from real affine geometry to complex geometry we construct from a real ane manifold with singularities a tropical manifold a degeneration of calabi yau manifolds this solves a fundamental problem in mirror symmetry furthermore a striking feature of our approach is that it yields an explicit and canonical order by order description of the degeneration via families of tropical trees this gives complete control of the b model side of mirror symmetry in terms of tropical geometry for example we expect that our deformation parameter is a canonical coordinate and expect period calculations to be expressible in terms of tropical curves we anticipate this will lead to a proof of mirror symmetry via tropical methods

conditions imposed by tacnodes and cusps the study of linear systems of algebraic plane curves with fixed imposed singularities is a classical subject which has recently experienced important progress the horace method introduced by a hirschowitz has been successfully exploited to prove many h1 vanishing theorems even in higher dimension other specialization techniques which include degenerations of the plane are due to z ran and c ciliberto and r miranda g m greuel c lossen and e shustin use a local specialization procedure together with the horace method to give the first asymptotically proper general existence criterion for singular curves of low degree in this paper we develop a specialization method which allows us to compute the dimension of several linear systems as well as to substantially improve the bounds given by greuel lossen and shustin for curves with tacnodes and cusps

on the cohomology of a simple normal crossings divisor abstract we establish a formula which decomposes the cohomologies of various sheaves on a simple normal crossings divisor snc d in terms of the simplicial cohomologies of the dual complex d with coefficients in a presheaf of vector spaces this presheaf consists precisely of the corresponding cohomology data on the components of d and on their intersections we use this formula to give a hodge decomposition for snc divisors and investigate the toric setting we also conjecture the existence of such a formula for effective non reduced divisors with snc support and show that this would imply the vanishing of the higher simplicial cohomologies of the dual complex associated to a resolution of an isolated rational singularity

admissible mimo singular observation lqg designs abstract the widely known lqg design method for linear time invariant mimo systems may lead under certain circumstances to closed loop systems with improper sensitivity matrices such systems have no stability robustness and we refer to them as inadmissible ones this phenomenon is analyzed in the paper necessary and sufficient conditions guaranteeing admissibility of lqg designs both in the frequency and the time domains are presented and proven these conditions are based on the available information in the statement of the problem thus enabling a priori detection of inadmissibility in optimal systems the key tool in the analysis is the extension of results from polynomial matrices to rational matrices a suboptimal design aimed directly at avoiding inadmissibility and which involves the minimum necessary changes in the lqg cost function is suggested illustrative examples are used to demonstrate the main results

on the extendability of projective surfaces and a genus bound for enriques fano threefolds we introduce a technique based on gaussian maps to study whether a surface can lie on a threefold as a very ample divisor with given normal bundle we give applications among which one to surfaces of general type and another to enriques surfaces in particular we prove the genus bound g 17 for enriquesfano threefolds moreover we find a new enriques fano threefold of genus 9 whose normalization has canonical but not terminal singularities and does not admit q smoothings

a note on the ordinal sum theorem and its consequence for the construction of triangular norms in this paper the well known ordinal sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms t norms among them one can find several new families of left continuous t norms too

a fock space approach to severi degrees the classical severi degree counts the number of algebraic curves of fixed genus and class passing through points in a surface we express the severi degrees of p1 p1 as matrix elements of the exponential of a single operator ms on fock space the formalism puts severi degrees on a similar footing as the more developed study of hurwitz numbers of coverings of curves the pure genus 1 invariants of the product e p1 with e an elliptic curve are solved via an exact formula for the eigenvalues of ms to initial order the severi degrees of p2 are also determined by ms via the 1 d 1 d2 disk multiple cover formula for calabi yau threefold geometries

on properties of uninorms with underlying t norm and t conorm given as ordinal sums uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory this paper presents some properties of uninorm like operations for which the underlying operations are given by ordinal sums if the underlying operations of a uninorm are given by ordinal sums then the cartesian product of the union of two arbitrary intervals one in 0 e and the other in e 1 where e is the neutral element of the uninorm is a set closed under the uninorm when transposing such a cartesian product to the unit square one obtains a uninorm like operation as a result we have described the uninorm like operations for which the underlying operations are basic pseudo t norms and pseudo t conorms and one of them is idempotent

