the equivalence between mann ishikawa iterations and multistep iteration abstract we show that the convergence of mann ishikawa iterations are equivalent to the convergence of a multistep iteration for various classes of operators

uniformization of mathcal g bundles we show some of the conjectures of pappas and rapoport concerning the moduli stack bung of g torsors on a curve c where g is a semisimple bruhat tits groupschemeon c inparticularweprovetheanalogoftheuniformizationtheoremof drinfeld simpson in this setting furthermore we apply this to compute the connected components of these moduli stacks and to calculate the picard group of bung in case g is simply connected

variations of mass formulas for definite division algebras abstract the aim of this paper is to organize some known mass formulas arising from a definite central division algebra over a global field and to deduce some more new ones

effortless critical representation of laplacian pyramid the laplacian pyramid lp is a multiresolution representation introduced originally for images and it has been used in many applications a major shortcoming of the lp representation is that it is oversampled the dependency among the lp coefficients is studied in this paper it is shown that whenever the lp compression filter is interpolatory the redundancy in the lp coefficients can be removed effortlessly by merely discarding some of the lp coefficients furthermore it turns out that the remaining now critically sampled lp coefficients are actually the coefficients of a wavelet filter bank as a result a new algorithm for designing a nonredundant wavelet filter bank from non biorthogonal lowpass filters is obtained our methodology presented in this paper does not depend on the spatial dimension of the data or the dilation matrix for sampling

encoding and progressive transmission of still pictures in ntsc composite format using transform domain methods coding schemes suitable for progressive transmission of still pictures in ntsc composite format are studied transform coding methods based on the discrete cosine transform dct and the walshhadamard transform wht are used the transform coefficients are segmented into groups having similar properties variable blocklength to variable length codes are used to encode the quantized coefficients for each of the groups progressive transmission is achieved by sending the coefficients belonging to particular groups in successive passes over the image results are presented for coding the ntsc signal sampled at four times the color subcarrier frequency with an orthogonal structure and at twice the subcarrier frequency with a hexagonal structure

a unifying framework for lossless and progressive image coding progressive coding is a desirable feature for image database telebrowsing or image transmissions over low bandwidth channels furthermore for some applications exact image reconstruction is required in this paper we show that most of the lossless and progressive coders can be described by a common nonlinear subband decomposition scheme this unifying framework provides useful guidelines for the analysis and improvement of the considered decomposition methods finally we compare the respective performances of these methods in terms of shannon entropy for several images and also evaluate their compression ability when combined with a hierarchical coding technique

irreducible cuspidal representations with prescribed local behavior let g be a simple algebraic group defined over the global field k in this paper we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of g with specified local behavior at a finite set of places of k and unramified elsewhere this sum is expressed as the product of the values of modified artin l functions at negative integers

on some haar measures on reductive groups we give a characteristic free proof of a theorem of b h gross comparing two haar measures on a reductive group over a local field as a consequence of this theorem we obtain an integration formula for adele groups over global function fields

equivalence theorems of the convergence between ishikawa and mann iterations with errors for generalized strongly successively φ pseudocontractive mappings without lipschitzian assumptions abstract in this paper the equivalence of the strong convergence between the modified mann and ishikawa iterations with errors in two different schemes by xu y g xu ishikawa and mann iteration process with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and liu l s liu ishikawa and mann iterative process with errors for nonlinear strongly accretive mappings in banach spaces j math anal appl 194 1995 114 125 respectively is proven for the generalized strongly successively pseudocontractive mappings without lipschitzian assumption our results generalize the recent results of the papers zhenyu huang f bu the equivalence between the convergence of ishikawa and mann iterations with errors for strongly successively pseudocontractive mappings without lipschitzian assumption j math anal appl 325 1 2007 586 594 b e rhoades s m soltuz the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps j math anal appl 289 2004 266 278 b e rhoades s m soltuz the equivalence between mann ishikawa iterations and multi step iteration nonlinear anal 58 2004 219 228 by extending to the most general class of the generalized strongly successively pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points u 1 x 1 in uniformly smooth banach spaces

