the matrix realization of affine jacobi varieties and the extended lotka volterra lattice we study completely integrable hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes of polynomial matrices let x be the algebraic curve given by the common characteristic equation for we construct the isomorphism from the set of representatives to an affine part of the jacobi variety of x this variety corresponds to the invariant manifold of the system where the hamiltonian flow is linearized as an application we discuss the algebraic complete integrability of the extended lotka volterra lattice with a periodic boundary condition

the small dispersion limit of the korteweg de vries equation iii in parts i and ii we have derived explicit formulas for the distribution limit u of the solution of the kdv equation as the coefficient of uxxx tends to zero this formula contains n parameters 1 n whose values as well as whose number depends on x and t in section 4 we have shown that for t tb n 1 and the value of was determined in section 5 we have shown that the parameters i satisfy a nonlinear system of partial differential equations in part iii section 6 we show that for t large n 3 and we determine the asymptotic behavior of 1 2 3 and of u and u2 for t large the explicit formulas show that u and u2 are o t 1 and o t 2 respectively see formulas 6 2 and 6 24 in section 7 we study initial data whose value tends to zero as x and to 1 as x if one accepts some plausible guesses about the behavior of solutions with such initial data we derive an explicit formula for the solution and determine the large scale asymptotic behavior of the solution the function s is expressible in terms of complete elliptic integrals a similar formula is derived for u2 in section 8 we indicate how to extend the treatment of this series of papers to multihumped but still negative initial data

unitarity of the knizhnik zamolodchikov bernard connection and the bethe ansatz for the elliptic hitchin systems we work out finite dimensional integral formulae for the scalar product of genus one states of the groupg chern simons theory with insertions of wilson lines assuming convergence of the integrals we show that unitarity of the elliptic knizhnik zamolodchikov bernard connection with respect to the scalar product of cs states is closely related to the bethe ansatz for the commuting hamiltonians building up the connection and quantizing the quadratic hamiltonians of the elliptic hitchin system

cohomological study on variants of the mumford system and integrability of the noumi yamada system the purpose of this paper is twofold the first is to apply the method introduced in the works of nakayashiki and smirnov 11 12 on the mumford system to its variants the other is to establish a relation between the mumford system and the isospectral limit mathcal q g i and mathcal q g ii of the noumi yamada system 15 as a consequence we prove the algebraically completely integrability of the systems mathcal q g i and mathcal q g ii and get explicit descriptions of their solutions

coisotropic deformations of associative algebras and dispersionless integrable hierarchies the paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies like the dispersionless kp and modified kp hierarchies and the universal whitham hierarchy of genus zero it stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras it discusses the link between the structure constants and hirota s tau function and shows that the dispersionless hirota bilinear equations are within this approach a way of writing the associativity conditions for the structure constants in terms of the tau function it also suggests a simple interpretation of the algebro geometric construction of the universal whitham equations of genus zero due to krichever

discretizations for the incompressible navier stokes equations based on the lattice boltzmann method a discrete velocity model with spatial and velocity discretization based on a lattice boltzmann method is considered in the low mach number limit a uniform numerical scheme for this model is investigated in the limit the scheme reduces to a finite difference scheme for the incompressible navier stokes equation which is a projection method with a second order spatial discretization on a regular grid the discretization is analyzed and the method is compared to chorin s original spatial discretization numerical results supporting the analytical statements are presented

the extended lotka volterra lattice and affine jacobi varieties of spectral curves based on the work by smirnov and zeitlin we study a simple realization of the matrix construction of the affine jacobi varieties we find that the realization is given by a classical integrable model the extended lotka volterra lattice we investigate the integrable structure of the representative for the gauge equivalence class of matrices which is isomorphic to the affine jacobi variety and make use of it to discuss the solvability of the model

the initial value problem for the whitham averaged system we study the initial value problem for the whitham averaged system which is important in determining the kdv zero dispersion limit we use the hodograph method to show that for a generic non trivial monotone initial data the whitham averaged system has a solution within a region in thex t plane for all time bigger than a large time furthermore the whitham solution matches the burgers solution on the boundaries of the region for hump like initial data the hodograph method is modified to solve the non monotone inx solutions of the whitham averaged system in this way we show that for a hump like initial data the whitham averaged system has a solution within a cusp for a short time after the increasing and decreasing parts of the initial data beging to interact on the cusp the whitham and burgers solutions are matched

