braid structure and raising lowering operator formalism in sutherland model we algebraically construct the fock space of the sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors for this purpose we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta the operators exchanging eigenvalues of two pseudomomenta have been known all the eigenstates are systematically produced by starting from the ground state and multiplying these operators by it

an almost sure large deviation principle for the hopfield model we prove a large deviation principle for the finite dimensional marginals of the gibbs distribution of the macroscopic overlap parameters in the hopfield model in the case where the number of random patterns m as a function of the system size n satisfies lim sup m n n 0 in this case the rate function is independent of the disorder for almost all realizations of the patterns

the riemann problem for a class of nonlinear degenerate equations in the present paper we study the riemann problem for degenerate equations in which the pressure is constant over some range of stains by the liu entropy condition the riemann solutions of twelve regions in the v u plane are completely constructed moreover we obtain the invariant regions for the riemann solutions c 2012 elsevier inc all rights reserved

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

observer based feedback boundary stabilization of the navier stokes equations abstract this paper aims at designing an observer based feedback law which locally stabilizes the solution to the two dimensional navier stokes equations with mixed boundary conditions we consider a finite number of controls acting on a portion of the boundary through robin boundary conditions and construct a linear luenberger observer based on the point observations of the linearized navier stokes equations the sensor location for the point observations is determined by the response of feedback functional gains we prove that the nonlinear system coupled with the observer through the feedback law is locally exponentially stable numerical experiments based on a taylor hood finite element method are presented to illustrate the design for different reynolds numbers

a new actuator activation policy for performance enhancement of controlled diffusion processes the present work aims at the development of a framework within which a moving actuator activation policy and feedback controller synthesis are integrated for diffusion processes modelled by parabolic partial differential equations it is assumed that the process of interest has either i multiple actuators and the desirable arrangement is to activate only one while keeping the remaining ones dormant or ii a single actuator capable of moving at a priori selected positions within the spatial domain practical advantages associated with arrangement i are energy cost savings and simplification of the local controller synthesis and the overall switching scheme and with ii is enhanced spatiotemporal disturbance compensation feedback controller synthesis methods based on linear matrix inequality techniques are employed for a finite dimensional galerkin approximation of the original distributed parameter system along with standard controllability criteria additional conditions are imposed that ensure robustness with respect to a certain class of disturbances the value of a performance functional is then explicitly calculated by solving a location parameterized family of lyapunov matrix equations and then optimized with respect to the set of admissible actuator locations finally a case study of a moving bed adsorber is presented where the performance enhancing capabilities of the proposed method is evaluated through simulation studies

integrable spin chain with reflecting end a new integrable spin chain of the haldane shastry type is introduced it is interpreted as the inverse square interacting spin chain with a reflecting end the lattice sites of this model consist of the square roots of the zeros of the laguerre polynomial using the exchange operator formalism the integrals of motion for the model are explicitly constructed

connection between yangian symmetry and the quantum inverse scattering method the quantum nonlinear schrodinger model with two component fermions exhibits a yangian symmetry when considered on an infinite interval we construct the generators of the yangian using dunkl operators we show an equivalence between the monodromy matrix constructed from the dunkl operators and that of the quantum inverse scattering method under the yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations

degenerations of sklyanin algebra and askey wilson polynomials a new trigonometric degeneration of the sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied a further contraction gives the standard quantum algebra uq sl 2 it is shown that the degenerate sklyanin algebra contains a subalgebra isomorphic to algebra of functions on the quantum sphere su 2 so 2 q12 the diagonalization of general quadratic form in its generators leads in the functional realization to the difference equation for askey wilson polynomials

symbolic dynamics and periodic orbits for the cardioid billiard the periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics the corresponding partition is mapped to a topologically well ordered symbol plane in the symbol plane the pruning front is obtained from orbits running either into or through the cusp we show that all periodic orbits correspond to maxima of the lagrangian and give a complete list up to code length 15 the symmetry reduction is done on the level of the symbol sequences and the periodic orbits are classified using symmetry lines we show that there exists an infinite number of families of periodic orbits accumulating in length and that all other families of geometrically short periodic orbits eventually get pruned all these orbits are related to finite orbits starting and ending in the cusp we obtain an analytical estimate of the kolmogorov sinai entropy and find a good agreement with the numerically calculated value and the one obtained by averaging periodic orbits furthermore the statistical properties of periodic orbits are investigated

gibbs states of the hopfield model in the regime of perfect memory we study the thermodynamic properties of the hopfield model of an autoassociative memory ifn denotes the number of neurons andm n the number of stored patterns we prove the following results ifm n 0 asn then there exists an infinite number of infinite volume gibbs measures for all temperaturest 1 concentrated on spin configurations that have overlap with exactly one specific pattern moreover the measures induced on the overlap parameters are dirac measures concentrated on a single point and the gibbs measures on spin configurations are products of bernoulli measures ifm n asn for small enough we show that for temperaturest smaller than somet 1 the induced measures can have support only on a disjoint union of balls around the previous points but we cannot construct the infinite volume measures through convergent sequences of measures