the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings abstract convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of browder petryshyn type are proved in banach spaces using a new composite implicit iteration scheme with errors the results presented in this paper generalize and improve the corresponding results of m o osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81

group schemes and local densities the subject matter of this paper is an old one with a rich history beginning with the work of gauss and eisenstein maturing at the hands of smith and minkowski and culminating in the fundamental results of siegel more precisely if l is a lattice over z for simplicity equipped with an integral quadratic form q the celebrated smith minkowski siegel mass formula expresses the total mass of l q which is a weighted class number of the genus of l q as a product of local factors these local factors are known as the local densities of l q subsequent work of kneser tamagawa and weil resulted in an elegant formulation of the subject in terms of tamagawa measures in particular the local density at a non archimedean place p can be expressed as the integral of a certain volume form ld over autzp l q which is an open compact subgroup of autqp l q the question that remains is whether one can find an explicit formula for the local density through the work of pall for p 6 2 and watson for p 2 such an explicit formula for the local density is in fact known for an arbitrary lattice over zp see p and wa the formula is obviously structured though cs seems to be the first to comment on this unfortunately the known proof as given in p and k does not explain this structure and involves complicated recursions on the other hand conway and sloane cs 13 have given a heuristic explanation of the formula in this paper we will give a simple and conceptual proof of the local density formula for p 6 2 the view point taken here is similar to that of our earlier work ghy and the proof is based on the observation that there exists a smooth affine group scheme g over zp with generic fiber autqp l q which satisfies g zp autzp l q this follows from general results of smoothening blr as we explain in section 3 for the purpose of obtaining an explicit formula it is necessary to have an explicit construction of g the main contribution of this paper is to give such an explicit construction of g in section 5 and to determine its special fiber in section 6 finally by comparing ld and the canonical volume form can of g we obtain the explicit formula for the local density in section 7 the smooth group schemes constructed in this paper should also be of independent interest

on the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings abstract the purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of h bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 b halpern fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 p l lions approximation de points fixes de contractions c r acad sci paris ser a 284 1977 1357 1359 s reich strong convergence theorems for resolvents of accretive operators in banach spaces j math anal appl 75 1980 287 292 z h sun strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings j math anal appl 286 2003 351 358 r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 h k xu m g ori an implicit iterative process for nonexpansive mappings numer funct anal optimiz 22 2001 767 773 y y zhou s s chang convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in banach spaces numer funct anal optimiz 23 2002 911 921

strong convergence theorem for uniformly l lipschitzian asymptotically pseudocontractive mapping in real banach space abstract let e be a real banach space let k be a nonempty closed and convex subset of e t k k a uniformly l lipschitzian asymptotically pseudocontractive mapping with sequence k n n 0 1 lim n k n 1 such that f t let n n 0 0 1 be such that n 0 n n 0 n 2 and n 0 n k n 1 suppose x n n 0 is iteratively defined by x n 1 1 n x n n t n x n n 0 and suppose there exists a strictly increasing continuous function 0 0 0 0 such that t n x x j x x k n x x 2 x x x k it is proved that x n n 0 converges strongly to x f t it is also proved that the sequence of iteration x n defined by x n 1 a n x n b n t n x n c n u n n 0 where u n n 0 is a bounded sequence in k and a n n 0 b n n 0 c n n 0 are sequences in 0 1 satisfying appropriate conditions converges strongly to a fixed point of t

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

progressive image transmission using vector quantization on images in pyramid form a progressive image transmission scheme in which vector quantization is applied to images represented by pyramids is proposed a mean pyramid representation of an image is first built up by forming a sequence of reduced size images by averaging over blocks of 2 2 pixels a difference pyramid is then built up by taking the differences between successive levels in the mean pyramid progressive transmission is achieved by sending all the nodes in the difference pyramid starting from the top level and ending at the bottom level the kth approximate image can be formed by adding the information of level k to the previously reproduced k 1 st approximation to gain efficiency vector quantization is applied to the difference pyramid of the image on a level by level basis if the errors due to quantization at level k are properly delivered and included in the next level k 1 then it is demonstrated that the original image can be reconstructed an entropy coder is used to encode the final residual error image losslessly thus ensuring perfect reproduction of the original image the experiments demonstrate that it is possible to achieve simultaneously lossless and progressive transmission with compression at the intermediate level the use of vector quantization results in a coding gain over that obtained using only a huffman coder excellent reproduction is achieved at a bit rate of only 0 06 bits pixel