classical functional bethe ansatz for sl n separation of variables for the magnetic chain it is desirable for one to be able to construct separation variables for systems with sl n r matrices or lax pairs this article relates and extends the two known methods of construction the sklyanin s functional bethe ansatz fba commun math phys 150 181 191 1992 was previously only known for sl 2 and sl 3 and associated r matrices the algebraic geometric method of adams harnad and hurtubise commun math phys 155 385 413 1993 has been shown to work for sl n but up until now only for linear poisson brackets in this article sklyanin s program is advanced by giving the fba for certain systems with sl n r matrices this is achieved by constructing rational functions a u and b u of the matrix elements of t u so that in the generic case the zeros xi of b u are the separation coordinates and the pi a xi provide their conjugate momenta it is shown that the separation variables thus defined are the same as those given as the simultaneous solutions of several equations in two

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

approximating the llr distribution for a class of soft output mimo detectors we present approximations of the llr distribution for a class of fixed complexity soft output mimo detectors such as the optimal soft detector and the soft output via partial marginalization detector more specifically in a mimo awgn setting we approximate the llr distribution conditioned on the transmitted signal and the channel matrix with a gaussian mixture model gmm our main results consist of an analytical expression of the gmm model including the number of modes and their corresponding parameters and a proof that in the limit of high snr this llr distribution converges in probability towards a unique gaussian distribution

equivalence of two graphical calculi the author considers the integrable systems which are connected with separation of variables in the helmholtz operator on the real riemannian spaces of constant curvature an isomorphism is given for these systems with a quantum hyperbolic gaudin magnet using this isomorphism the complete classification of all separable coordinate systems on the manifolds considered is provided by means of the corresponding l operators for the gaudin magnet

chern simons states at genus one we present a rigorous analysis of the schrodinger picture quantization for thesu 2 chern simons theory on 3 manifold torusxline with insertions of wilson lines the quantum states defined as gauge covariant holomorphic functionals ofsu 2 connections on the torus are expressed by degree 2k theta functions satisfying additional conditions the conditions are obtained by splitting the space of semistablesu 2 connections into nine submanifolds and by analyzing the behavior of states at four codimension 1 strata we construct the knizhnik zamolodchikov bernard connection allowing to compare the states for different complex structures of the torus and different positions of the wilson lines by letting two wilson lines come together we prove a recursion relation for the dimensions of the spaces of states which together with the unproven absence of states for spins 1 2 level implies the verlinde dimension formula

quadrics on complex riemannian spaces of constant curvature separation of variables and the gaudin magnet integrable systems that are connected with orthogonal separation of variables in complex riemannian spaces of constant curvature are considered herein an isomorphism with the hyperbolic gaudin magnet previously pointed out by one of the authors extends to coordinates of this type the complete classification of these separable coordinate systems is provided by means of the corresponding l matrices for the gaudin magnet the limiting procedures or e calculus which relate various degenerate orthogonal coordinate systems play a crucial role in the classification of all such systems

a kinetic equation with kinetic entropy functions for scalar conservation laws we construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws in particular we prove that it is well posed uniformly in e the microscopic scale we also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions analogous to boltzmann s microscopich function such that they recover krushkov type entropy inequality on the macroscopic scale finally we prove by both bv compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case that the local density of kinetic particles admits a continuum limit as it converges strongly with e 0 to the unique entropy solution of the corresponding conservation law

hamiltonian formalism of whitham type hierarchies and topological landau ginsburg models we show that the bi hamiltonian structure of the averaged gelfand dikii hierarchy is involved in the landau ginsburg topological models fora n series the casimirs for the first p b give the correct coupling parameters for the perturbed topological minimal model the correspondence coupling parameters primary fields is determined by the second p b the partition function at the tree level and the chiral algebra for lg models are calculated for any genusg

