rational approximation to the thomas fermi equations abstract we show that a simple and straightforward rational approximation to the thomas fermi equation provides the slope at origin with unprecedented accuracy and that pade approximants of relatively low order are far more accurate than more elaborate approaches proposed recently by other authors we consider both the thomas fermi equation for isolated atoms and for atoms in strong magnetic fields

accurate calculation of the solutions to the thomas fermi equations abstract we obtain highly accurate solutions to the thomas fermi equations for atoms and atoms in very strong magnetic fields we apply the pade hankel method numerical integration power series with pade and hermite pade approximants and chebyshev polynomials both the slope at origin and the location of the right boundary in the magnetic field case are given with unprecedented accuracy

n point deformation of algebraic k3 surfaces we construct a set of noncommutative geometries by performing n point deformation of algebraic k3 surfaces first we consider two point deformation of algebraic k3 surfaces by performing algebraic deformation of a pair of commutative algebraic k3 surfaces in this case the moduli space of the noncommutative deformations is of dimension 19 the same as the moduli dimension of the complex deformations of commutative algebraic k3 surfaces then we extend this method to the n point case in the n point case the dimension of deformation moduli space becomes 19n n 1 2

on a perturbation treatment of a model for mhd viscous flow we discuss the solution of a nonlinear ordinary differential equation that appears in a model for mhd viscous flow caused by a shrinking sheet we propose an accurate numerical solution and derive simple analytical expressions our results suggest that a recent perturbation treatment of the same problem exhibits a pathological behaviour and conjecture its probable cause

strong morita equivalence of higher dimensional noncommutative tori ii we show that two c algebraic noncommutative tori are strongly morita equivalent if and only if they have isomorphic ordered k0 groups and centers extending n c phillips s result in the case that the algebras are simple this is also generalized to the twisted group c algebras of arbitrary finitely generated abelian groups

finitized conformal spectrum of the ising model on the cylinder and torus abstract the spectrum of the critical ising model on a lattice with cylindrical and toroidal boundary conditions is calculated by commuting transfer matrix methods using a simple truncation procedure we obtain the natural finitizations of the conformal spectra recently proposed by melzer these finitizations imply polynomial identities which in the large lattice limit give rise to the rogers ramanujan identities for the c 1 2 virasoro characters

quantum thetas on noncommutative bb t d with general embeddings in this paper we construct quantum theta functions over noncommutative t a with general embeddings manin has constructed quantum theta functions from the lattice embedding into vector space x finite group we extend manin s construction of quantum thetas to the case of general embedding of vector space x lattice x torus it turns out that only for the vector space part of the embedding there exists the holomorphic theta vector while for the lattice part there does not furthermore the so called quantum translations from embedding into the lattice part become non additive while those from the vector space part are additive

paths and partitions combinatorial descriptions of the parafermionic states the zk parafermionic conformal field theories despite the relative complexity of their modes algebra offer the simplest context for the study of the bases of states and their different combinatorial representations three bases are known the classic one is given by strings of the fundamental parafermionic operators whose sequences of modes are in correspondence with restricted partitions with parts at distance k 1 differing at least by 2 another basis is expressed in terms of the ordered modes of the k 1 different parafermionic fields which are in correspondence with the so called multiple partitions both types of partitions have a natural bressoud path representation finally a third basis formulated in terms of different paths is inherited from the solution of the restricted solid on solid model of andrews baxter forrester the aim of this work is to review in a unified and pedagogical exposition these four different combinatorial representations of the states of the zk parafermionic models

theta vectors and quantum theta functions in this paper we clarify the relation between manin s quantum theta function and schwarz s theta vector we do this in comparison with the relation between the kq representation which is equivalent to the classical theta function and the corresponding coordinate space wavefunction we first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting when the translation operators of the phase space are not commuting then the kq representation is no longer meaningful we explain why manin s quantum theta function obtained via algebra quantum torus valued inner product of the theta vector is a natural choice for the quantum version of the classical theta function we then show that this approach holds for a more general theta vector containing an extra linear term in the exponent obtained from a holomorphic connection of constant curvature than the simple gaussian one used in manin s construction