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

a note on the continuity of solutions of parametric linear programs this note shows that if a parametric linear program min cx ax b1 b2 x 0 has optimal solutions in an interval left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right for then depending on degeneracy the solutions is a continuous vector function or a continuous point to set mapping in the latter case an algorithm is introduced to solve the problem and generate a continuous vector solution in left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right

orientation sensitive interpolative pyramids for lossless and progressive image coding this paper presents a modified jpeg coder that is applied to the compression of mixed documents containing text natural images and graphics for printing purposes the modified jpeg coder proposed in this paper takes advantage of the distinct perceptually significant regions in these documents to achieve higher perceptual quality than the standard jpeg coder the region adaptivity is performed via classified thresholding being totally compliant with the baseline standard a computationally efficient classification algorithm is presented and the improved performance of the classified jpeg coder is verified

a logarithmic interpretation of edixhoven s jumps for jacobians let a be an abelian variety over a discretely valued field edixhoven has defined a filtration on the special fiber of the neron model of a that measures the behavior of the neron model under tame base change we interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where a is the jacobian of a curve c and we give a compact explicit formula for the jumps in terms of the combinatorial reduction data of c

optimal pyramidal decomposition for progressive multidimensional signal coding using optimal quantizers optimal hierarchical coding is sought for progressive or scalable multidimensional signal transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal coders are determined for images quantized using the optimal vector lloyd max quantizers a rigorous general statistical model of a vector lloyd max quantizer is used consisting of a linear time invariant filter followed by additive noise uncorrelated with the input given arbitrary analysis filters the optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal multidimensional signal decompositions these structures produce replicas of the original image which at lower resolutions retain as much similarity to the original as possible this is highly useful for the progressive coding of two or three dimensional 2 d or 3 d images needed in applications such as fast browsing through image databases furthermore the minimization of the variance of the error image leads to minimization of the variance of the quantization noise for this image and hence to its optimally efficient compression experimental results illustrate the implementation and performance of the optimal pyramids in application for the coding of still 2 d images

progressive image transmission by transform coefficient residual error quantization a progressive image transmission scheme based on iterative transform coding structure is proposed for application in interactive image communication over low bandwidth channels the scheme not only provides progressive transmission but also guarantees lossless reproduction combined with a degree of compression the image to be transmitted undergoes an orthogonal transform and the transform coefficients are quantized scalar or vector before transmission the novelty is that the residual error array due to quantization is iteratively fedback and requantized scalar or vector the coded residual error information is progressively transmitted and utilized in reconstructing the successive approximations it is shown that the average reconstruction error variance converges to zero as the number of iterative stages approaches infinity in practice lossless reproduction can be achieved with a small number of iterations by using an entropy coder on the final residual error image computer simulation results demonstrate the effectiveness of the technique

comparative performance of pyramid data structures for progressive image transmission a review of various pyramid data structures for progressive image transmission focusing on the steps involved in forming the pyramid and the performance comparisons is presented the simple mean pyramid its variants including the truncated mean reduced sum difference reduced difference and s transform pyramids and the more general laplacian pyramid are discussed it is also shown that the use of an interpolation function improves the quality of the full resolution approximations both objectively and subjectively

optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images optimal hierarchical coding is sought for progressive or scalable image transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal and subband image coders are determined for images subject to corruption by quantization or transmission noise given arbitrary analysis filters and assuming adequate knowledge of the noise statistics optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal and subband image decompositions experimental results illustrate the implementation and performance of the optimal coders

stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces in this paper we introduce the new iterative sequences with errors approximating the common fixed point for a couple of quasi contractive mappings and show the stability of the iterative procedures with errors in q uniformly smooth banach spaces our results extend improve and unify the corresponding results of chidume osilike liu and others