relaxation of nonlinear oscillations in bcs superconductivity the diagonal case of the sl 2 richardson gaudin quantum pairing model is known to be solvable as an abel jacobi inversion problem the effect of random time dependent perturbations of the single particle spectrum on the exact solution is an open question of considerable physical relevance weak perturbations introduce a new slow time scale while preserving the nonlinear character of the dynamics in this paper such perturbations are considered it is shown that the long time asymptotics can be obtained by a deformation of the original integrable system equivalent to phase averaging over the fast time scale

spectral curve darboux coordinates and hamiltonian structure of periodic dressing chains a chain of one dimensional schrodinger operators connected by successive darboux transformations is called the darboux chain or dressing chain the periodic dressing chain with period n has a control parameter alpha if alpha not 0 the n periodic dressing chain may be thought of as a generalization of the fourth or fifth depending on the parity of n painleve equations the n periodic dressing chain has two different lax representations due to adler and to noumi and yamada adler s 2 times 2 lax pair can be used to construct a transition matrix around the periodic lattice one can thereby define an associated spectral curve and a set of darboux coordinates called spectral darboux coordinates the equations of motion of the dressing chain can be converted to a hamiltonian system in these darboux coordinates the symplectic structure of this hamiltonian formalism turns out to be consistent with a poisson structure previously studied by veselov shabat noumi and yamada

the small dispersion limit of the korteweg de vries equation ii in part i the scattering transform method is used to study the weak limit of solutions to the initial value problem for the korteweg devries kdv equation as the dispersion tends to zero in that limit the associated schrodinger operator becomes semiclassical so the exact scattering data is replaced by its corresponding wkb expressions only nonpositive initial data are considered in that case the limiting reflection coefficient vanishes the explicit solution of kay and moses for the reflectionless inverse transform is then analyzed and the weak limit valid for all time is characterized by a quadratic minimum problem with constraints this minimum problem is reduced to a riemann hilbert problem in function theory in parts ii and iii we use function theoretical methods to solve the riemann hilbert problem in terms of solutions to an auxiliary initial value problem the weak limit satisfies the kdv equation with the dispersive term dropped until its derivatives become infinite up to that time the weak limit is a strong l2 limit at later times the weak limit is locally described by whitham s averaged equations or more generally by the equations found by flaschka et al using multiphase averaging for large times behavior of the weak limit is studied directly from the minimum problem

cohomological structure in soliton equations and jacobian varieties on etudie la structure des orbites du systeme dynamique definie par la hierarchie kp totale on montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une algebre commutative le systeme dynamique kp restreint a chaque orbite determine un systeme dynamique de mouvements lineaires sur lui par rapport a la structure lineaire du groupe de cohomologie

systems of conservation laws with invariant submanifolds systems of conservation laws with coinciding shock and rarefaction curves arise in the study of oil reservoir simulation multicomponent chromatogra phy as well as in the study of nonlinear motion in elastic strings here we characterize this phenomenon by deriving necessary and sufficient conditions on the geometry of a wave curve in order that the shock wave curve coincide with its associated rarefaction wave curve for a system of conservation laws this coinci dence is the one dimensional case of a submanifold of the state variables being invariant for the system of equations and the necessary and sufficient conditions are derived for invariant submanifolds of arbitrary dimension in the case of 2 x 2 systems we derive explicit formulas for the class of flux functions that give rise to the coupled nonlinear conservation laws for which the shock and rarefaction wave curves coincide introduction systems of conservation laws which have coinciding shock and rarefaction curves arise in the study of oil reservoir simulation nonlinear wave motion in elastic strings as well as in multicomponent chromatography 1 4 5 6 9 11 12 these systems have many interesting features the riemann problem for these equations can be explicitly solved in the large and wave interactions have a simplified structure even in the presence of a nonconvex flux function for this reason these systems represent some of the few examples for which the cauchy problem has been solved for arbitrary data of bounded variation also hyperbolic degeneracies appear in each of these systems in the present paper we are concerned with characterizing the phenomenon of coinciding shock and rarefaction curves this phenomenon turns out to be a special case of the general phenomenon of a submanifold of r being invariant for weak solutions of a given system of n conservation laws invariant manifolds of higher dimension also appear in physical conservation equations in which the conserved quantities represent concentrations i e when the concentrations c of any of the species vanish the system must reduce to a lower order system that expresses the conservation of the remaining species thus c 0 defines a manifold which is invariant in the sense that solutions that start on the manifold remain there for all time moreover such an invariant manifold of dimension n 1 is the boundary of an dimensional invariant region in the sense of chueh conley and smoller 14 in the case of

