premixed flame shapes and polynomials abstract the nonlinear nonlocal michelson sivashinsky equation for isolated crests of unstable flames is studied using pole decompositions as starting point polynomials encoding the numerically computed 2 n flame slope poles and auxiliary ones are found to closely follow a meixner pollaczek recurrence accurate steady crest shapes ensue for n 3 squeezed crests ruled by a discretized burgers equation involve the same polynomials such explicit approximate shapes still lack for finite n pole decomposed periodic flames despite another empirical recurrence

unitary random matrix ensemble with governable level confinement a family of unitary ensuremath alpha ensembles of random matrices with governable confinement potential v x ensuremath sim ensuremath vert x mathrm ensuremath vert mathrm ensuremath alpha is studied employing exact results of the theory of nonclassical orthogonal polynomials the density of levels two point kernel locally rescaled two level cluster function and smoothed connected correlations between the density of eigenvalues are calculated for strong ensuremath alpha g1 and border ensuremath alpha 1 level confinement it is shown that the density of states is a smooth function for ensuremath alpha g1 and has a well pronounced peak at the band center for ensuremath alpha ensuremath le 1 the case of border level confinement associated with transition point ensuremath alpha 1 is reduced to the exactly solvable pollaczek random matrix ensemble unlike the density of states all the two point correlators remain after proper rescaling universal down to and including ensuremath alpha 1 textcopyright 1996 the american physical society

sivashinsky equation for corrugated flames in the large wrinkle limit sivashinsky s acta astron 4 1177 1977 nonlinear integrodifferential equation for the shape of corrugated one dimensional flames is ultimately reducible to a 2n body problem involving the 2n complex poles of the flame slope thual frisch and henon j phys france 46 1485 1985 derived singular linear integral equations for the pole density in the limit of large steady wrinkles n 1 which they solved exactly for monocoalesced periodic fronts of highest amplitude of wrinkling and approximately otherwise here we solve those analytically for isolated crests next for monocoalesced then bicoalesced periodic flame patterns whatever the large amplitudes involved we compare the analytically predicted pole densities and flame shapes to numerical results deduced from the pole decomposition approach good agreement is obtained even for moderately large ns the results are extended to give hints as to the dynamics of supplementary poles open problems are evoked

on 2d elliptic discontinuous galerkin methods we discuss the discretization using discontinuous galerkin dg formulation of an elliptic poisson problem two commonly used dg schemes are investigated the original average flux proposed by bassi and rebay j comput phys 1997 131 267 and the local discontinuous galerkin ldg siam j numer anal 1998 35 2440 2463 scheme in this paper we expand on previous expositions discontinuous galerkin methods theory computation and applications springer berlin 2000 135 146 siam j sci comput 2002 24 2 524 547 int j numer meth engng 2003 58 2 1119 1148 by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the dg method through consideration of standard c0 type expansion bases as opposed to elementally orthogonal expansions with the matrix formulation we are able to apply static condensation techniques to improve efficiency of the direct solver when high order expansions are adopted the use of c0 type expansions also permits the direct enforcement of dirichlet boundary conditions through a lifting approach where the ldg flux does not require further stabilization in our construction we also adopt a formulation of the continuous dg fluxes that permits a more general interpretation of their numerical implementation in particular it allows us to determine the conditions under which the ldg method provides a near local stencil finally a study of the conditioning and the size of the null space of the matrix systems resulting from the dg discretization of the elliptic problem is undertaken copyright 2005 john wiley sons ltd

