distributivity equation in the class of 2 uninorms this paper is mainly devoted to solving the functional equation of distributivity between aggregation operators with 2 neutral element our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e g triangular norms conorms uninorms nullnorms and implications one of the recent generalizations covering both uninorms and nullnorms are 2 uninorms which form a class of commutative associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements in this work the distributivity of two binary operators from the class of 2 uninorms is considered in particular all possible solutions of the distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized

some results about nullnorms on bounded lattices abstract nullnorms as a generalization of the concepts of t norms and t conorms admit a zero element to be any element in a bounded lattice in this paper we discuss the characterization of idempotent nullnorms on bounded lattices and investigate some of the main properties of them we propose some new methods yielding nullnorms in particular idempotent nullnorms on bounded lattices with the fixed zero element under some additional constraints moreover some illustrative examples are presented to demonstrate the feasibility of the proposed methods

precise asymptotic of eigenvalues of resonant quasilinear systems in this work we study the sequence of variational eigenvalues of a system of resonant type involving p and q laplacians on rn with a coupling term depending on two parameters and satisfying p q 1 we show that the order of growth of the kth eigenvalue depends on k o k n

the distributive equations for idempotent uninorms and nullnorms the distributive equations only involving idempotent uninorms and nullnorms are investigated the following two cases are proved i as for a nullnorm with an idempotent uninorm having distributivity the necessary and sufficient conditions are given ii as for an idempotent uninorm with a nullnorm having distributivity the necessary and sufficient conditions are given also

construction of nullnorms on bounded lattices and an equivalence relation on nullnorms abstract in this study we present two methods for the construction of nullnorms on bounded lattices based on the existence of t norms as well as t conorms on an arbitrary bounded lattice l we demonstrate that these methods differ from the existing approaches mainly because of their more generalized structures an equivalence relation is also defined based on a class of nullnorms and some properties of this relation are examined

estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems we consider solutions to the nonlinear eigenvalue problem a x u ui xf x j o ing2 u o on dol u 7 0o where is a quasilinear strongly coupled second order elliptic system of partial differential equations and q c ru is a smooth bounded domain we obtain lower bounds for x in the case where f x u has linear growth and relations between x s2 and ess sup i i when f yx u has subor superlinear growth the estimates are based on integration by parts and application of certain sobolev inequalities we briefly discuss extensions to higher order systems

lower bounds for generalized eigenvalues of the quasilinear systems abstract in this paper we establish several new lyapunov type inequalities for two classes of one dimensional quasilinear elliptic systems of resonant type which generalize or improve all related existing ones then we use the lyapunov type inequalities obtained in this paper to derive a better lower bound for the generalized eigenvalues of the one dimensional quasilinear elliptic system with the dirichlet boundary conditions

the fredholm alternative at the first eigenvalue for the one dimensionalp laplacian abstract in this work we study the range of the operatoru u p 2 u 1 u p 2 u u 0 u t 0 p 1 we prove that all functionsh c1 0 t satisfying t0 h t sinp pt t dt 0 lie in the range but that ifp 2 andh 0 the solution set is bounded here sin pt t is a first eigenfunction associated to 1 we also show that in this case the associated energy functionalu 1 p t0 u p 1 p t0 u p t0 huis unbounded from below if 1 2 onw1 p0 0 t 1corresponds precisely to the best constant in thelp poincare inequality moreover we show that unlike the linear casep 2 forp 2 the range contains a nonempty open set inl 0 t

a combinatorial approach to nonlocality and contextuality so far most of the literature on quantum contextuality and the kochen specker theorem seems either to concern particular examples of contextuality or be considered as quantum logic here we develop a general formalism for contextuality scenarios based on the combinatorics of hypergraphs which significantly refines a similar recent approach by cabello severini and winter csw in contrast to csw we explicitly include the normalization of probabilities which gives us a much finer control over the various sets of probabilistic models like classical quantum and generalized probabilistic in particular our framework specializes to quantum nonlocality in the case of bell scenarios which arise very naturally from a certain product of contextuality scenarios due to foulis and randall in the spirit of csw we find close relationships to several graph invariants the recently proposed local orthogonality principle turns out to be a special case of a general principle for contextuality scenarios related to the shannon capacity of graphs our results imply that it is strictly dominated by a low level of the navascues pironio acin hierarchy of semidefinite programs which we also apply to contextuality scenarios