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

isospectral hamiltonian flows in finite and infinite dimensions the approach to isospectral hamiltonian flow introduced in part i is further developed to include integration of flows with singular spectral curves the flow on finite dimensional ad invariant poisson submanifolds of the dual widetilde gl r of the positive part of the loop algebra widetilde gl r is obtained through a generalization of the standard method of linearization on the jacobi variety of the invariant spectral curves these curves are embedded in the total space of a line bundlet p1 c allowing an explicit analysis of singularities arising from the structure of the image of a moment map tilde j r m n r times m n r to widetilde gl r from the space of rank r deformations of a fixedn n matrixa it is shown how the linear flow of line bundles e t to tilde s over a suitably desingularized curve tilde s may be used to determine both the flow of matricial polynomialsl and the hamiltonian flow in the spacemn r mn r in terms of functions the resulting flows are proved to be completely integrable the reductions to subalgebras developed in part i are shown to correspond to invariance of the spectral curves and line bundles e t to tilde s under certain linear or anti linear involutions the integration of two examples from part i is given to illustrate the method the rosochatius system and the cnls coupled non linear schrodinger equation

driven cavity flows by efficient numerical techniques abstract efficient and reliable numerical techniques of high order accuracy are presented for solving problems of steady viscous incompressible flow in the plane and are used to obtain accurate solutions for the driven cavity a solution is obtained at reynolds number 10 000 on a 180 180 grid the numerical methods combine an efficient linear system solver an adaptive newton like method for nonlinear systems and a continuation procedure for following a branch of solutions over a range of reynolds numbers

hyperelliptic prym varieties and integrable systems we introduce two algebraic completely integrable analogues of the mumford systems which we call hyperelliptic prym systems because every hyperelliptic prym variety appears as a fiber of their momentum map as an application we show that the general fiber of the momentum map of the periodic volterra lattice is an affine part of a hyperelliptic prym variety obtained by removing n translates of the theta divisor and we conclude that this integrable system is algebraic completely integrable

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

finite temperature correlation functions from discrete functional equations we present a new approach to the static finite temperature correlation functions of the heisenberg chain based on functional equations an inhomogeneous generalization of the n site density operator is considered the lattice path integral formulation with a finite but arbitrary trotter number allows us to derive a set of discrete functional equations with respect to the spectral parameters we show that these equations yield a unique characterization of the density operator our functional equations are a discrete version of the reduced q knizhnik zamolodchikov equations which played a central role in the study of the zero temperature case as a natural result and independent of the arguments given by jimbo et al 2009 j phys a math theor 42 304018 we prove that the inhomogeneous finite temperature correlation functions have the same remarkable structure as for zero temperature they are a sum of products of nearest neighbour correlators

a general formula for soliton form factors in the quantum sine gordon model a general formula for soliton form factors of several local fields in the quantum sine gordon model is presented

separation of variables in the bc type gaudin magnet an integrable system is introduced based on the poisson rs matrix structure this is a generalization of the gaudin magnet and in the sl 2 case is isomorphic to the generalized neumann model the separation of variables is discussed for both the classical and quantum cases

nonlinear chains and painleve equations abstract ode systems which define a periodically closed sequence of backlund transformations bt and which are equivalent to the painleve equations p2 p6 are presented transformation properties of painleve equations can be easily derived from the discrete symmetries of these systems

