commutant structure of u n 1 u transformations in this paper we have found irreducible representations irreps of the algebra of partially transposed permutation operators on the last subsystem we give here the direct method of irreps construction for an arbitrary number of subsystems n and local dimension d our method is inspired by the representation theory of the symmetric group s n the theory of brauer algebras and walled brauer algebras

irreducible representations of brauer algebras irreducible representations of brauer algebras are constructed by using the induced representation and the linear equation method as examples some matrix representations of brauer algebras df n with f or 5 are presented

subduction coefficients of brauer algebras and racah coefficients of o n and sp 2 m ii racah coefficients irreducible representations of brauer algebras are discussed in the non standard basis a method for evaluating subduction coefficients sdcs i e the transformation coefficients between standard and non standard bases of brauer algebras is outlined non trivial sdcs of for are derived racah coefficients of o n and sp 2m can be derived from subduction coefficients of brauer algebras by using the schur weyl duality relation between and o n or sp 2m

the induced representations of brauer algebras and the clebsch gordan coefficients of induced representations of from with are discussed the induction coefficients idcs or the outer product reduction coefficients of with up to a normalization factor are derived by using the linear equation method weyl tableaux for the corresponding gel fand basis of so n are defined the assimilation method for obtaining clebsch gordan coefficients of so n in the gel fand basis for no modification rule involved couplings from idcs of brauer algebras is proposed some isoscalar factors of for the resulting irrep with are tabulated

on the vectoral ekeland s variational principle and minimal points in product spaces abstract phelps 13 noticed that the scalar ekeland s variational principle evp is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order attouch and riahi 1 showed that evp is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions taking these into account gopfert and tammer 6 7 established a maximal point theorem in a product space the aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial evp

an improved completion theorem of fuzzy metric spaces in this paper we continue to investigate the completion of a fuzzy metric space in the sense of kaleva and seikkala as such an improved completion theorem is proved which is an essential generalization of the corresponding result of kaleva back in 1985 is also an improvement on the recent result given by huang and wu in 2008

the variational principle and fixed point theorems in certain topological spaces abstract the main purpose of this paper is to introduce the concept off type topological spaces and to establish a variational principle and a fixed point theorem in the kind of spaces which extend ekeland s variational principle and caristi s fixed point theorem respectively

analytical expressions for some multiplicity free isoscalar factors of sf sf 1 an algebraic routine for the evaluation of analytical expressions for isoscalar factors isfs of sf sf 1 is formulated based on the linear equation method lem and the analytical continuation of the rank f as examples isfs of sf sf 1 for the coupling f 1 1 f 1 1 f 1 1 f 2 2 f 2 1 1 f 2 1 1 are tabulated the results demonstrate that the number of isf tables can be greatly reduced compared with corresponding numerical results produced using other methods

fixed point theorems for nonlinear contractions in kaleva seikkala s type fuzzy metric spaces in this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces in the sense of kaleva and seikkala is discussed nonlinear contractions of the boyd wong s type alber guerre delabriere s type and kannan reich s type are considered and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented respectively also some error estimates are given for iterations to approximate fixed point previous work with respect to fixed point in fuzzy metric spaces is based on the t conorm max the presented work does away with this restriction by proposing weaker conditions defining a generic class of suitable binary operations as applications the corresponding fixed point theorems for menger probabilistic metric spaces are obtained

gauge transformation in einstein yang mills theories we discuss the relation between space time diffeomorphisms and gauge transformations in theories of the yang mills type coupled with einstein s general relativity we show that local symmetries of the hamiltonian and lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the legendre map although pure yang mills gauge transformations are projectable by themselves diffeomorphisms are not instead the projectable symmetry group arises from infinitesimal diffeomorphism inducing transformations which must depend on the lapse function and shift vector of the space time metric plus associated gauge transformations our results are generalizations of earlier results by ourselves and by salisbury and sundermeyer

