LEFT INVERSES AND RIGHT INVERSES OF A STRONG ENDOMORPHISM OF A GRAPH

In this paper, we characterize left inverses and right inverses of a strong endomorphism of a graph under some certain Green's equivalence conditions. In addition, the number of them is also given.

A construction of quasi-hereditary endomorphism algebras

In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras.

Shadowing and Inverse Shadowing for C^1 Endomorphisms

In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.

An Extended Ockham Algebra with Endomorphism Kernel Property

An algebraic structure A is said to have the endomorphism kernel property if every congruence on A, other than the universal congruence, is the kernel of an endomorphism on A. In this paper, we consider the EKP （that is, endomorphism kernel property） for an extended Ockham algebra A. In particular, we describe the structure of the finite symmetric extended de Morgan algebras having EKP.

Unstable manifolds for endomorphisms

A detailed presentation of an unstable manifold theorem for non invertible differentiable maps of finite dimensional manifolds is given.

Inverses and Pseudo-Inverses of a Strong Endomorphism of a Graph

In this paper,we explicitly describe all the inverses and pseudo-inverses of a strong endomorphism of a graph.The number of them is determined.In addition,we give a characterization of a strong endomorphism whose pseudo-inverse set coincides with its inverse set.The graph,each strong endomorphism of which has this property,is also investigated.

The Join of Split Graphs Whose Half-strong Endomorphisms Form a Monoid

In this paper, the half-strong endomorphisms of the join of split graphs are investigated. We give the conditions under which the half-strong endomorphisms of the join of split graphs form a monoid.

Classification of Special Anosov Endomorphisms of Nil-manifolds

In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γbe a covering map of a nil-manifold and denote by A:N/Γ→N/Γthe nil-endomorphism which is homotopic to f.If f is a special TA-map,then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A.

Finite Abelian Groups with the Strong Endomorphism Kernel Property

An endomorphism h of a group G is said to be strong whenever for every congruenceθon G,(x,y)∈θimplies(h(x),h(y))∈θfor every x,y∈G.A group G is said to have the strong endomorphism kernel property if every congruence on G is the kernel of a strong endomorphism.In this note,we study the strong endomorphism kernel property in the class of Abelian groups.In particular,we show that a finite Abelian group has the strong endomorphism kernel property if and only if it is cyclic.

Existence of periodic points of endomorphisms of a circle

A theorem of Block and Franke is improved on the existence of periodic points for a map of a circle to itself and a proof which seems more understandable is given.

On Endomorphism Monoids of Finite Kleene Algebras

An endomorphism monoid of an algebra A.is said to be a band if every endomorphism on A is an idempotent,and it is said to be a demi-band if every noninject ive endomorphism on A is an idempotent.We precisely determine finite Kleene algebras whose endomorphism monoids are demi-bands and bands via Priestley duality.

ISOMORPHISMS BETWEEN ENDOMORPHISM RINGS OF FREE MODULES

In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.

Local Unstable Entropy and Local Unstable Pressure for Partially Hyperbolic Endomorphisms

In this paper,local unstable metric entropy,local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated.Specially,two variational principles concerning relationships among the above mentioned numbers are formulated.

Classification of holomorphic endomorphisms of Hopf manifolds

We give a complete classification of holomorphic endomorphisms of Hopf manifolds in dimensions two and three.In particular,we show that these endomorphisms are automorphisms except for the diagonal class,in which case they are quasi-homogeneous.

Symmetric Extended MS-algebras with the Strong Endomorphism Kernel Property

An endomorphism on an algebra A is said to be strong if it is compatible with every congruence on A.If every congruence on A,other than the universal congruence,is the kernel of a strong endomorphism on A,then A is said to have the strong endomorphism kernel property.In this paper,we shall give a complete description of the structure of those symmetric extended MS-algebras that have this property via Priestley duality.

On the Arithmetic of Endomorphism Ring End (Zp×Zpm)

For a prime p,let E_（p,p^m）={（a p^（m-1） b d）｜a,b,c∈Z_p,d∈Z_（p^m）}. We first establish a ring isomorphism from Z_（p,p^m） onto E_（p,p^m）. Then we provide a way to compute-d and d^（-1） by using arithmetic in Z_p and Z_（p^m）, and characterize the invertible elements of E_（p,p^m）. Moreover, we introduce the minimal polynomial for each element in E_（p,p^m） and give its applications.

SOME TOPOLOGICAL PROPERTIES OF ENDOMORPHISMS OF THE UNIT CIRCLE

In this paper, we give a simple proof for some topological properties of endomorphisms on the unit circle.

CONNECTIONS AND GEODESIC CHARACTERISTIC OF EQUATIONSOF MOTION FOR CONSTRAINED MECHANICAL SYSTEMS

The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from the case in an autonomous mechanical system.

HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS

Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（F） be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn（F） such that F M^Pn（F）. A map f ： F→R is called a homomorphism if f（AB） = f（A）f（B） for any A, B ∈F. In particular, f is called an endomorphism if F = R. The structure of all homomorphisms from F to R （respectively, all endomorphisms of Mn（F）） is described.

AN APPROACH TO CONSTRUCT AN END-REGULAR GRAPH

Abstract In this paper,an approach to construct a nontrivial end regular graph of any order under some conditions are given.