vector quantization of speech and speech like waveforms an algorithm for the design of vector quantizers that are locally optimum in the sense of minimizing an average quantitative distortion measure is used to design 1 and 2 bit sample vector quantizers for both real sampled speech and a simulated speech like auto regressive random process both weighted and unweighted squared error distortion measures are considered several comparisons are made and discussed based on the average distortions of the vector quantization schemes the results for the simulated speech are compared to mathematical performance bounds from information theory to provide an indication of how nearly globally optimal vector quantization is for such highly correlated sources a comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and hence of the applicability of information theory bounds and code designs based on probabilistic models the signal to quantization noise ratios of vector quantizers designed to minimize squared error distortion are compared to those of several popular speech waveform coding systems of similar rates

interframe predictive coding of images using hybrid vector quantization the temporal and spatial redundancies of image sequences can be reduced by prediction and vector quantization respectively the robustness of the coder is increased through the use of a hybrid two stage vector quantizer the first stage is of the linde buzo gray type the second stage encodes the residual error of the first stage using a lattice vector quantizer

standard monomial theory for g2 let g be a semi simple algebraic group and b a borel subgroup let x be a schubert variety in g b let l be an ample line bundle on g b as well as its restriction to x a standard monomial theory for schubert varieties in g b is developed in 9 11 8 10 as a generalization of the classical hodge young theory cf 3 4 this theory consists in the construction of a characteristic free basis for h0 x l this theory is extended to schubert varieties in the infinite dimensional flag variety ln b in 13 see also 12 in this paper we extend the theory to schubert varieties in the infinite dimensional flag variety p2n b

a pyramid vector quantizer the geometric properties of a memoryless laplacian source are presented and used to establish a source coding theorem motivated by this geometric structure a pyramid vector quantizer pvq is developed for arbitrary vector dimension the pvq is based on the cubic lattice points that lie on the surface of an l dimensional pyramid and has simple encoding and decoding algorithms a product code version of the pvq is developed and generalized to apply to a variety of sources analytical expressions are derived for the pvq mean square error mse and simulation results are presented for pvq encoding of several memoryless sources for large rate and dimension pvq encoding of memoryless laplacian gamma and gaussian sources provides rose improvements of 5 64 8 40 and 2 39 db respectively over the corresponding optimum scalar quantizer although suboptimum in a rate distortion sense because the pvq can encode large dimensional vectors it offers significant reduction in rose distortion compared with the optimum lloyd max scalar quantizer and provides an attractive alternative to currently available vector quantizers

sharing secret images using shadow codebooks abstract a practical specific r n threshold scheme for secret digital images is proposed in this paper by this scheme we divide a secret digital image into n pieces and distribute them to n participants the secret digital image can be reconstructed when and only when r or more participants cooperate for it the time complexity of this proposed scheme is independent of the size of the secret image in this scheme the setup phase is bounded by i j r 1 2 2 module multiplications plus i j r 1 module additions where i j is the size of the codebook except the time needed for generating the codebook the reconstructing phase is bounded by o r log2 r this scheme also achieves perfect secrecy

two secret sharing schemes based on boolean operations traditional secret sharing schemes involve complex computation a visual secret sharing vss scheme decodes the secret without computation but each shadow is m times as big as the original probabilistic vss solved the computation complexity and space complexity problems at once in this paper we propose a probabilistic 2 n scheme for binary images and a deterministic n n scheme for grayscale images both use simple boolean operations and both have no pixel expansion the 2 n scheme provides a better contrast and significantly smaller recognized areas than other methods the n n scheme gives an exact reconstruction

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

tangent cones to schubert varieties in types an bn and cn abstract we study tangent cones to schubert subvarieties of the flag variety of a complex reductive group g let t be a maximal torus of g b be a borel subgroup of g containing t be the root system of g with respect to t w be the weyl group of and f g b be the flag variety we prove that if every irreducible component of is of type b n or c n and w 1 w 2 are two distinct involutions in w then the tangent cones at the point p e b to the corresponding schubert subvarieties x w 1 x w 2 of f do not coincide as subschemes of the tangent space t p f we also show that if every irreducible component of is of type a n or c n then the reduced tangent cones to x w 1 and x w 2 do not coincide as subvarieties of t p f

