continuity of gaussian local times continuity in the time parameter is considered for a natural version of the local time for stationary gaussian processes bounds are given for the local and uniform modulus of continuity which are applicable in cases not covered by kono notably when the incremental variance is a regularly varying function of index two

on fuzzy linear representations of finite groups abstract a linear representation of a finite group g in a finite dimensional vector space v induces through zadeh s extension principle a function 9 from igto into igl v where gl v is the group of all linear automorphisms of v if w is a fuzzy subspace of v the group of all fuzzy linear automorphisms of w gl w is a subgroup of gl v w is said to be stable under the action of a fuzzy subgroup a of g if 9 a is a subset of gl w i e 9 a is zero at every f inside gl v and outside gl q if w is stable under the action of a then its support subspace is stable under the action of the support subgroup of a in the crisp sense finally we show that if there are two stable fuzzy subspaces one of them is contained in the other then the smaller one has a fuzzy direct summand in the bigger which is also a stable fuzzy subspace

fuzzy semistar operations on overrings abstract in this paper we reinvestigate the notion of fuzzy semistar operation introduced in 5 we show how a fuzzy semistar operation on an integral domain r induces canonically a fuzzy semistar operation on an overring t of r and conversely how a fuzzy semistar operation on t induces canonically a semistar operation on r as an application new characterizations of prufer domains and complete description of the set of all fuzzy semistar operations of finite character on prufer domains are obtained we also characterize conducive domains

k fuzzy ideals in semirings abstract we introduce the k fuzzy ideal of a semiring also we construct an extension of a fuzzy ideal in a k semiring and study the quotient structure of a k semiring by a fuzzy ideal

tl subrings and tl ideals part 4 radicals of tl ideals abstract in this paper the notion of the radicals of l subsets and tl ideals of a ring is introduced and studied where t is an infinitely distributive t norm on a given complete brouwerian lattice l our main objective is to present basic properties about the radicals of tl ideals in preparation for the forthcoming two papers

fuzzy ideals and semiprime fuzzy ideals in semigroups in this paper we investigate relationships between different definitions of fuzzy ideals of a fuzzy semigroup the equivalence of different definitions of fuzzy ideals of a fuzzy semigroup is obtained we show that the lattice of all f fuzzy ideals of a fuzzy semigroup x is a complete sublattice of the lattice of all fuzzy sets in x when f is an infinitely distributive weak pseudo t norm on l a definition of f semiprime fuzzy ideal of a fuzzy semigroup is given a description of all f semigroups in which every f fuzzy ideal is f semiprime is obtained

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

fuzzy homomorphisms of rings abstract in this paper we introduce the concept of fuzzy homomorphisms of rings we prove for fuzzy homomorphisms analogues of the homomorphism theorems of ordinary ring homomorphisms

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

basis functions for triangular and quadrilateral high order elements in this paper we present a unified description of new spectral bases suitable for high order hp finite element discretizations on hybrid two dimensional meshes consisting of triangles and quadrilaterals all bases presented are for c0 continuous discretizations and are described both as modal and as mixed modal nodal expansions general jacobi polynomials of mixed weights are employed that accommodate automatic exact numerical quadratures generalized tensor products and variable expansion order in each element the approximation properties of the bases are analyzed in the context of the projection linear advection and diffusion operators

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

r primary l representations of l ideals we examine the basic properties of prime l ideals primary l ideals and r radicals of l ideals where l is a completely distributive lattice we determine to what extent every l ideal has an r primary l representation

fuzzy direct sums of fuzzy rings abstract in this paper we introduce the concepts of the fuzzy weak direct sum and the fuzzy complete direct sum of fuzzy subrings of commutative rings we prove some basic properties analogous to those of ordinary rings

tl subrings and tl ideals part 1 basic concepts abstract in 25 27 we put forward a rudimentary frame of the theory of tl subalgebras in 26 we established a theory of tl subgroups and tl subgroups in this paper we will continue our work in concern with basic ideas provided in 25 27 introduce the notions of tl subrings and tl ideals of a ring and study some of their properties where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

fuzzy nil radicals and fuzzy primary ideals abstract the purpose of this paper is to extend the concept of a fuzzy set by introducing the concept of a fuzzy nil radical of a fuzzy ideal in a ring using this concept a fuzzy primary ideal is defined some fundamental results concerning these notions are proved

