lagrangian hamiltonian unified formalism for field theory the rusk skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems it incorporates all the characteristics of lagrangian and hamiltonian descriptions of these systems including dynamical equations and solutions constraints legendre map evolution operators equivalence etc in this work we extend this unified framework to first order classical field theories and show how this description comprises the main features of the lagrangian and hamiltonian formalisms both for the regular and singular cases this formulation is a first step toward further applications in optimal control theory for partial differential equations

the approximation of left continuous t norms a discrete t norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t norms we show that any left continuous t norm can in a natural sense be approximated by a discrete t norm with an arbitrary precision

berezin toeplitz quantization and composition formulas abstract extending results in l a coburn the measure algebra of the heisenberg group j funct anal 161 1999 509 525 l a coburn on the berezin toeplitz calculus proc amer math soc 129 11 2001 3331 3338 we derive composition formulas for berezin toeplitz operators with i g unbounded symbols in the range of certain integral transforms the question whether a finite product of berezin toeplitz operators is an operator of this type again can be answered affirmatively in several cases but there are also well known counter examples we explain some consequences of such formulas to c algebras generated by toeplitz operators

mtl algebras arising from partially ordered groups after dropping the implication like operation and reversing the order an mtl algebra becomes a partially ordered structure l 0 1 based on the single addition like operation furthermore may be restricted to a partial but cancellative addition without loss of information we deal in this paper with the case that the resulting partial algebra l 0 1 is embeddable into the positive cone of a partially ordered group it turns out that most of the examples of mtl algebras known at present can be represented in this way so the systematisation of a considerable class of mtl algebras is achieved and the methods of their construction are brought onto a common line

commuting toeplitz operators on the segal bargmann space abstract consider two toeplitz operators t g t f on the segal bargmann space over the complex plane let us assume that g is a radial function and both operators commute under certain growth condition at infinity of f and g we show that f must be radial as well we give a counterexample of this fact in case of bounded toeplitz operators but a fast growing radial symbol g in this case the vanishing commutator t g t f 0 does not imply the radial dependence of f finally we consider toeplitz operators on the segal bargmann space over c n and n 1 where the commuting property of toeplitz operators can be realized more easily

commutative c algebras of toeplitz operators and quantization on the unit disk abstract a family of recently discovered commutative c algebras of toeplitz operators on the unit disk can be classified as follows each pencil of hyperbolic straight lines determines a set of symbols consisting of functions which are constant on the corresponding cycles the orthogonal trajectories to lines forming a pencil the c algebra generated by toeplitz operators with such symbols turns out to be commutative we show that these cases are the only possible ones which generate the commutative c algebras of toeplitz operators on each weighted bergman space

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

a note on minimal axiomatisations of some extensions of mtl abstract the rotation of the product t norm provides the tool to show that ukasiewicz logic cannot be axiomatised as an extension of mtl by means of any set of axioms with at most one variable as a corollary also bl cannot be axiomatised from mtl by means of single variable axioms

fock sobolev spaces and their carleson measures abstract we study a class of holomorphic spaces f p m consisting of entire functions f on c n such that f is in the fock space f p for all multi indices with m we prove a useful fourier characterization namely f f p m if and only if z f z is in f p for all with m we obtain duality and interpolation results for these spaces including the interesting fact that for 0 p 1 f p m f m we also characterize carleson measures for f p m in terms of simple polynomial growth conditions

on a class of left continuous t norms in this paper we study the subclass of left continuous t norms n which are definable by an arbitrary continuous t norm and a weak i e non necessarily involutive negation n by putting x n y 0 if x n y x n y x y otherwise thus generalizing the construction of the so called nilpotent minimum t norms we provide the characterization of weak negations compatible with a given continuous t norm and conversely which are the continuous t norms compatible with a given weak negation function

multivector field formulation of hamiltonian field theories equations and symmetries we state the intrinsic form of the hamiltonian equations of first order classical field theories in three equivalent geometrical ways using multivector fields jet fields and connections thus these equations are given in a form similar to that in which the hamiltonian equations of mechanics are usually given then using multivector fields we study several aspects of these equations such as the existence and non uniqueness of solutions and the integrability problem in particular these problems are analysed for the case of hamiltonian systems defined in a submanifold of the multimomentum bundle furthermore the existence of first integrals of these hamiltonian equations is considered and the relation between cartan noether symmetries and general symmetries of the system is discussed noether s theorem is also stated in this context both the classical version and its generalization to include higher order cartan noether symmetries finally the equivalence between the lagrangian and hamiltonian formalisms is also discussed