the induction coefficients of the hecke algebra and the clebsch gordan coefficients of the quantum group suq n i special gel fand basis a general procedure for evaluating the induction coefficients idcs or the outer product reduction coefficients of the hecke algebra hf q of the af 1 type is formulated based on the linear equation method analytical expressions for the idc s of hf q are tabulated for f 4 it is also proved that these idcs are the clebsch gordan coefficients for the special gel fand basis of the quantum group suq n

equivalence classes of perturbations in cosmologies of bianchi types i and v interpretation in the preceding paper 26 gauge invariant variables were defined that characterize an almost bianchi type i or almost bianchi type v universe filled with a nonbarotropic perfect fluid one can think of these basic variables denoted collectively by d as having at least two aspects first d gives an explicit i e analytical representation of the equivalence class of perturbations in fact this equivalence class is uniquely determined from d and vice versa second any gauge invariant quantity with respect to a bianchi type i or bianchi type v background model is obtainable linearly from d through purely algebraic and differential operations among many other things the above properties of d facilitate new insights into the question of why a standard and well known formulation based on the stewart walker lemma does not enable one to describe the equivalence classes of perturbations and to find gauge invariant variables independent of d if we pose an analogous question in regard to almost robertson walker universe models a different but none the less instructive answer is obtained in this case the stewart walker lemma provides a complete framework both for constructing all gauge invariant variables and for determining the equivalence classes of perturbations because of the sometimes confusing statements in the literature nontrivial comparisons with other work on linear perturbations in anisotropic background models are made we also present what we believe are some interesting applications of our ideas to the subject of quantum field theory in curved space time

structure and properties of the algebra of partially transposed permutation operators we consider the structure of algebra of operators acting in n fold tensor product space which are partially transposed on the last term using purely algebraical methods we show that this algebra is semi simple and then considering its regular representation we derive basic properties of the algebra in particular we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations it appears that there are two kinds of irreducible representations of the algebra the first one is strictly connected with the representations of the group s n 1 induced by irreducible representations of the group s n 2 the second kind is structurally connected with irreducible representations of the group s n 1

an extension of ekeland s variational principle in fuzzy metric space and its applications abstract an extension of ekeland s variational principle in fuzzy metric space which is an essential and the most general improvement of ekeland s variational principle in fuzzy metric space up to now is established as an application we obtain caristi s coincidence theorem for set valued mappings in fuzzy metric spaces further a direct simple proof of the equivalence between the two theorems is given some applications of these results to probabilistic metric spaces are presented all these results even in usual metric space are also the latest

surface charge algebra in gauge theories and thermodynamic integrability surface charges and their algebra in interacting lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus in the case of exact solutions and symmetries the surface charges are interpreted as a pfaff system integrability is governed by frobenius theorem and the charges associated with the derived symmetry algebra are shown to vanish in the asymptotic context we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended comparison with hamiltonian and covariant phase space methods is made all approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

combinatorics of transformations from standard to non standard bases in brauer algebras transformation coefficients between standard bases for irreducible representations of the brauer centralizer algebra and split bases adapted to the subalgebra f1 f2 f are considered after providing the suitable combinatorial background based on the definition of the i coupling relation on nodes of the subduction grid we introduce a generalized version of the subduction graph which extends the one given in chilla 2006 j phys a math gen 39 7657 for symmetric groups thus we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space an ordering relation on the grid is also given and then as in the case of symmetric groups the choices of the phases and of the free factors governing the multiplicity separations are discussed

lagrangian approach to the physical degree of freedom count in this paper we present a lagrangian method that allows the physical degree of freedom count for any lagrangian system without having to perform neither dirac nor covariant canonical analyses the essence of our method is to establish a map between the relevant lagrangian parameters of the current approach and the hamiltonian parameters that enter in the formula for the counting of the physical degrees of freedom as is given in dirac s method once the map is obtained the usual hamiltonian formula for the counting can be expressed in terms of lagrangian parameters only and therefore we can remain in the lagrangian side without having to go to the hamiltonian one using the map it is also possible to count the number of first and second class constraints within the lagrangian formalism only for the sake of completeness the geometric structure underlying the current approach developed for systems with a finite number of degrees of freedom is uncovered with the help of the covariant canonical formalism finally the method is illustrated in several examples including the relativistic free particle