smoothness of the density for solutions to gaussian rough differential equations we consider stochastic differential equations driven by a multi dimensional gaussian process under the assumption that the vector fields satisfy hormander s bracket condition we demonstrate that the solution admits a smooth density for any strictly positive time t provided the driving noise satisfies certain non degeneracy assumptions our analysis relies on an interplay of rough path theory malliavin calculus and the theory of gaussian processes our result applies to a broad range of examples including fractional brownian motion with hurst parameter greater than 1 4 the ornstein uhlenbeck process and the brownian bridge returning after time t

fuzzy primary representations of fuzzy ideals abstract let r be a commutative ring with identity and let a be a fuzzy ideal of r then a is said to have a fuzzy primary representation if a is the intersection of a finite number of fuzzy primary ideals we show that every fuzzy ideal a of r such that a 0 1 has a fuzzy primary representation if and only if r is artinian we show that uniqueness properties for reduced primary representations of ideals in the usual sense carry over to fuzzy ideals

mixed finite elements of least squares type for elasticity abstract in terms of stress and displacement the linear elasticity problem is discretized by a least squares finite element method in the case of a convex polygonal domain the stress is approximated by the lowest order raviart thomas nedelec flux element and the displacement by the linear c0 element we obtain coerciveness and optimal h1 l2 and h div error bounds uniform in lame constant for displacement and stress respectively our method also allows the use of any other combination of conforming elements for stress and displacement e g c0 elements for all variables

fuzzy ideals and fuzzy subalgebras of lie algebras abstract a fuzzy idea l of a lie algebra l factors it into a lie algebra l l called a fuzzy quotient lie algebra this fuzzy algebra lie algebra is always a fuzzy partition of l and a fuzzy partition of l will be a fuzzy quotient lie algebra if and only if its associated fuzzy similarity relation is compatible with the lie algebra operations relationship between the operations of the lie algebras l i t and zadeh s extension principle are studied we also study homomorphisms of lie algebras and the relationship between them and fuzzy ideals and fuzzy subalgebras of the domains and the co domains of these homomorphisms finally solvability of fuzzy ideals and studied in defining these solvable fuzzy ideals we use zadeh s extension principle

some comments on spectrums of prime fuzzy ideals of a ring abstract common and distinctive features of two prime spectrums one obtained by kumar and kohli using 2 valued prime fuzzy ideals and the other obtained by the author using not so restrictive definition of prime fuzzy ideals are discussed it is also shown that some results claimed by kumar and kohli regarding spectrum of 2 valued prime fuzzy ideals need some corrections

fuzzy partitions and fuzzy quotient rings abstract the cosets of a fuzzy ideal m in a ring a form another ring a m called the fuzzy quotient ring of a and m we show that a m is always a fuzzy partition of a and a fuzzy partition of a will be a fuzzy quotient ring with respect to some fuzzy ideal if and only if its associated fuzzy similarity relation is compatible with the ring operations we also discuss relationships between the two operations of the fuzzy quotient ring a m and the extensions over ia of the two operations of a by zadeh s extension principle we study relationships between the level ring structures of a fuzzy quotient ring and the level relations of its associated fuzzy similarity relations we introduce and study a new notion of the factorization of a ring homomorphism through fuzzy quotients finally a relationship between fuzzy prime ideals and fuzzy similarity relation has been established

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

fuzzy subrings and ideals redefined abstract v q fuzzy subrings and ideals of a ring are defined the concepts of v q fuzzy semiprime prime semi primary primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained v q fuzzy cosets determined by v q fuzzy ideals and v q fuzzy radicals of v q fuzzy ideals are discussed

fuzzy ideals and fuzzy bi ideals in fuzzy semigroups abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra such as fuzzy left right ideal and fuzzy bi ideal in fuzzy semigroup through the new approach of fuzzy space and fuzzy group introduced by dib 1994 our notion of fuzzy ideal and fuzzy bi ideal includes the classical concepts of fuzzy ideal and fuzzy bi ideal of ordinary semigroup many counterexamples are also given

on a certain mixed variational theorem and a proposed application formulation d une equation variationnelle pour les deplacements et certaines contraintes en vue d une application aux plaques elastiques stratifiees isotropes et anisotropes

