logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

vacuum expectation values of products of chiral currents in 3 1 dimensions an algebraic rule is presented for computing expectation values of products of local nonabelian charge operators for fermions coupled to an external vector potential in 3 1 space time dimensions the vacuum expectation value of a product of four operators is closely related to a cyclic cocycle in noncommutative geometry of alain connes the relevant representation of the current is constructed using kirillov s method of coadjoint orbits

new construction of solvable lattice models including an ising model in a field in this letter we report a new construction to obtain restricted solid on solid rsos models out of loop models the method is a generalization of ideas developed by owczarek and baxter and by pasquier in particular we consider a solvable o n model and point out that some of the rsos models thus obtained admit an off critical extension among these models we find a spin 1 ising model which is solvable not only at the critical point but also in a fieldlike deviation away from it we calculate the critical exponent ensuremath delta 15 directly from the relation between the free energy and the field this is the first determination of this exponent without the use of scaling relations

steffensen type inequalities for fuzzy integrals we provide several steffensen type inequalities for the sugeno integral the inequalities are of the form a b f g d a a a f d b or a b f g d a b b f d b where a b are constants is a fuzzy measure on r g a b 0 1 f a b r is nonincreasing or nondecreasing and b a a b g d we show that some of our sufficient conditions are also necessary

on steffensen pairs in the article we establish some general steffensen pairs by the use of mathematical induction and properties of the generalized weighted mean values

low temperature series expansions for the spin 1 ising model the finite lattice method of series expansion has been used to extend low temperature series for the partition function order parameter and susceptibility of the spin 1 ising model on the square lattice a new formalism is described which uses two distinct transfer matrix approaches in order to significantly reduce computer memory requirements and which permits the derivation of the series to 79th order subsequent analysis of the series clearly confirms that the spin 1 model has the same dominant critical exponents as the spin 1 2 ising model accurate estimates for both the critical temperature and non physical singularities are obtained in addition evidence for a non analytic confluent correction with exponent delta 1 1 1 or 0 1 is found

index formulas for generalized wiener hopf operators and boson fermion correspondence in 2n dimensions the kernels of operators associated with special chiral gauge trans formations kinks in the 2 dimensional dirac theory are explicitly deter mined the result is used to obtain index formulas for fredholm operators corresponding to continuous chiral gauge transformations moreover the fock space quadratic forms corresponding to the kinks are proved to converge to the dirac field as the kink size goes to zero it is also shown that for n i 2 mod4 the majorana field can be reached in a similar fashion

the failure of a conjectured s4 symmetry in the three state checkerboard potts model low temperature expansions are obtained for the three state potts model on the checkerboard lattice the four boltzmann weights were set to various integer multiples of a low temperature variable x the series were evaluated to order x19 but it was found that the conjectured s4 symmetry failed at order x14 for the zero field partition function the spontaneous magnetisation and the zero field susceptibility

large q expansion of the specific heat for the two dimensional q state potts model we have calculated the large q expansion for the specific heat at the phase transition point in the two dimensional q state potts model to the 23rd order in 1 sqrt q using the finite lattice method the obtained series allows us to give highly convergent estimates of the specific heat for q 4 on the first order transition point the result confirm us the correctness of the conjecture by bhattacharya et al on the asymptotic behavior of the specific heat for q to 4

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

the q state potts ferromagnet on d dimensional hypercubic lattices we use a high temperature star graph expansion to compute the free energy and the susceptibility of a q state potts model for arbitrary q on d dimensional hypercubic lattices the series are to order o 10 in the expansion variable nu ek 1 ek q 1 we show how to compute the expectation value of any operator on a finite graph for arbitrary number q of states of the potts model

series studies of the potts model i the simple cubic ising model the finite lattice method of series expansion is generalized to the q state potts model on the simple cubic lattice it is found that the computational effort grows exponentially with the square of the number of series terms obtained unlike two dimensional lattices where the computational requirements grow exponentially with the number of terms for the ising q 2 case the authors have extended the low temperature series for the partition functions magnetization and zero field susceptibility to u26 from u20 the high temperature series for the zero field partition function is extended from nu 18 to nu 22 subsequent analysis gives critical exponents in agreement with those from field theory