commutants of toeplitz operators with radial symbols on the fock sobolev space abstract in the setting of the fock space over the complex plane bauer and lee have recently characterized commutants of toeplitz operators with radial symbols under the assumption that symbols have at most polynomial growth at infinity their characterization states if one of the symbols of two commuting toeplitz operators is nonconstant and radial then the other must be also radial we extend this result to the fock sobolev spaces

triangular norms position paper iii continuous t norms this third and last part of a series of position papers on triangular norms for parts i and ii see e p klement r mesiar e pap triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press e p klement r mesiar e pap triangular norms position paper ii general constructions and parameterized families submitted for publication presents the representation of continuous archimedean t norms by means of additive generators and the representation of continuous t norms by means of ordinal sums with archimedean summands both with full proofs finally some consequences of these representation theorems in the context of comparison and convergence of continuous t norms and of the determination of continuous t norms by their diagonal sections are mentioned

poly poisson sigma models and their relational poly symplectic groupoids the main idea of this paper is to describe the integration procedure for poly poisson structures that is to find a poly symplectic groupoid integrating a poly poisson structure in terms of topological field theories namely via the path space construction this will be given in terms of the poly poisson sigma model and we prove that every poly poisson structure has a natural integration via relational poly symplectic groupoids extending known results for poisson structures we provide familiar examples trivial linear constant and symplectic within this formulation and give some applications of this construction regarding the classification of poly symplectic integrations as well as morita equivalence of poly poisson manifolds the main idea of this paper is to describe the integration procedure for poly poisson structures that is to find a poly symplectic groupoid integrating a poly poisson structure in terms of topological field theories namely via the path space construction this will be given in terms of the poly poisson sigma model and we prove that every poly poisson structure has a natural integration via relational poly symplectic groupoids extending known results for poisson structures we provide familiar examples trivial linear constant and symplectic within this formulation and give some applications of this construction regarding the classification of poly symplectic integrations as well as morita equivalence of poly poisson manifolds

mellin transform monomial symbols and commuting toeplitz operators abstract in this paper we give necessary and sufficient conditions for a symbol that produces a toeplitz operator on the bergman space that commutes with another such operator whose symbol is a monomial the result is stated in terms of the mellin transform of the symbol as a corollary we show that a toeplitz operator with a radial symbol may only commute with another such operator with a radial symbol

n symplectic algebra of observables in covariant lagrangian field theory n symplectic geometry on the adapted frame bundle l e e of an n m k dimensional fiber bundle e m is used to set up an algebra of observables for covariant lagrangian field theories using the principle bundle l e j1 we lift a lagrangian l j1 r to a lagrangian l l l e r and then use l to define a modified n symplectic potential l on l e the cartan hamilton poincare chp rn valued 1 form if the lifted lagrangian is nonzero then l e d l is an n symplectic manifold to characterize the observables we define a lifted legendre transformation l from l e into le the image ql l l e is a submanifold of le and ql d ql is shown to be an n symplectic manifold we prove the theorem that l l ql and pull back the reduced canonical n symplectic geometry on ql to l e to define the algebras of observables on the n symplectic manifold l e d l to find the reduced n symplectic algebra on ql we set up the equations of n symplectic reduction and apply the general theory to the mo

product logic and probabilistic ulam games there is a well known game semantics for lukasiewicz logic introduced by daniele mundici namely the renyi ulam game records in a reny ulam game are coded by functions which constitute an mv algebra and it is possible to prove a completeness theorem with respect to this semantics in this paper we investigate some probabilistic variants of the renyi ulam game and we prove that some of them constitute a complete game semantics for product logic whilst some other constitute a game semantics for a logic between pmtl and product logic

on the failure of standard completeness in πmtl for infinite theories it is well known that hajek s basic fuzzy logic bl lukasiewicz logic and product logic are not strongly standard complete on the other hand esteva and godo s monoidal t norm based logic mtl and its involutive extension imtl are strongly standard complete in this paper we show that pmtl an extension of mtl by the axioms characteristic of product logic does not enjoy the strong standard completeness theorem like bl lukasiewicz and product logic

geometry of multisymplectic hamiltonian first order field theories in the jet bundle description of field theories multisymplectic models in particular there are several choices for the multimomentum bundle where the covariant hamiltonian formalism takes place as a consequence several proposals for this formalism can be stated and on each one of them the differentiable structures needed for setting the formalism are obtained in different ways in this work we make an accurate study of some of these hamiltonian formalisms showing their equivalence in particular the geometrical structures canonical or not needed for the hamiltonian formalism are introduced and compared and the derivation of hamiltonian field equations from the corresponding variational principle is shown in detail furthermore the hamiltonian formalism of systems described by lagrangians is performed both for the hyper regular and almost regular cases finally the role of connections in the construction of hamiltonian field theories is clarified