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

on the free energy of the hopfield model the general theory of inhomogeneous mean field systems of raggio and werner provides a variational expression for the almost sure limiting free energy density of the hopfield model h n p xi s frac 1 2n sum limits i j 1 n sum limits mu 1 n xi i mu xi j mu s i s j for ising spinssi andp random patterns 1 2 n under the assumption that mathop lim limits n to gamma n 1 sum limits i 1 n delta xi i lambda xi i xi i 1 xi i 2 xi i p exists almost surely in the space of probability measures overp copies of 1 1 including an external field term p h i 1 n i si we give a number of general properties of the free energy density and compute it for a p 2 in general and b p arbitrary when is uniform and at most the two componentsh 1 andh 2 are nonzero obtaining the almost sure formula f beta h tfrac 1 2 f ew beta h mu 1 h mu 2 tfrac 1 2 f ew beta h mu 1 h mu 2 for the free energy wherefcw denotes the limiting free energy density of the curie weiss model with unit interaction constant in both cases we obtain explicit formulas for the limiting almost sure values of the so called overlap parameters m n mu beta h n 1 sum limits i 1 n xi i mu left langle s i right rangle in terms of the curie weiss magnetizations for the general i i d case with prob i 1 1 2 we obtain the lower bound 1 4 2 p 1 for the temperaturetc separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero this lower bound is exact forp 2 or e 0 or e 1 2 forp 2 we identify an intermediate temperature region between t 1 4 2 and tc 1 4 2 where the overlap vector is homogeneous i e all its components are equal and nonzero t marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct we conjecture that the homogeneous nonzero regime exists forp 3 and that t max 1 4 2 p 1 0

convergence of the viscosity solutions for the system of nonlinear elasticity abstract in this paper some special entropy pairs of lax type are constructed for the system of nonlinear elasticity in which the progressive terms are functions of a single variable the necessity estimates for the major terms are obtained by using the theory of singular perturbation of the ordinary differential equations the special entropy pairs are used to prove that the family of young measures uniquely determined by the viscosity solution sequence is a family of dirac measures hence a convergence theorem on the viscosity solutions is established by applying the method of compensated compactness

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

minimum cost input output design for large scale linear structural systems in this paper we provide optimal solutions to two different but related input output design problems involving large scale linear dynamical systems where the cost associated to each directly actuated measured state variable can take different values but is independent of the input output performing the task under these conditions we first aim to determine and characterize the input output placement that incurs in the minimum cost while ensuring that the resulting placement achieves structural controllability observability further we address a constrained variant of the above problem in which we seek to determine the minimum cost placement configuration among all possible input output placement configurations that ensures structural controllability observability with the lowest number of directly actuated measured state variables we develop new graph theoretical characterizations of cost constrained input selections for structural controllability and properties that enable us to address both problems by reduction to a weighted maximum matching problem efficiently addressed by algorithms with polynomial time complexity in the number of state variables finally we illustrate the obtained results with an example

numerical demonstration of the semiclassical matrix element probability distribution between integrability and chaos in this letter i report on the first successful verification of the semiclassical matrix element probability distribution for the hamiltonian systems between integrability and chaos as for all the other statistical properties of quantum dynamical systems e g level spacing distribution phase space localization of eigenstates etc the semiclassical limit was found to converge extremely slowly so a rather abstract dynamical system was used namely the standard map on a torus in order to clearly demonstrate the semiclassical regime

h optimal actuator location in many control applications there is freedom to place the actuators the actuator location should be chosen to optimize certain performance objectives in this paper h performance with state feedback is considered that is both the controller and the actuator locations are chosen to minimize the effect of disturbances on the output a framework for calculating h optimal actuator locations is developed conditions for well posedness of the h optimal actuator location problem are presented many optimal actuator problems involve systems modelled by partial differential equations and conditions under which approximations yield reliable results are given a derivative free optimization algorithm to calculate h optimal actuator locations is described the results are illustrated using several examples