noether s theorem and gauge transformations application to the bosonic string and cp n 12 model new results on the theory of constrained systems are applied to characterize the generators of noether s symmetry transformations as a byproduct an algorithm to construct gauge transformations in hamiltonian formalism is derived this is illustrated with two relevant examples

covariant differential identities and conservation laws in metric torsion theories of gravitation i general consideration arbitrary diffeomorphically invariant metric torsion theories of gravity are considered it is assumed that lagrangians of such theories contain derivatives of field variables tensor densities of arbitrary ranks and weights up to a second order only the generalized klein noether methods for constructing manifestly covariant identities and conserved quantities are developed manifestly covariant expressions are constructed without including auxiliary structures like a background metric in the riemann cartan space the following manifestly generally covariant results are presented a the complete generalized system of differential identities the klein noether identities is obtained b the generalized currents of three types depending on an arbitrary vector field displacements are constructed they are the canonical noether current symmetrized belinfante current and identically conserved hilbert bergmann current in particular it is stated that the symmetrized belinfante current does not depend

minimization theorems for fixed point theorems in fuzzy metric spaces and applications abstract in this paper we establish a minimization theorem in fuzzy metric spaces and make use of the result to obtain a fixed point theorem in fuzzy metric spaces which is similar to the downing kirk fixed point theorem in metric spaces as the consequences we obtain caristi s fixed point theorem and ekeland s variational principle in fuzzy metric spaces and also give a direct simple proof of the equivalence between these two theorems some applications of these results to probabilistic metric spaces are presented

classification selection rules and symmetry properties of the clebsch gordan coefficients of symmetric group new analytical expressions for clebsch gordan coefficients cgcs of symmetric group are formulated based on the racah factorization lemma as examples cgcs for the coupling f 1 1 f 1 1 and f 1 1 f 2 2 are tabulated we have introduced a new technique called the clebsch gordan sequences cgss cgss provide a partial understanding of vanishing of cgcs and an explanation of new symmetry properties of multiplicity free cgcs

origin of the lagrangian constraints and their relation with the hamiltonian formulation the theory of presymplectic systems is used for the study of mechanical systems described by singular lagrangians in order to clarify the geometric meaning of the euler lagrange equations for such systems the two different types of primary constraint functions arising in the lagrangian formulation are analyzed by means of the relation between the image under the vertical endomorphism of the kernel of the presymplectic form l and its vertical part the connection with the hamiltonian dirac theory is also studied and the theory is illustrated with several examples

noether currents and charges for maxwell like lagrangians the hilbert noether theorem states that a current associated with diffeomorphism invariance of a lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential application of the noether procedure to physical lagrangians yields however meaningful and measurable currents the well known solution to this paradox is to involve the variation of the metric tensor such procedure for the field considered on a fixed flat background is sophisticated logically one needs to introduce the variation of a fixed field and formal we analyse the noether procedure for a generic diffeomorphism invariant p form field model we show that the noether current of the field considered on a variable background coincides with the current treated in a fixed geometry consistent description of the canonical energy momentum current is possible only if the dynamics of the geometry gravitation is taken into account however even the truncated consideration yields the proper expression we examine the examples of the free p form gauge field theory the gr in the coframe representation and the metric free electrodynamics although the variation of a metric tensor is not acceptable in the latter case the noether procedure yields the proper result

general quadratic gauge theory constraint structure symmetries and physical functions how can we relate the constraint structure and constraint dynamics of the general gauge theory in the hamiltonian formulation to specific features of the theory in the lagrangian formulation especially relate the constraint structure to the gauge transformation structure of the lagrangian action how can we construct the general expression for the gauge charge if the constraint structure in the hamiltonian formulation is known whether we can identify the physical functions defined as commuting with first class constraints in the hamiltonian formulation and the physical functions defined as gauge invariant functions in the lagrangian formulation the aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions to fulfil such a programme we demonstrate the existence of the so called superspecial phase space variables in terms of which the quadratic hamiltonian action takes a simple canonical form on the basis of such a representation we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation we then use these results to identify the two definitions of physical functions and thus prove the dirac conjecture

