relating invariant linear form and local epsilon factors via global methods we use the recent proof of jacquet s conjecture due to harris and kudla hk and the burger sarnak principle see bs to give a proof of the relationship between the existence of trilinear forms on representations of gl 2 k u for a non archimedean local field k u and local epsilon factors which was earlier proved only in the odd residue characteristic by this author in p1 theorem 1 4 the method used is very flexible and gives a global proof of a theorem of saito and tunnell about characters of gl 2 using a theorem of waldspurger w theorem 2 about period integrals for gl 2 and also an extension of the theorem of saito and tunnell by this author in p3 theorem 1 2 which was earlier proved only in odd residue characteristic in the appendix to this article h saito gives a local proof of lemma 4 which plays an important role in the article

parameterizing quasi periodicity generalized poisson summation and its application to modified fibonacci antenna arrays the fairly recent discovery of quasi crystals whose x ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity has motivated studies of the wave dynamical implications of aperiodic order within the context of the radiation properties of antenna arrays an instructive novel canonical example of wave interactions with quasi periodic order is illustrated here for one dimensional array configurations based on the modified fibonacci sequence with utilization of a two scale generalization of the standard poisson summation formula for periodic arrays this allows for a quasi floquet analytic parameterization of the radiated field which provides instructive insights into some of the basic wave mechanisms associated with quasi periodic order highlighting similarities and differences with the periodic case examples are shown for quasi periodic infinite and spatially truncated arrays with brief discussion of computational issues and potential applications

local e factors and characters of gl 2 introduction the representation theory of gl 2 k for k a nonarchimedean local field is somewhat more complicated than the corresponding theory for gl 2 r in particular the formulas for the characters of discrete series representation of gl 2 r have a concise closed form while the published character formulas for supercuspidal representations of gl 2 k occupy several pages 10 14 the purpose of this paper is to give a concise formula for the character of certain infinite dimensional representations of gl 2 k the representations considered are admissible in the sense that the stabilizer of a vector in the representation space is open in gl 2 k and the subspace stabilized by an open compact subgroup of gl 2 k is finite dimensional irreducible admissible representations ir of gl 2 k satisfy schur s lemma so that the center k of gl 2 k acts by multiplication by a quasicharacter there exists a locally constant character function ch defined on a dense open subgroup of gl 2 k which determines the isomorphism class of ir 7 section 7 jacquet and langlands 7 section 2 introduced factors e 10 x attached to the twist of ir by quasicharacters x of k which describe the action of r in a specific model for each separable quadratic extension l of k there exists an irreducible admissible representation bcl k 1r of gl 2 l the base change of ir to l 9 section 2 this representation of gl 2 l enters into the expression for the character the main result of this paper is the following formula recall that conjugacy classes of nonsplit cartan subgroups are parameterized by quadratic separable field extensions l of k via embeddings of l in gl 2 k

some characteristics of radiation from linearly phased sequentially excited periodic rectangular arrays of dipoles floquet wave and element by element summation representations are implemented to investigate the radiation from a periodic rectangular array of linearly phased sequentially pulsed dipoles in the frequency and time domains a synthetic aperture type formulation for floquet wave representation and an asymptotic formulation for the element by element summation representation are developed numerical results are presented to demonstrate the efficiency of the floquet wave representation in terms of radiating non radiating and diffracted wave constituents and then validated via comparison with direct summation over the contributions of individual dipole radiations