on monodromies of a degeneration of irreducible symplectic kahler manifolds we study the monodromy operators on the betti cohomologies associated to a good degeneration of irreducible symplectic manifold and we show that the unipotency of the monodromy operator on the middle cohomology is at least the half of the dimension this implies that the mildest singular fiber of a good degeneration with non trivial monodromy of irreducible symplectic manifolds is quite different from the generic degeneration of abelian varieties or calabi yau manifolds

enumerative geometry of singular plane curves general points in the plane the answer is easy for 6 1 namely 3 d l 2 but otherwise was to my knowledge unknown until now we are going to develop a recursive procedure for solving such problems to make the recursion possible it will be necessary to consider a generalization of independent interest of the above problem let s be the blow up of ip 2 at a point p with exceptional divisor e1 and a fixed line section eo we call s an irreducible fan a curve c c s is said to be of type d e if it is the proper transform of a curve of degree d in z having multiplicity e at p one then asks how many curves c c s of given type d e having only smooth branches of given configuration along e0 w e1 and otherwise having a given number of nodes as their only singularities pass through the appropriate number of points of s some of which may be on e o w e we will solve this problem by recursion on d e the recursion is based on degenerating the surface s to a surface called a 2 fan of the form so 1 w s 2 with si s i i 2 using and suitably enhancing methods of 3 we can describe a suitable part of the limit on so of the relevant families of curves of type d e on s d e 1 in terms of similar families of curves of type d e and e e e e d on 1 and 2 respectively

continuous triangular subnorms triangular subnorms are associative commutative non decreasing operations on the unit interval upper bounded by the minimum continuous triangular subnorms are shown to be ordinal sum of archimedean continuous t subnorms with at most one proper t subnorm summand special attention is paid to generate continuous t subnorms an application of continuous t subnorms to the construction of left continuous t norms is shown several illustrative examples are included

mathematics underlying the f theory heterotic string duality in eight dimensions we give an analytic description of the moduli space of classical vacua for f theory compactified on elliptic k3 surfaces on open tubular regions near the two type ii boundary divisors the structure of these open sets is related to the total spaces of certain holomorphic theta fibrations over the corresponding boundary divisors as the two type ii divisors can be naturally identified as moduli spaces of elliptic curves and flat g bundles with g e8 e8 or spin 32 one is led to an analytic isomorphism between these open domains and regions of the moduli spaces of heterotic string theory compactified on the two torus corresponding to large volumes of the torus this provides a proof for the classical version of f theory heterotic string duality in eight dimensions a description of the type ii boundary points in terms of elliptic stable k3 surfaces is also given

uniruledness of strata of holomorphic differentials in small genus abstract we address the question concerning the birational geometry of the strata of holomorphic and quadratic differentials we show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on k3 and del pezzo surfaces respectively restricting to genus 3 g 6 we construct projective bundles over a rational varieties that dominate the holomorphic strata with length at most g 1 hence showing in addition that these strata are unirational

logarithmic hodge witt sheaves on normal crossing varieties in this paper we define two kinds homological and cohomological of etale logarithmic hodge witt sheaves on normal crossing varieties over a perfect field of positive characteristic and discuss some fundamental properties in particular puity and duality

a characterization of a class of uninorms with continuous underlying operators in this paper all uninorms locally internal in the region a e given by the complement in 0 1 2 of 0 e 2 e 1 2 where e is the neutral element of the uninorm having continuous underlying operators are studied and characterized by distinguishing some cases when the underlying t norm and t conorm are not given by ordinal sums it is proved that uninorms locally internal in a e are in fact all possible uninorms with these underlying operators except when both the t norm and the t conorm are strict in which case there is also the class of representable uninorms leading to a finite number of possibilities when at least one of the continuous underlying operators is given by an ordinal sum again there are other possible uninorms than those that are locally internal in a e but all uninorms with this property are also characterized in this case infinitely many possibilities can appear depending on the set of idempotent elements of the uninorm

