migrative uninorms and nullnorms over t norms and t conorms in this paper the notions of migrative uninorms and nullnorms over a fixed t norm t and over a fixed t conorm s are introduced and studied all cases when the uninorm u lies in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations of u and t and for all possible combinations of u and s a similar study is done for nullnorms

multilinear calderon zygmund theory abstract a systematic treatment of multilinear calderon zygmund operators is presented the theory developed includes strong type and endpoint weak type estimates interpolation a multilinear t 1 theorem and a variety of results regarding multilinear multiplier operators

migrative t norms with respect to continuous ordinal sums abstract in this paper we study and characterize continuous migrative t norms t with respect to a continuous t norm t0 depending on whether is an idempotent element of t0 or not the t0 migrative property restricts the ordinal sum structure of t especially locally i e at or around it outside this well defined neighbourhood of the t norm t can be arbitrary under the only condition of keeping it continuous the investigation exploits the ordinal sum structure of continuous t norms and our former results related to the migrative property

on the migrativity of triangular subnorms the a t migrative triangular subnorms where t stands for the three prototype triangular norms namely the product the lukasiewicz t norm and the minimum are investigated in detail the paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous additive generator is a t migrative with respect to any of the three prototype triangular norms

a hormander type multiplier theorem for multilinear operators abstract in this paper we prove a hormander type multiplier theorem for multilinear operators as a corollary we can weaken the regularity assumption for multilinear fourier multipliers to assure the boundedness

migrativity property for uninorms the migrative uninorms over a fixed uninorm with different neutral elements are presented all cases when both uninorms lay in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations the solutions obtained generalize the results where both uninorms have the same neutral elements

on continuous triangular norms that are migrative in this paper we completely describe all continuous migrative triangular norms since the migrative property excludes both idempotent and nilpotent classes the characterization and construction is carried out by solving a functional equation for additive generators of strict t norms we also study cases when the construction results in a smooth generator

the migrativity equation for uninorms revisited abstract the migrativity equation with interesting applications in decision making and image processing has been extensively discussed involving different kinds of aggregation functions from t norms and t conorms to uninorms nullnorms and some generalizations of them in recent papers the already known results concerning the migrativity of two uninorms are based on the assumption that both uninorms belong to one of the most studied classes of uninorms in this paper we will explore the migrativity equation involving uninorms in a most general setting specifically we will study the migrativity between two uninorms in the cases when the second uninorm lies in any of the most studied classes of uninorms but the first one is any uninorm with no further assumptions we will show along the paper that many new solutions appear from this new point of view that were not included in the previous approaches

a generalization of the migrativity property of aggregation functions this paper brings a generalization of the migrativity property of aggregation functions suggested in earlier work of some of the present authors by imposing the a migrativity property of durante and sarkoci for all values of a instead of a single one replacing the algebraic product by an arbitrary aggregation function b naturally leads to the properties of a b migrativity and b migrativity this generalization establishes a link between migrativity and a particular case of aczel s general associativity equation already considered by cutello and montero as a recursive formula for aggregation following a basic investigation emphasis is put on aggregation functions that can be represented in terms of an additive generator more specifically strict t norms strict t conorms and representable uninorms

on migrativity property for uninorms recently u 0 migrative uninorms u were introduced and discussed where u and u 0 are two uninorms with neutral element e in this paper we will further study u 2 migrative uninorms u 1 where u 1 and u 2 are two uninorms with different neutral elements e 1 and e 2 respectively all cases when the uninorm u 1 and u 2 are in different families out of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations of u 1 and u 2

migrative uninorms and nullnorms over t norms and t conorms revisited abstract in 2015 mas et al investigated the migrativity of uninorms and nullnorms over any fixed t norm and t conorm first they introduced the concept of migrative uninorm over any fixed t norm in addition they showed equivalent characterizations of the migrativity equation when the uninorm belongs to one certain class e g u min u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 and then they gave the notion of migrative uninorms over any fixed t conorm and proposed the migrativity equation using an analogous method finally they discussed the migrativity of nullnorms over any fixed t norm and t conorm and obtained equivalent characterizations of the related migrativity equations respectively however they did not discuss the migrativity property of a conjunctive resp disjunctive uninorm non locally internal on the boundary over any fixed t norm resp t conorm and the migrativity property of a conjunctive resp disjunctive uninorm locally internal on the boundary over any continuous t norm resp t conorm to fill the gap in this paper we explore some new results on the migrativity property of a conjunctive resp disjunctive uninorm over any fixed t norm resp t conorm and give some new characterizations of the migrativity property of nullnorms over any fixed t norm and t conorm respectively

supermigrativity of aggregation functions abstract a functional inequality called supermigrativity was recently introduced for bivariate semi copulas and applied in various problems arising in the study of aging properties of stochastic systems here we revisit this notion and extend it to the case of aggregation functions in higher dimensions in particular we show how supermigrativity can be expressed via monotonicity of a function with respect to logarithmic majorization ordering of real vectors various alternative characterizations of supermigrativity are illustrated together with some of its weaker versions several examples show similarities and differences between the bivariate and the general case

generalizing the migrativity of continuous t norms this paper generalizes the migrativity of triangular norms t norms for short precisely we find those continuous t norms t which satisfy t l 1x l 2y email protected 3t x y where l email protected 0 1 i 1 2 3 are given it is worth pointing out that this paper provides a new characterization of the product t norm

supermigrative semi copulas and triangular norms a semi copula s 0 1 2 0 1 is called supermigrative if it is commutative and satisfies s ax y s x ay for all email protected 0 1 and for all x email protected 0 1 such that y

the hormander multiplier theorem ii the bilinear local l 2 case we use wavelets of tensor product type to obtain the boundedness of bilinear multiplier operators on mathbb r n times mathbb r n associated with hormander multipliers on mathbb r 2n with minimal smoothness we focus on the local l 2 case and we obtain boundedness under the minimal smoothness assumption of n 2 derivatives we also provide counterexamples to obtain necessary conditions for all sets of indices

