fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

fuzzy completely irresolute and fuzzy weakly completely irresolute functions abstract the aim of this paper is to introduce two new classes of functions called fuzzy completely irresolute and fuzzy weakly completely irresolute functions their characterizations examples compositions of these functions their relationships with other functions and preservations of some fuzzy spaces under these functions are studied

on two weakers forms of continuous order homomorphisms the aim of this paper is to find further connections between two different current researches on fuzzy topology the one based on the concepts of neighborhood filter and zadeh function and the other based on the concepts of remote neighborhood ideal and order homomorphism on fuzzy lattices to approach this the paper studies two weaker forms of continuous order homomorphisms the semi continuous order homomorphism and the weakly semi continuous order homomorphism between l fuzzy topological spaces these order homomorphisms can be characterized in each of the notions remote neighborhood neighborhood ideal filter and molecular net in addition some relations connecting weakly semi continuous order homomorphisms semi hausdorff l fts and urysohn l fts have also been established

automorphisms of the canonical anticommutation relations and index theory let h be a complex hilbert space p an orthogonal projection on h and p the complementary projection if g is any symmetrically normed ideal in the ring of bounded operators on h then we consider the group of unitary operators on h such that p up and p u p lie in g when g is the hilbert schmidt class these unitaries define automorphisms of the c algebra b of the canonical anticommutation relations over h which are implementable in the representation of b determined by p we investigate the structure of the group u proving in particular that it has infinitely many connected components uk labelled by the fredholm index of p u p the connected component of the identity u0 is generated by unitaries of the form exp ia with a self adjoint and p a p in g finally we consider an application of these results to two dimensional field theory showing in particular that the charge and chiral charge quantum numbers arise as the fredholm indices of p up for certain unitary u on l2 r c2

loop groups anyons and the calogero sutherland model the positive energy representations of the loop group of u 1 are used to construct a boson anyon correspondence we compute all the correlation functions of our anyon fields and study an anyonic w algebra of unbounded operators with a common dense domain this algebra contains an operator with peculiar exchange relations with the anyon fields this operator can be interpreted as a second quantized calogero sutherland cs hamiltonian and may be used to solve the cs model in particular we inductively construct all eigenfunctions of the cs model from anyon correlation functions for all particle numbers and positive couplings

on fuzzy semi preopen sets and fuzzy semi precontinuity the purpose of this paper is to introduce and study the concepts of fuzzy semi preopen sets and fuzzy semi precontinuous mappings in fuzzy topological spaces

a superversion of quasifree second quantization i charged particles a formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented the second quantization of one particle observables leads to current superalgebras and a super schwinger term shows up anticommuting parameters are introduced in order to construct super bogoliubov transformations mixing bosons and fermions as an application representations of lie superalgebras are given which are semidirect products of extensions of affine kac moody algebras and the virasoro algebra and of the super virasoro algebra

on fuzzy t continuous mappings abstract the concepts of fuzzy almost continuous fuzzy continuous and fuzzy weakly continuous mappings have been introduced by yalvac and by mukherjee and sinha the aim of this paper is mainly to study and to find the mutual interrelations among these concepts

fuzzy weak totally semicontinuous and fuzzy weak totally precontinuous mappings abstract the aim of this paper is to introduce some new classes of mappings called fuzzy weak totally continuous fuzzy totally precontinuous fuzzy weak totally semicontinuous fuzzy totally m precontinuous fuzzy totally m precontinuous and fuzzy totally irresolute mappings their compositions their relationships with other mappings preservations of some fuzzy spaces under these mappings and some examples are studied we also prove that the property that the mapping is fuzzy totally semicontinuous and fuzzy totally precontinuous is equivalent to the property that the mapping is fuzzy totally continuous

on fuzzy semi irresolute and strongly irresolute functions abstract in this paper two classes of functions between fuzzy topological spaces are introduced under the terminologies fuzzy semi irresolute and strongly irresolute functions each of which is independent of the fuzzy continuity of chang 1968 the class of fuzzy irresolute functions as recently introduced by mukherjee and sinha 1989 is seen to lie strictly between these two classes several characterizations of these functions along with their relationships with certain other types of functions are investigated

v algebras a particular class of unbounded operator algebras we consider a weak unbounded commutant for a set of unbounded operators and we examine op algebras which coincide with some of their bicommutant this class of op algebras called v algebras shows some properties close to those which hold true for bounded operator algebras

