quantized knizhnik zamolodchikov equations quantum yang baxter equation and difference equations for q hypergeometric functions thesl2 quantized knizhnik zamolodchikov equations are solved inq hypergeometric functions new difference equations are derived for generalq hypergeometric functions the equations are given in terms of quantum yang baxter matrices and have the form similar to quantum knizhnik zamolodchikov equations for quantum affine algebras introduced by frenkel and reshetikhin

exchange dynamical quantum groups for any simple lie algebra and any complex number q which is not zero or a nontrivial root of unity but may be equal to 1 we construct a dynamical quantum group hopf algebroid whose representation theory is essentially the same as the representation theory of the quantum group uq this dynamical quantum group is obtained from the fusion and exchange relations between intertwining operators in representation theory of uq and is an algebraic structure standing behind these relations

global attractivity and positive almost periodic solution for delay logistic differential equation abstract in this paper we establish some sufficient conditions for the global attractivity of positive solutions and the unique existence of positive almost periodic solutions for delay logistic differential equations of the form x t r t x t a t b t x t l x t our results extend and improve corresponding ones in the literature

streamwise upwind algorithm for computing unsteady transonic flows past oscillating wings a streamwise upwind algorithm has been extended to compute unsteady flows with a moving grid system and applied to compute flows over oscillating wings at transonic mach numbers comparisons have been made between results obtained from this upwind algorithm using both temporally nonconservative and conservativeimplicit methods with the results obtained from a central difference method and also with experimental data the efficiency and practicality of the temporally nonconservative implicit solver are illustrated results to show the robustness and accuracy of the upwind method for unsteady computations compared to the central difference method are presented

global attractivity in delayed differential equations with applications to food limited population model abstract a new criterion is built which guarantees the global attractivity of zero solution for equation having the form x t 1 x t f t x t the behavior of global solution on r is also addressed as an application we study the existence of globally attractive positive almost periodic solution for the food limited single population model our results improve those in literature

the duality of glm n and glk gaudin models abstract we establish a duality of the non periodic gaudin model associated with superalgebra gl m n and the non periodic gaudin model associated with algebra gl k the hamiltonians of the gaudin models are given by expansions of a berezinian of an m n m n matrix in the case of gl m n and of a column determinant of a k k matrix in the case of gl k we obtain our results by proving capelli type identities for both cases and comparing the results

implicit time stepping methods for the navier stokes equations a novel two factor approximate factorization for three dimensional flows is described the method uses a preconditioned conjugate gradient solver for one of the factors and this solution is based on a method developed for two dimensional flows this two dimensional method is described and its performance is summarized for steady and unsteady flows the two factor method is then given larger time steps can be used with this method than is possible with the more conventional three factor method test results for the transonic steady flow over the onera m6 wing are given

multiple orthogonal polynomials and a counterexample to the gaudin bethe ansatz conjecture jacobi polynomials are polynomials whose zeros form the unique solution of the bethe ansatz equation associated with two irreducible modules we study sequences of polynomials whose zeros form the unique solution of the bethe ansatz equation associated with two highest weight irreducible modules with the restriction that the highest weight of one of the modules is a multiple of the first fundamental weight we describe the recursion which can be used to compute these polynomials moreover we show that the first polynomial in the sequence coincides with the jacobi pineiro multiple orthogonal polynomial and others are given by wronskian type determinants of jacobi pineiro polynomials as a byproduct we describe a counterexample to the bethe ansatz conjecture for the gaudin model

deforming mesh for computational aeroelasticity using a nonlinear elastic boundary element method a nonlinear elastic boundary element method nbem approach is developed as an innovative deforming mesh generator for computational aeroelastic simulation the computational fluid dynamics cfd mesh is assumed to be embedded in an infinite nonlinear elastic medium of a hardening material leading to the formulation of a pseudononlinear elastostatic problem whereas the cfd surface mesh is treated as a boundary element model and the cfd flowfield grid as domain sample points the nbem approach solves navier s equations using a particular solution scheme that removes the requirement of the domain integral in the conventional nbem formulation the nbem approach has a unified feature that is applicable to all mesh systems including unstructured multiblock structured and overset grids an optimization strategy is employed to determine the optimum hardening material properties by minimizing the mesh distortion in the viscous region where grid orthogonality must be preserved three test cases are performed to demonstrate the robustness and effectiveness of the nbem approach for deforming mesh generation