sensor placement for optimal estimation of vector valued diffusion processes abstract diffusion processes are commonplace in many scientific disciplines as they describe a broad range of physical phenomenon consider a diffusion process observed through linear sensors with additive white noise we derive the optimal placement of these sensors for estimating this process where optimality is defined in terms of the mean squared estimation error mse of the state given past observations we consider two cases first we assume the sensors to be orthogonal we show in this case that the minimum mse is related to the nuclear norm of the system matrix of the process second we remove the orthogonality constraint and show that the mse is related to the schatten p norm of the system matrix of the process and the optimal sensors are proportional its matrix cube root we present simulation results illustrating the fact that the gain afforded by optimizing the choice of sensors depends on the ratio p n where n is the dimension of the system and p the dimension of the wiener processes driving it and this gain is in general large especially when p n is small

linear quadratic optimal actuator location in control of vibrations diffusion and many other problems governed by partial differential equations there is freedom in the choice of actuator location the actuator location should be chosen to optimize performance objectives in this paper we consider linear quadratic performance two types of cost are considered the choice depends on whether the response to the worst initial condition is to be minimized or whether the initial condition is regarded as random in practice approximations are used in controller design and thus in selection of the actuator locations the optimal cost and location of the approximating sequence should converge to the exact optimal cost and location in this work conditions for this convergence are given in the case of linear quadratic control examples are provided to illustrate that convergence may fail when these conditions are not satisfied

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

topics in quantum integrable systems recent developments in the theory of quantum integrable particle systems in one dimension with inverse square interactions are reviewed first the yangian symmetry is introduced and the energy spectra of the related spin models are discussed the character of the su n 1 wznw theory is shown to be closely related with the rogers szego polynomial second the infinite dimensional representation for solutions of the yang baxter equation and the reflection equation is given based on the representation the dunkl operators associated with the classical root systems are constructed the macdonald polynomial and its generalization are discussed in connection with the eigenstates for the trigonometric case finally some results on short range interacting systems are mentioned

numerical accuracy of bogomolny s semiclassical quantization scheme in quantum billiards we use the semiclassical quantization scheme of bogomolny to calculate eigenvalues of the limacon quantum billiard corresponding to a conformal map of the circle billiard we use the entire billiard boundary as the chosen surface of section and use a finite approximation for the transfer operator in coordinate space computation of the eigenvalues of this matrix combined with a quantization condition determines a set of semiclassical eigenvalues which are compared with those obtained by solving the schrodinger equation the classical dynamics of this billiard system undergoes a smooth transition from integrable circle to completely chaotic motion thus providing a test of bogomolny s semiclassical method in coordinate space in terms of the morphology of the wavefunction we analyse the results for billiards which exhibit both soft and hard chaos

the distribution of the partition function of the hopfield model with finite number of patterns we derive the leading term in the large n asymptotic expansion of the partition function of the hopfield model with finite number of patterns we show that this leading order term is deterministic in the high temperature region in the low temperature region and at the critical point it is random with the distribution governed by normal or iterated exponential distributions

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

computational design of optimal output feedback controllers we consider the problem of designing feedback control laws when a complete set of state variables is not available for linear autonomous systems with quadratic performance criterion the design problem consists of choosing an appropriate matrix of feedback gains according to a certain objective function in the literature the performance of quasi newton methods has been reported to be substandard we try to explain some of these observations and to propose structured quasi newton updates these methods which take into account the special structure of the problem show considerable improvement in the convergence using test examples from optimal output feedback design we also can verify these results numerically

affine hecke algebra macdonald polynomials and quantum many body systems the macdonald operators associated with the classical root systems are constructed based on the infinite dimensional representation for solutions of the yang baxter equation and the reflection equation

representation of the yangian invariant motif and the macdonald polynomial the representation of the yangian invariant motif is considered the relationship with the rogers szego polynomial is studied whose one parameter deformation is the macdonald polynomial we propose the deformation of the motifs which provides a new realization of the macdonald polynomials for the one row young diagrams

quantum integrability of the generalized elliptic ruijsenaars models the quantum integrability of the generalized elliptic ruijsenaars models is shown these models are mathematically related to the macdonald operator and the macdonald koornwinder operator which appeared in the q orthogonal polynomial theories we construct these integrable families by using the yang baxter equation and the reflection equation