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

backlund transformations for the sl 2 gaudin magnet elementary one and two point backlund transformations are constructed for the generic case of the sl 2 gaudin magnet the spectrality property is used to construct these explicitly given poisson integrable maps which are time discretizations of the continuous flows with any hamiltonian from the spectral curve of the 2 2 lax matrix

separation of variables in the classical integrable sl 3 magnetic chain there are two fundamental problems studied by the theory of hamiltonian integrable systems integration of equations of motion and construction of action angle variables a third problem however should be added to the list separation of variables though much simpler thant the two others it has important relations to quantum integrability separation of variables is constructed for thesl 3 magnetic chain an example of an integrable model associated to a nonhyperelliptic algebraic curve

schlesinger transformations and quantum r matrices schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues we study schlesinger transformations for twisted valued connections on the torus a universal construction is presented which gives the elementary two point transformations in terms of belavin s elliptic quantum r matrix in particular the role of the quantum deformation parameter is taken by the difference of the two poles whose residue eigenvalues are shifted elementary one point transformations acting on the residue eigenvalues at a single pole are constructed in terms of the classical elliptic r matrix the action of these transformations on the function of the system may completely be integrated and we obtain explicit expressions in terms of the parameters of the connection in the limit of a rational r matrix our construction and the quotients reduce to the classical results of jimbo and miwa in the complex plane

the τ function of the universal whitham hierarchy matrix models and topological field theories the universal witham hierarchy is considered from the point of view of topological field theories the function for this hierarchy is defined it is proved that the algebraic orbits of whitham hierarchy can be identified with various topological matter models coupled with topological gravity

reduced qkz equation and correlation functions of the xxz model correlation functions of the xxz model in the massive and massless regimes are known to satisfy a system of linear equations the main relations among them are the difference equations obtained from the qkz equation by specializing the variables 1 2n as 1 n n 1 1 1 we call it the reduced qkz equation in this article we construct a special family of solutions to this system they can be written as linear combinations of products of two transcendental functions open image in new window with coefficients being rational functions we show that correlation functions of the xxz model in the massive regime are given by these formulas with an appropriate choice of open image in new window we also present a conjectural formula in the massless regime

algebraic varieties in the birkhoff strata of the grassmannian gr 2 harrison cohomology and integrable systems the local properties of the families of algebraic subsets wg in the birkhoff strata 2g of gr 2 containing the hyperelliptic curves of genus g are studied it is shown that the tangent spaces tg for wg are isomorphic to the linear spaces of 2 coboundaries particular subsets in wg are described by the integrable dispersionless coupled kdv systems of hydrodynamical type defining a special class of 2 cocycles and 2 coboundaries in tg it is demonstrated that the blows ups of such 2 cocycles and 2 coboundaries and gradient catastrophes for associated integrable systems are interrelated

derivation of the lattice boltzmann method by means of the discrete ordinate method for the boltzmann equation in this note we show that the lattice boltzmann bgk method in common use can be derived from the boltzmann equation itself according to the present derivation it is apparent that the equation thus derived can be reduced to the navier stokes equation at a limit of small knudsen number since the equation thus derived is the boltzmann equation itself hence the present derivation method gives us a simple and flexible recipe to construct the lattice boltzmann method and makes it easy to construct an extended lattice boltzmann method in various ways 15 refs 1 fig

regular article a new discrete velocity method for navier stokes equations the relation between the lattice boltzmann method which has recently become popular and the kinetic schemes which are routinely used in computational fluid dynamics is explored a new discrete velocity method for the numerical solution of navier stokes equations for incompressible fluid flow is presented by combining both the approaches the new scheme can be interpreted as a pseudo compressibility method and for a particular choice of parameters this interpretation carries over to the lattice boltzmann method

kinetic derivation of a finite difference scheme for the incompressible navier stokes equation in the present paper the low mach number limit of kinetic equations is used to develop a discretization for the incompressible navier stokes equation the kinetic equation is discretized with a first and second order discretization in space the discretized equation is then considered in the low mach number limit using this limit a second order discretization for the convective part in the incompressible navier stokes equation is obtained numerical experiments are shown comparing different approaches

kinetic schemes in the case of low mach numbers originally kinetic schemes have been used as numerical methods to solve the system of compressible euler equations in gas dynamics the main idea in the approach is to construct the numerical flux function based on a microscopical description of the gas in this article the schemes are investigated in the case of isentropic euler equations and low mach numbers expanding the microscopical velocity distribution naturally leads to new kinetic schemes with strong resemblance to lattice boltzmann methods by adjusting the parameters of the kinetic scheme the numerical viscosity can be used to reproduce a given physical viscosity in this way a finite difference solver for the incompressible navier stokes equation is obtained its close relation to the lattice boltzmann approach is highlighted

