distribution of periodic torus orbits and duke s theorem for cubic fields we study periodic torus orbits on spaces of lattices using the action of the group of adelic points of the underlying tori we define a natural equivalence relation on these orbits and show that the equivalence classes become uniformly distributed this is a cubic analogue of duke s theorem about the distribution of closed geodesics on the modular surface suitably interpreted the ideal classes of a cubic totally real field are equidistributed in the modular 5 fold sl3 z sl3 r so3 in particular this proves a stronger form of the folklore conjecture that the collection of maximal compact flats in sl3 z sl3 r so3 of volume infinity

optimal low dispersion low dissipation lbm schemes for computational aeroacoustics lattice boltmzann methods lbm have been proved to be very effective methods for computational aeroacoustics caa which have been used to capture the dynamics of weak acoustic fluctuations in this paper we propose a strategy to reduce the dispersive and disspative errors of the two dimensional 2d multi relaxation time lattice boltzmann method mrt lbm by presenting an effective algorithm we obtain a uniform form of the linearized navier stokes equations corresponding to the mrt lbm in wave number space using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods we propose a class of minimization problems to optimize the free parameters in the mrt lbm we obtain this way a dispersion relation preserving lbm drp lbm to circumvent the minimized dispersion error of the mrt lbm the dissipation relation precision is also improved and the stability of the mrt lbm with the small bulk viscosity is guaranteed von neuman analysis of the linearized mrt lbm is performed to validate the optimized dispersion dissipation relations considering monochromatic wave solutions meanwhile dispersion and dissipation errors of the optimized mrt lbm are quantitatively compared with the original mrt lbm finally some numerical simulations are carried out to assess the new optimized mrt lbm schemes

unitary representations and theta correspondence for type i classical groups in this paper we discuss the positivity of the hermitian form p introduced by li in invent math 27 1989 237 255 let g1 g2 be a type i dual pair with g1 the smaller group let p be an irreducible unitary representation in the semistable range of y mg1 mg2 see communications in contemporary mathematics vol 2 2000 pp 255 283 we prove that the invariant hermitian form p is positive semidefinite under certain restrictions on the size of g2 and a mild growth condition on the matrix coefficients of p therefore if p does not vanish y mg1 mg2 p is unitary theta correspondence over r was established by howe in j amer math soc 2 1989 535 552 li showed that theta correspondence preserves unitarity for dual pairs in stable range our results generalize the results of li for type i classical groups invent math 27 1989 237 the main result in this paper can be used to construct irreducible unitary

godement jacquet l functions and full theta lifts we relate poles of local godement jacquet l functions to distributions on matrix spaces with singular supports as an application we show the irreducibility of the full theta lifts to mathrm gl n mathrm f of generic irreducible representations of mathrm gl n mathrm f where mathrm f is an arbitrary local field

application of lattice boltzmann method to sensitivity analysis via complex differentiation sensitivity analysis of flows computed by lattice boltzmann method via complex differentiation is proposed the theoretical work is illustrated and the proposed method assessed considering the d2q9 scheme along with the differentiation of the lattice boltzmann equation boundary condition implementation is also detailed some examples illustrate the capability of the proposed method

lp fourier and fourier stieltjes algebras for locally compact groups abstract let g be a locally compact group and 1 p a continuous unitary representation g b h of g is an l p representation if the matrix coefficient functions s s x x lie in l p g for sufficiently many x h the l p fourier algebra a l p g is defined to be the set of matrix coefficient functions of l p representations similarly the l p fourier stieltjes algebra b l p g is defined to be the weak closure of a l p g in the fourier stieltjes algebra b g these are always ideals in the fourier stieltjes algebra containing the fourier algebra a g in this paper we investigate how these spaces reflect properties of the underlying group and study the structural properties of these algebras as an application of this theory we characterize the fourier stieltjes ideals of sl 2 r

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

effective equidistribution of shears and applications a shear is a unipotent translate of a cuspidal geodesic ray in the quotient of the hyperbolic plane by a non uniform discrete subgroup of text psl 2 mathbb r possibly of infinite co volume we prove the regularized equidistribution of shears under large translates with effective that is power saving rates we also give applications to weighted second moments of gl 2 automorphic l functions and to counting lattice points on locally affine symmetric spaces

