a cellular automaton model of excitable media iii fitting the belousov zhabotinskiic reaction abstract we obtain a set of parameter values for our cellular automaton model that gives a reasonably good description of the belousov zhabotinskii reaction as determined by comparison with experimental results and with calculations on the oregonator a differential equation model of the chemical system

a q deformation of wakimoto modules primary fields and screening operators theq vertex operators of frenkel and reshetikhin are studied by means of aq deformation of the wakimoto module for the quantum affine algebrau q widehat mathfrak s mathfrak l 2 at an arbitrary levelk 0 2 a fock module version of theq deformed primary field of spinj is introduced as well as the screening operators which anti commute with the action ofu q widehat mathfrak s mathfrak l 2 up to a total difference of a field a proof of the intertwining property is given for theq vertex operators corresponding to the primary fields of spinj 1 2z 0 a sample calculation of the correlation function is also given

a cellular automaton model of excitable media ii curvature dispersion rotating waves and meandering waves abstract a cellular automaton model of excitable media recently introduced by the authors is examined in more detail here we show that i the model is consistent with a linear dependence of wave speed on wave front curvature in two dimensional space ii the model exhibits a stepwise increasing relation between wave speed and temporal period the dispersion relation whose precise shape can be controlled by parameter settings iii the model generates rigidly rotating spiral waves whose frequency speed and core size are consistent with theoretical expectations and iv spiral waves rotate non rigidly showing short term flowerlet meandering which seems to arise by bifurcation from the rigidly rotating solution and long term irregular wandering over large distances these observations are consistent with many known features of wave propagation in two dimensional continuous excitable media governed by reaction diffusion equations suggesting that our cellular automaton model is not only a fast but also a reliable method for investigating the behavior of excitable media

discrete maximum principles for finite element solutions of some mixed nonlinear elliptic problems using quadratures the discrete maximum principles are proved for finite element solutions of some nonlinear elliptic problems with mixed boundary conditions the effect of quadrature rules used for the construction of the stiffness matrices is taken into account

on the lipschitz continuity of derivatives for some scalar nonlinearities vector nonlinearities determined by a scalar function arise in various mathematical models the numerical solution of the corresponding partial differential equations often rely on the lipschitz continuity of the derivative of the nonlinear operator in this paper a simple sufficient condition is given for the required lipschitz continuity also providing an easily computable estimate of the lipschitz constant some discussion is included for the corresponding elliptic operators

a time space finite element discretization technique for the calculation of the electromagnetic field in ferromagnetic materials the stability of time stepping methods for parabolic differential equations is mostly a critical issue furthermore solving such equations with a classical time stepping approach can be very expensive because many small time steps have to be taken if steep gradients occur in the solution even if these occur only in a narrow part of the space domain in this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a time slab this technique may be repeatedly applied to obtain further parts of the solution in subsequent time intervals it will be shown that with the proposed method the solution can be computed cheaply even if it has steep gradients and that stability is automatically guaranteed for the solution of the non linear algebraic equations on each time slab fast iterative methods can be used

the reconstruction of local quantum operators for the boundary xxz spin heisenberg chain the method of the reconstruction of local quantum operators in terms of the elements of the quantum monodromy matrix is applied to the xxz spin heisenberg chain with integrable boundary conditions

spiral selection as a free boundary problem abstract we present a new formulation of the spiral selection problem for the belousov zhabotinsky reaction in particular we focus on deriving an exact integro differential shape equation and discuss the possible behavior of solutions to this equation we also present some new results on the asymptotic far from core structure of spirals in the fife scaling regime

a geometrical theory for spiral waves in excitable media in this paper we develop a geometrical theory for waves in excitable reacting media using singular perturbation arguments and dispersion of traveling plane wave trains we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems governed by the eikonal equation using this theory we study the effect of curvature on waves in excitable media specifically rotating spiral patterns in planar regions from this theory we are able to determine the frequency and wavelength for spiral patterns in excitable nonoscillatory media