fluctuation of the free energy in the hopfield model we prove that in the ergodic region t j2 1 r the deviation of the total free energy of the hopfield neural network converges in distribution asn to a shifted gaussian variable moreover the free energy per site converges in probability to lim 1 n ln n

yang baxter equation in long range interacting systems we consider the su p spin chains with long range interactions and the spin generalization of the calogero sutherland models we show that their properties derive from a transfer matrix obeying the yang baxter equation we obtain the expression of the conserved quantities of the dynamical models and we diagonalise them in the spin chain case we establish the connection between the degeneracies of the spectrum and the representation theory of the yangians we use a correspondence with the dynamical models to diagonalise the hamiltonian finally we extend the previous results to the case of a trigonometric r matrix

positively invariant regions for a problem in phase transitions positively invariant regions for the system v t p w x e v xx w t v x e w x are constructed where p p w 0 w e 0 such a choice of p is motivated by the maxwell construction for a van der waals fluid the method of an analysis is a modification of earlier ideas of chueh conley smoller 1 the results given here provide e independent l bounds on the solution w v

universal lax pairs for spin calogero moser models and spin exchange models for any root system and a set of vectors which form a single orbit of the reflection weyl group g generated by a spin calogero moser model can be defined for each of the potentials rational hyperbolic trigonometric and elliptic for each member of to be called a site we associate a vector space v whose element is called a spin its dynamical variables are the canonical coordinates of a particle in rr r rank of and spin exchange operators which exchange the spins at the sites and s here s is the reflection generated by for each and a spin exchange model can be defined the hamiltonian of a spin exchange model is a linear combination of the spin exchange operators only it is obtained by freezing the canonical variables at the equilibrium point of the corresponding classical calogero moser model for ar and set of vector weights it reduces to the well known haldane shastry model universal lax pair operators for both spin calogero moser models and spin exchange models are presented which enable us to construct as many conserved quantities as the number of sites for degenerate potentials

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

backstepping observers for linear pdes on higher dimensional spatial domains the extension of the backstepping based state observer design is considered for systems governed by parabolic pdes defined on a higher dimensional cuboidal spatial domain with the measured output being restricted to a single boundary hyperplane thereby a suitable coordinate and state transformation is employed which allows for the application of the backstepping method for the determination of a luenberger type state observer with observer corrections entering the pde and the boundary condition this ensures that the observer error dynamics follows the behavior of a predefined exponentially stable target system in view of a practical realization of the proposed observer approach the idealized system output previously assumed as measurable on the entire boundary hyperplane is reconstructed from a limited set of optimally located measurements by means of a least squares approximation the observer error convergence and the applicability of the proposed approach are confirmed analytically and are evaluated in numerical simulations

conserved operators of the generalized elliptic ruijsenaars models we construct the integrable families of the generalized elliptic ruijsenaars models by use of the yang baxter equation and the reflection equation the higher order conserved operators of these models are explicitly presented

involutive generators and actions for the group phi 2 the automorphisms of the free group f2 form the group phi 2 three involutions are shown to generate phi 2 the homomorphism h2 phi 2 to gl 2 z induced by the abelianization h1 f2 to z2 is generated by three affine reflections r3 to r3 the actions of phi 2 induced by the homomorphisms f2 to su 2 su 1 1 sl 2 c are generated by algebraic involutions and geometric reflections

exact solution and surface critical behaviour of open cyclic sos lattice models we consider the l state cyclic solid on solid lattice models under a class of open boundary conditions the integrable boundary face weights are obtained by solving the reflection equations functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions the eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic bethe ansatz for a special case of crossing parameter the finite size corrections to the eigenspectra of the critical models are obtained from which the corresponding conformal dimensions follow the calculation of the surface free energy away from criticality yields two surface specific heat exponents and where coprime to l these results are in agreement with the scaling relations and

current distribution and local power dissipation in the two component deterministic percolation model the authors have investigated the current distribution and local power dissipation in the two component deterministic percolation model in which the ratio of conductance h is regarded as a small parameter the iterative nature of the model enables them to find exact recursion relations for the current distribution for an extremely small h such that hlphi 1 where l is the size of the lattice and phi the crossover exponent they find that d alpha approximately exp a alpha b log l 2 log l 3 where d alpha d alpha is the number of currents with alpha log ii alpha d alpha ii is the current in bond i and a b are constants the current distribution is well approximated by a gaussian with the mean varying with the size as log l 2 while the variance as log l 3 as a result both the most probable current and the minimum current scale with l as exp constant log l 2 similar results are obtained for the distribution of local power dissipation