bubble stabilization of discontinuous galerkin methods we analyze the stabilizing effect of the introduction of suitable bubble functions in dg formulations for linear second order elliptic problems working for the sake of simplicity on laplace operator in particular we find that the addition of a single b ubble per element can stabilize the non symmetric formulation of baumann oden most commonly used dg methods need the addition of suitable stabilizing terms in order to provide good convergence properties the typical stabilizing procedure consists in the introduction of penalty terms that penalize the jumps across neigh boring elements sometimes in hyperbolic or in convection dominated problems one also use upwind techniques consisting in replacing the average u u 2 on an internal edge with the upwind value that is u or u according with the direction of the wind this however in most cases can be seen again as a jump stabilization 15 13 10 another possible way of stabilizing dg methods consists in the addition of suit able terms this time internal to each element of the so ca lled hughes francatype in general the integral of the original equation or one of t he original equations written in strong form inside each element in terms of the finite element unknowns trial functions multiplied by a similar expression act ing on the test functions the most famous stabilization of this type for standard galerkin methods is surely the supg stabilization of convection dominated equations 12 a typical problem in these cases is the choice of the proper stabilization coefficient to be put in front of the stabilizing term in a recent paper see 6 we pointed out that in dg methods the jumps are themselves to be regarded as equations so that jump stabilizations and hence upwind could be regarded as hughes franca stabilizations as well and indeed the optimal choice of the coefficient in a jump stabilizatio n term is still a subject that might need a further investigation

scaling properties of the eigenvalue spacing distribution for band random matrices the authors show that the spacing distribution for eigenvalues of band random matrices is described by a single parameter b2 n where b is the band half width and n is the size of the matrices it is also shown that the eigenvalue s density obeys the semicircle law the found scaling behaviour suggests that the fluctuation properties in the intermediate regime between wigner dyson and poisson are universal

the isomonodromy approach to matric models in 2d quantum gravity we consider the double scaling limit in the hermitian matrix model for 2d quantum gravity associated with the measure exp sum limits j 1 n t j z 2j n geqq 3 we show that after the appropriate modification of the contour of integration the cross migdal douglas shenker limit to the painleve i equation in the generic case of the pure gravity is valid and calculate the nonperturbative parameters of the corresponding painleve function our approach is based on the wkb analysis of the l a pair corresponding to the discrete string equation in the framework of the inverse monodromy method here we extend our results which were obtained before for the particular casesn 2 3 our analysis complements the isomonodromy approach proposed by g moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself

meixner pollaczek polynomials and the heisenberg algebra an alternative proof is given for the connection between a system of continuous hahn polynomials and identities for symmetric elements in the heisenberg algebra which was first observed by bender mead and pinsky phys rev lett 56 2445 1986 j math phys 28 509 1987 the continuous hahn polynomials turn out to be meixner pollaczek polynomials use is made of the connection between laguerre polynomials and meixner pollaczek polynomials the rodrigues formula for laguerre polynomials an operational formula involving meixner pollaczek polynomials and the schrodinger model for the irreducible unitary representations of the three dimensional heisenberg group

two level overlapping schwarz algorithms for a staggered discontinuous galerkin method two overlapping schwarz algorithms are developed for a discontinuous galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions the discontinuous galerkin formulation is based on a staggered discretization introduced by chung and engquist siam j numer anal 47 2009 pp 3820 3848 for the acoustic wave equation two types of coarse problems are introduced for the two level schwarz algorithms the first is built on a nonoverlapping subdomain partition which allows quite general subdomain partitions and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation condition number bounds are established and numerical results are presented

largest eigenvalue distribution in the double scaling limit of matrix models a coulomb fluid approach using thermodynamic arguments we find that the probability that there are no eigenvalues in the interval s infinity in the double scaling limit of hermitian matrix models is o exp s2 gamma 2 as s to infinity here gamma m 1 2 m 1 2 determines the mth multi critical point of the level density sigma x alpha b 1 x b 2 gamma x in b b and b2 alpha n furthermore the size of the transition zone where the eigenvalue density becomes vanishingly small at the tail of the spectrum is approximately n gamma 1 2 gamma 1 in agreement with earlier work based upon the string equation

stability of pole solutions for planar propagating flames i exact eigenvalues and eigenfunctions it is well known that the nonlinear pde describing the dynamics of a hydrodynamically unstable planar flame front admits exact pole solutions as equilibrium states such a solution corresponds to a steadily propagating cusp like structure commonly observed in experiments in this work we investigate the linear stability of these equilibrium states the steady coalescent pole solutions in previous similar studies either a truncated linear system was numerically solved for the eigenvalues or the initial value problem for the linearized pde was numerically integrated in order to examine the evolution of initially small disturbances in time in contrast our results are based on the exact analytical expressions for the eigenvalues and corresponding eigenfunctions in this paper we derive the expressions for the eigenvalues and eigenfunctions their properties and the implication on the stability of pole solutions is discussed in a paper which will appear later

