particle lattices and fuzzy particle lattices abstract this paper introduces several new concepts a particle in a lattice which is a generalization of an atom in a distributive lattice by weakening the minimality property of atom a particle lattice which is a generalization of distributive complete atomic lattices by replacing atoms by particles a fuzzy particle lattice a particle lattice with an order reversing involution a particulate boolean algebra a fuzzy particle lattice whose involution is a complementation operator and other related concepts points fuzzy points boundary points and boundary quasi points the paper establishes representation theorems for fomse of these concepts establishes connections between others and some well established lattice theoretic concepts and provides some elementary properties for some of the new concepts

pairs of positive solutions for singular p laplacian equations with a p superlinear potential abstract we consider a singular parametric elliptic equation driven by the p laplacian and with a p superlinear potential which does not satisfy the ambrosetti rabinowitz condition using variational arguments combined with truncation techniques and the method of upper and lower solutions we show that there exists a 0 such that if the parameter is in 0 then the problem has two ordered smooth positive strong solutions

an exact estimate result for singular p laplacian equations with sign changing potential abstract in this paper we study the multiplicity of positive solutions for a singular p laplacian problem with sign changing potential by the nehari method and some analysis techniques we obtain two positive solutions and point out one of the two positive solutions is a ground state solution moreover we provide an exact estimate to ensure the singular p laplacian problem has two positive solutions

independent elements integrally closed ideals and quasi unmixedness abstract let i a denote the integral closure of an ideal i in a noetherian ring a then it is shown that sup a i the maximum number of elements which are i n a independent as n exists and is equal to min height i a p z z p is a prime divisor of i n a for all large n and z is a minimal prime ideal in the completion a p of a p from this it follows that a is locally quasi unmixed if and only if sup a i height i for all ideals i in a

sub supersolution method for a quasilinear elliptic problem involving the 1 laplacian operator and a gradient term abstract in this work we study a quasilinear elliptic problem involving the 1 laplacian operator and a gradient term the problem requires the definition of a suitable sense of solution which allows us to show the existence of a solution in b v having no jump part despite the lack of regularity of the solutions we develop a sub supersolution approach together with a thorough analysis of the distributional derivative of the functions in b v

combined effects of singular and sublinear nonlinearities in some elliptic problems abstract we consider a parametric singular dirichlet equation with the singular term u appearing in the left hand side we establish the existence and nonexistence of positive solutions as the parameter 0 and the exponent 0 of the singularity vary in particular we show that for all 0 and all 1 the problem has no positive solution our approach combines truncation arguments with the method of upper and lower solutions

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

multiple solutions for a class of singular quasilinear problems abstract in this paper we use sub supersolution and minimax methods to show the existence and multiplicity of solutions for the following class of singular quasilinear problems u u 2 u a x u h x u in u 0 in u 0 on where is a bounded smooth domain of r n n 3 the function a x is nonnegative 0 is a constant and the nonlinearity h x u is continuous in our first result the nonlinearity h has an arbitrary polynomial growth and we obtain the existence of a solution for the problem via sub supersolution method for the second result h has subcritical growth and we show the existence of a second solution by applying the mountain pass theorem

monoidal extensions of a locally quasi unmixed ufd abstract let r be a locally quasi unmixed domain a b 1 b n an asymptotic sequence in r i a b 1 b n r and s r b 1 a b n a r i a the monoidal transform of r with respect to i it is shown that s is a locally quasi unmixed domain a b 1 a b n a is an asymptotic sequence in s and there is a one to one correspondence between the asymptotic primes a i of i and the asymptotic primes a a s of a s i s moreover if a b 1 b n is an r sequence this extends to a one to one correspondence between ass r r i and ass s s a s in the case that r is a unique factorization domain the height one prime ideals of s are examined to determine how far s is from being a ufd a complete description is given of which height one prime ideals p of s are principal or have a principal primary ideal in the case that p r has height 1 if the prime divisors of a satisfy a mild condition a similar description is given in the case that p r has height 1 these are applied to give similar results for the rees ring r 1 t i t where t is an indeterminate

some results on fuzzy supratopological spaces abstract in this note we study some results on the concepts of supracompactness and supracompactness in a fuzzy supratopological space we introduce the notions of hausdorffnessand lindelofness in a fuzzy supratopological space and characterize their properties interms of supracompactness we also introduce and study the concept of fuzzy supra regular space

on the kernel of a monadic transformation abstract let j b0 b1 bh a be an ideal in a noetherian ring a such that b0 is nonnilpotent and let b a x1 xh then a complete description of the asymptotic essential and quintessential prime divisors of k b0x1 b1 b0xh bh b is given and a more detailed description of these prime divisors of k and of ker b a b 1 b 0 b h b 0 is given when b0 b1 bh are an asymptotic essential or a sequence also it is shown that there exists a unique essential prime divisor of k if and only if b0 b1 bh are an essential sequence and a has exactly one prime divisor of zero