diagrammatics for su 2 invariant matrix product states we report on a systematic implementation of su 2 invariance for matrix product states mps with concrete computations cast in a diagrammatic language as an application we present a variational mps study of a spin 1 2 quantum chain for efficient computations we make systematic use of the su 2 symmetry at all steps of the calculations i the matrix space is set up as a direct sum of irreducible representations ii the local matrices with state valued entries are set up as superposition of su 2 singlet operators iii products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols the remaining numerical computations like the diagonalization of the associated transfer matrix and the minimization of the energy expectation value are done in spaces free of symmetry degeneracies the energy expectation value is a strict upper bound of the true ground state energy and yields definite conclusions about the accuracy of density matrix renormalization group results reported in the literature furthermore we present explicit results with accuracy better than 10 4 for nearest and next nearest neighbour spin correlators and for general dimer dimer correlators in the thermodynamical limit of the spin heisenberg chain with frustration

on stability and uniqueness of stationary one dimensional patterns in the belousov zhabotinsky reaction in this paper a numerical solution technique is presented for obtaining time independent spatial patterns of chemical concentration in the belousov zhabotinsky reaction the oregonator model of the reaction is assumed and the concentrations of each of the three principal intermediate species are expressed as fourier series in the spatial variable and the coefficients are then obtained by a straightforward galerkin technique results of extensive numerical calculation are discussed and it is demonstrated that in many instances the spatial pattern obtained is not unique in the sense that at least two different patterns could be produced at the same values of the chemical rate constants and diffusion coefficients the problem of whether the steady patterns are stable in time to small perturbations is discussed in detail a criterion for stability of patterns of infinitesimal amplitude is established and it is shown that when all the diffusion coefficients are equal there can be no stable small amplitude solutions however in the non linear case large amplitude quasi stable patterns have been discovered and these are discussed

a q operator identity for the correlation functions of the infinite xxz spin chain an explicit construction for q operators of the finite xxz spin chain with twisted boundary conditions is presented the massless and the massive regimes are considered as well as the root of unity case it is explained how these results yield an alternative expression for the trace function employed in the description of the correlation functions of the inhomogeneous xxz model on the infinite lattice by boos jimbo miwa smirnov and takeyama

traces on the sklyanin algebra and correlation functions of the eight vertex model we propose a conjectural formula for correlation functions of the z invariant inhomogeneous eight vertex model we refer to this conjecture as ansatz it states that correlation functions are linear combinations of products of three transcendental functions with theta functions and derivatives as coefficients the transcendental functions are essentially logarithmic derivatives of the partition function per site the coefficients are given in terms of a linear functional tr on the sklyanin algebra which interpolates the usual trace on finite dimensional representations we establish the existence of tr and discuss the connection to the geometry of the classical limit we also conjecture that the ansatz satisfies the reduced qkz equation as a non trivial example of the ansatz we present a new formula for the next nearest neighbour correlation functions

unitary representations of uq 2 ℝ the modular double and the multiparticle q deformed toda chain the paper deals with the analytic theory of the quantum q deformed toda chains the technique used combines the methods of representation theory and the quantum inverse scattering method the key phenomenon which is under scrutiny is the role of the modular duality concept first discovered by l faddeev in the representation theory of noncompact semisimple quantum groups explicit formulae for the whittaker vectors are presented in terms of the double sine functions and the wave functions of the n particle q deformed open toda chain are given as a multiple integral of the mellin barnes type for the periodic chain the two dual baxter equations are derived

bosonic representations of yangian double with on the basis of the rtt ttr formalism we introduce the quantum double of the yangian for with a central extension the gauss decomposition of the t matrices gives us the so called drinfel d generators using these generators we present some examples of both finite and infinite dimensional representations that are quite natural deformations of their corresponding affine counterpart