theory of random matrices with strong level confinement orthogonal polynomial approach strongly non gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in the presence and the absence of a hard edge in their energy spectra employing a theory of polynomials orthogonal with respect to exponential weights we calculate with an asymptotic accuracy the two point kernel over all distance scale and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the end points of the spectrum we also obtain the exact expressions for density of levels one and two point green s functions and prove that a universal local relationship exists for the suitably normalized and rescaled connected two point green s function the connection between the structure of the szeg o function entering strong polynomial asymptotics and mean field equation is traced textcopyright 1996 the american physical society

a priori error analyses of a stabilized discontinuous galerkin method abstract we introduce a new stabilized discontinuous galerkin method within a new function space setting that is closely related to the discontinuous galerkin formulation by oden babuska and baumann 1 but involves an extra stabilization term on the jumps of the normal fluxes across the element interfaces the formulation satisfies a local conservation property and we prove well posedness of the new formulation a priori error estimates are derived which are verified by 1d and 2d experiments on a reaction diffusion type model problem

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

a discrete approach to monotonicity of zeros of orthogonal polynomials we study the monotonicity with respect to a parameter of zeros of orthogonal polynomials our method uses the tridiagonal jacobi matrices arising from the three term recurrence relation for the polynomials we obtain new results on monotonicity of zeros of associated laguerre al salam carlitz meixner and pollaczek polynomials we also derive inequalities for the zeros of the al salam carlitz and meixner polynomials

asymptotics of the largest zeros of some orthogonal polynomials we study the asymptotics of the largest zeros of the wilson hermite and q laguerre polynomials using two distinct techniques the first is based on the coulomb fluid technique developed in a previous paper where the primary input is the weight function while the second uses the method of chain sequences which supplies inequalities for the largest zeros using the recurrence coefficients we also investigate the asymptotics of the largest zeros of the polynomials orthogonal to the weight functions for c 0 and m a positive even integer

existence results for singular critical elliptic problems in rn abstract in the paper we consider the following semilinear elliptic problems with critical sobolev hardy exponents p s u x 2 u v x u k x u 2 s 2 x s u in r n lim x u x 0 where n 3 0 n 2 2 2 0 0 s 2 2 s 2 n s n 2 under suitable conditions we prove that p s has at least one nontrivial solution by means of linking theorem also via the pseudo index theory we consider the multiplicity of nontrivial solutions for p s

the meixner pollaczek polynomials and a system of orthogonal polynomials in a strip considered in this paper are two systems of polynomials that are orthogonal systems for two different but related inner product spaces one of these systems is a special case of the symmetric meixner pollaczek polynomial systems pn x 2 2 and it turns out that this system is closely related to a system of orthogonal polynomials in the strip s z 1 im z 1 moreover there are some simple operators that connect the systems with each other we have designated the special case of the symmetric meixner pollaczek polynomial systems by n and the latter system on the strip by n and we have been able to show that this system is the limiting case of the symmetric meixner pollaczek polynomial systems pn x 2 2 as 0

three systems of orthogonal polynomials and l 2 boundedness of two associated operators abstract in this paper we describe three systems of orthogonal polynomials belonging to the class of meixner pollaczek polynomials and establish some useful connections between them in terms of three basic operators that are related to them furthermore we investigate boundedness properties of two other operators both as convolution operators in the translation invariant case where we use fourier transforms and for the weights related to the relevant orthogonal polynomials we consider only the most important but also simplest case of l 2 spaces however in subsequent papers we intend to extend the study to l p spaces 1 p

