THE 'HYBRID' TECHNIQUE FOR RISK ANALYSIS OF SOME DISEASES

51. IntroductionSince the theory of fuszy set was introduced by Lotfi A. Zadeh in 1965, fuzzy techniquehas developed rapidly and has been successfully aPplied into many fields.In receat yeaJrs3 a new and promising way of using the fuzzy technique is combinedwith other deterministic and statistica1 methods. The so-called 'hybrid' technique has beenaPplied to insurance business and achieved positive results (see [1, 2], etc.).Based on the data obtained from a survey recelltly made in a commun…     

The Supremum and Infimum of the Set of Fuzzy Numbers and Its Application

In 1986,Goetschel and Voxman represented a fuzzy number by two usualfunctions,which promote further development of the theory and application of fuzzynumbers.For example,we can embbed the fuzzy number space E~1 into a concreteBanach space by using this representation theorem(see[2—4]).     

ON THE RELIABILITY OF MEDIUM LOGIC(ML)

Medium logic (ML) is set up for the common theoritical foundation of the classical mathematics and fuzzy mathematics. It has been formalized as a new theory of logic. See note (1) and note (2). As mathematical logic the ML's construct reches the study of the informal deductive inference by means of studying the formal inference in it, and it demands the formal inference of ML reliable reflected the deductive inference. For this reason, this paper deals with its reliability. The result shows that the formal inference of M L consists with deductive inference, and that ML reliably reflects the deductive inference.     

BIFURCATION OF PERIODIC ORBITS OF A THREE-DIMENSIONAL SYSTEM

§ 1 . IntroductionThere has been a general theory on bifurcation of periodic orbits for two or higher-dimensional systems, and the theory for two-dimensional systems is much richer than thatfor higher-dimensional systems (see [1–11]). We have a relative…     

THE OPERATIONAL VIEWPOINT AND SOME OF ITS CONSEQUENCES: A SHORT REVIEW

This paper presents first results on fuzzy set theory (with the emphasis on probability theoretical aspects) from an operational viewpoint, a new approach that claims to be a way out of some of the difficulties and to present a consistent framework for the set-theoretical aspects of fuzzy set theory (e.g.the complementation paradoxes vanish, and fuzzy sets become a topos under this interpretation). As a preliminary conclusion of this approach we conjecture that the concept of fuzzy set has two essentially different semantical dimensions, which have not sufficiently been separated in the traditional theory, they may be considered either as an evaluation over a universe (i.e. as a connotation) or as a collection of evaluated object (i.e.as a denotation).     

Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters

Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderón's identity. This is inspired by the work of discrete Littlewood-Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe's covering lemma in multiparameter setting.     

SOME ASYMPTOTIC INFERENCE IN QUASI-LIKELIHOOD NONLINEAR MODELS:A GEOMETRIC APPROACH

§ 1　IntroductionIt is well known that quasi-likelihood models introduced by Wedderburn[1 ] greatlywiden the scope of generalized linear models by using a much weaker assumption in whichonly the firstand second moments ofresponse vector Yare needed to replace the full distri-butional assumption about Y in the models.It has drawn considerable attention in recentliterature(e.g.see[2～ 6] and so on) .However,little work has been done on the issuefrom a geometric viewpoint.The purpose of this p…     

A SURVEY OF SOME ASPECTS ON THE RESEARCH WORK OF FUZZY TOPOLOGY IN CHINA

The fundamental concept of a fuzzy set,introduced by Zadeh in 1965 [34] provides a natural foundation for treating mathematically the fuzzy phenomena which exist prevasively in our real world and for building new branches of fuzzy mathematics.In the area of fuzzy topology much research has been carried out since 1968 [1].     

Boundary Unique Continuation Properties for Elliptic Operators With Singular Potentials

0 Introduction Because of applications to control theory, see Schmit and Week's work in [1], the following unique continuation question (UCP) was raised in [2-3]: if u is a harmonic function in a connected Lipschitz domainΩ, vanishing continuously on an open subsetΓof the boundary (?)Ωand whose normal derivative vanishes on a subset of Γof positive surface measure, does it follows that u is identically zero inΩ? On the other hand, the unique continuation problem has been focusing on second order equations in which the coefficients of the lower-order terms are allowed to be     

RESEARCH ANNOUNCEMENTSOn the Simultaneous Pell Equations x~2-D_(1y)~2=δ and z~2 - D_(2y)~2 =δ