on the physical part of the factorized correlation functions of the xxz chain it was recently shown by jimbo et al 2008 arxiv 0811 0439 that the correlation functions of a generalized xxz chain associated with an inhomogeneous six vertex model with a disorder parameter and with arbitrary inhomogeneities on the horizontal lines factorize and can all be expressed in terms of only two functions and here we approach the description of the same correlation functions and in particular of the function from a different direction we start from a novel multiple integral representation for the density matrix of a finite chain segment of length m in the presence of a disorder field we explicitly factorize the integrals for m 2 based on this we present an alternative description of the function in terms of the solutions of certain linear and nonlinear integral equations we then prove directly that the two definitions of describe the same function the definition in the work of jimbo et al 2008 arxiv 0811 0439 was crucial for the proof of the factorization the definition given here together with the known description of in terms of the solutions of nonlinear integral equations is useful for performing e g the trotter limit in the finite temperature case or for obtaining numerical results for the correlation functions at short distances we also address the issue of the construction of an exponential form of the density matrix for finite

density matrix elements and entanglement entropy for the spin 1 2 xxz chain at δ 1 2 we have analytically obtained all the density matrix elements up to six lattice sites for the spin 1 2 heisenberg xxz chain at 1 2 we use the multiple integral formula of the correlation function for the massless xxz chain derived by jimbo and miwa as for the spin spin correlation functions we have newly obtained the fourth and fifth neighbour transverse correlation functions we have calculated all the eigenvalues of the density matrix and analyse the eigenvalue distribution using these results the exact values of the entanglement entropy for the reduced density matrix up to six lattice sites have been obtained we observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory

critical correlations in a z invariant inhomogeneous ising model abstract we study the critical spin spin correlation function in the z invariant inhomogeneous ising model which includes the rectangular triangular honeycomb and checkerboard lattices as special cases using quadratic difference equations we derive various explicit representations for the correlation function confirming and simplifying also a miraculous result of baxter

form factors and action of on cycles let be a sequence of skew symmetric polynomials in x1 xl satisfying degxjpn l n 1 whose coefficients are symmetric laurent polynomials in z1 zn we call p an cycle if holds for all n l these objects arise in integral representations for form factors of massive integrable field theory i e the su 2 invariant thirring model and the sine gordon model the variables a logxa are the integration variables and j logzj are the rapidity variables to each cycle there corresponds a form factor of the above models conjecturally all form factors are obtained from the cycles in this paper we define an action of on the space of cycles there are two sectors of cycles depending on whether n is even or odd using this action we show that the character of the space of even resp odd cycles which are polynomials in z1 zn is equal to the level 1 irreducible character of with lowest weight 0 resp 1 we also suggest a possible tensor product structure of the full space of cycles

free boson representation of dyℏ gln k and dyℏ sln k we construct a realization of the yangian double dy h over bar gl n k and dy h over bar sl n k for an arbitrary level k in terms of free boson fields with a continuous parameter in the h over bar 0 limit this realization becomes the wakimoto realization of affine lie algebras gl n and sl n respectively the vertex operators and the screening currents are also constructed with the same spirits the screening currents commute with dy h over bar sl n module total difference c 1998 american institute of physics s0022 2488 98 00104 2

spiral waves in the belousov zhabotinskii reaction abstract the beautiful spiral waves of oxidation in the belousov zhabotinskii reaction are the source of many interesting and important questions about periods structures in excitable media it has long been known that these spirals are similar to involutes of circles at least some distance from the center but until now no way has been known to determine the correct wavelength and frequency in this paper we show that the parameters of a spiral wave can be viwed s eigenvalues of a problem with unique solution the critical ingredients of the theory are the effects of curvature on the propagation of wavefronts in two dimensional media and the dispersion of plane waves our analytical results are shown to be in good agreement with experimental data for the belousov zhabotinskii reagent

a note on the high temperature expansion of the density matrix for the isotropic heisenberg chain abstract gohmann klumper and seel derived the multiple integral formula of the density matrix of the xxz heisenberg chain at finite temperatures we have applied the high temperature expansion hte method to isotropic case of their formula in a finite magnetic field and obtained coefficients for several short range correlation functions for example we have succeeded to obtain the coefficients of the hte of the third neighbor correlation function j z j 3 z for zero magnetic field up to the order of 25 these results expand our previous results on the emptiness formation probability z tsuboi m shiroishi j phys a math gen 38 2005 l363 l370 condmat 0502569 to more general correlation functions