new orthogonality relations for the continuous and the discrete q ultraspherical polynomials abstract in a recent contribution n m atakishiyev a u klimyk on discrete q ultraspherical polynomials and their duals j math anal appl 306 2005 637 645 the so named discrete q ultraspherical polynomials were introduced as a specialization of the big q jacobi polynomials and their orthogonality established for values of the parameter outside its commonly known domain but inside the range of validity of the conditions of favard s theorem in this paper we consider both the continuous and the discrete q ultraspherical polynomials and we prove that their orthogonality is guaranteed for the whole range of the allowed parameters even in those intriguing cases in which the three term recurrence relation breaks down the presence of either the askey wilson divided difference operator in the continuous case or the q derivative operator in the discrete one provides the q sobolev character of the non standard inner products introduced in our approach

two dimensional yang mills theory painleve equations and the six vertex model we show that the chiral partition function of two dimensional yang mills theory on the sphere can be mapped to the partition function of the homogeneous six vertex model with domain wall boundary conditions in the ferroelectric phase a discrete matrix model description in both cases is given by the meixner ensemble leading to a representation in terms of a stochastic growth model we show that the partition function is a particular case of the z measure on the set of young diagrams yielding a unitary matrix model for chiral yang mills theory on s2 and the identification of the partition function as a tau function of the painlev v equation we describe the role played by generalized non chiral yang mills theory on s2 in relating the meixner matrix model to the toda chain hierarchy encompassing the integrability of the six vertex model we also argue that the thermodynamic behaviour of the six vertex model in the disordered and antiferroelectric phases are captured by particular q deformations of two dimensional yang mills theory on the sphere

the laplacian on a random one dimensional lattice the authors study the spectrum of minus the laplacian on a random one dimensional lattice it extends monotonically throughout the positive real axis with a continuum limit behaviour for small values the authors find as expected localisation effects throughout the whole range they use a variety of techniques which are shown to be consistent and in agreement with a monte carlo simulation they include small and large disorder expansions direct integral equations for probability distributions as well as the replica method the latter is also used to investigate green functions

correlation functions in disordered systems recently we found that the correlation between the eigenvalues of random hermitian matrices exhibits universal behavior here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous work to the case in which the random matrix evolves in time or varies as some external parameters vary we compute the current current correlation function discuss various generalizations and compare our work with the work of other authors we study the distribution of eigenvalues of hamiltonians consisting of a sum of a deterministic term and a random term the correlation between the eigenvalues when the deterministic term is varied is calculated

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

solutions for semilinear elliptic problems with critical sobolev hardy exponents in rn abstract let n 3 0 s 2 0 n 2 2 2 and 2 s 2 n s n 2 be the critical sobolev hardy exponents via variational methods and the analytic technique we prove the existence of a nontrivial solution to the singular semilinear problem u u x 2 u u 2 s 2 x s u f u u h r 1 r n for n 4 0 1 and suitable functions f u

spectral fluctuation properties of hamiltonian systems the transition region between order and chaos the authors study numerically the classical dynamical behaviour and the spectral fluctuation properties of a class of hamiltonian systems with two degrees of freedom the quantum mechanical properties of these systems are monotonic but non universal functions of the fraction of classical phase space filled by chaotic trajectories it is found that the observed spectral fluctuation measures can be reproduced by a random matrix model which depends on one parameter only

low order discontinuous galerkin methods for second order elliptic problems we consider dg methods for second order scalar elliptic problems using piecewise affine approximation in two or three space dimensions we prove that both the symmetric and the nonsymmetric versions of the dg method have regular system matrices without penalization of the interelement solution jumps provided boundary conditions are imposed in a certain weak manner optimal convergence is proved for sufficiently regular meshes and data we then propose a dg method using piecewise affine functions enriched with quadratic bubbles using this space we prove optimal convergence in the energy norm for both a symmetric and nonsymmetric dg method without stabilization all of these proposed methods share the feature that they conserve mass locally independent of the penalty parameter

