on fuzzy spaces and fuzzy group theory abstract the concept of fuzzy space is introduced this concept corresponds to the concept of the universal set in the ordinary case the algebra of fuzzy spaces and fuzzy subspaces is studied using the concept of fuzzy space and fuzzy binary operation a new approach to study fuzzy group theory is given this approach can be considered as a generalization and reformulation of the rosenfeld theory of fuzzy subgroups therefore it is an active tool to develop the theory of fuzzy groups

generalized synchronization in linearly coupled time periodic systems abstract we consider the synchronization of a network of linearly coupled and not necessarily identical oscillators we present an approach to the existence of the synchronization manifold which is based on some results developed by r smith for the study of periodic solutions of odes our framework allows the study of a large class of systems and does not assume that they are small perturbations of linear systems moreover it provides a practical way to compute estimations on the parameters of the system for which generalized synchronization occurs additionally we give a new proof of the main result of r smith on invariant manifolds using wazewski s principle several examples of application are presented

inference of fuzzy relational tableaux from fuzzy exemplifications the paper describes a method for deriving fuzzy relational tableaux from fuzzy exemplifications in particular the work by thole zimmerman and zysno 4 is cited as they derive an operator for and using data derived from human subjects the method results in an operator or operators which is a maximal restriction of the operators implied by the data results showing the process are described and a value of and is derived using data presented in 4

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

fuzzy sylow subgroups abstract an attempt is made to define a fuzzy sylow p subgroup of a finite group some basic results regarding sylow p subgroups are extended to the fuzzy setting in particular fuzzy versions of sylow s theorems are obtained

on t fuzzy subfield and t fuzzy vector subspaces abstract in this paper we improve the definition of t fuzzy subfield and observe some of its properties the concept of t fuzzy vector subspaces of a t fuzzy subfield of a field will also be investigated and we further introduce the concept of t fuzzy subalgebra

join reducibility of fuzzy subgroups abstract we show that the lattice of all normal fuzzy subgroups of a group g is a sublattice of the lattice of all fuzzy subgroups of g and discuss join ir reductibility of fuzzy subgroups and representations of fuzzy subgroups as joins of join irreducible fuzzy subgroups

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

t fuzzy prime ideals abstract the purpose of this paper is to define study and characterize the t fuzzy prime ideals t fuzzy strongly prime ideals and t s fuzzy weakly prime ideals proving the inclusion relationships that are satisfied among them the t fuzzy comaximal ideals and fuzzy maximal ideals are also investigated

bounded domains of negative multipliers abstract a natural problem associated with coupling of non autonomous oscillators and synchronization is described it leads to a question about the boundedness of a domain associated with a derived quadratic form properties of real symmetric matrices with bounded domains are developed and unboundedness is translated into satisfiability of a certain lyapunov like matrix form eventually the real symmetric matrices associated with unbounded domains are explicitly characterized in terms of inertia explicit matrices a consequence of the characterization is that large irreducible matrices are likely to have bounded domains

fuzzy subgroups fuzzy ideals and fuzzy cosets some properties abstract as an application of fuzzy subgroups a necessary and sufficient condition for a p group to be cyclic is obtained a procedure to construct the fuzzy subgroup generated by a fuzzy subset of a group is provided also the effect of a homomorphism on the sum product intersection of two fuzzy ideals is studied some elementary properties of the ring fuzzy cosets of a fuzzy ideal are also obtained

fuzzy subgroups as union of two fuzzy subgroups abstract the problem of writing a fuzzy subgroup of a group g as a union of two fuzzy subgroups has been discussed by dixit et al in this paper an attempt has been made to study this problem further in a broader framework of nontrivial decomposition of a fuzzy subgroup thus something more than the settlement of the question of the possibility of having nonequivalent fuzzy subgroups in this union raised by the author at the end of the section 3 of their paper has been proved