idempotent nullnorms on bounded lattices abstract nullnorms are generalizations of triangular norms and triangular conorms with a zero element to be an arbitrary point from a bounded lattice in this paper we study and discuss the existence of idempotent nullnorms on bounded lattices considering an arbitrary distributive bounded lattice l we show that there exists a unique idempotent nullnorm on l we prove that an idempotent nullnorm may not always exist on an arbitrary bounded lattice furthermore we propose a construction method to obtain idempotent nullnorms on a bounded lattice l with an additional constraint on a for the given zero element a l 0 1

two simple proofs of the kochen specker theorem a new proof of the kochen specker theorem uses 33 rays instead of 117 in the original proof if the number of dimensions is increased from 3 to 4 only 24 rays are needed

greechie diagrams nonexistence of measures in quantum logics and kochen specker type constructions we use greechie diagrams to construct finite orthomodular lattices realizable in the orthomodular lattice of subspaces in a three dimensional hilbert space such that the set of two valued states is not large i e full separating unital nonempty resp we discuss the number of elements of such orthomodular lattices of their sets of ortho generators and of their subsets that do not admit a large set of two valued states we show connections with other results of this type

on the generalized spectrum for second order elliptic systems description qualitative et quantitative detaillee du spectre generalise reel pour les systemes elliptiques du second ordre application de la theorie des perturbations lineaires des methodes de prolongement et de la caracterisation variationnelle des valeurs propres de courant hilbert

on the extension of nullnorms and uninorms to fuzzy truth values abstract in this work by applying zadeh s extension principle we extend type 1 proper nullnorms and proper uninorms to fuzzy truth values the definitions of type 2 nullnorms and uninorms are introduced we mainly discuss in which subalgebras of fuzzy truth values extended proper nullnorms and proper uninorms are type 2 nullnorms and uninorms respectively

a characterization of idempotent nullnorms nullnorms are generalization of triangular norms and conorms with a zero element anywhere in the unit interval nullnorms are built up from triangular norms and triangular conorms if nullnorm is idempotent then it is composed of a minimum and a maximum the idea of this paper is to find minimal assumptions on an operation in order to get an idempotent nullnorm

eigenvalues of the p laplacian in fractal strings with indefinite weights in this paper we study the spectral counting function of the weighted p laplacian in fractal strings where the weight is allowed to change sign we obtain error estimates related to the interior minkowski dimension of the boundary we also find the asymptotic behavior of eigenvalues

characterizing idempotent nullnorms on a special class of bounded lattices abstract nullnorms with a zero element being at any point of a bounded lattice are an important generalization of triangular norms and triangular conorms this paper obtains an equivalent characterization for the existence of idempotent nullnorms with the zero element a on any bounded lattice containing only two distinct elements incomparable with a furthermore some basic properties for the bounded lattice containing only two distinct elements incomparable with a are presented

the modularity condition for uninorms and t operators in this work we study the functional equation given by the modularity condition f x g y z g f x y z for all z x where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

representation of nullnorms on bounded lattices abstract recently nullnorms on bounded lattices have been frequently investigated by many researchers in this paper we give the full characterization for quite a general class of nullnorms on bounded lattices and represent them by their underlying t norms and t conorms an example is given to show the relationship between each block of the nullnorms we also fully determine the values of arbitrary nullnorms when only one of the two variables is comparable with the absorbing elements for the rest cases we give some necessary conditions