synchronization multistability and basin crisis in coupled pendula abstract the synchronization dynamics of two linearly coupled pendula is studied in this paper based on the lyapunov stability theory and linear matrix inequality lmi some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling k th for the on set of full synchronization is obtained the numerical value of k th determined from the average energies of the systems is in good agreement with theoretical analysis prior to the on set of synchronization the boundary crisis of the chaotic attractor is identified in the bistable states where two asymmetric periodic attractors co exist it is shown that the coupled pendula can attain multistable states via a new dynamical transition the basin crisis that occur prior to the on set of stable synchronization the essential feature of basin crisis is that the two co existing attractors are destroyed while new three or more co existing attractors of the same or different periodicity are created in addition the linear perturbation technique and the routh hurwitz criteria are employed to investigate the stability of steady states and clearly identify the different types of bifurcations likely to be encountered finally two parameter phase plots show various regions of chaos hyperchaos and periodicity

synchronization and desynchronization under the influence of quasiperiodic forcing we study the influence of quasiperiodic forcing on synchronization and desynchronization using two coupled quasiperiodically forced logistic maps as a paradigm we show that due to the forcing the synchronization region in parameter space shrinks the loss of transverse stability of the synchronized attractors leads to desynchronization two types of such blowout bifurcations are described namely the blowout bifurcations of synchronized quasiperiodic motion on invariant curves and synchronized strange nonchaotic attractors both yielding desynchronized chaotic attractors

pattern avoidance and rational smoothness of schubert varieties abstract letwbe an element of the weyl groupsn and letxwbe the schubert variety associated towin the flag manifoldsln c b lakshmibai and sandhya showed thatxwis smooth if and only ifwavoids the patterns 4231 and 3412 using two tests for rational smoothness from carrell and peterson we show that rational smoothness ofxwis characterized by pattern avoidance for typesbandcas well a key step in the proof of this result is a sequence of rules for factoring the poincare polynomials for the cohomology ring ofxw generalizing the work of gasharov patterns can also be used to characterize actual smoothness of schubert varieties

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

basin bifurcations in quasiperiodically forced coupled systems we study the effect of quasiperiodic forcing on a system of coupled identical logistic maps upon a variation of system parameters a variety of different dynamical regimes can be observed including phenomena such as bistability and multistability at the bifurcation to bistability in a manner reminiscent of attractor expansion at interior crises there is an abrupt change in the size of attractor basins in the bistable region attractor basins undergo additional bifurcations wherein holes and islands are created within the basins when system parameters change these can be understood by examining critical surfaces for the coupled system

bases for some reciprocity algebras i for a complex vector space v let p v be the algebra of polynomial functions on v in this paper we construct bases for the algebra of all gl n c x gl m1 c x gl m2 c x x gl mr c highest weight vectors in p c n c m where m m 1 m r and mj n for all 1 j r and the algebra of gl n c x gl k c x gl 1 c highest weight vectors in p c n c k c n c l

affine structures and a tableau model for e_6 crystals abstract we provide the unique affine crystal structure for type e 6 1 kirillov reshetikhin crystals corresponding to the multiples of fundamental weights s 1 s 2 and s 6 for all s 1 in bourbaki s labeling of the dynkin nodes where 2 is the adjoint node our methods introduce a generalized tableaux model for classical highest weight crystals of type e and use the order three automorphism of the affine e 6 1 dynkin diagram in addition we provide a conjecture for the affine crystal structure of type e 7 1 kirillov reshetikhin crystals corresponding to the adjoint node

btc image coding using vector quantization this paper describes source encoding of the outputs of a block truncation coder btc namely the overhead statistical information and the truncated block the statistical overhead and the truncated block exhibit properties which can be effectively used for their quantization as vectors vector quantization of these btc outputs results into reduction of the bit rate of the coder the bit rate reduces up to 1 5 bits pel if vector quantization is used on one of the outputs i e either the overhead information or the truncated block by vector quantizing both the btc outputs the bit rate can he reduced up to 1 0 bits pel without introducing many perceivable errors in the reconstructed output

a new approach to image sharing with high security threshold structure image sharing is an attractive research subject in computer image techniques and in the information security field this article presents a novel scheme of image sharing with a t n high security threshold structure the scheme can encode secret images into n shadow images in such a way that all the shadow images are in a perfect and ideal t n threshold structure while each shadow image has its own visual content assigned at random the most common method to implement image sharing is based on interpolation polynomial over the field fp 0 1 2 m p 1 shamir 1979 in this article the authors present a new approach to image sharing and its computation based on algebraic geometry code over the pixel value field gf 2m

a new image coding algorithm using variable rate side match finite state vector quantization a new side match vector quantizer newsmvq is presented in this paper three techniques are incorporated to improve the image quality encoding speed and bit rate for compressing images the experimental result shows i the encoding time of newsmvq is almost 7 times faster than that of smvq ordinary fixed rate side match vector quantizer and csmvq variable rate smvq and ii newsmvq outperforms smvq and csmvq in terms of bit rate versus image quality tradeoffs