Let Z, N, Q be the sets of all integers, positive integers and rational numbers, respectively.Let D1, D2 be distinct positive integers, and let . The simultaneous Pell equationsarise in connection with a variety of classical problems on number theory and arithmetic algebraicgeometry. As has been noted by K. One[1], the solutions (x, y, z) of (1) imply the existence ofrational points of infinite order on the elliptic curveLet p, q be twin primes withRecently, Qiu Derong and Zhang Xianke[2…     

CHIRAL RING OF Sp（N） AND SO（N） SUPERSYMMETRIC GAUGE THEORY IN FOUR DIMENSIONS＊＊

The chiral ring of classical supersymmetric Yang-Mills theory with gauge group Sp(N) or SO(N) is computed, extending previous work (of Cachazo, Douglas, Seiberg, and the author) for SU(N). The result is that, as has been conjectured, the ring is generated by the usual glueball superfield S - Tr WαWα, with the relation Sh = 0, h being the dual Coxeter number. Though this proposition has important implications for the behavior of the quantum theory, the statement and (for the most part) the proofs amount to assertions about Lie groups with no direct reference to gauge theory.     

Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

Low-level Separation Axioms in Topological Molecular Lattices

Compactness,one of the most important notions in topological molecular lattices(TMLs for short)(see [1]), has not yet been defined reasonably in TMLs. Fuzzytopology, the blue-print on which the theory of TML was established,presages that asatisfactory solution to the problem of compactness is always associated with the studyof points, support points and separation axioms. In[2], the concept of component of     

THE NUMBER OF ROOTED NEARLY CUBIC C-NETS

1. IntroductionW.T. Tutte's original papers[1--3) on the enumerative theory of rooted planar maps havebrought forth a series of papers on enumerating triangulations. The enumeration of generalrooted planar maps has then also been investigated and a number of elegant results havebeen obtained, although relatively fewer than that of triangulations. As the dual case oftriangulations, the enumerative theory of cubic maps has also been developed, though thereare a lot of problems waiting for solut…     

THE EQUIVALUED BOUNDARY VALUE PROBLEMS FOR THE MINIMAL SURFACE EQUATION

There has been a long history on the study of the minimal surface equation (see [1]—[3]), For a tightly stretched uniform membrane in balance, its place can be discribed by the minimal surface equation. In this paper we will discuss boundary value problems of the minimal surface equation with equivalued boundary conditions on a complex connected domain. The physical meaning of such pro-     

MULTI-DIMENSIONAL QUANTITATIVE RESULTS FOR PROBABILITY MEASURES APPROXIMATING THE UNIT MEASURE

Introduction The convergence of a sequence of positive linear operators{L_j}_(j∈IN) to the identity operator I acting on C([a,b]), [a,b]IR,has been studied extensively by P. P. Korovkin (1953) (see [8]).Later on O. Shisha and B. Mond (1968) put this convergence in aquantitative form. And E. Censor (1971) produced similar quantita-tive results on IR~k,     

The Asymptotic Properties of the Extremal Rings in Space and the Proof of the Anderson's Conjecture

For n≥3,1≤p≤n-1,and 0<α<1,the ring R_n,p(a)may be described as theopen unit ball in n-space minus a closed concentric p—dimensional ball of radiusα,its modulus is denoted by modR_n,p(a).Because these rings have the importantextremal properties indicated in[1],the problem of evaluating the modulus mod-R_n,p(α)is very interesting.On this problem,much research work has been done(see[1]and[2]).In this paper,the following results are obtained.     

SMALLEST g-SUPERSOLUTION FOR BSDE WITH CONTINUOUS DRIFT COEFFICIENTS

91. IntroductionSince the result of monotonic lied theorem of BSDE and its aPPlication to nonlinearDoolyMeyer decomposition theorem, the smallest g-supersolution with a constraint on (Y, Z)(see [1]), some developments have been done, for example, in 14], where by a penallzationmethod, Chen and Peng discussed nonlinear Doob-Meyer decomposition theorem ash theBSDE introduced by Duffie and EPsteinI3]. In [51 Lin discussed the smallest g-supersolutionto BSDE with a constraint on (y,z) wi…     

Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals

Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.     

THE EQUIVALUED BOUNDARY VALUE PROBLEMS FOR THE MINIMAL SURFACE EQUATION

There has been a long history on the study of the minimal surface equation(see[1]—[3]).For a tightly stretched uniform membrane in balance,its place can be discribed by the minimal surface equation.In this paper we will discuss boundary value problems of the minimal surface equation with equivalued boundary conditions on a complex connected domain.The physical meaning of such problems will be given later. The linear approximation of the minimal