a quick perturbative method for schrodinger equations within the framework of perturbation theory we propose firstly an iterative method which may serve as a source of optimal unperturbed solutions in both one and more dimensions it combines the runge kutta and newton algorithm and its efficiency is illustrated on a few quartic oscillators secondly admitting also an arbitrary perturbation of potentials we generalize the existing runge kutta one dimensional rayleigh schrodinger constructions of energies and wavefunctions to more dimensions

rapidly decreasing functions in reduced algebras of groups let r be a group we associate to any length function l on r the space h r of rapidly decreasing functions on r with respect to l which coincides with the space of smooth functions on the k dimensional torus when r zk we say that r has property rd if there exists a length function l on r such that h r is contained in the reduced c algebra c r of r we study the stability of property rd with respect to some constructions of groups such as subgroups over groups of finite index semidirect and amalgamated products finally we show that the following groups have property rd 1 finitely generated groups of polynomial growth 2 discrete cocompact subgroups of the group of all isometries of any hyperbolic space

generalized complex geometry generalized complex geometry encompasses complex and symplectic ge ometry as its extremal special cases we explore the basic properties of this geometry including its enhanced symmetry group elliptic deforma tion theory relation to poisson geometry and local structure theory we also dene and study generalized complex branes which interpolate be tween at bundles on lagrangian submanifolds and holomorphic bundles on complex submanifolds

batalin vilkovisky algebras and two dimensional topological field theories by a batalin vilkovisky algebra we mean a graded commutative algebraa together with an operator a a 1 such that 2 0 and a a is a graded derivation ofa for alla a in this article we show that there is a natural structure of a batalin vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions we make use of a technique from algebraic topology the theory of operads

fermionic solution of the andrews baxter forrester model i unification of tba and ctm methods the problem of computing the one dimensional configuration sums of the abf model in regime iii is mapped onto the problem of evaluating the grandcanonical partition function of a gas of charged particles obeying certain fermionic exclusion rules we thus obtain a newfermionic method to compute the local height probabilities of the model combined with the originalbosonic approach of andrews baxter and forrester we obtain a new proof of some of melzer s polynomial identities in the infinite limit these identities yield rogers ramanujan type identities for the virasoro characters l 1 r l r q as conjectured by the stony brook group as a result of our work the corner transfer matrix and thermodynamic bethe ansatz approaches to solvable lattice models are unified

on the uniqueness of l _ infty bootstrap quasi isomorphisms are seiberg witten maps in the context of the recently proposed l bootstrap approach the question arises whether the so constructed gauge theories are unique solutions of the l relations physically it is expected that two gauge theories should be considered equivalent if they are related by a field redefinition described by a seiberg witten map to clarify the consequences in the l framework it is proven that seiberg witten maps between physically equivalent gauge theories correspond to certain relations of quasi isomorphisms of the underlying l algebras the proof suggests an extension of the definition of a seiberg witten map to the closure conditions of two gauge transformations and the dynamical equations of motion in the context of the recently proposed l bootstrap approach the question arises whether the so constructed gauge theories are unique solutions of the l relations physically it is expected that two gauge theories should be considered equivalent if they are related by a field redefinition described by a seiberg witten map to clarify the consequences in the l framework it is proven that seiberg witten maps between physically equivalent gauge theories correspond to certain relations of quasi isomorphisms of the underlying l algebras the proof suggests an extension of the definition of a seiberg witten map to the closure conditions of two gauge transformations and the dynamical equations of motion

q trinomial identities we obtain connection coefficients between q binomial and q trinomial coefficients using these one can transform q binomial identities into q trinomial identities and back again to demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of berkovich mccoy and pearce which have recently arisen in their study of the 2 1 and 1 5 perturbations of minimal conformal field theory