on fuzzy semiprimary ideals in this paper semiprimary ideals are redefined in terms of fuzzy points and it is proved that this definition is equivalent to that of kumar 1991 several results regarding semiprimary and fuzzy semiprimary ideals are derived it is shown by examples that the characterization of semiprimary ideals by prime radicals does not hold for this definition of fuzzy semiprimary ideals

a local time approach to the self intersections of brownian paths in space we study the brownian functional alpha x b int limits b int delta x w t w s dsdt wherewt is a brownian path in two or three dimensions forb off the diagonal we identify x b with a local time and establish the holder continuity of x b in bothx andb

spectrum of prime fuzzy ideals abstract a topological space called a spectrum of prime fuzzy ideals and denoted by fspec r is obtained by introducing a topology on the set of prime fuzzy ideals of a ring r the prime fuzzy ideals used here introduced by the author elsewhere are not necessarily two valued the topology introduced is compact and the usual nonfuzzy prime spectrum spec r is a subspace of fspec r and dense in it situations under which fuzzy spectrums of different rings are homeomorphic are discussed in particular fspec r is proved to be homeomorphic to fspec r frad r where frad r is the fuzzy prime radical of r the correspondence associating a ring r to the topological space fspec r is shown to define a contravarient functor from the category of rings with unity into the category of compact topological spaces

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

some results on l fuzzy modules abstract an l fuzzy quotient module of a module is redefined and a modular complete pseudo complemented lattice structure is given to the set of all l fuzzy modules of a given module some isomorphisms between the lattices or posets of l fuzzy modules are obtained finally a galois connection is established between two lattices of l fuzzy modules of homomorphic modules

correspondence theorem for fuzzy ideals abstract the ring r j of cosets of a fuzzy ideal j of a ring r is defined and shown to be isomorphic to a factor ring of r in a natural way if f r r is an epimorphism of rings a one to one order preserving correspondence is established between the fuzzy ideals of r and those of r which are constant on the kernel of f this generalizes the correspondence theorem of non fuzzy ideals

characterisation of fuzzy semiprime ideals of the ring of integers z abstract the aim of the paper is to characterise fuzzy semiprime ideals of the ring of integers z

length functions and fuzzy groups fuzzy sets were introduced by zadeh 7 in 1965 and fuzzy groups by rosenfeld 4 in 1971 fuzzy groups were also considered by anthony and sherwood i in 1979 and in 1981 the theory was developed by das 2 as in the paper of das 2 we also show how a fuzzy subgroup of a group g is determined by a chain of subgroups of g however we wish to point out that fuzzy subgroups are constructed in a way which is analogous to that of constructing certain length functions of g wilkens s 61 thus in section 3 we consider the theory of length functions and we show the connection between certain length functions and fuzzy subgroups of a group in section 4 we apply the structural results of section 3 on finite solvable groups and we gain a generalization of a theorem of das 2 our notation is standard however we use the symbol e to denote the identity element of a group g and i denotes a real number we start with a preliminary section where we briefly analyse the definition of a fuzzy subgroup given by rosenfeld 4 naturally we use this definition of a fuzzy subgroup throughout the paper

fuzzy semiprimary ideals of rings abstract the concept of fuzzy ideals is extended by introducing fuzzy semiprimary ideals in rings this class of fuzzy ideals generalizes the class of fuzzy semiprimary ideals it is shown that there do exist fuzzy ideals which are fuzzy semiprimary but not fuzzy primary a study of i the level ideals of a fuzzy semiprimary ideal ii the characteristic function of a semiprimary ideal iii the zero divisors in the ring of all fuzzy cosets of a fuzzy semiprimary ideal and iv the algebraic nature of direct and inverse images of fuzzy semiprimary ideals under homomorphisms is carried out

a characterization of fuzzy subgroups abstract an ordinary subgroup of a group g is 1 a subset of g 2 closed under the group operation in a fuzzy subgroup it is precisely these two notions that lose their deterministic character a fuzzy subgroup of a group g associates with each group element a number the larger the number the more certainly that element belongs to the fuzzy subgroup the closure property is captured by the inequality x y t x y in a rosenfeld s original definition t was the function minimum however any t norm t provides a meaningful generalization of the closure property two classes of fuzzy subgroups are investigated the fuzzy subgroups in one class are subgroup generated those in the other are function generated each fuzzy subgroup in these classes satisfies the above inequality with t given by t a b max a b 1 0 while the two classes look different each fuzzy subgroup in either is isomorphic to one in the other it is shown that a fuzzy subgroup satisfies the above inequality with t minimum if and only if it is subgroup generated of a very special type finally these notions are applied to some abstract pattern recognition problems