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

lattice boltzmann method with selective viscosity filter for high reynolds number flows the lattice boltzmann method suffers from numerical instabilities that can induce local blowup of the computation the von neumann stability analysis applied to the lbe bgk and lbe mrt models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes as it is done in the lbe mrt model an increase of the bulk viscosity is an efficient way of damping spurious oscillations however this stabilization method induces an over damping of acoustic waves some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes three different lattice boltzmann algorithms based on filtering step are proposed the fully filtered lbe the lbe with filtered macroscopic quantities and the lbe with filtered collision operator the behavior of several explicit filter stencils is studied in the fourier space for a given filter stencil the filtered collision operator approach leads to the highest cut off wavenumber in this case the theoretical wavenumber dependent viscosity is n k c s 2 t email protected k 1 2 where f k is the filter shape and s the filter strength under resolved simulations high reynolds number are performed on the case of the doubly periodic shear layers the performance of the three filtered lbe is found to be the same as the mrt model for stability control propagation of acoustic plane waves is also simulated with the three filtering algorithms the measured dissipation of acoustic wave compares well with the theoretical results

comparison between lattice boltzmann method and navier stokes high order schemes for computational aeroacoustics computational aeroacoustic caa simulation requires accurate schemes to capture the dynamics of acoustic fluctuations which are weak compared with aerodynamic ones in this paper two kinds of schemes are studied and compared the classical approach based on high order schemes for navier stokes like equations and the lattice boltzmann method the reference macroscopic equations are the 3d isothermal and compressible navier stokes equations a von neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions three physical modes are recovered and the corresponding theoretical dispersion relations are obtained then the same analysis is made on the space and time discretization of the navier stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions different orders of discretization are considered with and without a uniform mean flow three different lattice boltzmann models are then presented and studied with the von neumann analysis the theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied it is shown that the dispersion error in the lattice boltzmann models is only due to the space and time discretization and that the continuous discrete velocity boltzmann equation yield the same exact dispersion as the navier stokes equations finally dispersion and dissipation errors of the different kind of schemes are quantitatively compared it is found that the lattice boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3 step runge kutta scheme in time the number of floating point operations at a given error level associated with these two kinds of schemes are then compared

effective equidistribution for closed orbits of semisimple groups on homogeneous spaces we prove effective equidistribution with polynomial rate for large closed orbits of semisimple groups on homogeneous spaces under certain technical restrictions notably the acting group should have finite centralizer in the ambient group the proofs make extensive use of spectral gaps and also of a closing lemma for such actions

on distinguished square integrable representations for galois pairs and a conjecture of prasad we prove an integral formula computing multiplicities of square integrable representations relative to galois pairs over p adic fields and we apply this formula to verify two consequences of a conjecture of dipendra prasad one concerns the exact computation of the multiplicity of the steinberg representation and the other the invariance of multiplicities by transfer among inner forms

noise source identification with the lattice boltzmann method in this paper the sound source identification problem is addressed with the use of the lattice boltzmann method to this aim a time reversed problem coupled to a complex differentiation method is used in order to circumvent the inherent instability of the time reversed lattice boltzmann scheme a method based on a split of the lattice boltzmann equation into a mean and a perturbation component is used lattice boltzmann method formulation around an arbitrary base flow is recalled and specific applications to acoustics are presented the implementation of the noise source detection method for two dimensional weakly compressible low mach number flows is discussed and the applicability of the method is demonstrated

connected lie groups and property rd for a locally compact group property rd gives a control on the convolution norm of any compactly supported measure in terms of the l 2 norm of its density and the diameter of its support we give a complete classification of those lie groups with property rd

asymptotic behavior results for nonlinear neutral delay difference equations abstract this paper is concerned with the nonlinear neutral delay difference equation x n c n x n m p n f x n k 0 n n n 0 where is the forward difference operator defined by x n x n 1 x n c n is a sequence of real numbers p n is a positive sequence f c r r m and k are positive integers n 0 is a nonnegative integer and n n 0 n 0 n 0 1 n 0 2 sufficient conditions are obtained under which every solution of equation is bounded and tends to a constant as n our results improve and extend some known results one example is given to illustrate our results

on the local global conjecture for integral apollonian gaskets we prove that a set of density one satisfies the local global conjecture for integral apollonian gaskets that is for a fixed integral primitive apollonian gasket almost every in the sense of density admissible passing local obstructions integer is the curvature of some circle in the gasket

the role of the ramanujan conjecture in analytic number theory we discuss progress towards the ramanujan conjecture for the group gln and its relation to various other topics in analytic number theory

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

uniform pointwise bounds for matrix coefficients of unitary representations on semidirect products abstract let k be a local field of characteristic 0 and let g be a connected semisimple almost k algebraic group suppose rank k g 1 and is an excellent representation of g on a finite dimensional k vector space v we construct uniform pointwise bounds for the k finite matrix coefficients restricted on g of all unitary representations of the semi direct product g v without non trivial v fixed vectors these bounds turn out to be sharper than the bounds obtained from g itself for some cases as an application we discuss a simple method of calculating kazhdan constants for various compact subsets of the pair g v v

on the discrete series of generalized stiefel manifolds a study of the discrete series of generalized stiefel manifolds is made using the oscillator representation new infinite families of such discrete series are constructed