local height probabilities in a composite andrews baxter forrester model we study the local height probabilities in a composite height model derived from the restricted solid on solid model introduced by andrews baxter and forrester and their connection with conformal field theory characters the obtained conformal field theories also describe the critical behavior of the model at two different critical points in addition at criticality the model is equivalent to a one dimensional chain of anyons subject to competing two and three body interactions the anyonic chain interpretation provided the original motivation to introduce the composite height model and by obtaining the critical behavior of the composite height model the critical behavior of the anyonic chains is established as well depending on the overall sign of the hamiltonian this critical behavior is described by a diagonal coset model generalizing the minimal models for one sign and by fateev zamolodchikov parafermions for the other

direct calculation of accurate siegert eigenvalues the roots of the hankel determinant built with the taylor coefficients of the regularized logarithmic derivative of the eigenfunction give both the bound state and siegert eigenvalues resonances of separable quantum mechanical systems we obtain accurate positions and widths for the resonances of some commonly chosen test examples

rogers ramanujan identities in the hard hexagon model the hard hexagon model in statistical mechanics is a special case of a solvable class of hard square type models in which certain special diagonal interactions are added the sublattice densities and order parameters of this class are obtained and it is shown that many rogers ramanujan type identities naturally enter the working

proof of the flohr grabow koehn conjectures for characters of logarithmic conformal field theory in a recent paper flohr grabow and koehn conjectured that the characters of the logarithmic conformal field theory ck 1 admit fermionic representations labelled by the lie algebra dk in this paper we provide a simple analytic proof of this conjecture

the andrews gordon identities and q multinomial coefficients we prove polynomial boson fermion identities for the generating function of the number of partitions of n of the form n sum j 1 l 1 j f j with f 1 leq i 1 f l 1 leq i 1 and f j f j 1 leq k the bosonic side of the identities involves q deformations of the coefficients of x a in the expansion of 1 x cdots x k l a combinatorial interpretation for these q multinomial coefficients is given using durfee dissection partitions the fermionic side of the polynomial identities arises as the partition function of a one dimensional lattice gas of fermionic particles

fermionic solution of the andrews baxter forrester model ii proof of melzer s polynomial identities we compute the one dimensional configuration sums of the abf model using the fermionic technique introduced in part i of this paper combined with the results of andrews baxter and forrester we prove polynomial identities for finitizations of the virasoro characters chi b a r 1 r q as conjectured by melzer in the thermodynamic limit these identities reproduce rogers ramanujan type identities for the unitary minimal virasoro characters conjectured by the stony brook group we also present a list of additional virasoro character identities which follow from our proof of melzer s identities and application of bailey s lemma

a generalization of connes kreimer hopf algebra bonsai hopf algebras introduced here are generalizations of connes kreimer hopf algebras which are motivated by feynman diagrams and renormalization we show that we can find operad structure on the set of bonsais we introduce a differential on these bonsai hopf algebras which is inspired by the tree differential the cohomologies of these are computed here and the relationship of this differential with the appending operation of connes kreimer hopf algebras is investigated

equivariant cohomology and the maurer cartan equation let g be a compact connected lie group acting smoothly on a manifold m goresky kottwitz macpherson described a small cartan model for the equivariant cohomology of m quasi isomorphic to the standard cartan complex of equivariant differential forms in this paper we construct an explicit cochain map from the small cartan model into the standard cartan model inducing an isomorphism in cohomology the construction involves the solution of a remarkable inhomogeneous maurer cartan equation this solution has further applications to the theory of transgression in the weil algebra and to the chevalley koszul theory of the cohomology of principal bundles

harmonic oscillations in a quasi relativistic regime a square root anharmonic oscillator potential is analysed as a model which simulates a quasi relativistic squeezing of the harmonic oscillator spectrum several eligible namely perturbative variational hill determinant and riccati pade methods of construction of its bound states are compared