the equivalence of the convergence of four kinds of iterations for a finite family of uniformly asymptotically o pseudocontractive mappings in this paper we prove the equivalences of the strong convergence each other the modified mann iterative process with errors the modified ishikawa iterative process with errors the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically o pseudocontractive mappings in arbitrary real banach space the results presented in this paper generalize and improve the corresponding results of roades soltuz and huang

haar measure and the artin conductor let g be a connected reductive group defined over a local non archimedean field k the group g k is locally compact and unimodular in gr a haar measure g was defined on g k using the theory of bruhat and tits in this note we give another construction of the measure g using the artin conductor of the motive m of g over k the equivalence of the two constructions is deduced from a result of prasad p 1 the root datum and motive of g in this section k is an arbitrary field and g is a connected reductive group over k we let k be an algebraic closure of k ks the separable closure of k in k and gal ks k let t b g be a maximal torus contained in a borel subgroup defined over ks let g b t be the based root datum defined by this choice we recall cf sp pg3 12 that x t t b x t t b 1 1 with x t and x t the character and cocharacter groups of t respectively and and the simple roots and coroots determined by b respectively let w ng t t be the weyl group of the finite group w acts as automorphisms of x t and is generated by the reflections s x x x 1 2 for the galois group acts as automorphisms of ie as automorphisms of the group x t preserving the finite set as follows if then we can find g g ks such that int g t g t g t and int g b g b g b with g well defined up to left multiplication by t ks hence it induces a well defined automorphism x t x t date 14th january 1997 1 2 benedict h gross and wee teck gan preserving hence we get a group homomorphism aut via acts on aut by inner automorphisms similarly if f g g is any automorphism of g over ks it induces an automorphism f of which depends only on the image of f in the quotient group outks g of outer automorphisms the resulting map outks g aut is an isomorphism which respects the respective galois actions on the two groups cf sp pg10 the galois group also acts on w via the formula s s 1 3 and the semi direct product w acts on the rational vector space e x t q 1 4 let r sym e w which is a graded q module let r be the ideal of elements of positive degree in r and define v r r 2 d 1vd 1 5 this is a graded q module and chevalley proved that dim v dim e cf ch steinberg extended the proof to show that e and v are isomorphic modules cf st pg22 we sketch a proof of this result that does not involve the classification of irreducible root systems proposition 1 6 the q modules e and v are isomorphic proof by the criterion in se pg 104 it suffices to show that for all the fixed spaces e and v have the same dimension for any graded module a am we define the poincare series of by p a t tr am t then p a b p a p b steinberg showed that there is an isomorphism of graded modules s e s vd a here a is finite dimensional with basis bw w w and action given by bw b w the degree of bw is the length l w of w with respect to the generators s furnished by this isomorphism yields the following identity of poincare series det 1 t e d 1 det 1 t vd

sato tate theorem for families and low lying zeros of automorphic l functions we consider certain families of automorphic representations over number fields arising from the principle of functoriality of langlands let g be a reductive group over a number field f which admits discrete series representations at infinity let l g widehat g rtimes mathrm gal bar f f be the associated l group and r l g rightarrow mathrm gl d mathbb c a continuous homomorphism which is irreducible and does not factor through mathrm gal bar f f the families under consideration consist of discrete automorphic representations of g mathbb a f of given weight and level and we let either the weight or the level grow to infinity we establish a quantitative plancherel and a quantitative sato tate equidistribution theorem for the satake parameters of these families this generalizes earlier results in the subject notably of sarnak prog math 70 321 331 1987 and serre j am math soc 10 1 75 102 1997 as an application we study the distribution of the low lying zeros of the associated family of l functions l s pi r assuming from the principle of functoriality that these l functions are automorphic we find that the distribution of the 1 level densities coincides with the distribution of the 1 level densities of eigenvalues of one of the unitary symplectic and orthogonal ensembles in accordance with the katz sarnak heuristics we provide a criterion based on the frobenius schur indicator to determine this symmetry type if r is not isomorphic to its dual r vee then the symmetry type is unitary otherwise there is a bilinear form on mathbb c d which realizes the isomorphism between r and r vee if the bilinear form is symmetric resp alternating then r is real resp quaternionic and the symmetry type is symplectic resp orthogonal

image interpolation for progressive transmission by using radial basis function networks investigates the application of a radial basis function network rbfn to hierarchical image coding for progressive transmission the rbfn is then used to generate an interpolated image from the subsampled version an efficient method of computing the network parameters is developed for reduction in computational and memory requirements the coding method does not suffer from problems of blocking effect and can produce the coarsest image quickly quantization error effects introduced at one stage are considered in decoding images at the following stages thus allowing lossless progressive transmission

the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps the convergence of modified mann iteration is equivalent to the convergence of modified ishikawa iterations when t is an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive map