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

a lookup conjecture for rational smoothness the purpose of this paper is to present a new combinatorial criterion for rational smooth ness of a point in a schubert variety the main result proves the criterion for schubert varieties associated to partial flag varieties of the form g p where g is semisimple of classical type and p is a maximal parabolic subgroup in the case where g p is of cominuscule type not necessarily clas sical we prove a stronger result we conjecture that the criterion is valid for all schubert varieties the paper also contains some general results related to rational smoothness in schubert varieties 1 introduction the purpose of this paper is to present a new combinato rial criterion for rational smoothness of a point in a schubert variety the main result proves the criterion for schubert varieties associated to certain partial flag varieties we conjecture that it is true in general the paper also contains some general results related to rational smoothness in schubert varieties we now explain our criterion in more detail let g be a complex semisimple

distortion free secret image sharing mechanism using modulus operator the t n threshold has been extended to secret image sharing due to its practicability in this article we provide a novel version that employs the modulus operator to embed the secret share into a host image the simulator shows that the modulus operator is useful for decreasing shadow image distortion using rabin s signature cryptosystem participants can detect if a cheater exists in the cooperation in particular the new mechanism permits involved members to restore a lossless secret image and to reconstruct a distortion free host image

upper semicontinuity of attractors and synchronization abstract in this paper we prove that diffusively coupled abstract semilinear parabolic systems synchronize we apply the abstract results obtained to a class of ordinary differential equations and to reaction diffusion problems the technique consists of proving that the attractors for the coupled differential equations are upper semicontinuous with respect to the attractor of a limiting problem explicitly exhibited in the diagonal

an algorithm for the design of labeled transition finite state vector quantizers a finite state vector quantizer fsvq is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder it can be viewed as an adaptive vector quantizer with backward estimation a vector generalization of an aqb system recently a family of algorithms for the design of fsvq s for waveform coding application has been introduced these algorithms first design an initial set of vector quantizers together with a next state function giving the rule by which the next quantizer is selected the codebooks of this initial fsvq are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm the next state function however is not modified from its initial form in this paper we present two extensions of the fsvq design algorithms first the algorithm for fsvq design for waveform coders is extended to fsvq design of linear predictive coded lpc speech parameter vectors using an itakura saito distortion measure second we introduce a new technique for the iterative improvement of the next state function based on an algorithm from adaptive stochastic automata theory the design algorithms are simulated for an lpc fsvq and the results are compared with each other and to ordinary memoryless vector quantization several open problems suggested by the simulation results are presented

a combinatorial approach to the singularities of schubert varieties schubert subvarieties of grassmannians and more generally varieties g p with g a linear algebraic group and p a parabolic subgroup have long been a rich source for algebraic geometers and topologists recent interest has focussed on their singularities which are of interest due to the relationship between the intersection homological properties of a singularity of a schubert variety in g p and invariants of composition series of verma modules kl gm this work presents a simple combinatorial algorithm for deciding whether a schubert variety in g p where g sl is singular this leads to a geometric characterization of the nonsingular schubert varieties as sequences of grassmannian bundles over grassmannians the combinatorial techniques are those of p of whose existence the author was unaware a more general result of this nature has been proved by seshadri and lakshmibai laks who use standard monomial theory to find the ideal of the singular locus of a schubert variety in g b where g is an algebraic group with a standard monomial theory and b is a bore1 subgroup of g ryan r has obtained results similar to ours using general techniques for understanding determinantal varieties the present work has the advantage of being quite elementary while sharing aspects of both of the above or special interest here are the combinatorial techniques which appear to be a basic connection between the singularities of schubert varieties the geometry of the tibres of springer s resolution of the singularities of the nilpotent scheme see wl and the kazhdan lusztig polynomials a related note w2 discusses some applications of these techniques to the computation of the kazhdan lusztig polynomials