quantum thetas on noncommutative bb t 4 from embeddings into lattice in this paper we investigate the theta vector and quantum theta function over noncommutative from the embedding of manin has constructed the quantum theta functions from the lattice embedding into vector space finite group we extend manin s construction of the quantum theta function to the embedding of vector space lattice case we find that the holomorphic theta vector exists only over the vector space part of the embedding and over the lattice part we can only impose the condition for the schwartz function the quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function however two subsequent quantum translations from the embedding into the lattice part are nonadditive contrary to the additivity of those from the vector space part

a nonlocal operator basis from the path representation of the cal m k 1 hbox k 2 and the cal m k 1 hbox 2k 3 minimal models we reinterpret a path describing a state in an irreducible module of the unitary minimal model in terms of a string of charged operators acting on the module s ground state path each such operator acts non locally on a path the path characteristics are then translated into a set of conditions on sequences of operators that provide an operator basis as an application we re derive the vacuum finite fermionic character by constructing the generating function of these basis states these results generalize directly to the models the close relatives of the unitary models in terms of path description

the anharmonic oscillator perturbation series for cubic and quartic energy distortion twenty five terms of the perturbation series are calculated for the first five energy levels of an oscillator with lambda x4 energy distortion and a similar calculation is carried out for the first six levels for lambda x3 distortion for the positive quartic the alternating series is summed using the aitken delta 2 transformation for lambda from 0 1 to 100 an exponential integral model and a truncated binomial model are used to transform the series for negative distortion energies and the complex energy eigenvalues are calculated for lambda from 0 01 to 1

morita equivalence of smooth noncommutative tori we show that in the generic case the smooth noncommutative tori associated with two n n real skew symmetric matrices are morita equivalent if and only if the matrices are in the same orbit of the natural so n n z action

the riccati pade method for coupled channel equations we present a method for calculating the energies of bound and quasibound states of quantum mechanical problems expressed in terms of coupled channel equations the approach is based on a rational approximation to the logarithmic derivative of the eigenfunction and leads to a simple quantization condition

exceptional structure of the dilute a 3 model e 8 and e 7 rogers ramanujan identities the dilute a3 lattice model in regime 2 is in the universality class of the ising model in a magnetic field here we directly establish the existence of an e8 structure in the dilute a3 model in this regime by expressing the one dimensional configuration sums in terms of fermionic sums which involve the e8 root system explicitly in the thermodynamic limit these polynomial identities yield a proof of the e8 rogers ramanujan identity recently conjectured by kedem et al 1993 the polynomial identities also apply to regime 3 which is obtained by transforming the modular parameter by q to 1 q in this case we find an a1xe7 structure and prove a rogers ramanujan identity of a1xe7 type finally in the critical q to 1 limit we give some intriguing expressions for the number of l step paths on the a3 dynkin diagram with tadpoles in terms of the e8 cartan matrix all our findings confirm the e8 and e7 structure of the dilute a3 model found recently by means of the thermodynamic bethe ansatz

symmetry of quantum torus with crossed product algebra in this paper we study the symmetry of quantum torus with the concept of crossed product algebra as a classical counterpart we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function an invariant function under the group action is constructed as a variant of the classical theta function then our main issue the crossed product algebra representation of a quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding we perform this analysis with manin s so called model ii quantum theta function approach the symplectic group sp 2n z satisfies the consistency condition of a crossed product algebra representation of quantum torus times the algebra of functions on the siegel space however only a subgroup of sp 2n z satisfies the consistency condition for orbifolding of the quantum torus

on an iteration method for eigenvalue problems we discuss a recently proposed asymptotic iteration method for eigenvalue problems we analyse its rate of convergence the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas

quantum open closed homotopy algebra and string field theory we reformulate the algebraic structure of zwiebach s quantum open closed string field theory in terms of homotopy algebras we call it the quantum open closed homotopy algebra qocha which is the generalization of the open closed homotopy algebra ocha of kajiura and stasheff the homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds in particular deformations by maurer cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories

homotopy classification of bosonic string field theory we prove the decomposition theorem for the loop homotopy lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given s matrix for the theory of open and closed strings we use results in open closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds as a further application of the open closed homotopy algebra we show that string field theory is background independent and locally unique in a very precise sense finally we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories

open closed homotopy algebra in mathematical physics in this paper we discuss various aspects of open closed homotopy algebras ochas presented in our previous paper inspired by zwiebach s open closed string field theory but that first paper concentrated on the mathematical aspects here we show how an ocha is obtained by extracting the tree part of zwiebach s quantum open closed string field theory we clarify the explicit relation of an ocha with kontsevich s deformation quantization and with the b models of homological mirror symmetry an explicit form of the minimal model for an ocha is given as well as its relation to the perturbative expansion of open closed string field theory we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

cut down method in the inductive limit decomposition of non commutative tori iii a complete answer in 3 dimension we use the cut down method and a multi dimensional continued fraction approximation to prove that any simple 3 torus is an inductive limit of direct sums of four circle algebras consequently simple 3 tori are classified by the orderedk0 group with distinguished order unit

categories of holomorphic line bundles on higher dimensional noncommutative complex tori we construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori our basic tools are heisenberg modules over noncommutative tori and complex holomorphic structures on them introduced by schwarz theta functions on noncommutative tori lett math phys 58 81 90 2001 we obtain differential graded dg categories as full subcategories of curved dg categories of heisenberg modules over the complex noncommutative tori also we present the explicit composition formula of morphisms which in fact depends on the noncommutativity

analytic continuation of taylor series and the boundary value problems of some nonlinear ordinary differential equations abstract we compare and discuss the respective efficiency of three methods with two variants for each of them based respectively on taylor maclaurin series pade approximants and conformal mappings for solving quasi analytically a two point boundary value problem of a nonlinear ordinary differential equation ode six configurations of ode and boundary conditions are successively considered according to the increasing difficulties that they present after having indicated that the taylor series method almost always requires the recourse to analytical continuation procedures to be efficient we use the complementarity of the two remaining methods pade and conformal mapping to illustrate their respective advantages and limitations we emphasize the importance of the existence of solutions with movable singularities for the efficiency of the methods particularly for the so called pade hankel method we show that this latter method is equivalent to pushing a movable pole to infinity for each configuration we determine the singularity distribution in the complex plane of the independent variable of the solution sought and show how this distribution controls the efficiency of the two methods in general the method based on pade approximants is easy to use and robust but may be awkward in some circumstances whereas the conformal mapping method is a very fine method which should be used when high accuracy is required

harmonic analysis on quantum tori this paper is devoted to the study of harmonic analysis on quantum tori we consider several summation methods on these tori including the square fej r means square and circular poisson means and bochner riesz means we first establish the maximal inequalities for these means then obtain the corresponding pointwise convergence theorems in particular we prove the noncommutative analogue of the classical stein theorem on bochner riesz means the second part of the paper deals with fourier multipliers on quantum tori we prove that the completely bounded l p fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension finally we present the littlewood paley theory associated with the circular poisson semigroup on quantum tori we show that the hardy spaces in this setting possess the usual properties of hardy spaces as one can expect these include the quantum torus analogue of fefferman s h 1 bmo duality theorem and interpolation theorems our analysis is based on the recent developments of noncommutative martingale ergodic inequalities and littlewood paley stein theory