time domain green s function for an infinite sequentially excited periodic planar array of dipoles the present paper is a continuation of previous explorations by the authors aimed at gaining a basic understanding of the time domain td behavior of large periodic phased i e sequentially turned on array antennas and related configurations our systematic investigation of the relevant canonical td dipole excited green s functions has so far included those for infinite and truncated sequentially pulsed line periodic arrays parameterized in terms of radiating propagating and nonradiating evanescent conical td floquet waves fw and truncation induced td fw modulated tip diffractions the present contribution extends these investigations to an infinite periodic sequentially pulsed planar array which generates pulsed plane propagating and evanescent fw starting from the familiar frequency domain fd transformation of the linearly phased element by element summation synthesis into summations of propagating and evanescent fws we access the time domain by fourier inversion the inversion integrals are manipulated in a unified fashion into exact closed forms which are parameterized by the single nondimensional quantity spl eta c v sup p sub u1 where v sup p sub u1 and c are the excitation phase speed along a preferred phasing direction u sub 1 in the array plane and the ambient wave speed respectively the present study deals with the practically relevant rapidly phased propagating case spl eta 1 regime for a future manuscript numerical reference data generated via element by element summation over the fields radiated by the individual dipoles with ultrawide band limited excitation are compared with results obtained much more efficiently by inclusion of a few td fws physical interpretation of the formal td fw solutions is obtained by recourse to asymptotics instantaneous frequencies and wavenumbers and related constructs of special interest is the demonstration that the td fws emerge along equal delay ellipses from the array plane this furnishes a novel and physically appealing interpretation of the planar array td fw phenomenology

the regularized siegel weil formula the second term identity and the rallis inner product formula in this paper we establish the second term identity of the siegel weil formula in full generality and derive the rallis inner product formula for global theta lifts for any dual pair as a corollary we resolve the non vanishing problem of global theta lifts initiated by steve rallis

graph based transductive learning for robust visual tracking in object tracking problem most methods assume brightness constancy or subspace constancy which are violated in practice in this paper the object tracking problem is considered as a transductive learning problem and a robust tracking method is proposed under intrinsic and extrinsic varieties the object not only fits the object model but also has the same cluster with the previous objects which are the labeled data by constraining the global and local information the cost function is constructed firstly the solution for minimizing the cost function can be solved by a simple linear algebra with graph laplacian moreover a novel graph is constructed over the positive samples and candidate patches which can simultaneously learn the object s global appearance model and the local intrinsic geometric structure of all the patches furthermore a heuristic positive samples selection scheme is adopted to make the method more effective the proposed method is tested on different videos which undergo large pose expression illumination and partial occlusion and compared with state of the art algorithms experimental results and comparative studies are provided to demonstrate the efficiency of the proposed method

ensemble tracking we consider tracking as a binary classification problem where an ensemble of weak classifiers is trained online to distinguish between the object and the background the ensemble of weak classifiers is combined into a strong classifier using adaboost the strong classifier is then used to label pixels in the next frame as either belonging to the object or the background giving a confidence map the peak of the map and hence the new position of the object is found using mean shift temporal coherence is maintained by updating the ensemble with new weak classifiers that are trained online during tracking we show a realization of this method and demonstrate it on several video sequences

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

local theta correspondence of tempered representations and langlands parameters in this paper we give an explicit determination of the theta lifting for symplectic orthogonal and unitary dual pairs over a nonarchimedean field f of characteristic 0 we determine when theta lifts of tempered representations are nonzero and determine the theta lifts in terms of the local langlands correspondence

twisted doubling integrals for classical groups we describe the twisted doubling integrals of cai friedberg ginzburg kaplan in a conceptual way this also extends the construction to the quaternionic unitary groups we carry out the unfolding argument uniformly in this article to do so we define a family of degenerate whittaker coefficients that are suitable in this setup and study some of their properties we also prove certain related global and local results that use the same tools

the gross prasad conjecture and local theta correspondence we establish the fourier jacobi case of the local gross prasad conjecture for unitary groups by using local theta correspondence to relate the fourier jacobi case with the bessel case established by beuzart plessis to achieve this we prove two conjectures of prasad on the precise description of the local theta correspondence for almost equal rank unitary dual pairs in terms of the local langlands correspondence the proof uses arthur s multiplicity formula and thus is one of the first examples of a concrete application of this global reciprocity law