identities between q hypergeometric and hypergeometric integrals of different dimensions abstract given complex numbers m1 l1 and nonnegative integers m2 l2 such that m1 m2 l1 l2 for any a b 0 min m2 l2 we define an l2 dimensional barnes type q hypergeometric integral ia b z m1 m2 l1 l2 and an l2 dimensional hypergeometric integral ja b z m1 m2 l1 l2 the integrals depend on complex parameters z and we show that ia b z m1 m2 l1 l2 equals ja b e z l1 l2 m1 m2 up to an explicit factor thus establishing an equality of l2 dimensional q hypergeometric and m2 dimensional hypergeometric integrals the identity is based on the gl k gl n duality for the qkz and dynamical difference equations

aeroelastic solutions using the nonlinear frequency domain method in this work both fully implicit time domain and nonlinear frequency domain methods are used to compute aeroelastic solutions in transonic flows specifically flutter boundaries for a two dimensional naca64a010 airfoil are calculated and compared with preexisting numerical results the second order backward difference time accurate scheme will serve as our numerical benchmark when determining the computational efficiency of the nonlinear frequency domain method comparable results between the time domain and nonlinear frequency domain approaches will further justify the nonlinear frequency domain method as an efficient alternative to the study of unsteady periodic problems a temporal resolution study will establish the required number of modes or time steps per period required for unsteady transonic flows

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

bispectral and gln glm dualities discrete versus differential we define integral transforms which establish a correspondence between spaces of quasi exponentials and spaces of quasi polynomials under certain conditions as a corollary of the properties of our transforms we obtain a correspondence between solutions to the bethe ansatz equations of two gln glm dual quantum integrable models one is the special trigonometric gaudin model and the other is the special xxx model

direct solution of two dimensional navier stokes equations for static aeroelasticity problems a new method has been developed to calculate the steady flow and structural deformations for fluid structure interaction problems the discretized fluid dynamic and structural equations are regarded as a single set of coupled nonlinear algebraic equations the equilibrium solution is directly obtained using newton s method the governing equations used for the fluid flow are the two dimensional navier stokes equations and a finite element model is used to represent the structure this paper describes the analytical method and presents sample calculations demonstrating the technique the results show rapid convergence and good agreement with experimental data nomenclature bw half bandwidth of tangent matrix d set of structural displacement variables e set of governing equations for the aeroelastic system f flux vector in x direction g flux vector in y direction h distance from nozzle throat to centerline number of fluid dynamic control volumes in streamwise direction j number of fluid dynamic control volumes in cross stream direction l reference length total length of nozzle n total number of variables in system p pressure pe exit static pressure pt total pressure r system residual r magnitude of residual r radius at nozzle throat t tangent matrix system jacobian t wall thickness u set of fluid dynamic variables x set of variables for the aeroelastic system ax change in system variables during a newton iteration x streamwise coordinate y cross stream coordinate

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

global attractivity in scalar delayed differential equations with applications to population models for the scalar delay differential equation x t 1 x t f t xt sufficient conditions for the global stability of the zero solution are given the behavior of global solutions on r is also addressed several applications to population models which improve known results are presented

a variational finite element method for stationary nonlinear fluid solid interaction we consider the problem of the interaction of a stationary viscous fluid with an elastic solid that undergoes large displacement the fluid is modeled by the stationary incompressible navier stokes equations in an eulerian frame of reference while a lagrangian reference frame and large displacement small strain theory is used for the solid a variational formulation of the problem is developed that ensures satisfaction of continuity of interface tractions and velocities the variational formulation is approximated by a galerkin finite element method yielding a system of nonlinear algebraic equations in unknown fluid velocities and pressures and solid displacements a newton like method is introduced for solution of the discrete system the method employs a modified jacobian that enables decomposition into separate fluid and solid subdomains this domain decomposition avoids possible ill conditioning of the jacobian as well as the need to compute and store geometric coupling terms between fluid and interface shape the capability of the methodology is illustrated by solution of a problem of the flow induced large displacements of an elastic infinite cylinder

jackson integrals of jordan pochhammer type and quantum knizhnik zamolodchikov equations we show that theq difference systems satisfied by jackson integrals of jordan pochhammer type give a class of the quantum knizhnik zamolodchikov equation for u q widehat mathfrak s mathfrak l 2 in the sense of frenkel and reshetikhin