fock representations of the affine lie algebra a 1 1 the aim of this note is to show that the affine lie algebraa1 1 has a natural family v of fock representations on the spacec xi yj i andj parametrized by v c2 by corresponding the highest weight of to each the parameter spacec2 forms a double cover of the weight spacec 0 c 1 with singularities at linear forms of level 2 this number is 1 times the dual coxeter number our results contain explicit realizations of irreducible non integrable highest wieghta1 1 modules for generic v

free field representation for massive integrable models a new approach to massive integrable models is considered it allows one to find symmetry algebras which define the spaces of local operators and to get general integral representations for form factors in thesu 2 thirring and sine gordon models

discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions one of the most important problems in numerical simulations is the preservation of qualitative properties of solutions of the mathematical models by computed approximations for problems of elliptic type one of the basic properties is the continuous maximum principle in our work we present several variants of the maximum principles and their discrete counterparts for scalar second order nonlinear elliptic problems with mixed boundary conditions the problems considered are numerically solved by the continuous piecewise linear finite element approximations built on simplicial meshes sufficient conditions providing the validity of the corresponding discrete maximum principles are presented geometrically they mean that the employed meshes have to be of acute or nonobtuse type depending of the type of the problem finally some examples of real life problems where the preservation of maximum principles plays an important role are presented

the critical an 1 1 chain we study the an 1 1 spin chain in the critical regime q 1 we give free boson realizations of the vertex operators and their duals using these free boson realizations we give integral representations for the correlation functions

on the vertex operators of the elliptic quantum algebra uq p sl2 k a realization of the elliptic quantum algebra uq p sl2 for any given level k is constructed in terms of three free boson fields and their accompanying twisted partners it can be viewed as the elliptic deformation of the wakimoto realization two screening currents are constructed they commute or anticommute with uq p sl2 modulo total q differences the free field realization for two types of vertex operators nominated as the type i and the type ii vertex operators is presented the twisted version of the two types of vertex operators are also obtained they all play crucial roles in calculating correlation functions

difference equations for the correlation functions of the eight vertex model the authors propose that the correlation functions of the inhomogeneous eight vertex model in the anti ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters solving the simplest difference equation they obtain the expression for the spontaneous staggered polarization conjectured by baxter and kelland 1974 they also discuss a related construction of vertex operators on the lattice

the elliptic quantum algebra u_ q hbox scriptsize p widehat sl_n and its vertex operators we construct a realization of the elliptic quantum algebra for any given level k in terms of free boson fields and their twisted partners it can be considered as the elliptic deformation of the wakimoto realization of the quantum affine algebra we also construct a family of screening currents which commute with the currents of up to total q differences and we give explicit twisted expressions for the type i and type ii vertex operators of by twisting the known results of the type i vertex operators of the quantum affine algebra and the new results of the type ii vertex operators of we obtained in this paper

spiral wave solutions for reaction diffusion equations in a fast reaction slow diffusion limit abstract a two species reaction diffusion equation is studied in a distinguished limit of fast reaction and slow diffusion asymptotic matching yields a spiral solution whose rotation frequency is a unique function of the physical parameters and the constant pitch of the spiral using an idea of fife the problem is first reduced to a free boundary problem the solution is obtained by matching the core where diffusion balances the curvature of the free boundary to the far field where the effects of diffusion are small the equations of motion are averaged over the rotation frequency to yield steady equations in the two regions helically symmetric solutions to the averaged equation reduce to solving a fourth order ode in the core region matched to a second order ode in the far field speculations on the dynamics of the system and coupling between the core and far field are presented

