中介逻辑的命题演算系统 (Ⅲ)

The paper is a continution of [1]、[2]、[4]、[5]. In this paper we shall introduceconjunction symbol"∧", disjunction symbol "∨" and equality value symbol " asdefining symbols of MP, which are read as "and"、"or"、"if and only if" respectively.With these symbols we shall go on to prove the formal theorems of MP. The list ofthe following formal theorems are in succssion of refernce.     

The Minimal Submanifolds in a Locally Symmetric and Conformally Flat Riemannian Manifold

In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in aLocally symmetric and conformally flat Riemannian mainfold N~(+p).When N~(+p)is a space S_(1)~(+p) of constantcurvature,our theorems reduce to the theorems of[1],[2].     

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…     

EKELAND'S VARIATIONAL PRINCIPLE AND CARISTI'S FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE

The main purpose of this paper is to establish the Ekeland's variational principle andCaristi's fixed point theorem in probabilistic metric spaces and to give a direct simple proofof the equivalence between these two theorems in the probabilistic metric space. The resultspresented in this paper generalize the corresponding results of [9--12].     

UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.     

Stability of Cubic Functional Equation in Three Variables

In this paper, we prove a generalization of Hyers＇ theorem on the sta- bility of approximately additive mapping and a generalization of Badora＇s theorem on approximate ring homomorphism. We also obtain more general stability theorem, which gives stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems in this paper are given following essentially the Hyers-Rassias approach to the stability of the functional equations connected with Ulam＇s problem.     

INFORMATION FLOW OF TREE (Ⅰ)Tree Flow Theorems

This paper is divided into two parts,where the general regularities of information flowin the tree graph are discussed.In the first part we discuss the equivalent theorems of thetree flow,the main sections are as follows:1.fundamental definitions;2.equivalent map-ping structure;3.equivalent partition of vector set*;4.theorems of tree flow.And in thesecond part we put stress on the establishment of tree flow equations.Here we present two most essential streams of information flowing in the tree,i.e.characteristic information flow F* and equivalent characteristic information flow F*θ~(F~*),therefore the interior relation in tree flow is explicited.The main conclusions in this paper are centralized in three theorems,they are respec-tively called tree flow theorem,tree flow theorem A and tree flow theorem B.The firsttheorem describes the equivalent partition of tree flow and the latter theorems then describethe equations of tree flow The basis of establishing these theorems is just the model of in-formation movement established in this paper,that is,α-equivalent structure.     

Two Theorems on Volume and Dihedral Angles of a n—dimensional Simplex

In this paper,we obtain thorem 1 on volum of a n-dimensional simplex and theorem 2 on dihedral angles of a simplex.Besides.We obtain Vasic inequality in E^n and its extension.The results in this paper contain and improve the results in paper[1]、[2]、[3]、[4].     

INFORMATION FLOW OF TREE (1) Tree Flow Theorems

This paper is divided into two parts, where the general regularities of information flow in the tree graph are discussed. In the first part we discuss the equivalent theorems of the tree flow, the main sections are as follows: 1. fundamental definitions; 2. equivalent mapping structure; 3. equivalent partition of vector set*; 4. theorems of tree flow. And in the second part we put stress on the establishment of tree flow equations.Here we present two most essential streams of information flowing in the tree, i.e. characteristic information flow F* and equivalent characteristic information flow *θ~κ (?), therefore the interior relation in tree flow is explicited.The main conclusions in this paper are centralized in three theorems, they are respectively called tree flow theorem, tree flow theorem A and tree flow theorem B. The first theorem describes the equivalent partition of tree flow and the latter theorems then describe the equations of tree flow. The basis of establishing these theorems is just th     

A Fixed Point Theorem and its Application to Best Approximation

The object of this paper is twofold. First, a fixed point theorem of G.L. Cain, Jr. and M. Z. Nashed [1] is generalized. Second, the theorem (Theoreml) is utilized to obtain theorems on best approximation which extend and unify the results of Meinardus [2], Singh [ 3—4 ], and Sahney Singh-Whitfield [5].     

HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD

A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper.For every convergence theorem,a convergence ball is respectively introduced,where the hypothesis conditions of the corresponding theorem can be satisfied.Since all of these convergence balls have the same center x~*,they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems.     

EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS

In recent years the Lie superalgebras have become a 8ubject of intere8t in both mathematicsand physic8[']--[41. We know that the embedding theorems of Z-graded Lie superalgebras andfiltered Lie superalgebras play an important role in the investigation of Lie superalgebras. Theembedding theorem of Z-greded Lie superalgebras is already proved in paper [5l. In this paperthe homomorphic realization Of Lie superalgebras is given and proved by tlle method of tlieReff6]. Using the result of honro…     

中介逻辑的命题运算系统(Ⅰ)

In this paper, we construct the propositional calculus system of mediumlogic MP under the view of medium principe. We first make out thevocabulary of MP and the rules of its formation and inference, and then, after a primary development, we reduce it to ten formal theorems (the formal relations of inference). More precisely, the theorems can be divided into 38 relations of inference, in which only 5 have alrealy been contained in the classiccal natural inference system P, this is to say, all the others are peculiar to tthe non-classical logic system MP.     

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.     

THE KERNELS OF PRODUCT TYPE ON LOCAL FIELDS(Ⅱ)

In paper[4],the kernel of product type on θ is introduced.It was shown in[4]that λ_n(x;r;s)is an approxi-mate identity.The purpose of this paper is to prove the directand inverse approximation theorems for the singular integral     

拓扑空间中新的广义L-KKM型定理及其应用

In this paper, some new generalized L-KKM type theorems with finitely open values and with finitely closed values are established without any convexity structure in topological spaces. As applications, some new matching theorem, fixed point theorem and existence the orem of equilibrium problem with lower and upper bounds are also given under some suitable conditions. These theorems presented in this paper unify and generalize some corresponding known results in recent literatures.     

On the Trace Embedding and Compact Properties of Finite Element Spaces

Ⅰ. Introduction In paper, the embedding theorem and the compact theorem of Rellich and Kondrachev for the Sobolev spaces are generalized to finite element spaces with certain properties. By means of them, the convergence of finite element methods for a class of nonlinear problems are proved in papers.In this paper, the trace embedding and compact theorems for Sobolev spaces will be generalized     

On a problem of Skiba from the Kourovka Notebook

In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.     

INTERPOLATION OF Ba SPACES

In this paper we advance the interpolation theorems of linear operator in Ba spaces. The conception of Ba spaces was first put forward by Ding Xiaxi in his discussion on the prior estimate of Laplace operator in some classical domains and in his study of the embedding theorem of Orlicz-Sobolev spaces, higher dimensional singular     

Stability of Functional Equations in Several Variables

We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.