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

bimigrativity of binary aggregation functions we introduce the notions of bimigrativity and total bimigrativity of an aggregation function w r t another aggregation function as a natural generalization of the notions of migrativity and bisymmetry we investigate the role of the presence of neutral or absorbing elements we also pay attention to the class of weighted quasi arithmetic means a well known class of bisymmetric aggregation functions

an extension of the migrative property for uninorms in this paper the notion of a migrative uninorms over a fixed uninorm u 0 with the same neutral element is introduced all uninorms u that are a migrative over a uninorm u 0 are studied all cases when u and u 0 have continuous underlying operations and belong to any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations

on the α migrativity of semicopulas quasi copulas and copulas in this paper we address the problem of a migrativity for a fixed a for semicopulas copulas and quasi copulas we introduce the concept of an a sum of semicopulas this new concept allows us to completely characterize a migrative semicopulas and copulas moreover a sums also provide a means to obtain a partial characterization of a migrative quasi copulas

a universal approach to vertex algebras abstract in this paper we characterize vertex algebras in the appropriate sense as algebras over a certain graded co operad we also discuss some applications and categorical ramifications of this characterization

on α β homogeneous copulas we introduce and characterize the family of a b homogeneous copulas and study some of its salient properties such as the greatest and the lowest copulas measures of association and the relationships with the a migrativity and invariant copulas

on the α migrativity of multivariate semi copulas in this paper we introduce and study the a migrative property for the class of multivariate semi copulas in particular a characterization of a migrative copulas is provided

real coextensions as a tool for constructing triangular norms we present in this paper a universal method of constructing left continuous triangular norms l c t norms the starting point is an arbitrary possibly finite totally ordered monoid fulfilling the conditions that are characteristic for l c t norms commutativity negativity and quanticity we show that under suitable conditions we can extend this structure by substituting each element for a real interval the process can be iterated and if the final structure obtained in this way is order isomorphic to a closed real interval its monoidal operation can up to isomorphism be identified with a l c t norm we specify the constituents needed for the construction in an explicit way we furthermore illustrate the method on the basis of a number of examples

migrativity property for uninorms and semi t operators in this paper the notions of migrative uninorms over semi t operators and migrative semi t operators over uninorms are introduced and investigated all solutions of the migrativity equations for all possible combinations of semi t operators and uninorms are characterized

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a note on the convex combinations of triangular norms we consider a property on binary operations which we call a migrativity and we use it to obtain t norms by means of convex combinations of two t norms one of them being discontinuous

the hormander multiplier theorem for multilinear operators in this paper we provide a version of the mikhlin hormander multiplier theorem for multilinear operators in the case where the target space is l p for pe 1 this extends a recent result of tomita 15 who proved an analogous result for p 1

some new results on the migrativity of uninorms over overlap and grouping functions abstract in 2018 qiao and hu 48 studied the migrativity of uninorms over overlap and grouping functions when the uninorm u belongs to one certain class e g u min u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 in addition they obtained some equivalent characterizations of them this paper will continue to consider the characterizations of this kind of migrativity equations by means of the ordinal sum of overlap and grouping functions we give the necessary and sufficient conditions for the solutions of the o migrativity equation when the uninorm u becomes a t norm or a conjunctive uninorm locally internal on the boundary and the g migrativity equation when the uninorm u becomes a t conorm or a disjunctive uninorm locally internal on the boundary respectively

an extension of the migrative property for triangular norms in this paper we extend the migrative property of triangular norms by allowing an arbitrary fixed t norm t 0 in the defining equation instead of the originally used product equivalent forms of this extended migrativity are also provided and proved two particular cases when t 0 is either the minimum or the lukasiewicz t norm are studied in these cases all continuous extended migrative t norms are characterized and represented the proofs are constructive which helps the reader to build up various families of extended migrative t norms

l 2 times l 2 rightarrow l 1 l2 l2 l1 boundedness criteria we obtain a sharp l 2 times l 2 rightarrow l 1 boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic dilations of a given function in terms of the l q integrability of this function precisely we show that boundedness holds if and only if q 4 we discuss applications of this result concerning bilinear rough singular integrals and bilinear dyadic spherical maximal functions our second result is an optimal l 2 times l 2 rightarrow l 1 boundedness criterion for bilinear operators associated with multipliers with l infty derivatives this result provides the main tool in the proof of the first theorem and is also manifested in terms of the l q integrability of the multiplier the optimal range is q 4 which in the absence of plancherel s identity on l 1 should be compared to q infty in the classical l 2 rightarrow l 2 boundedness for linear multiplier operators