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

variable preconditioning for strongly nonlinear elliptic problems abstract variable preconditioning has earlier been developed as a realization of quasi newton methods for elliptic problems with uniformly bounded nonlinearities this paper presents a generalization of this approach to strongly nonlinear problems first on an operator level then for elliptic problems allowing power order growth of nonlinearities numerical tests reinforce the convergence results

hyperbolic reaction diffusion equations and chemical oscillations in the brusselator abstract hyperbolic reaction diffusion equations are discussed with the example of the brusselator in this paper their behavior is compared with that of the parabolic reaction diffusion equations conventionally used in connection with oscillating chemical reactions and chemical waves it is shown by using the example of the brusselator that an approximate dispersion relation computed from the hyperbolic reaction diffusion equations has a qualitatively correct wave number dependence whereas the parabolic equations do not yield a dispersion relation when a similar method is used it is also shown that chaotic solutions can arise in the case of hyperbolic reaction diffusion equations linear stability characteristics can be quite different in the two cases of evolution equations

effect of diffusion on patterns in excitable belousov zhabotinskii systems travelling wave patterns occur frequently in chemically reacting systems these include planar fronts target patterns and spiral structures we review the dispersion relation for planar waves including the effects of diffusion in the slow field for a simplified piecewise linear model with a focus on the scaling behavior with respect to the relative rate of the fast and slow reactions we discuss the implications of these results for spirals showing the origins of fife scaling and deriving a boundary integral formulation of the spiral equations we discuss the generalization to more realistic models in particular the popular oregonator model for belousov zhabotinskii reactions

an iterative algorithm for finite element analysis in this paper we state in a new form the algebraic problem arising from the one field displacement finite element method fem the displacement approach in this discrete form can be considered as the dual approach force or equilibrium with subsidiary constraints this approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration this new form of the problem leads to an inexpensive improvement of fem computations which acts at local elementary and global levels we demonstrate the numerical performances of this approach which is independent of the mesh structure using the gmres algorithm we build for nonsymmetric problems a new algorithm based upon the discretized field of strain the new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process the sizes of the different operators arising in these new forms are linear functions of integration rule which is of great interest in the case of reduced integration

variable preconditioning via quasi newton methods for nonlinear problems in hilbert space the aim of this paper is to develop stepwise variable preconditioning for the iterative solution of monotone operator equations in hilbert space and apply it to nonlinear elliptic problems the paper is built up to reflect the common character of preconditioned simple iterations and quasi newton methods the main feature of the results is that the preconditioners are chosen via spectral equivalence the latter can be executed in the corresponding sobolev space in the case of elliptic problems which helps both the construction and convergence analysis of preconditioners this is illustrated by an example of a preconditioner using suitable domain decomposition

preconditioning operators and sobolevgradients for nonlinear elliptic problems a preconditioning framework is presented for the iterative solution of nonlinear elliptic problems based on the preconditioning operator approach various fixed preconditioning operators are used in the iteration which can be interpreted as a weighted sobolev gradient method

emptiness formation probability of the xxz spin heisenberg chain at δ using a multiple integral representation for the correlation functions we compute the emptiness formation probability of the xxz spin heisenberg chain at anisotropy we prove that it is expressed in terms of the number of alternating sign matrices

the chiral space of local operators in su 2 invariant thirring model the space of local operators in the su 2 invariant thirring model su 2 itm is studied by the form factor bootstrap method by constructing sets of form factors explicitly we define a susbspace of operators which has the same character as the level one integrable highest weight representation of this makes a correspondence between this subspace and the chiral space of local operators in the underlying conformal field theory the su 2 wess zumino witten model at level one

isomorphism of two realizations of quantum affine algebra u_q widehat mathfrak g mathfrak l text n text we establish an explicit isomorphism between two realizations of the quantum affine algebra u q widehat mathfrak g mathfrak l text n text given previously by drinfeld and reshetikhin semenov tian shansky our result can be considered as an affine version of the isomorphism between the drinfield jimbo and the faddeev reshetikhin takhtajan constructions of the quantum algebra u q mathfrak g mathfrak l n