network oriented dyadic time domain green s function for a sequentially excited infinite planar array of dipoles in free space during the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas infinite periodic structures frequency selective surfaces and related applications with emphasis on gaining physical insight into the phenomenology of short pulse radiation the present contribution shows the current status of our network oriented dyadic time domain green s function td gf for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short pulsed radiation by infinite periodic arrays the dispersive effects of the td floquet waves fw and the consequences of a te and tm field decomposition are discussed in details in this network formulation the equivalent td transmission line tl voltages and currents excited by equivalent td current generators are determined an expression for the tm voltage tl gf is provided for the first time in terms of incomplete lipschitz hankel integrals and bessel functions together with some remarks for its evaluation as shown in previous publications for the scalar potentials real td physical observables are determined by pairing td floquet waves with positive and negative indices it is shown that the vectorial td radiated field is reconstructed at any time with the superposition of a few td fws

asymptotic high frequency green s function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions this paper deals with the derivation and physical interpretation of a uniform high frequency representation of the green s function for a large planar rectangular phased array of dipoles with weakly varying excitation thereby our earlier published results valid for equiamplitude excitation and those for tapered illumination in one dimension are extended to tapering along both dimensions including dipole amplitudes tending to zero at the edges as previously the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high frequency asymptotic reduction yields a series of propagating and evanescent floquet waves fws together with corresponding fw modulated diffracted fields which arise from fw scattering at the array edges and vertexes to accommodate the weak amplitude tapering new generalized periodicity modulated edge and vertex slope transition functions are introduced accompanied by a systematic procedure for their numerical evaluation special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields a sample calculation is included to demonstrate the accuracy of the asymptotic algorithm the resulting array green s function forms the basic building block for the full wave analysis of planar weakly amplitude tapered phased array antennas and for the description of electromagnetic radiation and scattering from weakly amplitude tapered rectangular periodic structures

endoscopy theta liftings and period integrals for the unitary group in three variables l packets for the quasi split unitary group in three variables u 3 we shall give an explicit parametrization of these l packets using theta liftings and describe some relations between the structure of l packets and certain period integrals we also prove that an endoscopic l packet contains a unique generic representation in local and global cases suppose that g is a reductive algebraic group over a local or global field

theta dichotomy for unitary groups some recent work of gross and prasad 14 suggests that the root numbers attached to certain symplectic representations of the weil deligne group of a local field f control certain branching rules for representations of orthogonal groups over f on a global level this local phenomenon should have implications for the structure of the value at the center of symmetry for certain l functions of arithmetic interest 12 this conjectural picture is based to some extent on the now classic work of tunnell 47 and waldspurger 49 as well as on the case of the triple product l function 13 34 17 in all of these examples the local root number detects the existence of a certain type of invariant linear functional it is possible to set up analogous conjectures for the isometry groups of hermitian or quaternion hermitian forms it turns out that root numbers also play a role in the local and global theta correspondence roughly speaking certain local root numbers should control the occurrence of representations in the local theta correspondence between groups of the same size e g for dual pairs of the form sp n o 2n 1 and u n u n as will be seen the theta correspondence for such pairs is connected with a certain induced representation in s at the point s 0 on the unitary axis by contrast the correspondence for the pairs sp n o 2n and sp n o 2n 2 discussed by prasad 35 is connected to the behavior of a similar induced representation at the points 12 in which case no epsilon factor arises in this paper we consider the local theta correspondence for unitary groups in the non archimedean case let f be a non archimedean local field of characteristic not equal to 2 and let e be a quadratic extension of f for further notation see the notation section at the end of this introduction let v and w be e vector spaces of dimensions m and n equipped respectively with a hermitian form v v e and a skew hermitian form w w e then the isometry groups g v and g w of the spaces v and w form a dual reductive pair in the symplectic group sp w where w v e w viewed as an f vector space of dimension 2mn and equipped with the symplectic form