asymptotic distribution of zeros of polynomials satisfying difference equations we propose a way to find the asymptotic distribution of zeros of orthogonal polynomials pn x satisfying a difference equation of the form b x pn x c x n pn x d x pn x 0 we calculate the asymptotic distribution of zeros and asymptotics of extreme zeros of the meixner and meixner pollaczek polynomials the distribution of zeros of meixner polynomials shows some delicate features we indicate the relation of our technique to the approach based on the nevai dehesa ullman distribution

a priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems we analyze three discontinuous galerkin approximations for solving elliptic problems in two or three dimensions in each one the basic bilinear form is nonsymmetric the first one has a penalty term on edges the second has one constraint per edge and the third is totally unconstrained for each of them we prove hp error estimates in the h1 norm optimal with respect to h the mesh size and nearly optimal with respect to p the degree of polynomial approximation we establish these results for general elements in two and three dimensions for the unconstrained method we establish a new approximation result valid on simplicial elements l2 estimates are also derived for the three methods

continuous hahn polynomials and the heisenberg algebra continuous hahn polynomials have surfaced in a number of somewhat obscure physical applications for example they have emerged in the description of two photon processes in hydrogen hard hexagon statistical mechanical models and clebsch gordan expansions for unitary representations of the lorentz group so 3 1 in this paper it is shown that there is a simple and elegant way to construct these polynomials using the heisenberg algebra

analysis of a family of discontinuous galerkin methods for elliptic problems the one dimensional case in this paper we analyze a family of discontinuous galerkin methods parameterized by two real parameters for elliptic problems in one dimension our main results are 1 a complete inf sup stability analysis characterizing the parameter values yielding a stable scheme and energy norm error estimates as a direct consequence thereof 2 an analysis of the error in l2 where the standard duality argument only works for special parameter values yielding a symmetric bilinear form and different orders of convergence are obtained for odd and even order polynomials in the nonsymmetric case the analysis is consistent with numerical results and similar behavior is observed in two dimensions

multilevel preconditioners for discontinuous galerkin approximations of elliptic problems with jump coefficients in this article we develop and analyze two level and multi level methods for the family of interior penalty ip discontinuous galerkin dg discretizations of second order elliptic problems with rough coecients exhibiting large jumps across interfaces in the domain these methods are based on a decomposition of the dg nite element space that inherently hinges on the diusion coecient of the problem our analysis of the proposed preconditioners is presented for both symmetric and non symmetric ip schemes and we establish both robustness with respect to the jump in the coecient and near optimality with respect to the mesh size following the analysis we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods

stabilization mechanisms in discontinuous galerkin finite element methods in this paper we propose a new general framework for dg methods which allows to uncover a basic mechanism that ensures suitable stability properties of the methods we show that such a mechanism is essentially the same for apparently unrelated stabilizations such as jump penalty upwinding and hughes franca type residual based stabilizations

nonlocal kardar parisi zhang equation to model interface growth the dynamics of the growth of interfaces in the presence of noise and when the normal velocity is constant in the weakly nonlinear limit are described by the kardar parisi zhang kpz equation in many applications however the growth is controlled by nonlocal transport which is not contained in the original kpz equation for these problems we are proposing an extension of the kpz model where the nonlocal contribution is expressed through a hilbert transform and can act to either stabilize or destabilize the interface the model is illustrated with a specific example from reactive infiltration the properties of the solution of the resulting equation are studied in one spatial dimension in the linear and the nonlinear limits for both stable and unstable growth we find that the early time behavior has a power law scaling similar to that of the kpz equation however in the case of stable growth the scaling of the saturation width is logarithmic which differs from the power law in the kpz equation this dependence reflects the stabilizing effect of nonlocal transport in the unstable case we obtain results similar to those of olami et al phys rev e 55 2649 1997

critique of the replica trick it is shown that the replica trick fails to give the correct non perturbative result for the two point function s2 of the gaussian unitary ensemble of n n random matrices the failure arises from an incorrect description of the symmetries of the random matrix system in the limit n to infinity the correct description which involves integration over both non compact and compact degrees of freedom is obtained by using the method of superfields some implications for the localisation transition in disordered electronic systems and the theory of the quantised hall effect are suggested

random matrix theory by the supersymmetry method beyond the sigma model abstract the leading correction to the smoothed connected energy density density correlation function is obtained for the large energy difference within the context of the gaussian random matrix theory in order to achieve this result the supersymmetry method is extended beyond the sigma model to include small quadratic fluctuations around the saddle point special care is taken to avoid the potential divergence arising from the unbounded nature of the saddle point also in the small energy difference regime the leading correction to a two point correlation function is obtained