independent elements and asymptotic sequences abstract some properties of a frequently used ring homomorphism are determined and then used to characterize asymptotic sequences in a noetherian ring a then it is shown that elements b1 bh in the jacobson radical of a are an asymptotic sequence if and only if b1n bhn are b1 bh na a independent for all n 1

on fuzzy t1 topological spaces on etudie diverses relations entre les differentes definitions des espaces topologiques t 1 flous

combined effects of singular and superlinear nonlinearities in some singular boundary value problems abstract this paper deals with a class of singular semilinear elliptic dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results

higher separation axioms in bifuzzy topological spaces abstract higher separation axioms for bifuzzy topological spaces namely p ti p tiw p regular and p normal i 2 2 1 2 have been defined relation between these axioms have been derived and some related results in this area have been proved

on inductive dimensions for fuzzy topological spaces an approach to the dimension theory for fuzzy topological spaces is being developed the appropriate context for this theory is not the category cft of chang fuzzy topological spaces or some of its modifications but the category hut introduced in the paper this category is a slight extension of the category h of hutton fuzzy topological spaces hutton 1980 the frames of this category allow us to make exposition simple and uniform and on the other hand to make it applicable in quite a general setting

bases of ideals and rees valuation rings let i be a regular proper ideal in a noetherian ring r we prove that there exists a simple free integral extension ring a of r such that the ideal ia has a rees good basis that is a basis c1 cg such that ciw iw for i 1 g and for all rees valuation rings w of ia moreover a may be constructed so that i ia and i have the same rees integers with possibly different cardinalities and ii ap is unramified over rp r for each asymptotic prime divisor p of ia indeed if h is a regular ideal in r such that each asymptotic prime divisor of h is contained in an asymptotic prime divisor of i then ii holds for ha if card reesh card reesi we prove that i also holds for ha and h if i b1 bg r and b1 bg is an asymptotic sequence we prove that b1 bg is a rees good basis of i

the second order expansion of solutions to a singular dirichlet boundary value problem abstract in this paper we mainly study the second order expansion of classical solutions in a neighborhood of to the singular dirichlet problem u b x g u a x f u u 0 x u 0 where is a bounded domain with smooth boundary in r n 0 the weight functions b a c loc are positive in and both may be vanishing or be singular on the boundary the function g c 1 0 0 satisfies lim t 0 g t and f c 0 0 we show that the nonlinear term a x f u does not affect the second order expansion of solutions in a neighborhood of to the problem for some kinds of functions b and a

on a singular nonlinear semilinear elliptic problem where k x c2 b v9 a p 0 1 and l is a real parameter such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts nonnewtonian fluids and also the theory of heat conduction in electrically conducting materials see 3 5 8 9 for a detailed discussion obviously 1 1 cannot have a solution u c2 v9 if k x is not vanishing near v however under various appropriate assumptions on k x we will obtain classical solutions of 1 1 for l belonging to a certain range and we will also obtain some uniqueness criteria here a classical solution is a solution u of 1 1 which belongs to c2 v mc v9 with u 0 in v we also study the boundary behaviour of solutions of 1 1 and we will show that the solution u of 1 1 lies in a certain holder class the special case when k x is negative and l 0 has been studied by several authors the existence and uniqueness of the solution were established by crandall rabinowitz and tartar 6 del pino 7 gomes 10 and lazer and mckenna

critical points and positive solutions of singular elliptic boundary value problems usually we do not think there is variational structure for singular elliptic boundary value problems so it cannot be considered by using critical points theory in this paper we use critical theory on certain convex closed sets to solve positive solutions for singular elliptic boundary value problems especially use the ordinary differential equation theory of banach spaces to obtain new results on the existence of multiple positive solutions the method is useful for other singular problems

fuzzy hausdorff topological spaces abstract we introduce the notion of a fuzzy hausdorff topological space and make a few observations to establish the appropriateness of this notion

fuzzy separation axioms and fuzzy continuity in fuzzy bitopological spaces abstract let x 1 2 be a bitopological space and i i 1 2 be the set of all lower semi continuous functions defined from x into the closed unit interval 0 1 in this paper we have succeeded in showing goodness of extension of separation axioms for fuzzy bitopological spaces namely we prove the space x 1 2 is p t i p t iw p regular and p normal iff the fuzzy bitopological space x 1 2 is p t i p t iw p regular and p normal