local times of fractional brownian sheets let b0h b0h t t i mathbb r n be a real valued fractional brownian sheet consider the n d gaussian random field bh defined by bh t bh1 t bhd t t i mathbb r n where bh1 bhd are independent copies of b0h in this paper the existence and joint continuity of the local times of bh are established

on radicals of fuzzy submodules and primary fuzzy submodules we define in this paper the concepts of the radical of fuzzy submodules and the primary fuzzy submodules and prove some of their properties

fuzzy prime ideals of a ring abstract this paper characterizes all fuzzy prime ideals p of an arbitrary ring r we show that a nonconstant fuzzy ideal p of r is prime if and only if p0 x r p x p 0 is a prime ideal of r p is two valued and p 0 1 examples are given showing that p0 is a prime ideal is not sufficient for p to be a fuzzy prime ideal and that p0 may be a prime ideal of r with the image of p being of arbitrary finite cardinality or being countably infinite

approximation du temps local des surfaces gaussiennes letx be a centered stationary gaussian stochastic process with ad dimensional parameter d 2 f its spectral measure int limits r d x 2 f dx infty x denotes the euclidean norm ofx we consider regularizations of the trajectories ofx by means of convolutions of the formxe t e x t where e stands for an approximation of unity as e tends to zero satisfying certain regularity conditions

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

isomorphism theorems and fuzzy k ideals of k semirings we define and study the fuzzy maximal k ideal of a k semiring also we characterize the quotient k semiring r a of a k semiring r by a fuzzy maximal k ideal a and we have some isomorphism theorems in commutative k semirings and further we have some properties of the quotient k semiring r a of all cosets of a fuzzy semiprimary semiprime primary prime k ideal a in a commutative k semiring r

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

mixed least squares finite element models for static and free vibration analysis of laminated composite plates abstract new mixed least squares finite element models are developed for static and free vibration analysis of laminated composite plates both models consider the first order shear deformation theory with generalized displacements and stress resultants as independent variables using equal and high order c 0 basis functions the mixed least squares formulation is a useful alternative to mixed weak form models as it develops into an unconstrained minimization variational problem and thereby allows the finite element approximating spaces to be chosen independently ultimately the model for static analysis yields a symmetric positive definite system of linear equations and the latest innovative model for free vibration analysis yields a symmetric quadratic eigenvalue problem the predictive capabilities of the proposed models are assessed by comparison with analytical solutions considering selected examples of both static and free vibration analysis of rectangular laminated composite plates with different boundary conditions and a range of side to thickness ratios from 10 to 500 in particular these mixed least squares models using high order basis functions are shown to be insensitive to shear locking

fuzzy nil radicals and fuzzy semiprimary ideals of rings abstract an attempt is made to define a fuzzy semiprimary ideal by using the idea of the fuzzy nil radical of a fuzzy ideal the level ideals of a such a fuzzy ideal are examined and the ring of fuzzy cosets of such a fuzzy ideal is studied the algebraic nature of such fuzzy ideals under homomorphisms is also ascertained

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

on l fuzzy residual quotient modules and p primary submodules in this paper we give some suitable definitions of the operations of l fuzzy modules and ideals and we prove some fundamental results analoguous to the ordinary modules and ideals also a characterization of l fuzzy p primary submodules is presented

prime and primary l fuzzy ideals of l fuzzy rings the aim of this paper is to give a definition of prime l fuzzy ideal and primary l fuzzy ideal of a fuzzy ring and to give their first properties as well as the relationship of these concepts with the concept of l fuzzy radical

holder conditions for the local times and the hausdorff measure of the level sets of gaussian random fields let y t t n be a real valued strongly locally nondeterministic gaussian random field with stationary increments and y 0 0 consider the n d gaussian random field defined by where x 1 x d are independent copies of y the local and global holder conditions in the set variable for the local time of x t are established and the exact hausdorff measure of the level set x 1 x is evaluated