elliptic algebra in the scaling limit the scaling limit of the elliptic algebra is investigated the limiting algebra is defined in terms of a continuous family of generators being fourier harmonics of gauss coordinates of the l operator the ding frenkel isomorphism between l operator s and current descriptions of the algebra is established and is identified with the riemann problem on a strip the representations coalgebraic structure and intertwining operators of the algebra are studied

quantum kz equation with q 1 and correlation functions of the xxz model in the gapless regime an integral solution to the quantum knizhnik zamolodchikov qkz equation with q 1 is presented upon specialization it leads to a conjectural formula for correlation functions of the xxz model in the gapless regime the validity of this conjecture is verified in special cases including the nearest neighbour correlator with an arbitrary coupling constant and general correlators in the xxx and xy limits

third neighbour and other four point correlation functions of spin 1 2 xxz chain the correlation functions of the spin 1 2 xxz chain in the ground state were expressed in the form of multiple integrals for 1 1 and 1 in particular adjacent four point correlation functions were given as certain four dimensional integrals we show that these integrals can be reduced to polynomials with respect to specific one dimensional integrals the results give the polynomial representation of the third neighbour correlation functions

correlation functions of the higher spin xxx chains using the algebraic bethe ansatz we consider the correlation functions of the integrable higher spin chains we apply a method recently developed for the spin heisenberg chain based on the solution of the quantum inverse problem we construct a representation for the correlation functions on a finite chain for arbitrary spin then we show how the string solutions of the bethe equations can be considered in the framework of this approach in the thermodynamic limit finally a multiple integral representation for the spin 1 zero temperature correlation functions is obtained in the thermodynamic limit

new formulae for solutions of quantum knizhnik zamolodchikov equations on level 4 we present a new form of solution to the quantum knizhnik zamolodchikov equation qkz on level 4 in a special case corresponding to the heisenberg xxx spin chain our form is equivalent to the integral representation obtained by jimbo and miwa in 1996 7 an advantage of our form is that it is reduced to the product of single integrals this fact is deeply related to a cohomological nature of our formulae our approach is also based on the deformation of hyper elliptic integrals and their main property deformed riemann bilinear relation jimbo and miwa also suggested a nice conjecture which relates solution of the qkz on level 4 to any correlation function of the xxx model this conjecture together with our form of solution to the qkz makes it possible to prove a conjecture that any correlation function of the xxx model can be expressed in terms of the riemann function at odd arguments and rational coefficients suggested in 8 9 this issue will be discussed in our next publication

yangian doubles of classical types and their vertex representations the yangian double dy gn is introduced for the classical types of gn o2n 1 sp2n and o2n via the gauss decomposition of the generator matrix the yangian double is given the drinfeld presentation in addition bosonization of level 1 realizations for the yangian double dy gn of non simply laced types are explicitly constructed

dynamical behavior in linearly coupled oregonators abstract tyson ann ny acad sci 316 1979 279 conjectured that the stable homogeneous positive steady state may coexist with stable echo wave meaning anti phase wave in linearly coupled oregonators and thus gave a conjecture on the bifurcation diagram of this system in this paper we rigorously prove stability of the in phase wave and existence of the anti phase wave our proof procedure actually gives a general method or line to deal with the analogous problem for instance to prove stability of the in phase wave following our line one may decompose the corresponding variational equations a four dimensional system into two independent planar systems also for instance existence of the anti phase wave can be concluded as existence and uniqueness of limit cycle of the associate oscillator in addition according to parameter regimes of existence of the anti phase wave and the stable homogeneous positive steady state we give their coexistence regime and specify it and in particular give the regime of the coupled coefficient the specified results show that the theoretical results are in good accord with tyson s numerical results

q special functions with q 1 and their application to discrete integrable systems solutions for certain discrete integrable systems are constructed by using integral solutions for hypergeometric q difference systems with q 1 we apply a solution for lauricella s d type hypergeometric q difference system with q 1 to construct a solution for the discrete kp hierarchy furthermore an integral solution of a q difference analogue of bessel s equation is newly introduced and applied to construct a solution for a q difference analogue of the cylindrical toda equation with q 1