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

fuzzy normal subgroups and fuzzy quotients abstract in case of groups a mormal subgroup n of a group g can be defined with three equivalent approaches namely i as a kernel of some group homomorphism ii as a subgroup commuting with every element of g and iii as the subgroup n closed with respect to conjugates of elements of n in case of generalizations of this concept to fuzzy sets the elementwise third approach is found more suitable and hence is widely adopted by many authors in this paper we further study this concept of fuzzy subgroups and introduce fuzzy quotients called fuzzy quotient groups for all 0 1 two different definitions of these fuzzy quotients have been given which are shown to lead to isomorphic structures we also study the direct products of fuzzy normal subgroups min product as per the terminology of sherwood 1983 and the problem of writing a fuzzy normal subgroups of a direct product of some groups as a direct product of certain fuzzy normal subgroups has been discussed in detail

generalized product of fuzzy subsets of a ring we define t intrinsic product of fuzzy subsets of an algebraic object more general than a ring and study some of its fundamental properties deep connection that exists between t intrinsic product and fuzzy subsets of a ring is brought to the surface the concepts of t fuzzy subring t fuzzy ideal and t fuzzy subgroup are redefined to include quite larger classes within their fold interconnection between these classes and t intrinsic product is studied in detail in the end we isolate different subclasses of the subsemigroup f r and reveal their ideal structure

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

the fuzzy normal subgroup using the concept of fuzzy spaces we define the fuzzy normal subgroup in a fuzzy group its relation with the classical fuzzy normal subgroup is studied

fuzzy partial groups abstract the fuzzification of partial monoids and partial groups has introduced in a little different way than that one usually found the notion of the t partial monoid on i has been investigated and is used to define different membership values for the partial identities which is consistent with the hall spirit of the fuzzification this is in fact the motivation of this paper examples have been given to get the generalization reasonable in fact the basic results of fuzzy groups and fuzzy monoids has been generalised

a sharp lower bound for the log canonical threshold in this note we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function varphi with an isolated singularity at 0 in an open subset of mathbb c n this threshold is defined as the supremum of constants c 0 such that e 2c varphi is integrable on a neighborhood of 0 we relate c varphi to the intermediate multiplicity numbers e j varphi defined as the lelong numbers of dd c varphi j at 0 so that in particular e 0 varphi 1 our main result is that c varphi geqslant sum j 0 n 1 e j varphi e j 1 varphi this inequality is shown to be sharp it simultaneously improves the classical result c varphi geqslant 1 e 1 varphi due to skoda as well as the lower estimate c varphi geqslant n e n varphi 1 n which has received crucial applications to birational geometry in recent years the proof consists in a reduction to the toric case i e singularities arising from monomial ideals

valuations and multiplier ideals this article is the third of a series of work on a new approach to the study of singularities of various objects in a local two dimensional setting our focus in the present paper is on multiplier ideals and singularity exponents in the discussion below we fix an equicharacteristic zero two dimensional regular local ring r m with algebraically closed residue field an important example is the ring r do o holomorphic germs at the origin in c2 in fj1 we introduced the space v consisting of all r u 00 valued valuations on r centered at m and normalized by m 1 this space is naturally a tree it is a union of uncountably many real segments patched together in such a way that v remains homotopic to a point it is also an r tree in the classical sense for a natural metric we hence call v the valuative tree it encodes in a natural way all possible blowups of r centered at m and therefore gives a way of measuring quite precisely singularities of different kinds of objects the points in v that are not ends form the subtree vqm of quasimonomial valuations these valuations which can alternatively be characterized as abhyankar valuations of rank 1 or as

valuative analysis of planar plurisubharmonic functions we show that valuations on the ring r of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions giving rise to generalized lelong numbers in the sense of demailly any plurisubharmonic function thus defines a real valued function on the set mathcal v of valuations on r and by way of a natural laplace operator defined in terms of the tree structure on mathcal v a positive measure on mathcal v this measure contains a great deal of information on the singularity at the origin under mild regularity assumptions it yields an exact formula for the mixed monge ampere mass of two plurisubharmonic functions as a consequence any generalized lelong number can be interpreted as an average of valuations using our machinery we also show that the singularity of any positive closed 1 1 current t can be attenuated in the following sense there exists a finite composition of blowups such that the pull back of t decomposes into two parts the first associated to a divisor with normal crossing support the second having small lelong numbers

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

on fuzzy subgroups and fuzzy ideals under triangular norms abstract in this communication we explicitly point out that the principal results of liu 1982 basically deduced from the definition of binary operation on the set f x of all fuzzy subsets of x also hold if one uses the weaker definition of product under triangular norm t fuzzy ideals with respect to the triangular norms are also defined

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

effectiveness of demailly s strong openness conjecture and related problems in this article stimulated by the effectiveness in berndtsson s solution of the openness conjecture and continuing our solution of demailly s strong openness conjecture we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result we explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier which is implicitly contained in guan and zhou 2014 arxiv 1401 7158 we also obtain optimal effectiveness of the conjectures of demailly kollar and jonsson mustat respectively

