generalized suq 1 2 gaudin model in this paper we propose the hamiltonians of the generalized suq 1 2 gaudin model corresponding to the periodic generalized t j model with the help of the well defined graded quantum determinant we obtain the eigenstate and eigenvalues of the generating function and the hamiltonians of the gaudin model in the fermionic background in the framework of the graded quantum inverse scattering method the bethe ansatz equations are also obtained

supersymmetric t j gaudin models and kz equations supersymmetric t j gaudin models with open boundary conditions are investigated by means of the algebraic bethe ansatz method off shell bethe ansatz equations of the boundary gaudin systems are derived and used to construct and solve the kz equations associated with sl 2 1 1 superalgebra

integral representation for the eigenstates of the spin system with inverse square interactions we consider the calogero sutherland moser system with spin 1 2 we give the integral representation for the ground state wavefunction excited states of the calogero spin model confined in the harmonic potential are also given

maximum l 2 convergence rates of the crank nicolson scheme to the stokes initial value problem let a denote the stokes operator and d a alpha the domain of its fractional powers a alpha we consider the homogeneous stokes initial value problem with initial data u 0 u 0 in d a 1 varepsilon varepsilon in 0 1 for stokes like equations the range varepsilon in 0 frac 1 4 is of special interest as any solution derived from varepsilon ge frac 1 4 would necessarily have to satisfy an additional in practice unverifiable compatibility condition at time t 0 approximating any strong solution u in c 0 0 infty d a 1 varepsilon in time direction on a finite time interval 0 t with a crank nicolson scheme we show convergence of order o frac tau 2 t 1 varepsilon which is maximal for the assumed regularity of the data and reflects the loss of regularity as t rightarrow 0 the error estimates are derived by energy and semigroup methods combined with a parabolic duality argument

global solutions to semilinear parabolic systems for small data abstract we consider semilinear parabolic systems u t au f u g u 0 u 0 a being the generator of an analytic semigroup with spectrum a in the right half plane for appropriate small data g u 0 global solutions are obtained if 0 belongs to the resolvent set and local existence is proved if 0 a the inverse function theorem is used in a class of functions which are holder continuous with respect to time t the asymptotic behaviour of the solution is given too as a first application we prove the existence of global respectively local solutions to the navier stokes equations in l spaces in bounded respectively unbounded domains second we consider the case where a is an elliptic operator of order 2 m and f has bounded growth third a quasilinear example where the nonlinearity involves derivatives of the same order as a is studied then an example of a nonautonomous nonlinearity is given and finally the convergence of solutions of the time dependent system to solutions of the stationary semilinear elliptic one is derived for 0 a

on integrable models related to the osp 1 2 gaudin algebra the osp 1 2 gaudin algebra is defined and integrable models described by it are considered the models include the osp 1 2 gaudin magnet and the dicke model related to it detailed discussion of the simplest cases of these models is presented the effect of the presence of fermions on the separation of variables is indicated

on the convergence of a time discretization scheme for the navier stokes equations version linearisee du schema d euler implicite utilisee pour l approximation des solutions des equations de navier stokes dans un domaine bidimensionnel

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

energy conserving lagrangian approximation for the equations of navier stokes on considere les equations de navier stokes stationnaires dans un domaine cylindrique borne 0 t ou t 0 et r 3 a une frontiere lisse on construit un quotient aux differences lagrangien conservant l energie qui approche le terme convectif non lineaire

the stabilized extrapolated trapezoidal finite element method for the navier stokes equations abstract we consider a fully discrete stabilized finite element method for the navier stokes equations which is unconditionally stable and has second order temporal accuracy of o k 2 hk spatial error the method involves a simple artificial viscosity stabilization of the linear system for the approximation of the new time level connected to anti diffusion of its effects at the old time level lowering the cell reynolds number of the oseen problem to o 1 the method requires only the solution of one linear system arising from an oseen problem per time step the effectiveness of the method is illustrated in several numerical experiments

off shell bethe ansatz equations and n point correlators in the su 2 wznw theory we prove that the wavevectors of the off shell bethe ansatz equation for the inhomogeneous su 2 lattice vertex model render in the quasiclassical limit the solutions of the knizhnik zamolodchikov equation

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

derivative estimates for the navier stokes equations in a three dimensional region on etablit des estimations fractionnaires pour les solutions de l equation de navier stokes dans le cas d un domaine avec une limite sur laquelle les composantes des solutions s annulent la condition de limite fixee appropriee pour des ecoulements visqueux

exact solution to a supersymmetric gaudin model we investigate a special case of the gaudin model related to the superalgebra osp 1 2 we present an exact solution to that system diagonalizing a complete set of commuting observables and providing the corresponding eigenvectors and eigenvalues the approach used in this paper is based on the co algebra symmetry of the model already known from the calogero gaudin system

gaudin magnet with boundary and generalized knizhnik zamolodchikov equation we consider the boundary quantum inverse scattering method established by sklyanin 1988 the gaudin magnet with boundary is diagonalized by taking a quasi classical limit of the inhomogeneous lattice using the method proposed by babujian 1993 the integral representation for the solution of the b type knizhnik zamolodchikov equation is explicitly constructed

an existence theorem for the navier stokes flow in the exterior of a rotating obstacle we consider the three dimensional navier stokes initial value problem in the exterior of a rotating obstacle it is proved that a unique solution exists locally in time if the initial velocity possesses the regularity l 1 2 this regularity assumption is the same as that in the famous paper of fujita kato an essential step for the proof is the deduction of a certain smoothing property together with estimates near t 0 of the semigroup which is not an analytic one generated by the operator in the space l 2 where stands for the angular velocity of the rotating obstacle and p denotes the projection associated with the helmholtz decomposition

nonlinear systems identification and control via dynamic multitime scales neural networks this paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network nn with different timescales two nn identifiers are proposed for nonlinear systems identification via dynamic nns with different timescales including both fast and slow phenomenon the first nn identifier uses the output signals from the actual system for the system identification in the second nn identifier all the output signals from nonlinear system are replaced with the state variables of the nns the online identification algorithms for both nn identifier parameters are proposed using lyapunov function and singularly perturbed techniques with the identified nn models two indirect adaptive nn controllers for the nonlinear systems containing slow and fast dynamic processes are developed for both developed adaptive nn controllers the trajectory errors are analyzed and the stability of the systems is proved simulation results show that the controller based on the second identifier has better performance than that of the first identifier

the bcs model and the off shell bethe ansatz for vertex models we study the connection between the bcs pairing model and the inhomogeneous vertex model the two spectral problems coincide in the quasi classical limit of the off shell bethe ansatz of the disordered six vertex model the latter problem is transformed into an auxiliary spectral problem which corresponds to the diagonalization of the integrals of motion of the bcs model a generating functional whose quasi classical expansion leads to the constants of motion of the bcs model and in particular the hamiltonian is identified

navier wall law for nonstationary viscous incompressible flows abstract we study the navier wall law for the two dimensional initial boundary value problem of the navier stokes equations in a domain with a rough boundary the navier wall law is verified for the initial data in c 1 class under the natural compatibility condition our proof relies on the boundary layer analysis and the l theory of the navier stokes equations in the half space