algebraic properties of toeplitz operators on generalized fock spaces on cd abstract we study two problems involving algebraic properties of toeplitz operators on generalized fock spaces on c d with weights of the form z 2 s e z 2 m m 1 s 0 we determine the commutant of a given toeplitz operator with a radial symbol which satisfies certain growth conditions we also discuss the equation t f t g 0 when f or g is radial

on covariant poisson brackets in classical field theory how to give a natural geometric definition of a covariant poisson bracket in classical field theory has for a long time been an open problem as testified by the extensive literature on multisymplectic poisson brackets together with the fact that all these proposals suffer from serious defects on the other hand the functional approach does provide a good candidate which has come to be known as the peierls de witt bracket and whose construction in a geometrical setting is now well understood here we show how the basic multisymplectic poisson bracket already proposed in the 1970s can be derived from the peierls de witt bracket applied to a special class of functionals this relation allows to trace back most if not all of the problems encountered in the past to ambiguities the relation between differential forms on multiphase space and the functionals they define is not one to one and also to the fact that this class of functionals does not form a poisson subalgebra

k cosymplectic manifolds and lagrangian field theories a geometrical description of classical field theories of first order is given the underlying k cosymplectic structure permits to derive the corresponding field equations

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

reduction of polysymplectic manifolds the aim of this paper is to generalize the classical marsden weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure this generalization allows us to reduce polysymplectic hamiltonian systems with symmetries such as those appearing in certain kinds of classical field theories as an application of this technique an analogue to the kirillov kostant souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed our procedure corrects some mistakes and inaccuracies in previous papers gunther 1987 j differ geom 25 23 53 munteanu et al 2004 j math phys 45 1730 51 on this subject

a general method for constructing left continuous t norms a new method for constructing left continuous t norms is introduced and analyzed in this paper we shall construct via embedding a left continuous t norm from any countable residuated totally and densely ordered commutative integral monoid moreover we can construct a left continuous t norm from any countable totally ordered commutative integral monoid which is not necessarily densely ordered and residuated a special case the embedding of such monoids on lexicographic product spaces is investigated in detail and several examples are demonstrated the results shed some light to chang s mv algebra to a recently proposed extraordinary t norm and to the standard semantics of the recently introduced logic ii mtl of hajek

nmł a schematic extension of f esteva and l godo s logic mtl abstract a schematic extension nm of f esteva and l godo s logic mtl is introduced in this paper based on a new left continuous but discontinuous t norm which was proposed by s jenei and can be regarded as a kind of distorted nilpotent minimum the semantics of nm is interpreted and the standard completeness theorem of nm is proved the fact that the maximum and the minimum are definable from the negation and implication in nm and nm is discovered which also leads to a modification of the nm axiom system

k symplectic formalism on lie algebroids in this paper we introduce a geometric description of lagrangian and hamiltonian classical field theories on lie algebroids in the framework of k symplectic geometry we discuss the relation between the lagrangian and hamiltonian descriptions through a convenient notion of legendre transformation the theory is a natural generalization of the standard one in addition other interesting examples are studied in particular systems with symmetry and poisson sigma models

observations on the monoidal t norm logic the paper is a contribution to the theory of the monoidal t norm based logic mtl and stronger logics analogous to the well known extensions of the basic fuzzy logic lukasiewicz godel and product logic main attention is payed to the logic iimtl mtl plus the characteristic axioms ii1 ii2 of product logic

on the n symplectic structure of faithful irreducible representations each faithful irreducible representation of an n dimensional vector space v1 on an n dimensional vector space v2 is shown to define a unique irreducible n symplectic structure on the product manifold v1 v2 the basic details of the associated poisson algebra are developed for the special case n n2 and 2n dimensional symplectic submanifolds are shown to exist

reduced classical field theories k cosymplectic formalism on lie algebroids in this paper we introduce a geometric description of lagrangian and hamiltonian classical field theories on lie algebroids in the framework of k cosymplectic geometry we discuss the relation between lagrangian and hamiltonian descriptions through a convenient notion of legendre transformation the theory is a natural generalization of the standard one in addition other interesting examples are studied mainly on reduction of classical field theories

gunther s formalism k symplectic formalism in classical field theory skinner rusk approach and the evolution operator the first aim of this paper is to extend the skinner rusk formalism on classical mechanics for first order field theories the second is to generalize the definition and properties of the evolution k operator on classical mechanics for first order field theories using in both cases gunther s formalism k symplectic formalism