continuous additive generators of continuous conditionally cancellative triangular subnorms the continuous conditionally cancellative t subnorms that posses a continuous additive generator are discussed conditions for a continuous conditionally cancellative t subnorm to have a continuous additive generator are described constructions of corresponding additive generators are also shown

severi degrees on toric surfaces ardila and block used tropical results of brugalle and mikhalkin to count nodal curves on a certain family of toric surfaces building on a linearity result of the first author we revisit their work in the context of the goettsche yau zaslow formula for counting nodal curves on arbitrary smooth surfaces addressing several questions they raised by proving stronger versions of their main theorems in the process we give new combinatorial formulas for the coefficients arising in the goettsche yau zaslow formulas and give correction terms arising from rational double points in the relevant family of toric surfaces

the geometry of the moduli space of odd spin curves the spin moduli spacesg is the parameter space of theta characteristics spin structures on stable curves of genus g it has two connected components s g ands g depending on the parity of the spin structure we establish a complete birational classication by kodaira dimension of the odd components g of the spin moduli space we show thats g is uniruled for g 12 and even unirational for g 8 in this range introducing the concept of cluster for the mukai variety whose one dimensional linear sections are general canonical curves of genus g we construct new birational models ofs g these we then use to explicitly describe the birational structure of s g for instance s 8 is birational to a locally trivial p 7 bundle over the moduli space of elliptic curves with seven pairs of marked points for g 12 we prove thats g is a variety of general type in genus 12 this requires the construction of a counterexample to the slope conjecture on eective divisors on the moduli space of stable curves of genus 12

uninorms continuous on 0 e 2 e 1 2 uninorms continuous on 0 e 2 e 1 2 are discussed archimedean uninorms continuous and cancellative on 0 e 2 e 1 2 are characterized and related non archimedean uninorms are also discussed the problem when is the border continuous projection of a t norm associative i e a t subnorm is also answered

degeneration of surfaces with trivial canonical bundle the object of this note is to prove the theorem stated below the main idea of the proof and much of the detail are already to be found in v i kulikov s important paper k our contribution to the proof and the differences with kulikov s paper are discussed later in this introduction theorem let wl x d be a semistable degeneration of surfaces such that

deforming stanley reisner schemes we study the deformation theory of projective stanley reisner schemes associated to combinatorial manifolds we achieve detailed descriptions of first order deformations and obstruction spaces versal base spaces are given for certain stanley reisner surfaces

on the recovery procedure for lqg systems abstract the loop transfer function recovery ltr procedure of doyle and stein 1979 ieee trans aut control ac 24 607 611 is re examined in the context of singular measurement lqg systems using existing closed form expressions for singular optimal estimation an alternative proof of the ltr is presented some of the structural properties of the ltr are obtained naturally using this approach it is shown that in the limit the control effort becomes infinite and therefore the critical tradeoff is between control effort and robustness

properties of uninorms with the underlying operations given as ordinal sums abstract uninorms as mixed aggregation operations on the unit interval have been widely used as logical connectives in fuzzy set theory this paper presents some properties of uninorms for which the underlying operations are given as ordinal sums specially we present the relations between two arbitrary summands and the value on cartesian product of their underlying intervals one in 0 e and the other in e 1 where e is neutral element of the uninorm whose results bring us a step closer to the structure of uninorms that have continuous underlying operations as a byproduct we characterize several special classes of uninorms that are different from the well studied classes of uninorms

projective degenerations of k3 surfaces gaussian maps and fano threefolds in this article we exhibit certain projective degenerations of smoothk3 surfaces of degree 2g 2 in g whose picard group is generated by the hyperplane class to a union of two rational normal scrolls and also to a union of planes as a consequence we prove that the general hyperplane section of suchk3 surfaces has a corank one gaussian map ifg 11 org 13 we also prove that the general such hyperplane section lies on a uniquek3 surface up to projectivities finally we present a new approach to the classification of prime fano threefolds of index one which does not rely on the existence of a line

distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t conorm this paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms in particular the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict from the obtained results it is deduced that distributivity and conditional distributivity are equivalent moreover we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict

gopakumar vafa bps invariants hilbert schemes and quasimodular forms i we prove a closed formula for leading gopakumar vafa bps invariants of local calabi yau geometries given by the canonical line bundles of toric fano surfaces it shares some sim ilar features with gottsche yau zaslow formula connection with hilbert schemes connection with quasimodular forms and qua dratic property after suitable transformation in part i of this paper we will present the case of projective plane more general cases will be presented in part ii the problem of counting curves in algebraic varieties dates back to the nineteenth century classical examples include the famous 27 lines on a cubic surface and the 2875 lines on a quintic 3 fold through the interaction with string theory spectacular progresses in this classi cal branch of algebraic geometry have been made over the years since 1990 s first of all gromov witten theory and its various variants have laid the foundation for the modern treatment of many classical enumerative problems and greatly expanded the range of enumerative problems being considered see pt for an introduction to some of the exciting developments the study of the problems of counting curves in surfaces and calabi yau 3 folds have served both as motivations and applications of gromov witten theory we will recall some results in these directions in 2 and 3 to serve as motivations for this work we emphasize on the following three salient features for the curving counting problems for algebraic surfaces connection with hilbert schemes connection with quasimod ular forms and quadratic properties of the node polynomials after suit able transformation our main results will show that these features are also shared in the curve counting problems of some noncompact calabi yau 3 folds arising as the the total space of the canonical line bundles of toric fano surfaces 1

extended limiting forms of optimum observers and lqg regulators the general problem of optimal estimation in singular observation systems is considered by generalizing the limiting procedure of friedland explicit and closed expressions for the transfer matrices of the optimum observer as well as for the optimal control law in the singular measurement lqg problem are derived the number of integrators that are required for the implementation of the singular optimum observer is shown for square systems to be equal to the number of the system s zeros the closed form of the optimum observer given here is advantageous as compared with existing procedures structural properties of the singular observation problem are discussed and the role of the zeros of the system in such problems is clarified the dual results for the case of stochastic cheap control are also given

moduli of nodal curves on k3 surfaces abstract we consider modular properties of nodal curves on general k3 surfaces let k p be the moduli space of primitively polarized k3 surfaces s l of genus p 3 and v p m k p be the universal severi variety of nodal irreducible curves in m l on s l k p we find conditions on p m for the existence of an irreducible component v of v p m on which the moduli map v m g with g m 2 p 1 1 has generically maximal rank differential our results which for any p leave only finitely many cases unsolved and are optimal for m 5 except for very low values of p are summarized in theorem 1 1 in the introduction

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

mirror symmetry via logarithmic degeneration data i this paper lays the foundations of a program to study mirror symmetry by studying the log structures of illusie fontaine and kato on degenerations of calabi yau manifolds the basic idea is that one can associate to certain sorts of degenerations of calabi yau manifolds a log calabi yau space which is a log structure on the degenerate fibre the log cy space captures essentially all the information of the degeneration and hence all mirror statements for the large complex structure limit given by the degeneration can already be derived from the log cy space in this paper we begin by discussing affine manifolds with singularities given such an affine manifold along with a polyhedral decomposition we show how to construct a scheme consisting of a union of toric varieties in certain non degenerate cases we can also construct log structures on these schemes conversely given certain sorts of degenerations one can build an affine manifold with singularities structure on the dual intersection complex of the degeneration mirror symmetry is then obtained as a discrete legendre transform on these affine manifolds thus providing an algebro geometrization of the strominger yau zaslow conjecture the deepest result of this paper shows an isomorphism between log complex moduli of a log cy space and log kahler moduli of its mirror

