关于Г-半环

Just as Nobusawa has extended the concept of ring to the concept of Γ-ring. we introduce in this paper a new concept of Γ-hemiring based on the concept of abelian additive hemigroup. And then, we extend the foundamental results associated with hemiring which are developed by Bourne and Zassenhaus to some analogous results associated with Γ-hemiring, such as the notions of ideal, zeroid, homomorphism and Jacobsonian radical and semi-radical in the case of Γ-hemiring. Finally, we have given some conditions for a Γ-hemiring being a Γ-ring.     

The Jacobson Relational Radical and the Jacobson Radical

In this paper it is shown that the intersection of all w-relations of a hemiring R is exactly the intersection of all primitive relations of this hemiring, and is called J-relational radical of the himiring R. Several properties of the J-relational radical are described. The radical R of a hemiring R is defined by the set {x\in R|x\tau 0}, where \tau is the J-relational radical of R. We obtain independently following results: 1.R is a right quasi-regular ideal which contains every right quasi-regular right ideal. 2.R=\cap {(0:M)|M,, irreducible cancellative right R-semimodule. The term "Jacobson semisimple” in ring theory is generalized to hemirings by defining “J-relational semisimple.” It is proved that if \tau is the Jacobson relational radical of a hemiring R, then R/\tau is J-relational semisimple. Finally the structure theorem of the hemirings is given. A hemiring is J-relational simisimple if and only if it is isomorphic to a subdirect sum of completely primitive hemirings.     

A Note on Ideals of a Three-Dimensional Associative Algebra

In this paper, we shall apply the theory of nilpotent radical to derive some results about ideals of a there-dimensional associative algebra over a field F and of an associative ring of order p~3 where p is a prime. These results are useful in studying the structure of the algebra and the ring.     

关于半局部群环

Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group.     

LIE IDEALS, MORITA CONTEXT AND GENERALIZED （α β）-DERIVATIONS

A classical problem in ring theory is to study conditions under which a ring is forced to become commutative. Stimulated from Jacobson＇s famous result, several tech- niques are developed to achieve this goal. In the present note, we use a pair of rings, which are the ingredients of a Morita context, and obtain that if one of the ring is prime with the generalized （α β）-derivations that satisfy certain conditions on the trace ideal of the ring, which by default is a Lie ideal, and the other ring is reduced, then the trace ideal of the reduced ring is contained in the center of the ring. As an outcome, in case of a semi-projective Morita context, the reduced ring becomes commutative.     

On computing Grbner bases in rings of differential operators

Insa and Pauer presented a basic theory of Grbner basis for differential operators with coeffcients in a commutative ring in 1998,and a criterion was proposed to determine if a set of differential operators is a Gro¨bner basis.In this paper,we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Grbner basis more effciently by this new criterion.     

Gr?bner bases in difference-differential modules with coefficients in a commutative ring

Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algorithmic approach for computing Grbner bases in difference-differential modules with coefficients in a commutative ring.We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem.Our result is a generalization of theories of Insa and Pauer,Ma et al.,Zhou and Winkler and includes them as special cases.     

EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES

In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces.Our first step is to give the representation of mild solution for this control system by utilizing the general method of Laplace transform and the theory of(α, γ)-regularized families of operators. Next, we study the solvability and controllability of nonlinear fractional control systems with damping under some suitable sufficient conditions. Finally, two examples are given to illustrate the theory.     

On the Compactness of Grunsky Differential Operators

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces. The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper the authors deal with the compactness of a Grunsky differential operator. They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.     

Seismic wave imaging in visco-acoustic media

Realistic representation of the earth may be achieved by combining the mechanical properties of elastic solids and viscous liquids. That is to say, the amplitude will be attenuated with different frequency and the phase will be changed in the seismic data acquisition. In the seismic data processing, this effect must be compensated. In this paper, we put forward a visco-acoustic wave propagator which is of better calculating stability and     

The Least Regular Order with Respect to a Regular Congruence on Ordered Γ-Semigroups

The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the Γ-semigroups. We can see that any semigroup can be considered as a Γ-semigroup. In this paper, we introduce and characterize the concept of the regular congruences on ordered Γ-semigroups and prove the following statements on an ordered Γ-semigroup M : (1) Every ordered semilattice congruences is a regular congruence. (2) There exists the least regular order on the Γ-semigroup M/ρ with respect to a regular congru- ence ρ on M . (3) The regular congruences are not ordered semilattice congruences in general.     