difference equations and highest weight modules of based on the trigonometric r matrix of a family of q deformed discrete knizhnik zamolodchikov equations is formulated solutions to them are constructed by using the generalization of the algebraic bethe ansatz developed to solve difference equations these solutions are shown to be of highest weight with respect to the underlying quantum group structure using the variant of the nested bethe ansatz method these results are extended to the higher ranked symmetry of

cohomology classes of conormal bundles of schubert varieties and yangian weight functions we consider the conormal bundle of a schubert variety s i in the cotangent bundle t mathrm mathrm gr of the grassmannian mathrm mathrm gr of k planes in mathrm mathbb c n this conormal bundle has a fundamental class kappa i in the equivariant cohomology h mathrm mathbb t t mathrm mathrm gr here mathrm mathbb t mathrm mathbb c n times mathrm mathbb c the torus mathrm mathbb c n acts on t mathrm mathrm gr in the standard way and the last factor mathrm mathbb c acts by multiplication on fibers of the bundle we express this fundamental class as a sum y i of the yangian y mathfrak gl 2 weight functions w j j we describe a relation of y i with the double schur polynomial s i a modified version of the kappa i classes named kappa i satisfy an orthogonality relation with respect to an inner product induced by integration on the non compact manifold t mathrm mathrm gr this orthogonality is analogous to the well known orthogonality satisfied by the classes of schubert varieties with respect to integration on mathrm mathrm gr the classes kappa i i form a basis in the suitably localized equivariant cohomology h mathrm mathbb t t mathrm mathrm gr this basis depends on the choice of the coordinate flag in mathrm mathbb c n we show that the bases corresponding to different coordinate flags are related by the yangian r matrix

q deformed kzb heat equation completeness modular properties and sl 3 z abstract we study the properties of one dimensional hypergeometric integral solutions of the q difference quantum analogue of the knizhnik zamolodchikov bernard equations on tori we show that they also obey a difference kzb heat equation in the modular parameter give formulae for modular transformations and prove a completeness result by showing that the associated fourier transform is invertible these results are based on sl 3 z transformation properties parallel to those of elliptic gamma functions

unsteady aerodynamic and aeroelastic calculations for wings using euler equations a procedure to solve simultaneously the euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings the euler flow equations are solved by a finite difference scheme with dynamic grids the coupled aeroelastic equations of motion are solved using the linear acceleration method the aeroelastic configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing the unsteady flow calculations are validated with the experiment both for a semi infinite wing and a wall mounted cantilever rectangular wing aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite element method the robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using potential equations are demonstrated

an application of aomoto gelfand hypergeometric functions to the su n knizhnik zamolodchikov equation solutions to the knizhnik zamolodchikov equation for verma modules of the lie algebra mathfrak s mathfrak l n 1 mathbb c are explicitly given by certain integrals called aomoto gelfand hypergeometric functions

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

the b and m shapiro conjecture in real algebraic geometry and the bethe ansatz we prove the b and m shapiro conjecture that if the wronskian of a set of polynomials has real roots only then the complex span of this set of polynomials has a basis consisting of polynomials with real coefficients this in particular implies the following result if all ramification points of a parametrized rational curve 1 r lie on a circle in the riemann sphere 1 then maps this circle into a suitable real subspace r r the proof is based on the bethe ansatz method in the gaudin model the key observation is that a symmetric linear operator on a euclidean space has real spectrum in appendix a we discuss properties of differential operators associated with bethe vectors in the gaudin model in particular we prove a statement which may be useful in complex algebraic geometry it claims that certain schubert cycles in a grassmannian intersect transversally if the spectrum of the corresponding gaudin hamiltonians is simple in appendix b we formulate a conjecture on reality of orbits of critical points of master functions and prove this conjecture for master functions associated with lie algebras of types a r b r and c r

matrix difference equations for the supersymmetric lie algebra sl 2 1 and the off shell bethe ansatz based on the rational r matrix of the supersymmetric sl 2 1 matrix difference equations are solved by means of a generalization of the nested algebraic bethe ansatz these solutions are shown to be of highest weight with respect to the underlying graded lie algebra structure

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

calculation of norms of bethe wave functions a class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered eigenfunctions of the hamiltonians are known for these models norms of these eigenfunctions in the finite box are calculated in the present paper these models include in particular the quantum nonlinear schrodinger equation and the heisenbergxxz model