cancellativity properties for t norms and t subnorms on the one hand cancellativity properties are mainly used to express to which extend the partial functions of a t subnorm t are injective on the other hand the zooms of t corresponding to its non trivial archimedean components are t subnorms that largely determine t fixing one out of four basic types of cancellativity cancellativity conditional cancellativity weak cancellativity and weak conditional cancellativity we figure out which less restrictive type of cancellativity expresses that all maximal archimedean zooms of t satisfy the given cancellativity property we lay bare the mutual relationships between all these types of cancellativity and solve an open problem posed by klement et al

triangular norm based predicate fuzzy logics the paper surveys the present state of knowledge on t norm based predicate fuzzy logics with their double semantics standard the set of truth values being the real interval 0 1 and general with abstract algebras of truth functions

triangular norm based graded convex fuzzy sets in this paper we develop the theory of graded convex fuzzy set graded strongly convex fuzzy set graded strictly convex fuzzy set based on triangular norms in which the degree of fuzzy convexity is described by one real number we also investigate some graded properties of these graded convex fuzzy sets and present the relations between these graded convex fuzzy sets and their topological properties and give several conditions for a fuzzy set to be a graded convex fuzzy set finally we generalize the notion of global maximizer and prove an important property of graded convex fuzzy sets

commuting toeplitz operators on the polydisk we obtain characterizations of essentially commuting toeplitz operators with pluriharmonic symbols on the bergman space of the polydisk we show that commuting and essential commuting properties are the same for dimensions bigger than 2 while they are not for dimensions less than or equal to 2 also the corresponding results for semi commutators are obtained

constraint field systems in multimomentum canonical variables to describe constraint field models we apply the multimomentum hamiltonian formalism where momenta correspond to derivatives of fields with respect to all world coordinates not only time if a lagrangian density is degenerate the euler lagrange equations are underdetermined and need additional gauge type conditions which remain elusive in general one gets these conditions automatically as a part of the hamilton equations but must consider a family of hamiltonian forms associated with the same lagrangian density in order to exhaust solutions of the euler lagrange equations the case of degenerate quadratic and affine lagrangian densities is elaborated as a result we get the universal procedure of describing constraint field systems

covariant hamilton equations for field theory we study the relations between the equations of first order lagrangian field theory on fibre bundles and the covariant hamilton equations on the finite dimensional polysymplectic phase space of covariant hamiltonian field theory if a lagrangian is hyperregular these equations are equivalent a degenerate lagrangian requires a set of associated hamiltonian forms in order to exhaust all solutions of the euler lagrange equations the case of quadratic degenerate lagrangians is studied in detail

on a kind of noether symmetries and conservation laws in k cosymplectic field theory this paper is devoted to studying symmetries of certain kinds of k cosymplectic hamiltonian systems in first order classical field theories thus we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of noether s theorem

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

the polysymplectic hamiltonian formalism in field theory and calculus of variations i the local case on presente un formalisme hamiltonien geometrique invariant pour des problemes variationnels a integrale multiple et des theories de champ le formalisme est base sur la notion de forme polysymplectique qui est une generalisation a valeur vectorielle des formes symplectiques on etudie des equations hamiltoniennes des transformations canoniques des systemes de lagrange des symetries des applications en pulsion de theorie du champ et une classification des systemes de theorie du champ g homogenes sur une generalisation des orbites coadjointes

the commutants of certain toeplitz operators on weighted bergman spaces abstract for 1 let a 2 be the corresponding weighted bergman space of the unit ball in c n for a bounded measurable function f let t f be the toeplitz operator with symbol f on a 2 this paper describes all the functions f for which t f commutes with a given t g where g z z 1 l 1 z n l n for strictly positive integers l 1 l n or g z z 1 s 1 z n s n h z for non negative real numbers s 1 s n and a bounded measurable function h on 0 1

non standard connections in classical mechanics in the jet bundle description of first order classical field theories there are some elements such as the lagrangian energy and the construction of the hamiltonian formalism which require the prior choice of a connection bearing these facts in mind we analyse the situation in the jet bundle description of time dependent classical mechanics we prove that this connection dependence also occurs in this case although it is usually hidden by the use of the natural connection given by the trivial bundle structure of the phase spaces under consideration however we also prove that this dependence is dynamically irrelevant except where the dynamical variation of the energy is concerned in addition the relationship between first integrals and connections is shown for a sufficiently large class of lagrangians