algebraic partial boolean algebras partial boolean algebras first studied by kochen and specker in the 1960s provide the structure for bell kochen specker theorems which deny the existence of non contextual hidden variable theories in this paper we study partial boolean algebras which are algebraic in the sense that their elements have coordinates in an algebraic number field several of these algebras have been discussed recently in a debate on the validity of bell kochen specker theorems in the context of finite precision measurements the main result of this paper is that every algebraic finitely generated partial boolean algebra b t is finite when the underlying space is three dimensional answering a question of kochen and showing that conway and kochen s infinite algebraic partial boolean algebra has minimum dimension this result contrasts the existence of an infinite non algebraic b t generated by eight elements in an abstract orthomodular lattice of height 3 we then initiate a study of higher dimensional algebraic partial boolean algebras first we describe a restriction on the determinants of the elements of b t that are generated by a given set t we then show that when the generating set t consists of the rays spanning the minimal vectors in a real irreducible root lattice b t is infinite just if that root lattice has an a5 sublattice finally we characterize the rays of b t when t consists of the rays spanning the minimal vectors of the root lattice e8

new construction of an ordinal sum of t norms and t conorms on bounded lattices abstract this paper introduces a new ordinal sum construction of t norms and t conorms on bounded lattices based on interior and closure operators the proposed method generalizes several known constructions and provides a simple tool to introduce new classes of t norms and t conorms

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

the distributivity condition for uninorms and t operators in this work we study the functional equation given by the distributivity condition f x g y z g f x y f x z for all x y z 0 1 where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

distributivity between uninorms and nullnorms recently the distributivity equation was investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms generally the assumption of associativity is not necessary in consideration of distributivity equation moreover if we omit commutativity assumption consideration of the left and right distributivity conditions is reasonable previous results about distributivity between uninorms and nullnorms can be obtained as simple corollaries

estimates for eigenvalues of quasilinear elliptic systems part ii abstract in this paper we find explicit lower bounds for dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p laplace equation also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value

kochen specker vectors some reference citations in the text of this paper are incorrect and should be amended as listed below the reference list is correct as published page 1579 line 5 23 34 38 39 should read 23 34 35 36 page 1579 line 9 40 should read 37 page 1580 line 8 31 33 35 should read 31 33 38 page 1580 line 14 36 should read 39 page 1580 line 36 36 should read 39 page 1580 line 38 37 should read 40 page 1580 line 42 38 should read 35 page 1581 line 3 of caption 33 35 should read 33 38 page 1583 line 12 41 should read 42 page 1587 line 9 39 should read 36 page 1587 line 11 39 should read 36 page 1587 line 18 38 39 should read 35 36 page 1587 line 37 39 should read 36 page 1589 line 18 39 46 47 should read 36 46 47 page 1590 line 2 39 should read 36 age 1590 line 3 39 should read 36

nullnorms on bounded lattices derived from t norms and t conorms abstract nullnorms with an annihilator a in any point of a bounded lattice are generalizations and unifications of t norms and t conorms this study continues to investigate the construction of nullnorms on bounded lattices we propose some methods to construct nullnorms derived from t norms and t conorms on bounded lattices where some sufficient and necessary conditions on theirs annihilator are required as a by product of these constructions idempotent nullnorms on bounded lattices are obtained further we provide some illustrative examples of the new classes of nullnorms idempotent nullnorms on bounded lattices

graph approach to quantum systems using a graph approach to quantum systems we show that descriptions of 3 dim kochen specker ks setups as well as descriptions of 3 dim spin systems by means of greechie diagrams a kind of lattice that we find in the literature are wrong correct lattices generated by mckay megill pavicic mmp hypergraphs and hilbert subspace equations are given to enable future exhaustive generation of 3 dim ks setups by means of our recently found stripping technique bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks orthogonal triples of elements up to 41 of them we obtain several new results on such lattices and hypergraphs in particular on properties such as superposition and orthoraguesian equations

new class of 4 dim kochen specker sets we find a new highly symmetrical and very numerous class millions of nonisomorphic sets of 4 dim kochen specker ks vector sets due to the nature of their geometrical symmetries they cannot be obtained from previously known ones we generate the sets from a single set of 60 orthogonal spin vectors and 75 of their tetrads which we obtained from the 600 cell by means of our newly developed stripping technique we also consider critical ks subsets and analyze their geometry the algorithms and programs for the generation of our ks sets are presented