on some weaker forms of fuzzy continuous and fuzzy open mappings on fuzzy topology spaces abstract the purpose of the present paper is to study some weaker forms of fuzzy continuous and fuzzy open maps between fuzzy topological spaces along with the introduction and investigations of a new class of non fuzzy continuous maps this latter type of mappings is seen to be independent of the other non continuous functions discussed here all these functions are characterized and certain properties concerning them are proved finally a comparative study as to their mutual dependence and interrelations under different conditions is taken up

supersymmetric quantum mechanics defined as sesquilinear forms a formulation of supersymmetric quantum mechanics in terms of sesquilinear forms is presented otherwise occurring rather complicated domain questions are solved in a simple and natural way the authors formulate the axioms and describe a number of models supersymmetry transformations are implemented as superunitary transformations in a space defined over a grassmann algebra generalised bogoliubov transformations acting in that space are also formulated

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

semi continous and semi closed mappings and semi connectedness in fuzzy setting abstract the aim of the paper is mainly to study and to find different characterizations of semi continuous and semi closed mappings between fuzzy topological spaces the notion of fuzzy semi open sets is used to define fuzzy ti spaces i 0 1 2 and these spaces are investigated under fuzzy semi continuity finally fuzzy semi connectedness is introduced and studied to some extent

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

fuzzy topology on fuzzy sets fuzzy semicontinuity and fuzzy semiseparation axioms the concept of a fuzzy topology on a fuzzy set was introduced in fuzzy set syst 45 1992 103 the aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined also we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept fuzzy semiconnected and fuzzy semicompact spaces are introduced and some of their properties are discussed

a supersymmetric generalization of von neumann s theorem a formulation of supersymmetric quantum mechanics is given and superunitary and generalized canonical transformations are defined acting in a module next it is assumed that there are operators that give an irreducible representation of the canonical commutation and anticommutation relations respectively and it is proved that two such representations are connected by a uniquely determined superunitary transformation under suitable domain assumptions this extends the well known uniqueness theorem of von neumann to canonical anti commutation relations using anticommuting parameters

operations and its applications on l fuzzy bitopological spaces part i abstract in this and a subsequent paper a new operation on the class of all l fuzzy subsets of a universe endowed with a fuzzy topological space is introduced to generalize several characterization and properties of some fuzzy bitopological concepts such as a fuzzy interior operators and some new classes of fuzzy separation axioms also the relation between these classes and the weaker and stronger forms in fuzzy bitopological spaces are investigated finally we showed that these axioms are good extension in the sense of lowen 1978 due to lowen in part ii this theory is applied on the mappings defined on l fuzzy bitopological spaces

on separation axioms and ti fuzzy continuity abstract we introduce and generalise concepts of t continuous functions in a fuzzy setting and study them in connection with the fuzzy continuity and fuzzy separation axioms some fuzzy topological properties are also investigated under such functions

semi open sets semi continuity and semi open mappings in fuzzy bitopological spaces abstract in this paper the concepts of fuzzy semi open sets fuzzy semi continuity and fuzzy semi open mappings due to azad j math anal appl 82 1981 14 32 have been generalized to the fuzzy bitopological setting and some of its basic properties are discussed several characterizing theorems of fuzzy semi continuity and its relationship with fuzzy continuity are investigated

fuzzy extremally disconnected spaces abstract an investigation of extremally disconnected fuzzy topological spaces is done in this paper such a class of spaces is characterized in various ways by using the concepts of q neighborhoods semi q neighbourhoods closure closure semi closure and related notions in fuzzy setting

fermion currents in 1 1 dimensions let f denote the fock space for a free massless fermion field in two space time dimensions if q and q5 denote the charge and chiral charge operators then f n1 n2fn1 n2 where fn1 n2 is the joint eigenspace of q and q5 with corresponding eigenvalues n1 and n2 the smeared time zero free fermion currents formally given by j f x x f x dx 0 1 f s r are in fact self adjoint densely defined operators on f and their exponentials generate a c algebra which leaves each subspace fn1 n2 invariant if a periodic box cutoff for the fermions is introduced uhlenbrock has shown that this c algebra acts irreducibly in each sector fn1 n2 we prove this same result without any cutoffs and determine the properties of the representations in each sector the importance of this result for the problem of constructing fermion fields from observables in two dimensional models such as those of thirring and schwinger is discussed