the construction of left continuous t norms a geometric approach in two dimensions abstract each t norm can be identified with its cayley tomonoid which consists of pairwise commuting order preserving functions from the real unit interval to itself cayley tomonoids provide an easily manageable yet versatile tool for the construction of t norms to give evidence to this claim we review and reformulate several construction methods that are known in the literature we adopt on the one hand a geometric point of view manipulations with t norms have often been inspired by their three dimensional graphs by means of cayley tomonoids the process gains the character of putting together the pieces of a jigsaw puzzle we consider on the other hand construction methods in their algebraic context we show that those constructions that correspond to certain tomonoid extensions can be described on the basis of cayley tomonoids in a particularly transparent way

h transformation of t norms cancellative t norms are generated only if they do not posses anomalous pairs and then they are isomorphic to subsemigroups of 0 a new construction method for t norms so called h transformation of t norms is introduced and studied generalizing a recent example of hajek h transformation allows to construct non generated cancellative left continuous t norms with prescribed number of non trivial archimedean components the unique t norm stable under h transformation is also described in an analogous way h transformation of residual implications is given finally a general h transformation based on cancellative discrete t conorms is proposed and examined

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

some geometric structures associated with a k symplectic manifold a canonical connection is attached to any k symplectic manifold we study the properties of this connection and its geometric applications to k symplectic manifolds in particular we prove that under some natural assumptions any k symplectic manifold admits an ehresmann connection discuss some corollaries of this result and find vanishing theorems for characteristic classes on a k symplectic manifold

the gunther s formalism in classical field theory momentum map and reduction the polysymplectic formalism in local field theory developed by gunther j diff geom 25 23 1987 is revised a new approach and new results on momentum maps and reduction are given

a new axiomatization for involutive monoidal t norm based logic on the real unit interval the notion of a girard monoid coincides with the notion of a t norm based residuated lattice with strong induced negation a geometrical approach toward these girard monoids based on the notion of rotation invariance is turned in an adequate axiomatization for the involutive monoidal t norm based residuated logic

on archimedean triangular norms abstract the behaviour of the additive generator functions related to a sequence of convergent continuous archimedean triangular norm where the limit triangular norm is continuous archimedean is examined in this paper it is proved that the related generator functions converge to the generator function of the limit triangular norm in some sense under the assumption that the limit triangular norm is strict a bit weaker convergence is proved if the limit triangular norm has 0 divisor an example is given for the fact that the stronger type of convergence cannot be obtained in the 0 divisor limit case

disjunctive elimination rule and its application in mtl firstly the disjunctive elimination rule is proved valid in esteva and godo s mtl and hajek s bl logics secondly from this rule a general method is presented for finitely axiomatizing the intersection of the sets of theorems of two given schematic extensions of mtl or bl thirdly the axiomatic system of nm is simplified by replacing the axiom schemata nm with another which is built up with one variable fourthly the intersection of the sets of tautologies of nm and g nm and p nm and l are finitely axiomatized by our method finally new axiom systems for lg email protected pg email protected are presented by our method and some comments are made on the relations between these systems and those given by cignoli et al

an answer to an open problem on triangular norms in this paper we shall give an answer to show that an open problem which is collected by klement et al in problems on triangular norms and related operators fuzzy sets and systems 145 2004 471 479 has a negative solution

k symplectic lie systems theory and applications abstract a lie system is a system of first order ordinary differential equations describing the integral curves of a t dependent vector field taking values in a finite dimensional real lie algebra of vector fields a so called vessiot guldberg lie algebra we suggest the definition of a particular class of lie systems the k symplectic lie systems admitting a vessiot guldberg lie algebra of hamiltonian vector fields with respect to the presymplectic forms of a k symplectic structure we devise new k symplectic geometric methods to study their superposition rules t independent constants of motion and general properties our results are illustrated through examples of physical and mathematical interest as a byproduct we find a new interesting setting of application of the k symplectic geometry systems of first order ordinary differential equations

extended hamiltonian systems in multisymplectic field theories we consider hamiltonian systems in first order multisymplectic field theories we review the properties of hamiltonian systems in the so called restricted multimomentum bundle including the variational principle which leads to the hamiltonian field equations in an analogous way to how these systems are defined in the so called extended symplectic formulation of nonautonomous mechanics we introduce hamiltonian systems in the extended multimomentum bundle the geometric properties of these systems are studied the hamiltonian equations are analyzed using integrable multivector fields the corresponding variational principle is also stated and the relation between the extended and the restricted hamiltonian systems is established all these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost regular field theories

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

hamiltonian systems on k cosymplectic manifolds the hamiltonian framework on symplectic and cosymplectic manifolds is extended in order to consider classical field theories to do this the notion of k cosymplectic manifold is introduced and a suitable hamiltonian formalism is developed so that the field equations for scalar and vector hamiltonian functions are derived