counting lattice points for a locally compact second countable group g and a lattice subgroup we give an explicit quantitative solution of the lattice point counting problem in general domains in g provided that i g has finite upper local dimension and the domains satisfy a basic regularity condition ii the mean ergodic theorem for the action of g on g holds with a rate of convergence the error term we establish matches the best current result for balls in symmetric spaces of simple higher rank lie groups but holds in much greater generality a significant advantage of the ergodic theoretic approach we use is that the solution to the lattice point counting problem is uniform over families of lattice subgroups provided they admit a uniform spectral gap in particular the uniformity property holds for families of finite index subgroups satisfying a quantitative variant of property we discuss a number of applications including counting lattice points in general domains in semisimple s algebraic groups counting rational points on group varieties with respect to a height function and quantitative angular or conical equidistribution of lattice points in symmetric spaces and in affine symmetric varieties we note that the mean ergodic theorems which we establish are based on spectral methods including the spectral transfer principle and the kunze stein phenomenon we formulate and prove appropriate analogues of both of these results in the set up of adele groups and they constitute a necessary step in our proof of quantitative results in counting rational points

radial rapid decay property for cocompact lattices abstract we study haagerup inequality for radial functions on uniform lattices in semisimple lie groups with respect to riemannian metrics and in some case to word metrics in particular we extend the swiatkowski valette results to any lattice acting properly and essentially transitively on classical buildings

subconvex equidistribution of cusp forms reduction to eisenstein observables let traverse a sequence of cuspidal automorphic representations of gl2 with large prime level unramified central character and bounded infinity type for g gl1 pgl2 let h g denote the assertion that subconvexity holds for g twists of the adjoint l function of with polynomial dependence upon the conductor of the twist we show that h gl1 implies h pgl2 in geometric terms h pgl2 corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term h gl1 to the special case in which the relevant sequence of measures is tested against an eisenstein series

best possible rates of distribution of dense lattice orbits in homogeneous spaces this paper establishes upper and lower bounds on the speed of approximation in a wide range of natural diophantine approximation problems the upper and lower bounds coincide in many cases giving rise to optimal results in diophantine approximation which were inaccessible previously our approach proceeds by establishing more generally upper and lower bounds for the rate of distribution of dense orbits of a lattice subgroup in a connected lie or algebraic group g acting on suitable homogeneous spaces g h the upper bound is derived using a quantitative duality principle for homogeneous spaces reducing it to a rate of convergence in the mean ergodic theorem for a family of averaging operators supported on h and acting on g in particular the quality of the upper bound on the rate of distribution we obtain is determined explicitly by the spectrum of h in the automorphic representation on l 2 g we show that the rate is best possible when the representation in question is tempered and show that the latter condition holds in a wide range of examples

uniform pointwise bounds for matrix coefficients of unitary representations and applications to kazhdan constants let k be a local field and g the group of k rational points of a connected reductive linear algebraic group over k with k semisimple rank g 2 let k be a good maximal compact subgroup of g for a unitary representation of g a vector v in is called kfinite if the subspace spanned bykv is finite dimensional we will use the termk matrix coefficients resp k finite matrix coefficients of to refer to its matrix coefficients with respect to k invariant resp k finite unit vectors following bt we denote by g the subgroup generated by the unipotent k split subgroups of g the main goal of the present paper is to construct a class of uniform pointwise bounds for the k finite matrix coefficients of all infinite dimensional irreducible unitary representations of g or more generally of all unitary representations of g without a non zero g invariant vector let a be a maximal k split torus and a the closed positive weyl chamber of a such that the cartan decomposition g ka k holds where is a finite subset of the

sparse equidistribution problems period bounds and subconvexity we introduce a geometric method to bound periods of automorphic forms the key features of this method are the use of equidistribution results in place of mean value theorems and the systematic use of mixing and the spectral gap applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of cm points to subconvexity of the triple product period in the level aspect over number fields which implies subconvexity for certain standard and rankin selberg l functions and to bounding fourier coefficients of automorphic forms

on the pair correlation density for hyperbolic angles we prove a conjecture of boca popa zaharescu on the density function for the pair correlation of hyperbolic angles in a growing orbit of a discrete lattice in psl2 r

triple product formula and the subconvexity bound of triple product l function in level aspect in this paper we derive a nice general formula for the local integrals of triple product formula whenever one of the representations has sufficiently higher level than the other two as an application we generalize venkatesh and woodbury s work on the subconvexity bound of triple product l function in level aspect allowing joint ramifications higher ramifications general unitary central characters and general special values of local epsilon factors

functions on symmetric spaces and oscillator representation in this paper we study the l 2 functions on u 2n o 2n and mp n r we relate them using the oscillator representation we first study some isometries between various l 2 spaces using the compactification we defined in h he an analytic compactification of the symplectic group j differential geom 51 1999 375 399 these isometries were first introduced by betten and olafsson in f betten g olafsson causal compactification and hardy spaces for spaces of hermitian type pacific j math 200 2

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

strong solidity of group factors from lattices in so n 1 and su n 1 abstract we show that the group factors l where is an icc lattice in either so n 1 or su n 1 n 2 are strongly solid in the sense of ozawa and popa 2010 13 this strengthens a result of ozawa and popa 2010 14 showing that these factors do not have cartan subalgebras