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

existence of solutions for elliptic equations with critical sobolev hardy exponents let omega subset of rn be a smooth bounded domain such that 0 is an element of omega n greater than or equal to 3 0 less than or equal to s 2 2 s 2 n s n 2 we prove the existence of nontrival solutions for the singular critical problem

a posteriori estimates for the bubble stabilized discontinuous galerkin method in this paper two reliable and efficient a posteriori error estimators for the bubble stabilized discontinuous galerkin bsdg method for diffusion reaction problems in two and three dimensions are derived the theory is followed by some numerical illustrations

the symmetric meixner pollaczek polynomials with real parameter abstract the symmetric meixner pollaczek polynomials p n x 2 2 for 0 are well studied polynomials these are polynomials orthogonal on the real line with respect to a continuous positive real measure for 0 p n x 2 2 are also polynomials however they are not orthogonal on the real line with respect to any real measure this paper defines a non standard inner product with respect to which the polynomials p n x 2 2 for 0 become orthogonal polynomials it examines the major properties of the polynomials p n x 2 2 for 0 which are also shared by the polynomials p n x 2 2 for 0

a penalty free nonsymmetric nitsche type method for the weak imposition of boundary conditions in this paper we show that the nonsymmetric version of nitsche s method for the weak imposition of boundary conditions is stable without penalty term for nonconforming elements we prove the same result for the symmetric formulation as well we prove optimal h 1 error estimates and l 2 error estimates that are suboptimal with half an order in h both the pure diffusion and the convection diffusion problems are discussed

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

nodal solutions for p laplace equations with critical growth abstract this paper is concerned with the existence and nodal character of the nontrivial solutions for the following quasilinear elliptic equations involving critical sobolev exponents 1 i 1 n x i u p 2 u x i u p 2 u u p 2 u f u u w r 1 p r n where p 2 and p np n p is the critical sobolev exponent for the embedding w r 1 p r n l p r n the function f satisfies some conditions given by f1 f2 f3 in the paper the main results obtained in this paper are that there exists at least a pair of nontrivial solutions for eq 1 provided that n p2 and there exists at least a pair of nontrivial solutions uk uk of eq 1 for each k n 0 such that both uk and uk possess exactly k nodes provided that f t 0 for t 0 and n p2 p 1 p

level curvature distribution for diffusive aharonov bohm systems analytical results we calculate analytically the distributions of level curvatures lc the second derivatives of eigenvalues with respect to a magnetic flux for a particle moving in a white noise random potential we find that the zakrzewski delande conjecture is still valid even if the lowest weak localization corrections are taken into account the ratio of mean level curvature modulus to mean dissipative conductance is proved to be universal and equal to 2 pi in agreement with available numerical data

hardy spaces for the strip abstract in this paper we shall study hardy spaces of analytic functions in a strip s our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense we also present an orthogonal in h 2 s basis of polynomials

distributions on partitions point processes and the hypergeometric kernel we study a 3 parametric family of stochastic point processes on the one dimensional lattice originated from a remarkable family of representations of the infinite symmetric group we prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel the kernel can be expressed through the gauss hypergeometric function we call it the hypergeometric kernel in a scaling limit our processes approximate the processes describing the decomposition of representations mentioned above into irreducibles as we showed in previous works the correlation functions of these limit processes also have determinantal form with so called whittaker kernel we show that the scaling limit of the hypergeometric kernel is the whittaker kernel integrable operator as defined by its izergin korepin and slavnov we argue that the hypergeometric kernel can be considered as a kernel defining a discrete integrable operator we also show that the hypergeometric kernel degenerates for certain values of parameters to the christoffel darboux kernel for meixner orthogonal polynomials this fact is parallel to the degeneration of the whittaker kernel to the christoffel darboux kernel for laguerre polynomials