uni nullnorms on bounded lattices abstract in this paper we study uni nullnorms with both neutral elements and zero elements on bounded lattices in order to illustrate the existence of uni nullnorms on bounded lattices we present two construction methods for obtaining such a uni nullnorm also we show two additional methods for the construction of idempotent nullnorms on bounded lattices which are generalizations of the one proposed by cayli and karacal furthermore we discuss the presence of idempotent uni nullnorms on bounded lattices and propose two construction methods to obtain an idempotent uni nullnorm on any bounded lattice

construction methods for idempotent nullnorms on bounded lattices abstract in this paper we discuss the presence of idempotent nullnorms on bounded lattices and investigate some properties of these operators we introduce two new methods for constructing idempotent nullnorms on bounded lattices for a zero element under a constraint that all elements incomparable with the zero element are comparable with each other in order to stress the role of this constraint satisfying that our constructions yield an idempotent nullnorm some illustrative examples are added

on coupled multiparameter nonlinear elliptic systems on considere le systeme de problemes non lineaires aux valeurs limites de dirichlet lu x f u x v x lv x g u x v x x domaine borne de r n l est un operateur aux derivees partielles lineaire fortement et uniformement elliptique et sont des parametres reels f g r 2 r des applications continues telles que f 0 0 0 g 0 0 on presente une analyse detaillee de l ensemble des solutions du point de vue de la theorie de la bifurcation a plusieurs parametres

lyapunov type inequalities for partial differential equations in this work we present a lyapunov inequality for linear and quasilinear elliptic differential operators in n dimensional domains we also consider singular and degenerate elliptic problems with ap coefficients involving the p laplace operator with zero dirichlet boundary condition as an application of the inequalities obtained we derive lower bounds for the first eigenvalue of the p laplacian and compare them with the usual ones in the literature

the influence of elasticity on analysis modern developments on examine plusieurs domaines de l analyse auxquels l elasticite a apporte une contribution importante questions de connectivite de la theorie globale des bifurcations particularites de l analyse non lineaire calcul des variations convergence faible inegalites variationnelles autres contributions

nullnorms on bounded lattices nullnorms are generalization of triangular norms and triangular conorms with a zero element in the interior of the unit interval in this paper we generalize nullnorms to an arbitrary bounded lattices we show the existence of nullnorms with zero element a for arbitrary element a l 0 1 using the fact that some t norms and t conorms on an arbitrary fixed bounded lattice l always exist as a by product we give a method of constructing nullnorms using this method we obtain also the smallest nullnorm and the greatest nullnorm with given zero element a some other construction methods for nullnorms are also added

answering an open problem on t norms for type 2 fuzzy sets abstract this paper proves that a binary operation on 0 1 ensuring that the binary operation is a t norm or is a t conorm is a t norm where and are special convolution operations defined by f g x sup f y g z y z x f g x sup f y g z y z x for any f g map 0 1 0 1 where and are a continuous t norm and a continuous t conorm on 0 1 answering negatively an open problem posed in 8 besides some characteristics of t norm and t conorm are obtained in terms of the binary operations and

distributivity between semi t operators and semi nullnorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this paper we describe the solutions of distributivity between semi t operators and semi nullnorms previous results about distributivity between nullnorms can be obtained as simple corollaries

infinitely distributive t norms on complete lattices and pseudo complements in this paper we have introduced the concepts of t prime element t prime radical element and t semi prime element and have studied their properties we have investigated the construction methods of new infinitely distributive t norms from given infinitely distributive t norms by means of t prime elements and pseudo complements if every element of l is t prime radical element then we show that l is a complete brouwerian lattice and email protected if l is an algebraic lattice t is a t norm on l and every compact element of l is idempotent then we obtain that email protected we show that l r is a complete lattice and that the restriction of t to l r is an infinitely distributive t norm on l r when t is an infinitely distributive t norm on l and 0 is a t prime we present infinitely distributive t norms on a complete sublattice l and study their properties