lattice realizations of unitary minimal modular invariant partition functions the conformal spectra of the critical dilute a d e lattice models are studied numerically the results strongly indicate that in branches one and two these models provide realizations of the complete a d e classification of unitary minimal modular invariant partition functions given by cappelli itzykson and zuber 1987 in branches three and four the results indicate that the modular invariant partition functions factorize similar factorization results are also obtained for two colour lattice models

a universal amplitude ratio for the q 4 potts model from a solvable lattice model the universal amplitude ratio r for the q 4 state potts model in two dimensions is determined by using results for the dilute a model in regime 1 the nature of the relationship between the potts model and the dilute a model is discussed

order parameters of the dilute a models the free energy and local height probabilities of the dilute a models with borken 2 symmetry are calculated analytically using inversion and corner transfer matrix methods these models possess four critical branches the first two branches provide new realizations of the unitary minimal series and the other two branches give a direct product of this series with an ising model we identify the integrable perturbations which move the dilute a models away from the critical limit generalized order parameters are defined and their critical exponents extracted the associated conformal weights are found to occur on the diagonal of the relevant kac table in an appropriate regime the dilute a3 model lies in the universality class of the ising model in a magnetic field in this case we obtain the magnetic exponent 15 directly without the use of scaling relations

triangular lattice potts models in this paper we study the 3 state potts model on the triangular lattice which has two and three site interactions using a peierls argument we obtain a rigorous bound on the transition temperature thereby disproving a conjecture on the location of its critical point low temperature series are generated and analyzed for three particular choices of the coupling constants a phase diagram is then drawn on the basis of these considerations our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order implying the existence of a multicritical point in the ferromagnetic region relation of the triangularq state potts model with other lattice statistical problems is also discussed in particular an ashkin teller model and the hard hexagon lattice gas solved by baxter emerge as special cases in appropriate limits

susceptibility amplitudes for the three and four state potts models abstract the finite lattice method of series expansions is used to calculate a number of extended series for susceptibilities of the three and four state potts models on the square lattice we analyse all these series and estimate their critical amplitudes we resolve an uncertainty in amplitude ratios for high to low temperature susceptibilities and thus provide confirmation of field theoretic predictions

mercer and wu srivastava generalisations of steffensen s inequality in this paper generalisations of steffensen s inequality obtained by pecaric mercer and wu srivastava are related some of this generalisations are showed to be equivalent and using wu srivastava refinement of steffensen s inequality refined versions of pecaric and mercer s results are obtained using wu srivastava sharpened and generalized version of mercer s result sharpened version of generalization given by pecaric is obtained furthermore weaker conditions for some generalisations and refinements are obtained moreover functionals defined as the difference between the left hand and the right hand side of generalizations and refinements of steffensen s inequality are studied new stolarsky type means using several families of exponentially convex functions related to defined functionals are generated

commutator anomalies and the fock bundle we show that the anomalous finite gauge transformations can be realized as linear operators acting on sections of the bundle of fermionic fock spaces parametrized by vector potentials and more generally by splittings of the fermionic one particle space into a pair of complementary subspaces on the lie algebra level we show that the construction leads to the standard formula for the relevant commutator anomalies

measures on infinite dimensional grassmann manifolds abstract a 1 parameter family of quasi invariant measures is presented these measures are cylinder measures in graph coordinates their characteristic functions are represented as integrals relative to an infinite product measure this is applied to the problem of determining the support properties of the measures one of the measures can be used to define the unitary structure for the basic representation of the affine extension of the restricted unitary group

a variant of jensen steffensen s inequality and quasi arithmetic means a variant of jensen steffensen s inequality is proved necessary and sufficient conditions for the equality in jensen steffensen s inequality are established several inequalities involving more than two monotonic functions and generalized quasi arithmetic means with not only positive weights are proved it is shown that such generalized quasi arithmetic means have the same comparability properties as those with positive weights