the cauchy problem for the integrable novikov equation in this paper we consider the cauchy problem for the integrable novikov equation by using the littlewood paley decomposition and nonhomogeneous besov spaces we prove that the cauchy problem for the integrable novikov equation is locally well posed in the besov space b p r s with 1 max 1 1 p 3 2 in particular when u 0 is an element of b p r s boolean and h l with 1 max 1 1 p 3 2 for all t is an element of 0 t we have that vertical bar vertical bar u t vertical bar vertical bar h l vertical bar vertical bar u 0 vertical bar vertical bar h l we also prove that the local well posedness of the cauchy problem for the novikov equation fails in b 2 3 2 infinity c 2012 elsevier inc all rights reserved

on fuzzy pairwise semi precontinuity abstract in this paper we generalize the concepts of fuzzy semi preopen semi preclosed sets and fuzzy semi precontinuous mappings due to park and lee fuzzy sets and systems 67 1994 359 364 into fuzzy bitopological setting and discuss some of its basic properties

fuzzy semi preopen sets and fuzzy semi precontinuous mappings abstract the aim of this paper is to introduce and discuss the concepts of fuzzy semi preopen sets and fuzzy semi precontinuous mappings

on fuzzy weakly semi continuous functions abstract this paper is devoted to the introduction and study of fuzzy weakly semi continuous functions between fuzzy topological spaces some properties of these functions are characterized in terms of quasi coincidence quasi neighborhoods neighborhoods etc furthermore some relations connecting fuzzy weakly semi continuous functions and fuzzy retractions have been established

i type of strong connectivity in l fuzzy topological spaces in this paper we mainly introduce and study r type of strong connectivity for a given l fuzzy topological space it preserves many good properties of connected sets in general topological spaces for example any union of r type of strongly connected sets with nonempty intersection is r type of strongly connected the images of irresolute order homomorphism of r type of strongly connected sets are r type of strongly connected

a class of strong forms of fuzzy complete continuity abstract the aim of this paper is devoted to make use of operations on ix of a fuzzy topological space x to unify and generalize classes of strong forms of fuzzy complete continuity furthermore we add more types of strong forms of fuzzy completely continuous functions by choosing special operations a comparison between these types of functions is of interest preservations of some fuzzy aspects under these functions are studied

some covariant representations of massless boson fields considers the c algebra of the canonical commutation relations ccr acted on by a group g of one particle symmetry transformations v a symplectic operator t defines a representation pi t pi f omicron t where pi f is the fock representation the automorphisms of the ccr algebra that are induced by g are shown to be continuously implemented in pi t if and only if a v g av g is a continuous hilbert schmidt 1 cocycle of g here a is related to t by t exp a a being a suitable bounded antilinear self adjoint operator some new examples of fully poincare covariant representations of massless fields in 1 1 dimensions are constructed

fuzzy less strongly semiopen sets and fuzzy less strong semicontinuity abstract in this paper we first introduce the concepts of a fuzzy less strongly semiopen set a fuzzy less strongly semiclosed set fuzzy less strong semi interior and fuzzy less strong semiclosure we study their properties and discuss the relationships between these concepts and relevant concepts in fuzzy topological space finally we introduce the fuzzy less strongly continuous fuzzy less strongly semiopen and fuzzy less strongly semiclosed mappings on fuzzy topological space and establish their various characteristic properties

directed family of fuzzy sets and fuzzy perfect maps the present paper deals with the perfect functions in fuzzy setting fuzzy filter bases of fuzzy sets are also studied vis a vis such functions finally certain fuzzy topological properties are taken up for their study with regard to fuzzy perfect functions

fuzzy completely pre irresolute and weakly completely pre irresolute mappings in this paper we introduce fuzzy completely pre irresolute and fuzzy weakly completely pre irresolute mappings between fuzzy topological spaces and study these mappings in relation to some other types of already known mappings

implementability of gauge transformations and quantization of fermions in external fields quantization of fermions in an external soliton field leading to a representation of the canonical anticommutation relation car which is inequivalent to the representation connected to the massive dirac operator is studied classes of gauge and axial gauge transformations that can be unitarily implemented are determined in the latter case quantization conditions for gauge functions are obtained integers entering can be interpreted as winding numbers

groups of automorphisms of the canonical commutation and anticommutation relations observables of supersymmetric quantum mechanics are coded by taking the antisymmetric tensor product with anticommuting parameters next the authors define superunitary transformations which mix bosonic and fermionic degrees of freedom in order to construct automorphisms of the canonical anti commutation relations c a cr conversely every automorphism of the c a cr is implemented by an essentially unique superunitary transformation