presymplectic current and the inverse problem of the calculus of variations the inverse problem of the calculus of variations asks whether a given system of partial differential equations pdes admits a variational formulation we show that the existence of a presymplectic form in the variational bicomplex when horizontally closed on solutions allows us to construct a variational formulation for a subsystem of the given pde no constraints on the differential order or number of dependent or independent variables are assumed the proof follows a recent observation of bridges hydon and lawson math proc cambridge philos soc 148 01 159 178 2010 and generalizes an older result of henneaux ann phys 140 1 45 64 1982 from ordinary differential equations odes to pdes uniqueness of the variational formulation is also discussed

a new young diagrammatic method for kronecker products of and a new simple young diagrammatic method for kronecker products of o n and sp 2m is proposed based on the representation theory of brauer algebras a general procedure for the decomposition of the tensor products of representations for o n and sp 2m is outlined which is similar to that for u n known as the littlewood rules together with trace contractions from a brauer algebra and some modification rules given by king

set valued ekeland variational principles in fuzzy metric spaces abstract in this paper we establish a general set valued ekeland s variational principle in fuzzy metric spaces where the objective function is a set valued map defined on a fuzzy metric space and taking values in a pre ordered locally convex space and the perturbation involves a quasi metric family generating the fuzzy topology of the domain space moreover the direction of the perturbation is a convex subset of the positive cone instead of a single positive vector in our general version the assumption that the objective function is lower semi continuous and one that the range of the function is lower bounded are both weakened from the general ekeland s variational principle we obtain several particular set valued ekeland s variational principles in fuzzy metric spaces which generalize and improve some related known results from these we deduce the corresponding caristi s fixed point theorems for set valued maps and the corresponding takahashi s non convex minimization theorems in set valued optimization finally we extend the obtained results to f type topological spaces

racah coefficients of quantum group uq n racah coefficients of uq n are derived from subduction coefficients of hecke algebras hf q by using the schur weyl duality relation between uq n and hf q the racah coefficients of uq n for the resulting irreps n1 n2 nk o with sigma i 1kni or 5 and some of them for the resulting irreps with multiplicity and sigma i 1kni or 6 are tabulated

the variational principle in fuzzy metric spaces and its applications abstract in this paper we prove a fixed point theorem and a variational principle in fuzzy metric spaces applying these results to some probabilistic metric spaces we obtain a corresponding fixed point theorem and a variational principle

coincidence theorems for set valued mappings and ekeland s variational principle in fuzzy metric spaces abstract in this paper we establish a coincidence theorem for set valued mappings in fuzzy metric spaces with a view to generalizing downing kirk s fixed point theorem in metric spaces as consequences we obtain caristi s coincidence theorem for set valued mappings and a more general type of ekeland s variational principle in fuzzy metric spaces further we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces some applications of these results to probabilistic metric spaces are presented

local symmetries and constraints the general relationship between local symmetries occurring in a lagrangian formulation of a field theory and the corresponding constraints present in a phase space formulation are studied first a prescription applicable to an arbitrary lagrangian field theory for the construction of phase space from the manifold of field configurations on space time is given next a general definition of the notion of local symmetries on the manifold of field configurations is given that encompasses as special cases the usual gauge transformations of yang mills theory and general relativity local symmetries on phase space are then defined via projection from field configuration space it is proved that associated to each local symmetry which suitably projects to phase space is a corresponding equivalence class of constraint functions on phase space moreover the constraints thereby obtained are always first class and the poisson bracket algebra of the constraint functions is isomorphic to the lie bracket algebra of the local symmetries on the constraint submanifold of phase space the differences that occur in the structure of constraints in yang mills theory and general relativity are fully accounted for by the manner in which the local symmetries project to phase space in yang mills theory all the field independent local symmetries project to all of phase space whereas in general relativity the nonspatial diffeomorphisms do not project to all of phase space and the ones that suitably project to the constraint submanifold are field dependent as by products of the present work definitions are given of the symplectic potential current density and the symplectic current density in the context of an arbitrary lagrangian field theory and the noether current density associated with an arbitrary local symmetry a number of properties of these currents are established and some relationships between them are obtained