time harmonic and transient scattering by finite periodic flat strip arrays hybrid ray floquet mode mom algorithm a frequency and short pulse sp time domain td study of two dimensional plane wave scattering from a finite periodic array of thin flat coplanar perfectly conducting strips is presented rigorous analytical numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments mom followed by frequency inversion the analytical portion is approximated so as to yield via high frequency asymptotics for a sufficiently large number of strips a hybrid ray floquet mode mom algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution of special interest are the td floquet modes with their space time dependent frequencies and wave numbers by superposition they can synthesize the highly resolved pulse train return under sp conditions attention is given also to direct sp td synthesis and to processing options for sp td data

howe correspondence for real unitary groups roger howe proved that for any reductive dual pair g g in the symplectic groupsp 2n r there is a one to one correspondence of irreducible admissible representations of some two fold covers ofgandg we determine this correspondence explicitly for dual pairs of the form u p q u r s withr s p q and describe it in terms of langlands parameters in this case the correspondence may be understood in a natural way as a correspondence of representations of the linear groups rather than the appropriate covers we show that every irreducible admissible representation ofu p q occurs in the correspondence with precisely one unitary group of equal rank this result verifies a conjecture of harris kudla and sweet who investigated the correspondence for unitary groups of equal size overp adic fields the correspondence of discrete series representations was determined by j s li for induced representations the correspondence is obtained in a natural way from the corresponding discrete series on the respective levi factors of the parabolic subgroups ofu p q andu r s generalizing a result of li we show that under the correspondence representations with nonzero cohomology are matched in an interesting way with unitarity not necessarily preserved the proof uses the induction principle which is due to kudla and an argument involvingk types and the space of joint harmonics howe

l functions and theta correspondence for classical groups using the doubling method of piatetski shapiro and rallis we develop a theory of local factors of representations of classical groups and apply it to give a necessary and sufficient condition for nonvanishing of global theta liftings in terms of analytic properties of the l functions and local theta correspondence

doubling constructions and tensor product l functions the linear case we present an integral representation for the tensor product l function of a pair of automorphic cuspidal representations one of a classical group the other of a general linear group our construction is uniform over all classical groups and is applicable to all cuspidal representations it does not require genericity the main new ideas of the construction are the use of generalized speh representations as inducing data for the eisenstein series and the introduction of a new global and local model which generalizes the whittaker model here we consider linear groups but our construction also extends to arbitrary degree metaplectic coverings this will be the topic of an upcoming work

robust discriminative tracking via landmark based label propagation the appearance of an object could be continuously changing during tracking thereby being not independent identically distributed a good discriminative tracker often needs a large number of training samples to fit the underlying data distribution which is impractical for visual tracking in this paper we present a new discriminative tracker via landmark based label propagation llp that is nonparametric and makes no specific assumption about the sample distribution with an undirected graph representation of samples the llp locally approximates the soft label of each sample by a linear combination of labels on its nearby landmarks it is able to effectively propagate a limited amount of initial labels to a large amount of unlabeled samples to this end we introduce a local landmarks approximation method to compute the cross similarity matrix between the whole data and landmarks moreover a soft label prediction function incorporating the graph laplacian regularizer is used to diffuse the known labels to all the unlabeled vertices in the graph which explicitly considers the local geometrical structure of all samples tracking is then carried out within a bayesian inference framework where the soft label prediction value is used to construct the observation model both qualitative and quantitative evaluations on the benchmark data set containing 51 challenging image sequences demonstrate that the proposed algorithm outperforms the state of the art methods

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

analysis of the rayleigh pulse seismologists make frequent use of wavelets also referred to as signals signatures or pulses particularly in such fields as seismic filtering wavelet processing wave propagation modeling and trace inversion whenever possible the actual seismic wavelet of the real source should be considered hosken 1988 however frequently particularly in wave propagation modeling one must consider a synthetic source wavelet this should if possible be given by a simple mathematical formula and possess an easy description for its most important spectral properties e g amplitude and phase spectrum main frequency hilbert transform etc moreover the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained

the hodge conjecture and arithmetic quotients of complex balls let s be a closed shimura variety uniformized by the complex n ball associated with a standard unitary group the hodge conjecture predicts that every hodge class in h 2k s mathbb q k 0 dots n is algebraic we show that this holds for all degrees k away from the neighborhood bigl tfrac13n tfrac23n bigr of the middle degree we also prove the tate conjecture for the same degrees as the hodge conjecture and the generalized form of the hodge conjecture in degrees away from an interval depending on the codimension c of the subvariety centered at the middle dimension of s these results are derived from a general theorem that applies to all shimura varieties associated with standard unitary groups of any signature the proofs make use of arthur s endoscopic classification of automorphic representations of classical groups as such our results rely on the stabilization of the trace formula for the disconnected groups gl n rtimes langle theta rangle associated with base change

visual tracking via discriminative sparse similarity map in this paper we cast the tracking problem as finding the candidate that scores highest in the evaluation model based upon a matrix called discriminative sparse similarity map dss map this map demonstrates the relationship between all the candidates and the templates and it is constructed based on the solution to an innovative optimization formulation named multitask reverse sparse representation formulation which searches multiple subsets from the whole candidate set to simultaneously reconstruct multiple templates with minimum error a customized apg method is derived for getting the optimum solution in matrix form within several iterations this formulation allows the candidates to be evaluated accurately in parallel rather than one by one like most sparsity based trackers do and meanwhile considers the relationship between candidates therefore it is more superior in terms of cost performance ratio the discriminative information containing in this map comes from a large template set with multiple positive target templates and hundreds of negative templates a laplacian term is introduced to keep the coefficients similarity level in accordance with the candidates similarities thereby making our tracker more robust a pooling approach is proposed to extract the discriminative information in the dss map for easily yet effectively selecting good candidates from bad ones and finally get the optimum tracking results plenty experimental evaluations on challenging image sequences demonstrate that the proposed tracking algorithm performs favorably against the state of the art methods

hermite rodriguez uwb circular arrays pulsed circular arrays are collecting growing interest in radar applications such as automotives and indoor navigations this contribution presents the analytic derivation of the space time and energy patterns of pulsed circular arrays in terms of geometrical and electrical parameters as well as of the signal distortion produced by the antennas response it is shown that the field emitted by circular arrays with many elements can be represented as a summation of a practically finite set of high order hermite rodriguez waveforms while the energy pattern is a generalized hypergeometric function the angular and temporal resolutions are finally related through handy formulas to the array size the input signals and to the antenna types

frequency and time domain green s functions for a phased semi infinite periodic line array of dipoles we extend a previous prototype study of felsen and capolino see ibid vol 48 p 921 931 june 2000 of frequency domain fd and time domain td green s functions for an infinite periodic phased line array of dipoles to account for the effects of truncation as modeled by a semi infinite array these canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular td plane phased arrays in the presentation we rely on the analytic results and phenomenologies pertaining to the infinite array which are reviewed major emphasis is then placed on the modifications introduced by the truncation finite poisson summation is used to convert the individual dipole radiations into collective truncated wavefields the fd and td floquet waves fw in the td exact closed form solutions are obtained and are examined asymptotically to extract fd and td periodicity matched conical truncated fw fields both propagating and nonpropagating corresponding tip diffracted periodicity matched spherical waves and uniform transition functions connecting both across the fd and td fw truncation boundaries these new effects can again be incorporated in a fw modulated geometrical theory of diffraction a numerical example of radiation from a finite phased td dipole array with band limited excitation demonstrates the accuracy and efficiency of the fw diffracted field asymptotic algorithm when compared with an element by element summation reference solution

e factor of representations of classical groups abstract we let g be the isometry group of a nondegenerate symmetric or skew symmetric form h on a space v over some local or global field k i e g u v h we let lg be the l group of go the identity component of g and r be the natural representation of this group we develop here a theory of l functions and e factors attached to this r in particular we develop a theory of local and global zeta integrals for such g we use very special intertwining operators therein we require an analysis of the proper normalization of such operators with such techniques we determine the correct e factors associated to local representations the issue of the correct local l factor is discussed