Structure of Two-Groups Associative Rings

Introduction.T.S.Ravisanker and U.S.Shukla [1] introduced the notion of a Weak ring A, more general than a ring and a ring in the sense of Nobusawa, and obtained analogical characterizations of the Jacobson radical for weak rings. It is clear that every ring A is a weak ring A for some abelian group (Theorem 3.1 in [2]. Therefore auther gives consideration to such a fact that A and are equal in the weak ring, moreover there is     

WELL-CONDITIONED FRAMES FOR HIGH ORDER FINITE ELEMENT METHODS

The purpose of this paper is to discuss representations of high order C⁰finite element spaces on simplicial meshes in any dimension.When computing with high order piecewise polynomials the conditioning of the basis is likely to be important.The main result of this paper is a construction of representations by frames such that the associated L²condition number is bounded independently of the polynomial degree.To our knowledge,such a representation has not been presented earlier.The main tools we will use for the construction is the bubble transform,introduced previously in[1],and properties of Jacobi polynomials on simplexes in higher dimensions.We also include a brief discussion of preconditioned iterative methods for the finite element systems in the setting of representations by frames.     

Representation Theorem for Mild C-existence Families

As we know,the representation theorem is one of the most important theorems foroperator semigroup theory.The representation theorem for exponentially bounded C-semigroup with dense range R(C) was given in [1 ] ,which was generalized to the casethat C does notnecessarily have dense range(see[2 ] ) .In this paper,more general caseis considered.We get a representation theorem for exponentially bounded mild C-exis-tence families.According to this,a simple proof of a construction theorem for C-s…     

European option pricing model in a stochastic and fuzzy environment

The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.     

SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN

The object of this paper is to study the non-tangential increasing properties of positiveharmonic function u in Lipschitz domain by means of Martin representation theory. A necessaryand sufficient condition of the control of growth of u near any fixed boundary point is obtained.It is shown that the non-tangential increasing degree of u near a boundary point is exactlythe local degree of its representation measure with respect to the harmonic measure. Someexamples are given.     

关于亚直接不可约完全左对称Г-环

A left ideal L of a Г-ring M is called left symmetric if aabβb∈L implies aacβb∈L, where a,b, c∈ M, a ,β∈Γ. A Γ-ring M is called to be a Γ-division ring if it has the left unity, and if left oprator ring R is a division ring.In this paper, the following results are pvoved:Suppose that every left ideal of a Γ-ring M is left symmetiic.If A is subdirectly irreducible with more than one element and with no nonzero nilpotents then it is a Γ-division ring.If M is subdirectly irreducible and if D≠M then M/D is a Γ-division ring where D=(a∈M|aΓb=0,0≠b∈M).     

THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR SOBOLEV EQUATIONS

1 IntroductionIn this paper we will continue the work in LZ' 3, 4J and analyze the effect of numerical integration for nonlinear Sobolev equationsProblems of this type have applications to the two-- temperature theory of heat conduction andsoil mechanics. The treatment of Galerkin's approximations to the solution of partial differential equations using fume element techniques results in a syStem of equations.Throughout this paper, we shall assume that the domain n is a polygonal, so that n=…     

POSITIVE SOLUTIONS TO SYSTEMS OF SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS WITH FIRST ORDER DERIVATIVES

This paper investigates the existence of positive solutions to systems of second order nonlocal boundary value problems with first order derivatives, in which the nonlinear term is not required to be continuous and involves first order derivatives. The main tool used in this paper is a fixed point index theory in a cone.     

On transcendental meromorphic functions with radially distributed values

The growth of transcendental meromorphic functions in terms of their ordersis investigated in this paper when they and their derivatives have radially distributed valuesfollowing the discussion of the author. A simple and elementary way to study such subjectsis exhibited in this paper; that is, once an estimation of B(r, *) in terms of a few c(r, **) inthe Nevanlinna theory on angular domains is established, we can produce one result thatthe order of a mermorphic function with radially distributed values related to C(r, **) canbe estimated under the assumption of existence of suitable deficient value. The results ob-tained in this paper lead us to a new singular direction in terms of Nevanlinna charactersticinstead of the order of meromorphic functions.