asymptotic sequences and rees rings abstract let b1 bs be an asymptotic sequence over an ideal i in a noetherian ring r and let bi b1 bi r then it is shown that certain sequences closely related to these elements are asymptotic sequences over r r bi over ti r r i and over u r r i where r r j is the rees ring of r with respect to the ideal j these results then imply that certain other sequences are asymptotic sequences over the corresponding ideals in the associated graded rings and in the monadic transformation rings as an application of the results it is shown that if r is local then each permutation of b1 bs is an asymptotic sequence over i and that b1 bs are an asymptotic sequence in r

existence theorems for the one dimensional singular p laplacian equation with sign changing nonlinearities in this paper general existence theorems are presented for the singular equation f p y f t y 0 y 0 y 1 0 throughout our nonlinearity is allowed to change sign

on the asymptotic sequences over an ideal abstract let i be an ideal of a noetherian ring r ratliff has shown that very many known results concerning r sequences and classical grade have a valid analogue for asymptotic sequences and asymptotic grade as a generalization of the concepts of asymptotic sequences and asymptotic grade we introduce the concepts of asymptotic i sequences and asymptotic i grade it is shown that they play a role analogous to asymptotic sequences and asymptotic grade

a comparison of some hausdorff notions in fuzzy topological spaces abstract several different notions of the hausdorff separation property for fuzzy topological spaces have appeared in the literature this paper is a study of the relationships between 12 of these concepts

separation axioms for fuzzy spaces abstract using the concepts of fuzzy points as introduced by wong 15 and of belonging to as introduced by r srivastava s n lal and a k srivastava 13 we introduce several notions of fuzzy separation axioms and examine their productivity relations between these axioms have been observed we also introduce four types of separated fuzzy sets and clarify some relations between them

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

on singular semilinear elliptic equations abstract for the semilinear elliptic equation u p x u 0 x r n n 3 0 we show via the barrier method the existence of a positive entire solution behaving like x 2 n near

classical and weak solutions of a singular semilinear elliptic problem the singular semilinear elliptic equation u p x f u 0 is shown to have a unique positive classical solution inrnthat decays to zero at ifp x is simply a nontrivial nonnegative continuous function satisfying 0 t max x t p x dt providedfis a non increasing continuously differentiable function on 0 it is also shown that the equation has a unique weakh10 solution on a bounded domain provided e0 f s ds andp x l2

fuzzy topological properties and hereditariness some known compactness notions and separation axioms already given in chang fuzzy topological spaces are extended to a more general context of categories where i topological spaces on arbitrary i sets are defined the invariance under morphisms in these categories and the usual hereditary conditions of the considered topological properties in such a context are investigated

positive solutions of the p laplace equation with singular nonlinearity abstract for a given bounded domain in r n with c 1 boundary for some 0 1 and a possibly singular nonlinearity f on 0 we give sufficient conditions on f so that the p laplace equation p u f x u admits a solution u w 0 1 p on the basis of a comparison principle we will give a sufficient condition under which such a problem admits a unique solution

a set of new separation axioms in l fuzzy topological spaces in this paper a set of new separation axioms in l fuzzy topological spaces are defined and studied we give several characterizations of these separation axioms and discuss certain relationships among them moreover some of their basic properties are also examined

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

existence and uniqueness of solutions for the lane emden and fowler type problem this paper deals with the existence and uniqueness of a positive solution to the semilinear elliptic equation of the lane emden and fowler type

the existence of three positive solutions of a singular p laplacian problem abstract we establish the existence of three positive solutions of the p laplacian problem which involves a singular nonlinearity three solutions are obtained by using the cutoff argument and the three critical points theorem proved by ricceri 2000 in 15 and bonanno 2003 in 12 provided the nonlinear term is a p 1 sublinear growth at infinity

on the goodness of some types of fuzzy paracompactness abstract we introduce in fuzzy topological spaces definitions of paracompactness almost paracompactness and nearly paracompactness all of which turn out to be good extensions of their classical topological counterparts fuzzy semi paracompact para s closed weakly compact and rs paracompact spaces are treated to a similar approach

existence and multiplicity of positive solutions for singular quasilinear problems in this work we combine perturbation arguments and variational methods to study the existence and multiplicity of positive solutions for a class of singular p laplacian problems in the first two theorems we prove the existence of solutions in the sense of distributions by strengthening the hypotheses in the third and last result we establish the existence of two ordered positive weak solutions

on a topological model for the category of fuzzy topological spaces i we study global properties of fuzzy topological spaces which depend only on open sets fuzzy continuous functions and the relations we obtain many known theorems as purely topological theorems

a singular semilinear problem with dependence on the gradient abstract in the present paper we study the problem of finding classical and weak solutions for a semilinear elliptic equation involving a singular term and a nonlinearity depending on the gradient the approach we follow based on a suitable combination of sub supersolutions techniques and fixed point theory is not quite the same in the two cases and requires different kind of assumptions