hodograph solutions of the dispersionless coupled kdv hierarchies critical points and the euler poisson darboux equation it is shown that the hodograph solutions of the dispersionless coupled kdv dckdv hierarchies describe critical and degenerate critical points of a scalar function which obeys the euler poisson darboux equation singular sectors of each dckdv hierarchy are found to be described by solutions of higher genus dckdv hierarchies concrete solutions exhibiting shock type singularities are presented

quantum spin chains and riemann zeta function with odd arguments the riemann zeta function is an important object of number theory we argue that it is related to the heisenberg spin 1 2 anti ferromagnet in the xxx spin chain we study the probability of formation of a ferromagnetic string in the anti ferromagnetic ground state in the thermodynamics limit we prove that for short strings the probability can be expressed in terms of the riemann zeta function with odd arguments

coisotropic deformations of algebraic varieties and integrable systems coisotropic deformations of algebraic varieties are defined as those for which an ideal of the deformed variety is a poisson ideal it is shown that coisotropic deformations of sets of intersection points of plane quadrics cubics and space algebraic curves are governed in particular by the dkp wdvv dvn d2dtl equations and other integrable hydrodynamical type systems particular attention is paid to the study of two and three dimensional deformations of elliptic curves the problem of an appropriate choice of the poisson structure is discussed

quasiclassical limit of coupled kdv equations riemann invariants and multi hamiltonian structure abstract we consider the quasiclassical limit of the first nontrivial flow in coupled kdv hierarchy written down in riemann invariants it assumes the extremely simple form r i k 1 n r k 2r i r x i i 1 n up to certain natural equivalence this turns out to be the only hydrodynamic system with n 1 compatible purely local hamiltonian structures

vector bundles and lax equations on algebraic curves the hamiltonian theory of zero curvature equations with spectral parameter on an arbitrary compact riemann surface is constructed it is shown that the equations can be seen as commuting flows of an infinite dimensional field generalization of the hitchin system the field analog of the elliptic calogero moser system is proposed an explicit parameterization of hitchin system based on the tyurin parameters for stable holomorphic vector bundles on algebraic curves is obtained

cohomologies of affine hyperelliptic jacobi varieties and integrable systems we study the affine ring of the affine jacobi variety of a hyperelliptic curve the matrix construction of the affine hyperelliptic jacobi varieties due to mumford is used to calculate the character of the affine ring by decomposing the character we make several conjectures on the cohomology groups of the affine hyperelliptic jacobi varieties in the integrable system described by the familly of these affine hyperelliptic jacobi varieties the affine ring is closely related to the algebra of functions on the phase space classical observables we show that the affine ring is generated by the highest cohomology group over the action of the invariant vector fields on the jacobi variety

a systematic granulized piecewise linear approximation to the jacobian logarithm a systematic granulized piecewise linear approximation to the jacobian logarithm is developed this approximation reverts to the jacobian approximation and the exact jacobian logarithm at the far extremes the utility of the derived approximation is demonstrated by applying it to the decoding of turbo coded mimo bicm id systems

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

improving the performance of sm mimo bicm id systems with llr distribution matching in this paper a distribution matching technique is proposed to process the extrinsic information produced by practical multiple antenna detectors with iteratively demodulated bit interleaved coded modulation bicm id it is shown that significant gains may be achieved by appropriately processing the extrinsic information generated by practical multiple antenna detectors before feeding it to the channel decoder the validity of the proposed matching technique is shown via simulation results applied to turbo coded bicm id systems using qrd m and list sphere detectors

numerical passage from kinetic to fluid equations a numerical way to pass from the bhatnagar gross krook model of the boltzmann equation to compressible euler equations is presented in order to do so a stable discretization of the kinetic equati