coincidence point theorems and minimization theorems in fuzzy metric spaces abstract in this paper some new versions of coincidence point theorems and minimization theorems for single valued and multi valued mappings in generating spaces of the quasi metric family are obtained as applications we utilize our main theorems to prove coincidence point theorems fixed point theorems and minimization theorems for single valued and multi valued mappings in fuzzy metric spaces and probabilistic metric spaces

reduced phase space quotienting procedure for gauge theories we present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration velocity space local expressions for a basis of this kernel are obtained using phase space procedures the obstructions to the formulation of the dynamics in the reduced phase space are identified and circumvented we show that this reduction procedure is equivalent to the standard dirac method as long as the dirac conjecture holds that the dirac hamiltonian containing the primary first class constraints with their lagrange multipliers can be enlarged to an extended dirac hamiltonian which includes all first class constraints without any change of the dynamics the quotienting procedure is always equivalent to the extended dirac theory even when it differs from the standard dirac theory the differences occur when there are ineffective constraints and in these situations we conclude that the standard dirac method is preferable at least for classical theories an example is given to illustrate these features as well as the possibility of having phase space formulations with an odd number of physical degrees of freedom

irreducible representations of hecke algebras in the nonstandard basis and subduction coefficients irreducible representations of hecke algebras of the type an 1 hn q are discussed in the nonstandard basis some subduction coefficients i e the transformation coefficients between the standard and nonstandard base of hn q are derived by using the linear equation method

covariant hamiltonian boundary conditions in general relativity for spatially bounded space time regions we investigate the covariant hamiltonian symplectic structure of general relativity for spatially bounded regions of space time with a fixed time flow vector for existence of a well defined hamiltonian variational principle taking into account a spatial boundary it is necessary to modify the standard arnowitt deser misner hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field the most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obtained from the symplectic current pulled back to the hypersurface boundary of the space time region a main result is that we obtain a covariant derivation of dirichlet neumann and mixed type boundary conditions on the gravitational field at a fixed boundary hypersurface together with the associated hamiltonian boundary terms as well we establish uniqueness of these boundary conditions under certain assumptions motivated by the form of the symplectic current our analysis uses a noether charge method which extends and unifies several results developed in recent literature for general relativity as an illustration of the method we apply it to the maxwell field equations to derive allowed boundary conditions and boundary terms for the existence of a well defined hamiltonian variational principle for an electromagnetic field in a fixed spatially bounded region of minkowski space time

subduction coefficients of birman wenzl algebras and racah coefficients of the quantum groups oq n and spq 2m i subduction coefficients irreducible representations of birman wenzl algebras cf r q in the non standard basis are discussed a procedure for evaluating subduction coefficients sdcs or the transformation coefficients between standard and non standard basis of birman wenzl algebras is formulated based on the linear equation method sdcs of cf r q with f 4 are derived racah coefficients of the quantum groups oq n and spq 2m can be obtained from sdcs of birman wenzl algebras cf r q by using the schur weyl brauer duality relation between birman wenzl algebras cf r q and the quantum groups oq n and spq 2m

set valued pseudo metric families and ekeland s variational principles in fuzzy metric spaces abstract in this paper we introduce a set valued pseudo metric family on a fuzzy metric space and the notion of compatibility between the set valued pseudo metric family and the original fuzzy metric by means of this notion we prove a general set valued evp where the perturbation involves a set valued pseudo metric family compatible with the original fuzzy metric from the general evp we deduce several particular evps which extend the evps in qiu 2013 36 and in gutierrez et al 2008 20 to fuzzy metric spaces by using set valued pseudo metric families and using the unified approach for approximate solutions introduced by gutierrez jimenez and novo we deduce a general version of set valued evp based on c efficient solutions in fuzzy metric spaces where c is a coradiant set contained in the order cone by choosing two specific versions of the coradiant set c in the general version of evp we obtain several particular set valued evps for efficient solutions in the sense of nemeth and of dentcheva and helbig respectively these evps improve and generalize the related known results