matrix theory compactification on noncommutative t4 z2 in this article we construct gauge bundles on a noncommutative toroidal orbifold t 4 z2 first we explicitly construct a bundle with constant curvature connections on a noncommutative t 4 following rieffel s method then applying the appropriate quotient conditions for its z2 orbifold we find a connes douglas schwarz type solution of matrix theory compactified on t 4 z2 when we consider two copies of a bundle on t 4 invariant under the z2 action the resulting higgs branch moduli space of equivariant constant curvature connections becomes an ordinary toroidal orbifold t4 z2

on operad structures of moduli spaces and string theory we construct a real compactification of the moduli space of punctured rational algebraic curves and show how its geometry yields operads governing homotopy lie algebras gravity algebras and batalin vilkovisky algebras these algebras appeared recently in the context of string theory and we give a simple deduction of these algebraic structures from the formal axioms of conformal field theory and string theory

smooth dense subalgebras of reduced group c algebras schwartz cohomology of groups and cyclic cohomology abstract we introduce the notion of schwartz co homology of a discrete group with a length function which is the natural generalization of the bounded cohomology of a discrete group we prove that if the length function is chosen to be a word length on a group of polynomial growth then its schwartz cohomology is canonically isomorphic to the usual group cohomology with complex coefficients using this result we will show that the group cohomology of a discrete group of polynomial growth is of polynomial growth in the sense of connes and moscovici and that there are no nontrivial idempotents in the group c algebra of a torsion free group of polynomial growth by the method of cyclic cohomology of connes

theta functions on noncommutative t4 we construct the so called theta vectors on noncommutative t4 which correspond to the theta functions on commutative tori with complex structures following the method of dieng and schwarz we first construct holomorphic connections and then find the functions satisfying the holomorphic conditions the theta vectors the holomorphic structure in the noncommutative t4 case is given by a 2 2 complex matrix and the consistency requires its off diagonal elements to be the same we also construct the tensor product of these functions satisfying the consistency requirement

spectral decomposition of path space in solvable lattice model we give thespectral decomposition of the path space of the u q widehat sl 2 vertex model with respect to the local energy functions the result suggests the hidden yangian module structure on the widehat sl 2 levell integrable modules which is consistent with the earlier work 1 in the level one case also we prove the fermionic character formula of the widehat sl 2 levell integrable representations in consequence

the anharmonic oscillator complex eigenvalues for the ground state with negative quartic or cubic energy distortion the perturbed ground state eigenvalues for the harmonic oscillator with negative quartic and with cubic energy distortion are calculated by numerical integration these agree with the author s results using an asymptotic series

a path integral approach to the kontsevich quantization formula we give a quantum field theory interpretation of kontsevich s deformation quantization formula for poisson manifolds we show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory its batalin vilkovisky quantization yields a superconformal field theory the associativity of the star product and more generally the formality conjecture can then be understood by field theory methods as an application we compute the center of the deformed algebra in terms of the center of the poisson algebra

tight bounds to the schrodinger equation eigenvalues increasing tight upper and lower bounds to the schrodinger equation eigenvalues are obtained from the riccati equation for the logarithmic derivative of the wavefunction the solution of this non linear equation is written as a pade approximant and the bounds are given by the roots of a sequence of determinants numerical results are shown for the anharmonic and quartic oscillators

a hill series method for resonances a simple algorithm is given to treat perturbed oscillator bound states and resonances the method is applied to a bound state problem for which the energy is a non analytic function of a perturbation parameter and also to two resonance problems one of which has a spectrum with an unusual dual nature

complex variable hvpt complex variable hypervirial perturbation theory is applied to the case of oscillator and coulomb potentials perturbed by a single term potential of the form vxn or vrn respectively the trial calculations reported show that this approach can produce accurate complex energies for resonant states via a simple and speedy calculation and can also be useful in studies of pt symmetry and tunnelling resonance effects