toroidal crossings and logarithmic structures abstract we generalize friedman s notion of d semistability which is a necessary condition for spaces with normal crossings to admit smoothings with regular total space our generalization deals with spaces that locally look like the boundary divisor in gorenstein toroidal embeddings in this situation we replace d semistability by the existence of global log structures for a given gerbe of local log structures this leads to cohomological descriptions for the obstructions existence and automorphisms of log structures we also apply toroidal crossings to mirror symmetry by giving a duality construction involving toroidal crossing varieties whose irreducible components are toric varieties this duality reproduces a version of batyrev s construction of mirror pairs for hypersurfaces in toric varieties but it applies to a larger class including degenerate abelian varieties

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

on the k 2 of degenerations of surfaces and the multiple point formula in this paper we study some properties of reducible surfaces in particular of unions of planes when the surface is the central fibre of an embedded flat degeneration of surfaces in a projective space we deduce some properties of the smooth surface which is the general fibre of the degeneration from some combinatorial properties of the central fibre in particular we show that there are strong constraints on the invariants of a smooth surface which degenerates to configurations of planes with global normal crossings or other mild singularities our interest in these problems has been raised by a series of interesting articles by guido zappa in the 1950 s

degenerations of planar linear systems fixing n general points pi in the plane what is the dimension of the space of plane curves of degree d having multiplicity mi at pi for each i in this article we propose an approach to attack this problem and demonstrate it by successfully computing this dimension for all n and for mi constant at most 3 this application while previously known see hi1 demonstrates the utility of our approach which is based on an analysis of the corresponding linear system on a degeneration of the plane itself leading to a simple recursion for these dimensions we also obtain results in the quasi homogeneous case when all the multiplicities are equal except one this is the natural family to consider in the recursion

characterization of uninorms with continuous underlying t norm and t conorm by their set of discontinuity points uninorms with continuous underlying t norm and t conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown this set is proved to be a subset of the graph of a special symmetric u surjective nonincreasing set valued function which gives us a necessary condition for a uninorm to have continuous underlying functions a sufficient condition for a uninorm to have continuous underlying operations is also given several examples are included

enumeration of rational curves with cross ratio constraints abstract in this paper we prove the algebraic tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor the map has prescribed tangency to the boundary divisor and certain quadruples of marked points have prescribed cross ratios in particular our results generalize the results of nishinou siebert 14 the proof is very short involves only the standard theory of schemes and works in arbitrary characteristic including the mixed characteristic case

remarks on uninorm aggregation operators it is proved that continuous uninorm aggregation operators are only t norms or t conorms some general constructions about uninorm aggregation operators are given

moduli of curves on enriques surfaces abstract we compute the number of moduli of all irreducible components of the moduli space of smooth curves on enriques surfaces in most cases the moduli maps to the moduli space of prym curves are generically injective or dominant exceptional behavior is related to existence of enriques fano threefolds and to curves with nodal prym canonical model

a simply connected surface of general type with p g 0 and k 2 2 in this paper we construct a simply connected minimal complex surface of general type with pg 0 and k2 2 using a rational blow down surgery and a gorenstein smoothing theory

modular properties of nodal curves on k3 surfaces in this article we are going to address the following issues 1 the first is a rigidity property for pairs s c consisting of a general projective k3 surface s and a curve c obtained as the normalization of a nodal hyperplane section hat c hookrightarrow s we prove that a non trivial deformation of a pair s c induces a non trivial deformation of c 2 the second question concerns the wahl map of curves c obtained as above we prove that the wahl map of the normalization of a nodal curve contained in a general projective k3 surface is non surjective in both cases we impose upper bounds on the number of nodes of hat c

on universal severi varieties of low genus k3 surfaces we prove the irreducibility of universal severi varieties parametrizing irreducible reduced nodal hyperplane sections of primitive k3 surfaces of genus g with 3 g 11 g 10