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

bihamiltonian geometry darboux coverings and linearization of the kp hierarchy we use ideas of the geometry of bihamiltonian manifolds developed by gel fand and zakharevich to study the kp equations in this approach they have the form of local conservation laws and can be traded for a system of ordinary differential equations of riccati type which we call the central system we show that the latter can be linearized by means of a darboux covering and we use this procedure as an alternative technique to construct rational solutions of the kp equations

performance assessment of mimo bicm demodulators based on mutual information we provide a comprehensive performance comparison of soft output and hard output demodulators in the context of non iterative multiple input multiple output bit interleaved coded modulation mimo bicm coded bit error rate ber widely used in literature for demodulator comparison has the drawback of depending strongly on the error correcting code being used this motivates us to propose the mutual information of the equivalent modulation channel comprising modulator wireless channel and demodulator as a code independent performance measure we present extensive numerical results for spatially independent identically distributed i i d ergodic and quasi static fading channels under perfect and imperfect channel state information these results reveal that the performance ranking of mimo demodulators is rate dependent and provide new insights regarding mimo bicm system design i e the choice of antenna configuration symbol constellation and demodulator for a given target rate

a kinetic construction of global solutions of first order quasilinear equations on considere le probleme de cauchy pour des equations quasilineaires d ordre 1 de type conservation dans la region t 0 u t i 1 u a i u x i 0 u x o u o x ou x x 1 x n u u x t et a i i 1 n sont des fonctions continument differentiables a valeurs reelles d une seule variable reelle

dual baxter equations and quantization of the affine jacobian a quantum integrable model is considered which describes a quantization of the affine hyper elliptic jacobian this model is shown to possess the property of duality a dual model with inverse planck constant exists such that the eigenfunctions of its hamiltonians coincide with the eigenfunctions of hamiltonians of the original model we explain that this duality can be considered as duality between homologies and cohomologies of quantized affine hyper elliptic jacobian

monodromy preserving deformation of linear ordinary differential equations with rational coefficients iii abstract a unified treatment of monodromy and spectrum preserving deformations is presented in particular a general procedure is described to reduce the latter into the former consistently the concept of the function previously introduced for the former 2 is extended to the isospectral context it is shown that the general monodromy and spectrum preserving deformation equations can be written as hirota s bilinear differential equations by using the functions as dependent variables

singular sector of the burgers hopf hierarchy and deformations of hyperelliptic curves we discuss the structure of shock singularities of the burgers hopf hierarchy it is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy the stratification is associated with the birkhoff decomposition of the grassmannian given by the set of linear spaces spanned by the hierarchy we then construct integrable hierarchy on each stratum and demonstrate that it describes a deformation of a hyperelliptic curve parametrizing the stratum the hierarchy is called the hidden burgers hopf hierarchy and we found the riemann invariant form and the hodograph solution

laplacian growth and whitham equations of soliton theory the laplacian growth the hele shaw problem of multiply connected domains in the case of zero surface tension is proven to be equivalent to an integrable system of whitham equations known in soliton theory the whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations through this connection the laplacian growth is understood as a flow in the moduli space of riemann surfaces

boltzmann type schemes for gas dynamics and the entropy property let h be a convex function a boltzmann equation is built following the b g k model for which h is an entropy in the fluid limit the compressible euler equations are obtained with a convex entropy naturally associated to h the motivation is to define numerical boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support the classical scheme obtained with h f f log f is based on the equilibrium density function exp v 2 2 which has infinite support

block implicit multigrid solution of navier stokes equations in primitive variables abstract a calculation procedure for rapid computation of steady multidimensional viscous flows is presented the method solves the navier stokes equations in primitive variables using a coupled block implicit multigrid procedure the procedure is applicable to finite difference formulations using staggered locations of the flow variables a smoothing technique called symmetrical coupled gauss seidel scgs is proposed and is empirically observed to provide good smoothing rates the viscous flow in a square cavity with a moving top wall is calculated for a range of reynolds numbers calculations with finite difference grids as large as 321 321 nodes have been made to test the accuracy and efficiency of the calculation scheme the cpu times for these calculations are observed to be significantly smaller than other solution algorithms with primitive variable formulation the calculated flow fields in the cavity are in good agreement with earlier studies of the same flow situation