current algebras in d 1 dimensions and determinant bundles over infinite dimensional grassmannians we extend the methods of pressley and segal for constructing cocycle representations of the restricted general linear group in infinite dimensions to the case of a larger linear group modeled by schatten classes of rank 1 p an essential ingredient is the generalization of the determinant line bundle over an infinite dimensional grassmannian to the case of an arbitrary schatten rank p 1 the results are used to obtain highest weight representations of current algebras with the operator schwinger terms ind 1 dimensions when the space dimensiond is any odd number

some improvements and generalizations of steffensen s integral inequality abstract in this paper the authors present several interesting results on improvements of steffensen s integral inequality moreover an error in a generalization of steffensen s inequality due to mercer p r mercer extensions of steffensen s inequality j math anal appl 246 2000 325 329 is corrected

classical mechanics and geometric quantization on an infinite dimensional disc and grassmannian we discuss the classical mechanics on the grassmannian and the disc modeled on the ideal l 2 we apply methods of geometric quantization to these systems their relation to a flat symplectic space is also discussed

on the bellman generalization of steffensen s inequality iii soit f x une fonction non negative non croissante sur a b et soit u une fonction convexe croissante pour u 0 avec 0 0 si g x est une fonction non decroissante non negative sur a b telle qu il existe la fonction non negative g 1 x definie par l equation g 1 x g x g 1 x 1 et que a b g 1 t dt 1 alors l inegalite suivante est valable a b f t g t dt a b g t dt 1 a a f t dt ou a b g t d

on the mickelsson faddeev extension and unitary representations the mickelsson faddeev extension is a 3 space analogue of a kac moody group where the central charge is replaced by a space of functions of the gauge potential this extension is a pullback of a universal extension where the gauge potentials are replaced by operators in a schatten ideal as in non commutative differential geometry our main result is that the universal extension cannot be faithfully represented by unitary operators on a separable hilbert space we also examine potential consequences of the existence of unitary representations for the mickelsson faddeev extension

high temperature series expansions for the q state potts model on a hypercubic lattice and critical properties of percolation we present results for the high temperature series expansions of the susceptibility and free energy of the q state potts model on a d dimensional hypercubic lattice zd for arbitrary values of q the series are up to order 20 for dimension d 1 limit of these series we estimate the percolation threshold pc and critical exponent gamma for bond percolation in different dimensions we also extend the 1 d expansion of the critical coupling for arbitrary values of q up to order d 9

extensions of steffensen s inequality we offer a new proof of the well known steffensen inequality whose context is sufficiently general that it engenders a number of extensions

a further refinement of a jordan type inequality and its application abstract by introducing taylor polynomials a new sharpened and generalized version of jordan s inequality is established the result is then used to obtain a substantially more refined inequality of jordan type moreover an application of the results presented here toward the improvement of the yang le inequality is also considered in this paper

the potts model on kagome and honeycomb lattices low temperature series have been derived for theq state potts model on the kagom e lattice qd 3 and 4 and for the 3 state honeycomb lattice the series are derived by the finite lattice method with many additional terms obtained by noting the structure of the correction terms accurate estimates of the critical points are found which confirm exact but not rigorous results in the case of the honeycomb lattice and refute previous conjectures in the case of the kagom e lattice in this paper we report on the derivation and analysis of low temperature series for the 3 state honeycomb and 3 and 4 state kagomlattice potts model from the series we obtain estimates for the critical points which for the honeycomb model confirms the validity of the exact but not rigorous result 7 and for the kagomlattice provides accurate results against which conjectures can be tested and found not to hold we comment on properties that the solution must have in an unsuccessful attempt to find an alternative conjecture in addition we obtain estimates for the location of various non physical singularities the remainder of the paper is organized as follows in section 2 we briefly describe the finite lattice method of series expansions give details regarding the specific implementations for the kagomand honeycomb lattices and show how the finite lattice method can be supplemented by an extension procedure allowing us to derive more series terms details regarding the analysis of the series are given in section 3 and the implications for possible conjectures for the critical point on the kagom