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

la formule des traces stable pour le groupe metaplectique les termes elliptiques soient f un corps de nombres et tilde g le revetement metaplectique de weil de g mathbb a f mathrm sp 2n mathbb a f nous stabilisons les termes elliptiques semi simples de la partie specifique de la formule des trace pour tilde g a l aide du transfert des fonctions test et du lemme fondamental etablis dans un article anterieur nous obtenons ainsi une expression en termes des integrales orbitales stables le long de certaines classes f elliptiques dans mathrm so 2n 1 times mathrm so 2n 1 ce que nous appelons equi singulieres pour les paires n n avec n n n une formule simple des coefficients est aussi obtenue

wavelet analysis of matrix valued time series the construction of matrixvalued filters for multiresolution analysis of matrixvalued timeseries is studied several different designs are explicitly derived corresponding to perfect reconstruction

epipelagic l packets and rectifying characters we provide an explicit construction of the local langlands correspondence for general tamely ramified reductive p adic groups and a class of wildly ramified langlands parameters furthermore we verify that our construction satisfies many expected properties of such a correspondence more precisely we show that each l packet we construct admits a parameterization in terms of the langlands dual group contains a unique generic element for a fixed whittaker datum satisfies the formal degree conjecture is compatible with central and cocentral characters provides a stable virtual character and satisfies the expected endoscopic character identities moreover we show that in the case of mathrm gl n our construction coincides with the established local langlands correspondence our techniques provide a general approach to the construction of the local langlands correspondence for tamely ramified groups and regular supercuspidal parameters

the equivalence between the convergence of ishikawa and mann iterations with errors for strongly successively pseudocontractive mappings without lipschitzian assumption abstract in this paper we prove some new equivalences between convergence of the ishikawa and mann iteration sequences with errors in two schemes by xu y g xu ishikawa and mann iteration process with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and liu l s liu ishikawa and mann iterative process with errors for nonlinear strongly accretive mappings in banach spaces j math anal appl 194 1995 114 125 respectively for strongly successively pseudocontractive mappings our main results improve and extend the corresponding results of the all references listed in this article

deterministic prediction in progressive coding deterministic prediction in progressive coding of images is investigated progressive coding first creates a sequence of resolution layers by beginning with an original image and reducing its resolution several times by factors of some natural number m the resultant layers are losslessly encoded beginning with the lowest resolution layer and then encoding each higher resolution image incrementally upon the previous one coding efficiency may be improved if knowledge of the rules which produced the lower resolution image of each pair is used to deterministically predict pixels of the higher so they need not be encoded given reduction rules expressing each low resolution pixel as a function of nearby high resolution pixels and previously generated low resolution pixels it is shown that finding a complete set of rules each of which deterministically predicts the value of a high resolution pixel when certain values are found in nearby low resolution pixels and previously coded high resolution pixels is np complete a recursive algorithm for solving the problem in optimal time as a depth first tree search is proposed and the characteristics of the resultant prediction process are studied

