphisms.

SOME CHARACTERISTIC THEOREMS OF ORDER-HOMOMORPHISMS

Ⅰ. INTRODUCTION In 1979, the author introduced the concept of order-homomorphisms on Fuzzes, and in Refs. [2,3], this notion has been studied more systematically. With the general mappings, functions of Zadeh’s type and Fuzz functions as its special exam-

On Certain Identities with Automorphisms on Lie Ideals in Prime and Semiprime Rings

Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t≥> 1 fixed integers with t ≤ m + n + s. Suppose that a is a non-trivial automorphism of R and let φ(x,y)=[x,y]^t -[x,y]^m[α([x,y]),[x,y]^n[x,y]^s. Thus,(a)if φ(u, v)= 0 for any u,v∈L, then L■Z(R);(b) if φ(u,v)∈ Z(R) for any u,v∈L, then either L■Z(R) or R satisfies S4, the standard identity of degree 4. We also extend the results to semiprime rings.

On the Construction of p-Harmonic Morphisms and Conformal Actions

We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.

Equivalent Conditions of Dominated Splitting for Volume-Preserving Diffeomorphisms

We discuss the equivalent conditions of dominated splitting for conservative diffeomorphisms in C^1 topology.

Preservation of Quasi-isomorphisms of Complexes

We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext〉I（X,Y） = 0 for each object X ∈ X and each object Y ∈ Y. We show that if A,B ∈ C^（R） are X-complexes and U, V ∈ Cr（R） are Y-complexes, then U V Hom（A, U） Hom（A, Y）; A B Hom（B, U） Hom（A, U）. As an application, we give a sufficient condition for the Hom evaluation morphism being invertible.

Covering Morphisms in a Pushout-Pullback Diagram

In a pushout-pullback diagram, which consists of four morphisms f ： A → B, g ： A → C, α ： C → D and β ： B → D, we give some relations among the covers of these four modules. If ker f∈I（ ）, then g ： A → C is -covering if and only if ： B → D is -covering. If every module has an -precover and kerf E I（ ）, then A and C have isomorphic -precovers if and only if B and D have isomorphic -precovers.

Relationship between HSP70-hom single nucleotide polymorphisms and hypertension

Objective To investigate the relationship between HSP70-hom(2437 T/C)single nucleotide polymorphism and hypertension,and to analyze the population distribution of this polymorphism.Methods Samples were collected through epidemiological surveys.The HSP70-hom single nucleotide polymorphisms were detected by the method of polymerase chain reaction-restriction

An Alternative Way to Mapping Cone: The Algebraic Topology of the Pinched Tensor

In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.

水平共形映射和调和Morphism

本文建立了Riemann流形之间水平共形映射之能量密度的基本公式．作为应用，得到了水平共形映射是水平相似映射的充要条件；分类了欧氏空间的开子集之间所有具有全测地纤维的水平共形映射；最后导出了由调和morphism的度量形变产生的水平共形映射力调和motphism的等价条件．因而改进和推广了Baird－Eells，Gudmundsson以及Baird的相应结果．

ON THE SUPERSTABILITY OF THE PEXIDER TYPE GENERALIZED TRIGONOMETRIC FUNCTIONAL EQUATIONS

The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.

On Polynomial Representations of Lie Algebras

We study polynomial representations of finite dimensional （R or C） Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle structures.