radicals of fuzzy ideals abstract there are several natural ways to fuzzify the concepts of prime ideal primary ideal the radical of an ideal and the primary representation of an ideal in a commutative ring in this paper we introduce some new approaches and compare them with known ones our main goal is to unify the various possible fuzzy primary representations of a fuzzy ideal to prepare the way for the study of fuzzy nonlinear systems of equations

on fuzzy rings abstract an internal description of the fuzzy subring fuzzy ideal generated by a finite fuzzy subset of a ring is provided also a fuzzy coset of a fuzzy ideal is defined and the set of all fuzzy cosets of a fuzzy ideal is given a ring structure a fuzzy semiprime ideal is also defined and some basic properties of this fuzzy ideal are studied

prime fuzzy ideals over noncommutative rings in this paper we introduce prime fuzzy ideals over a noncommutative ring this notion of primeness is equivalent to level cuts being crisp prime ideals it also generalizes the one provided by kumbhojkar and bapat in 1993 which lacks this equivalence in a noncommutative setting semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes this allows us to introduce the fuzzy prime radical and contribute to establish the basis of a fuzzy noncommutative ring theory

certain fuzzy ideals of rings redefined abstract an attempt is made to redefine fuzzy semiprimary fuzzy primary fuzzy prime and fuzzy maximal ideals of rings these fuzzy ideals are characterized by their level ideals fuzzy analogues of various results concerning semiprimary primary prime and maximal ideals are obtained the concept of a fuzzy nil radical of a fuzzy ideal is also formulated and discussed

prime l fuzzy ideals and primary l fuzzy ideals abstract in this paper the concepts of a primary l fuzzy ideal and a prime l fuzzy ideal and p primary are introduced and some fundamental propositions proved in particular a structural theorem for a primary l fuzzy ideal belonging to a prime l fuzzy ideal is given

a characterization of l fuzzy prime ideals abstract in this paper the concepts of a l fuzzy prime and a l fuzzy completely prime ideal are given and some fundamental lemmas are proved in particular bijections among some of the l fuzzy prime ideals of two homomorphic rings are constructed also a characterization of a l fuzzy prime ideal of a ring is given

local examination of fuzzy intersection equations abstract we extend the primary representation theory for a fuzzy ideal of a commutative ring with identity in order to apply primary representation theory to a local examination of fuzzy intersection equations we show that a system of fuzzy intersection equations can be examined locally to obtain the general solution to the crisp part of the system

on prime and primary fuzzy ideals and their radicals abstract the merits and demerits of various definitions of prime and primary fuzzy ideals are discussed and new definitions are suggested it is shown that the new definitions are more satisfactory the nil radical is defined as against the prime radical of a fuzzy ideal some theorems regarding the nil radical are proved it is shown that the two radicals coincide when the grade membership lattice is totally ordered

radicals of tl ideals in this paper we first introduce several different definitions of radicals of tl ideals in a commutative ring with identity and study their basic properties then discuss several kinds of primary tl ideals where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

not so fuzzy fuzzy ideals abstract a characterization of rings which are both artinian and noetherian is obtained they are proved to be the rings whose fuzzy ideals assume only finitely many distinct values prime fuzzy ideals have been defined and conditions have been obtained under which they have only two distinct values

primary tl submodules and p primary tl submodules abstract in this paper we introduce the concepts of primary tl submodules and p primary tl submodules of m where m is a module i e left module over a given commutative ring with identity and t an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l we also give complete characterization of primary tl submodules and study the primary decomposition of tl submodules

a note on l fuzzy primary and semiprime ideals abstract in this note we introduce a definition for l fuzzy primary ideal in term of l fuzzy points and prove that this definition is equivalent to one of malik and mordeson 1991 where l 0 1 moreover l fuzzy semiprime ideals are introduced and some equivalent conditions of an l fuzzy semiprime ideal are proved

fuzzy subgroup some characterizations ii abstract we consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups given a finite chain of subgroups of a group g we prove that there exists a fuzzy subgroup of g whose level subgroups are exactly the subgroups of this chain as a corollary we obtain an interpretation of the number of chains of subgroups of a group g in which a subgroup h is a member when the group g is a supersolvable group some further interpretation of this number is obtained