macdonald polynomials from sklyanin algebras a conceptual basis for the p adics quantum group connection we establish a previously conjectured connection betweenp adics and quantum groups we find in sklyanin s two parameter elliptic quantum algebra and its generalizations the conceptual basis for the macdonald polynomials which interpolate between the zonal spherical functions of related real andp adic symmetric spaces the elliptic quantum algebras underlie thez n baxter models we show that in then limit the jost function for the scattering offirst level excitations in the 1 1 dimensional field theory model associated to thez n baxter model coincides with the harish chandra likec function constructed from the macdonald polynomials associated to the root systema 1 the partition function of thez 2 baxter model itself is also expressed in terms of this macdonald harish chandrac function albeit in a less simple way we relate the two parametersq andt of the macdonald polynomials to the anisotropy and modular parameters of the baxter model in particular thep adic regimes in the macdonald polynomials correspond to a discrete sequence of xxz models we also discuss the possibility of q deforming euler products

boundary k matrix elliptic dunkl operator and quantum many body systems the infinite dimensional representation of the boundary k operator the solution of the reflection equation is considered the trigonometric k matrix is studied as a degenerate case of the elliptic operator a method to construct the elliptic dunkl operator is proposed and the relationship with the quantum many body problem is also discussed

optimal actuator sensor location for active noise regulator and tracking control problems in this paper we investigate the problem of finding the optimal location of sensors and actuators to achieve reduction of the noise field in an acoustic cavity we offer two control strategies the first is based on linear quadratic tracking where the offending noise is tracked and the second considers the formulation of the harmonic control strategy as a periodic static output feedback control problem the first method which is based on full state information is suitable for optimal location of actuators while the second strategy can extend the results to finding optimal location of sensors as well as actuators for both methods we consider the optimization of an appropriate quadratic performance criterion with respect to the location of the actuators and or the sensors numerical examples are presented to compare the effectiveness of each control strategy and also the effect of optimal placement of actuators and sensors

intermediate statistics in the regime of mixed classical dynamics we explain the arguments in support of the berry robnik 1984 17 2413 picture of the energy level statistics in the asymptotic strict far semiclassical limit of sufficiently small where the entire energy spectrum can be represented as a statistically independent superposition of regular and irregular level sequences the regular ones obeying the poissonian statistics and the irregular ones the rmt statistics goe or gue we generalize the results to describe not only the level spacing distribution the number variance and the delta statistics but also arbitrary statistics the probability to find k levels inside an interval of length l after unfolding very useful and effective approximations for are described we demonstrate very clearly that this regime is excellently described by this picture for k as high as the outer energy scale even when taking into account the regular component and only one the dominant chaotic component this we show numerically for the compactified standard map and for the quartic 2d billiard

integrable n particle hamiltonians with yangian or reflection algebra symmetry we use the dunkl operator approach to construct one dimensional integrable models describing n particles with internal degrees of freedom these models are described by a general hamiltonian belonging to the centre of the yangian or the reflection algebra which ensures that they admit the corresponding symmetry in particular the open problem of the symmetry is answered for the bn type sutherland model with spin and for a generalized bn type nonlinear schrodinger hamiltonian

wavefunctions expectation values and scars on poincare sections a scattering approach using the scattering approach to quantization we define an appropriate representation of the billiard wavefunction on the scattering poincar section the expectation values of smooth operators in terms of these poincar section wavefunctions are expressed as sums over periodic orbits a special operator is used to define scars on the section and the relation to scars in configuration space is discussed and demonstrated numerically

rigorous results on the thermodynamics of the dilute hopfield model we study the hopfield model of an autoassociative memory on a random graph onn vertices where the probability of two vertices being joined by a link isp n assuming thatp n goes to zero more slowly thano 1 n we prove the following results 1 if the number of stored patternsm n is small enough such thatm n np n 0 asn then the free energy of this model converges upon proper rescaling to that of the standard curie weiss model for almost all choices of the random graph and the random patterns 2 if in additionm n ln n ln 2 we prove that there exists fort 1 a gibbs measure associated to each original pattern whereas for higher temperatures the gibbs measure is unique the basic technical result in the proofs is a uniform bound on the difference between the hamiltonian on a random graph and its mean value