compression of laplacian pyramids through orthogonal transforms and improved prediction scalable representation of visual signals such as image and video signals has become a subject of active research since early 1980s scalability allows the adaptation of the bit rate and or the resolution of the transmitted data to the network bandwidth and or the rendering capability of the receiving device for many years spatial scalability has been achieved through wavelets but recently the laplacian pyramid lp has become an alternative choice because of reduced aliasing in the lower resolutions in this paper we focus on the coding efficiency of the lp with a view to transmitting it over a communication channel in particular we aim to improve the compression efficiency of the lp detail layers through improved interlayer prediction and orthogonal spatial transforms first we consider an lp in the open loop configuration and propose to improve its rate distortion performance by compressing it to a critically sampled representation we derive four different orthogonal spatial transforms from the upsampling and downsampling filters that can achieve this representation and apply them on the detail layers the application of these transforms to the detail layers renders a fixed number of transform coefficients either zero or redundant thus making their transmission unnecessary then we consider the compression of an lp in the closed loop configuration through similar spatial transforms because of the introduction of quantization in the prediction loop these spatial transforms applied on the detail layers do not produce the same number of zero or redundant transform coefficients as in the open loop case nevertheless the insight obtained from the open loop coding leads us to enhance the interlayer prediction and the subsequent application of the spatial transforms to the new detail layers aims to achieve better energy compaction

sign changes in harmonic analysis on reductive groups let g be a connected reductive group over a field f in this note the author constructs an element e g of the brauer group of f the square of this element is trivial for a local field e g may be regarded as an element of i and is needed for harmonic analysis on reductive groups over that field for a global field there is a product formula the purpose of this note is to provide a cohomological interpretation of the sign changes in harmonic analysis on reductive groups over local fields that are caused by inner twistings the best understood example occurs in the work of shelstad 8 on inner twistings of real groups theorem 6 3 of that paper gives the following character identity 1 q g q g x here g is a connected reductive group over r g is its quasi split inner form x and x are stabilized characters of matched tempered l packets of g r and g r and y and y are matched regular semisimple elements of g r and g r the sign change in the character identity is q g q g where q g is one half of the dimension of the symmetric space attached to g more precisely attached to the simply connected cover of the derived group of g although q g may be only half integral the difference q g q g is always integral it is reasonable to expect an analogous character identity for groups g over a nonarchimedean local field f we can determine what the sign change must be by considering the steinberg characters of g f and g f since these should be related by the character identity let r g denote the f rank of the derived group of g the steinberg character of g f has value i r g on the elliptic regular set of g f and hence the sign change in the character identity must be l r g r g there are two groups for which the character identity has been proved the multiplicative group of a central division algebra of dimension d2 over f for d 2 see proposition 15 5 on p 484 of 4 and d 3 see theorem 1 of 1 later in this paper we will use a cohomological construction to define a sign e g 1 for any connected reductive group g over a local field let g denote a quasi split inner form of g we will show that e g l r g r g when the base received by the editors may 10 1982 1980 mathematics subject classification primary 22e50 partially supported by the national science foundation under grant mcs 78 02331 1983 american mathematical society 0002 9947 82 0000 11 93 03 25

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

on an exact mass formula of shimura in a series of recent papers g shimura obtained an exact formula for the mass of a maximal lattice in a quadratic or hermitian space over a totally real number field using bruhat tits theory we obtain a quick and more conceptual proof of his formula when the form is totally definite

a reduced laplacian pyramid for lossless and progressive image communication the laplacian pyramid lp is appropriate for lossy image compression conversely the reduced difference pyramid rdp having as many data as pixels gives a better performance with lossless encoding a reduced lp is designed by discarding the anti aliasing filter and adopting a half band interpolator thus retaining three over four of the lp coefficients lossless coding outperforms both lp and rdp especially when dealing with medical images

arithmetic invariants of discrete langlands parameters the local langlands correspondence can be used as a tool for making verifiable predictions about irreducible complex representations of p adic groups and their langlands parameters which are homomorphisms from the local weil deligne group to the l group in this article we refine a conjecture of hiraga ichino and ikeda which relates the formal degree of a discrete series representation to the value of the local gamma factor of its parameter we attach a rational function in x with rational coefficients to each discrete parameter which specializes at x q the cardinality of the residue field to the quotient of this local gamma factor by the gamma factor of the steinberg parameter the order of this rational function at x 0 is also an important invariant of the parameter it leads to a conjectural inequality for the swan conductor of a discrete parameter acting on the adjoint representation of the l group we verify this conjecture in many cases when we impose equality we obtain a prediction for the existence of simple wild parameters and simple supercuspidal representations both of which are found and described in this article

counting maximal arithmetic subgroups we study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semisimple lie group using an extension of the method developed by borel and prasad