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

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

a solution of an l 2 extension problem with an optimal estimate and applications in this paper we prove an l 2 extension theorem with an optimal estimate in a precise way which implies optimal estimate versions of various well known l 2 extension theorems as applications we give proofs of a conjecture of suita on the equality condition in suita s conjecture the so called l conjecture and the extended suita conjecture as other applications we give armative answer to a question by ohsawa about limiting case for the extension operators between the weighted bergman spaces and we present a relation of our result to berndtsson s important result on log plurisubharmonicity of the bergman kernel

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

a new approach to fuzzy groupoids abstract we establish a new approach to fuzzy groupoids a concept of fuzzy binary operation is introduced in terms of the concepts of fuzzy cartesian product and fuzzy function introduced by the authors in a foregoing paper having defined a fuzzy binary operation the concepts of fuzzy groupoid subgroupoid homomorphism etc are introduced and investigated a theory of fuzzy groupoids is built up this approach is both intrinsic and more general than the well known current approach

characterization of multiplier ideal sheaves with weights of lelong number one abstract in this article we characterize plurisubharmonic functions of lelong number one at the origin such that the germ of the associated multiplier ideal sheaf is nontrivial in arbitrary complex dimension their singularity must be the sum of a germ of smooth divisor and of a plurisubharmonic function with zero lelong number we also present a new proof of the related well known integrability criterion due to skoda

generalized fuzzy quotient subgroups abstract in this paper we consider the fuzzy subgroup of a given group defined by generalized triangular norms and conorms introduced by yager 1986 the definitions of a anti fuzzy subgroup and a anti pseudo fuzzy subgroup are reviewed then a generalized fuzzy cayley theorem as well as a partial generalization of fuzzy lagrange theorem are given also a unified approach for studying fuzzy quotient subgroups is discussed some correspondence theorems for several kinds of fuzzy subgroups are proved and examples of generalized triangular norms conorms are given

on some product of fuzzy subgroups abstract a kind of product of fuzzy subsets subgroups of a group is defined analogously to the pointwise product of functions via a triangular norm t we call this product the t product some properties of the t product of fuzzy subgroups of a group are investigated in particular we are interested in the fuzzy subgroups of the internal direct product of subgroups of a group

a proof of demailly s strong openness conjecture in this article we solve the strong openness conjecture on the multiplier ideal sheaf associated to any plurisubharmonic function which was posed by demailly the multiplier ideal sheaf associated to a plurisubharmonic function which is an invariant of the singularities of the psh function plays an important role in several complex variables and complex geometry various properties about the multiplier ideal sheaves associated to plurisubharmonic functions have been discussed e g see 25 7 30 31 demailly s strong openness conjecture means that the strong openness property about the multiplier ideal sheaf holds in the present article we establish such a useful strong openness property on the multiplier ideal sheaf associated to any plurisubharmonic function i e demailly s strong openness conjecture is true 1 1 organization of the paper the paper is organized as follows in the present section we recall the statement of the strong openness conjecture posed by demailly and present the main result of the present paper a solution of the strong openness conjecture in section 2 we recall or give some preliminary lemmas used in the proof of the main result in section 3 we give the proof of the strong openness conjecture and present some consequences by combining the conjecture with some well known results

divisible and pure fuzzy subgroups abstract as a continuation to the study of fuzzy subgroups which was given by a rosenfeld s sessa p s das h sherwood and others we introduce the concepts of divisible and pure fuzzy subgroups and prove some of their properties

products of fuzzy subgroups fuzzy subgroups are different from ordinary subgroups in that one cannot tell with certainty which group elements belong and which do not of course this requires an appropriate modification of the closure property which takes the form of an inequality in this paper a study of products of fuzzy subgroups is begun some results are expected the product of fuzzy subgroups is a fuzzy subgroup products with the same but permuted factors are isomorphic and there is a natural isomorphism from any factor into the product functions called t norms are used to construct products of fuzzy subgroups different t norms yielding different products since a fuzzy subgroup must satisfy an inequality generalizing closure and the strength of that inequality is important some results relate the t norm used in forming the product to the strength of the ensuing inequality when can complicated fuzzy subgroups be expressed as products of simple ones this question is addressed for fuzzy subgroups of finite abelian groups

tl subrings and tl ideals part 2 generated tl ideals abstract in this paper we introduce and discuss the tl left right two sided ideal generated by an l subset t being an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l