breakdown of universality in multi cut matrix models we solve the puzzle of the disagreement between orthogonal polynomials methods and mean field calculations for random n n matrices with a disconnected eigenvalue support we show that the difference does not stem from a 2 symmetry breaking but from the discreteness of the number of eigenvalues this leads to additional terms quasiperiodic in n which must be added to the naive mean field expressions our result invalidates the existence of a smooth topological large n expansion and some postulated universality properties of correlators we derive the large n expansion of the free energy for the general two cut case from it we rederive by a direct and easy mean field like method the two point correlators and the asymptotic orthogonal polynomials we extend our results to any number of cuts and to non real potentials

wrinkled flames and geometrical stretch localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity s are studied a stretch affected nonlinear and nonlocal equation derived from an inhomogeneous michelson sivashinsky equation is used as a starting point and pole decompositions are used as a tool analytical and numerical descriptions of isolated centered or multicrested wrinkles with steady shapes in a frame and various amplitudes are provided their number increases rapidly with 1 s 0 a large constant s 0 weakens or suppresses all localized wrinkles the larger the wrinkles the easier the suppression whereas s 0 strengthens them oscillations of s further restrict their existence domain self similar evolutions of unstable many crested patterns are obtained a link between stretch nonlinearity and instability with the cutoff size of the wrinkles in turbulent flames is suggested open problems are evoked

asymptotics of extreme zeros of the meixner pollaczek polynomials we study the asymptotics of the smallest and largest zeros of the symmetric and asymmetric meixner pollaczek polynomials using two techniques one is a coulomb fluid technique developed earlier where the primary input is the weight function the second uses the method of chain sequences which supplies inequalities for the largest zeros from the knowledge of the recurrence coefficients an upper bound for the largest zero of meixner polynomials is also given

thermodynamic limit of the six vertex model with domain wall boundary conditions we address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model here we compare the bulk free energy for periodic and domain wall boundary conditions using a determinant representation for the partition function with domain wall boundary conditions we derive toda differential equations and solve them asymptotically in order to extract the bulk free energy we find that it is different and bears no simple relation to the free energy for periodic boundary conditions the six vertex model with domain wall boundary conditions is closely related to algebraic combinatorics alternating sign matrices this implies new results for the weighted counting for large size alternating sign matrices finally we comment on the interpretation of our results in particular in connection with domino tilings dimers on a square lattice

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

bubble stabilized discontinuous galerkin method for parabolic and elliptic problems in this paper we give an analysis of a bubble stabilized discontinuous galerkin method for elliptic and parabolic problems the method consists of stabilizing the numerical scheme by enriching the discontinuous affine finite element space elementwise by quadratic bubbles this approach leads to optimal convergence in the space and time discretization parameters

some remarks on a paper by l carlitz we study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by l carlitz we show that they are a special case of the sheffer polynomials and point out some interesting connections with certain sobolev orthogonal polynomials

analysis of a nonsymmetric discontinuous galerkin method for elliptic problems stability and energy error estimates in this paper we analyze a nonsymmetric discontinuous galerkin method for elliptic problems proposed by oden babuska and baumann our main results are a complete inf sup stability analysis and as a consequence error estimates in a mesh dependent energy norm allowing variable meshsize and order of polynomials the analysis is carried out in two spatial dimensions on an unstructured triangulation

random unitary matrices permutations and painleve this paper is concerned with certain connections between the ensemble of n n unitary matrices specifically the characteristic function of the random variable tr u and combinatorics specifically ulam s problem concerning the distribution of the length of the longest increasing subsequence in permutation groups and the appearance of painleve functions in the answers to apparently unrelated questions among the results is a representation in terms of a painleve v function for the characteristic function of tr u and using recent results of baik deift and johansson an expression in terms of a painleve ii function for the limiting distribution of the length of the longest increasing subsequence in the hyperoctahedral groups