classification of varieties with canonical curve section via gaussian maps on canonical curves the purpose of this article is to develop further a method to classify varieties x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i having canonical curve section using gaussian map computations in a previous article we applied these techniques to classify prime fano threefolds that is fano threefolds whose picard group is generated by the hyperplane bundle in this article we extend this method and classify fano threefolds of higher index and mukai varieties i e varieties of dimension four or more with canonical curve sections first we determine when the hilbert scheme inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i of such varieties x is nonempty moreover in the case of picard number one we prove that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i is irreducible and that the examples of fano iskovskih and mukai form a dense open subset of smooth points of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i

on the stability robustness of the continuous time lqg optimal control the robustness properties of the lqg optimal controller that is obtained by the asymptotic recovery method are discussed it is shown that in spite of the good recovered stability margins the resulting closed loop design is inherently unrobust in the sense that small parameter variations in the plant and or small realization errors in the controller may lead to an instantaneous instability of the design

a single point characterization of representable uninorms we study uninorms of which both the underlying t norm and underlying t conorm are strict such uninorms are the only candidates for being representable by an additive generator we prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the remaining open part of the unit square more explicitly such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments if this single value coincides with one of these bounds then the value of the uninorm at any point in the remaining open part is determined by the same bound

counting rational curves on text k3 surfaces the aim of these notes is to explain the remarkable formula found by yau and zaslow y z to express the number of rational curves on a k3 surface projective k3 surfaces fall into countably many families fg g 1 a surface in fg admits a gdimensional linear system of curves of genus g a naive count of constants suggests that such a system will contain a positive number say n g of rational highly singular curves the formula is

a conjectural generating function for numbers of curves on surfaces i give a conjectural generating function for the numbers of nodal curves in a linear system of dimension on an algebraic surface it reproduces the results of vainsencher v for the case le 6 and kleiman piene k p for the case le 8 the numbers of curves are expressed in terms of five universal power series three of which i give explicitly as quasimodular forms this gives in particular the numbers of curves of arbitrary genus on a k3 surface and an abelian surface in terms of quasimodular forms generalizing the formula of yau zaslow for rational curves on k3 surfaces the coefficients of the other two power series can be determined by comparing with the recursive formulas of caporaso harris for the severi degrees in 2 we verify the conjecture for genus 2 curves on an abelian surface we also discuss a link of this problem with hilbert schemes of points

rational curves on k3 surfaces we show that projective k3 surfaces with odd picard rank contain infinitely many rational curves our proof extends the bogomolov hassett tschinkel approach i e uses moduli spaces of stable maps and reduction to positive characteristic

uninorms in fuzzy systems modeling abstract fuzzy systems modeling provides a framework in which input output relationships can be modeled by partitioning the input into fuzzy regions for which we can describe the output the fuzzy modeling inference process the procedure used to obtain the output of a fuzzy systems model for a given input is shown to involve an aggregation step in which the contributions of the different components of the fuzzy systems model are combined it is shown that the uninorm operator provides a general class of operators to implement this step the uninorm it is recalled is an operator that provides a generalization of the t norm and t conorm by allowing the identity element to be any value in the unit interval another step in the inference process is the determination of the contribution of each component of the model based on its relevancy to the current input the performance of this step requires the use of an operator related to the implication operator which we call a relevancy transformation ret operator it is shown that the form of this ret operator is dependent upon the identity value of the uninorm used in the aggregation step we provide some general formulations for this class of operators we show how the well known forms of fuzzy inference are special cases of our uninorm based approach

uninorms on bounded lattices with the underlying t norms and t conorms abstract uninorms are a generalization of the concepts of triangular norms t norms and triangular conorms t conorms that admit a neutral element as any element in a bounded lattice in this study we discuss the characterization of uninorms on bounded lattices we introduce some new constructions for uninorms on bounded lattices which are derived from both t norms and t conorms in particular two idempotent uninorms on bounded lattices are obtained we also provide some corresponding examples to help understand the structure of these new classes of uninorms in addition we provide an answer to the open problem proposed by cayli 2019 14