diffusion and wave propagation in cellular automaton models of excitable media in this paper the authors 1 examine general masks as discrete approximations to the diffusion equation showing how to calculate the diffusion coefficient from the elements of the mask 2 combine the mask with a thresholding operation to simulate the propagation of waves in excitable media showing that for well chosen masks the waves obey a linear speed curvature relation with slope given by the predicted diffusion coefficient and 3 assess the utility of different masks in terms of computational efficiency and adherence to a linear speed curvature relation

form factors of boundary fields for the a2 affine toda field theory in this paper we carry out the boundary form factor program for the a2 affine toda field theory at the self dual point the latter is an integrable model consisting of a pair of particles which are conjugated to each other that is and possessing two bound states resulting from the scattering processes 1 1 2 and 2 2 1 we obtain solutions up to four particle form factors for two families of fields which can be identified with spinless and spin 1 fields of the bulk theory previously known as well as new bulk form factor solutions are obtained as a particular limit of ours minimal solutions of the boundary form factor equations for all an affine toda field theories are given which will serve as the starting point for a generalization of our results to higher rank algebras

large distance asymptotic behavior of the emptiness formation probability of the xxz spin 1 2 heisenberg chain using its multiple integral representation we compute the large distance asymptotic behaviour of the emptiness formation probability of the xxz spin 1 2 heisenberg chain in the massless regime

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

on the updating and assembly of the hessian matrix in finite element methods abstract for many nonlinear differential equation solvers the assembly of the hessian matrix is an expensive task hence numerical methods like the damped inexact newton method see 3 11 are often too expensive to use as the hessian matrix has to be updated many times the goal of this paper is to show that in some special but frequently occurring cases where the hessian has a speical structure updating it is not more expensive than updating the gradient vector if a particular factorization of the stiffness matrix is used in these cases most of the computing time spent in the nonlinear solver will be used to solve linear systems of equations and the assembly of the hessian usually becomes a minor task the present paper extends earlier results of this nature in 4 6

dispersion of traveling waves in the belousov zhabotinskii reaction abstract we use perturbation and numerical methods to calculate the dispersion relation for periodic wave train solutions of diffusion reaction equations modeling the belousov zhabotinskii reaction these results are compared with experimental data for the belousov zhabotinskii reagent and shown to be in good agreement

singular perturbation theory of traveling waves in excitable media a review abstract waves of chemical or electrical activity traveling through space have been observed in several contexts chemical reaction mixtures in non convecting liquid phase cell suspensions nerve axons and neuromuscular tissues typically wave supporting preparations are excitable that is they respond and sensitivity to perturbations are rapidly damped out but suprathreshold disturbances trigger an abrupt and substantial response the abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious but the analysis of propagating waves in one spatial dimension is straightforward and several fundamentally different ways we compare and contrast the approaches taken by greenberg zykov fife krinskii and his collaborators and ourselves with particular emphasis on the case of rotating spiral waves our intention is to bring some order to the important but difficult theory of propagating waves in two dimensional excitable media in conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three dimensional space

integral representation of the density matrix of the xxz chain at finite temperatures we present an integral formula for the density matrix of a finite segment of the infinitely long spin xxz chain this formula is valid for any temperature and any longitudinal magnetic field

matrix models with hard walls geometry and solutions we discuss various aspects of most general multisupport solutions to matrix models in the presence of hard walls i e in the case where the eigenvalue support is confined to subdomains of the real axis the structure of the solution at the leading order is described by semiclassical or generalized whitham krichever hierarchies as in the unrestricted case derivatives of tau functions for these solutions are associated with families of riemann surfaces with possible double points and satisfy the witten dijkgraaf verlinde verlinde equations we then develop the diagrammatic technique for finding free energy of this model in all orders of the t hooft expansion in the reciprocal matrix size generalizing the feynman diagrammatic technique for the hermitian one matrix model due to eynard