conformal mappings versus other power series methods for solving ordinary differential equations illustration on anharmonic oscillators the simplicity and the efficiency of a quasi analytical method for solving nonlinear ordinary differential equations ode is illustrated on the study of anharmonic oscillators ao with a potential v x x2 x2m m 0 the method bervillier 2008 nucl phys b801 296 applies a priori to any ode with two point boundaries one being located at infinity the solution of which has fixed singularities in the complex plane of the independent variable x a conformal mapping of a suitably chosen angular sector of the complex plane of x upon the unit disc centered at the origin makes convergent the transformed taylor series of the generic solution so that the boundary condition at infinity can be easily imposed in principle this constraint when applied on the logarithmic derivative of the wavefunction determines the eigenvalues to an arbitrary level of accuracy in practice for 0 or slightly negative the accuracy of the results obtained is astonishingly large with regard to the modest computing power used various aspects of the method and comparisons with some seemingly similar methods based also on expressing the solution as a taylor series are shortly reviewed presented and discussed

homotopy algebras inspired by classical open closed string field theory we define a homotopy algebra associated to classical open closed strings we call it an open closed homotopy algebra ocha it is inspired by zwiebach s open closed string field theory and also is related to the situation of kontsevich s deformation quantization we show that it is actually a homotopy invariant notion for instance the minimal model theorem holds also we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

q trinomial coefficients and the dilute a model we express the configuration sums of the dilute model in regimes and in terms of q trinomial coefficients we then extend previous results to give expressions for all phases and regimes for odd l for finite system size

accurate eigenvalues and eigenfunctions for quantum mechanical anharmonic oscillators the representation of the taylor expansion of the logarithmic derivative of the wavefunction by means of a pade approximant followed by an appropriate quantization condition proves a powerful way of obtaining accurate eigenvalues of the schrodinger equation in this paper we investigate in detail some of the interesting features of this approach termed riccati pade method rpm by means of its application to anharmonic oscillators we analyse the occurrence of many roots in the neighborhoods of the physical eigenvalues in the weak coupling regime and also obtain accurate coefficients of the strong coupling expansion we finally investigate the global and the local accuracy of the rpm eigenfunctions

comment on an application of the asymptotic iteration method to a perturbed coulomb model we discuss a recent application of the asymptotic iteration method aim to a perturbed coulomb model contrary to what was argued before we show that the aim converges and yields accurate energies for that model we also consider alternative perturbation approaches and show that one of them is equivalent to that recently proposed by another author

polynomial identities indices and duality for the n 1 superconformal model sm 2 4v we prove polynomial identities for then 1 superconformal modelsm 2 4v which generalize and extend the known fermi bose character identities our proof uses theq trinomial coefficients of andrews and baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq series on the fermionic side we use these polynomials to demonstrate a dual relation underq q 1 betweensm 2 4v andm 2v 1 4v we also introduce a genralization of the witten index which is expressible in terms of the rogers false theta functions

categories of holomorphic vector bundles on noncommutative two tori in this paper we study the category of standard holomorphic vector bundles on a noncommutative two torus we construct a functor from the derived category of such bundles to the derived category of coherent sheaves on an elliptic curve and prove that it induces an equivalence with the subcategory of stable objects by the homological mirror symmetry for elliptic curves this implies an equivalence between the derived category of holomorphic bundles on a noncommutative two torus and the fukaya category of the corresponding symplectic commutative torus

models for classifying spaces and derived deformation theory using the theory of extensions of l l l algebras we construct rational homotopy models for classifying spaces of fibrations giving answers in terms of classical homological functors namely the chevalley eilenberg and harrison cohomology we also investigate the algebraic structure of the chevalley eilenberg complexes of l l l algebras and show that they possess along with the gerstenhaber bracket an l l l structure that is homotopy abelian

on noncommutative multi solitons solitons in noncommutative scalar field theories possess many stringy features in particular multi solitons in these theories behave like multiple d branes a useful moduli space description for multi solitons exists which reproduces stringy features of d brane moduli spaces in a simple way via properties of special projection operators in particular they are equivalent to a hilbert scheme resolution of symmetric product spaces