3 2 type criteria for global attractivity of lotka volterra competition system without instantaneous negative feedbacks this paper deals with a two species lotka volterra competition model with discrete delays but without instantaneous negative feedbacks motivated by wright s 3 2 global attractivity result for the delayed scalar logistic equation we establish some new 3 type criteria for global attractivity of the positive equilibrium of the system these criteria provide convenient and better than some existing estimates for the diagonal delays

on representations of the elliptic quantum group e τ η sl 2 we describe representation theory of the elliptic quantum groupe sl 2 it turns out that the representation theory is parallel to the representation theory of the yangiany sl 2 and the quantum loop group u q widetilde sl 2 we introduce basic notions of representation theory of the elliptic quantum groupe sl 2 and construct three families of modules evaluation modules cyclic modules one dimensional modules we show that under certain conditions any irreducible highest weight module of finite type is isomorphic to a tensor product of evaluation modules and a one dimensional module we describe fusion of finite dimensional evaluation modules in particular we show that under certain conditions the tensor product of two evaluation modules becomes reducible and contains an evaluation module in this case the imbedding of the evaluation module into the tensor product is given in terms of elliptic binomial coefficients we describe the determinant element of the elliptic quantum group representation theory becomes special ifn m l wheren m l are integers we indicate some new features in this case

hypergeometric solutions of trigonometric kz equations satisfy dynamical difference equations abstract the trigonometric kz equations associated to a lie algebra g depend on a parameter h where h g is a cartan subalgebra a system of dynamical difference equations with respect to compatible with the kz equations is introduced by v tarasov and the second author 2000 internat math res notices 15 801 829 we prove that the standard hypergeometric solutions of the trigonometric kz equations associated to sl n also satisfy the dynamical difference equations

vortical flow computations on swept flexible wings using navier stokes equations a procedure to couple the navier stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of swept flexible wings the navier stokes flow equations are solved by a finite difference scheme with dynamic grids the coupled aeroelastic equations of motion are solved using the linear acceleration method the configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing the calculations are compared with the experiment when available effects of flexibility sweep angle and pitch rate are demonstrated for flows with vortices

the quantum inverse scattering method approach to correlation functions the inverse scattering method approach is developed for calculation of correlation functions in completely integrable quantum models with ther matrix of xxx type these models include the one dimensional bose gas and the heisenberg xxx model the algebraic questions of the problem are considered

divisors on general curves and cuspidal rational curves in t roduc t ion 371 0 pre l iminar ies 377 1 a pl i icker formula 378 2 d imens iona l t ransversa l i ty 380 3 d i m e n s i o n of families of r a t iona l curves with fixed degree and ass igned cusps in a project ive space 383 4 l inear series on curves with universa l s ingular i t ies 386 5 l inear series and project ive embedd ings of general curves 391 6 embedd ings of general cuspidal curves 400 7 degenera t ion of schuber t in tersect ions some special cases 403 8 degene ra t ion of schuber t in tersect ions ma in results 407 9 g c is reduced for general cuspidal r a t iona l c 414

conservative load projection and tracking for fluid structure problems the loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes some techniques developed to solve the problems of the load transfer and interface surface tracking are presented the main criterion is to achieve conservation of total loads and total energy the load projection scheme is based on gaussian integration and fast interpolation algorithms for unstructured grids the surface tracking algorithm also based on interpolation is important for many applications including aeroelastic deformation of wings due to aerodynamic loads the methodologies not only improve present fluid structure interaction simulations but also increase the range of their applicability these techniques are of general character and can be used in other multidisciplinary applications as well

a multidimensional generalization of the barnes integral and the continuous hahn polynomial employing a multidimensional generalization of the beta integral of barnes we derive an expression of the continuous hahn polynomials motivation of the present work is to study such integrals from the viewpoint of a finite difference version of the de rham theory

how to regularize singular vectors and kill the dynamical weyl group abstract let g be a simple lie algebra and let m be the verma module over g with highest weight for a finite dimensional g module u we introduce a notion of a regularizing operator acting in u which makes the meromorphic family of intertwining operators m m u holomorphic and conjugates the dynamical weyl group operators aw end u to constant operators we establish fundamental properties of regularizing operators including uniqueness and prove the existence of a regularizing operator in the case g sl 3

periodic solutions of periodic delay lotka volterra equations and systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic lotka volterra equations and systems with distributed or state dependent delays our results substantially extend and improve existing results