multiplicities of points on a schubert variety in a minuscule gp in this paper we prove the results announced in 13 let g be a semi simple simply connected algebraic group defined over an algebraically closed field k let t be a maximal torus b a bore1 subgroup b 3 t let w be the weyl group of g let r resp r be the set of roots resp positive roots relative to t resp b let s be the set of simple roots in r let p be a maximal parabolic subgroup in g with associated fundamental weight w let w be the weyl group of p and wp be the set of minimal representatives of w w for w e wp let e w be the point and x w the schubert variety in g p associated to w in this paper we deter mine the multiplicity m w of x w at e z where e z e x w for all minuscule p s and also for p pgn g being of type c here pun denotes the maximal parabolic subgroup obtained by omitting a the determina tion of m w is done as follows let l be the ample generator of pic g p a basis has been constructed for x w l in terms of standard monomials on x w cf 16 11 i let u be the unipotent subgroup of g generated by u et r rp here r denotes the set of roots of p and u denotes the unipotent subgroup of g associated to tl e r then u e r gives an affme neighborhood of e z in g p let a be the affine algebra of u e z and a a where is the ideal of elements of a that vanish on x w n u e z let m be the maximal ideal in a h corresponding to e r then using the results of 16 111 we obtain a basis of m f this enables us to obtain an inductive formula for f the hilbert polynomial of x w at e t cf corollaries 3 8 and 4 11 and also express m w in terms of m w s x w s being the schubert divisors in x w such that e t e x w cf theorems 3 7 and 4 10 using this we

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

a criterion for smoothness of schubert varieties insp 2n b abstract in this paper we give a criterion for a schubert variety x w in sp 2 n b to be smooth the criterion is given in terms of the permutation giving w

straightening for standard monomials on schubert varieties abstract we give an elementary proof of the following known fact any multihomogenous component in the homogeneous coordinate ring of a schubert variety insidegln bhas basis given by the standard monomials 6

irreducible representations of semisimple algebraic groups and supersolvable lattices abstract let be the cross section lattice of an irreducible representation of a semisimple algebraic group certain combinatorial properties of are studied supersolvable s are determined in terms of dynkin diagrams the characteristic polynomial of a supersolvable is computed

a generalization of the littlewood richardson rule for the general linear group gz the littlewood richardson rule see 18 193 gives a method to calculate the decomposition of a tensor product of two irreducible g representations the aim of this article is to give a generalization of this rule for all simple simply connected algebraic groups of type a b c d g2 and e we obtain also partial results for g of type f4 e and es the restrictions in the last three cases come from the fact that for the formulation of the decomposition rules we need the notion of a standard young tableau such a notion has been developed by seshadri lakshmibai musili and rajeswari in a series of articles see ll 13 14 16 but not yet for all representations of the last three exceptional groups the advantage of the notion of a young tableau developed by seshadri et al is that it is independent of the type of the group for the convenience of the reader not used to this notion we give first a seperate proof for g sz using the classical notion of a standard young tableau of course for applications the classical notion is much more appropriate in the appendix we give a translation of the notion of a standard young tableau in the sense of seshadri et al into the classical notion of a young tableau for g sp2 and spin in 3 8 we give also such a translation for g g for the other exceptional groups such a translation is not known to the author let p be a dominant weight for g and denote by i the corresponding simple g module we assume that the character of vp is given by ct eycr where the sum has to be taken over all standard young tableaux f of shape p p and v 5 is the weight of the tableau y now by the

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

mixed ladder determinantal varieties abstract we investigate ladder determinantal varieties defined by ideals of minors of possibly different sizes in the different regions the steps of one sided ladders l these varieties are an important generalization of the classical ladder determinantal varieties i e with equal size minors since they are very closely related to schubert varieties this being the first main result of this paper we show that they correspond to opposite cells in schubert varieties in flag varieties of type a n in consequence one deduces the normality and the cohen macaulayness of these one sided ladder determinantal varieties with ideals of mixed size minors as well as the fact that they have rational singularities next we show that up to products by affine spaces each of these varieties is a basic open set in a classical ladder determinantal variety i e with equal size minors and that it contains as a basic open set another classical ladder determinantal variety this result along with a general localisation lemma used to show it enables us to compute the divisor class group and singular locus of the coordinate rings of these varieties as well as to determine when they are gorenstein

synchronization and control of coupled ginzburg landau equations using local coupling in this paper we discuss the properties of a recently introduced coupling scheme for spatially extended systems based on local spatially averaged coupling signals see z tasev et al int j bifurcation chaos appl sci eng to be published and l junge et al int j bifurcation chaos appl sci eng 9 2265 1999 using the ginzburg landau model we performed an extensive numerical examination of this coupling scheme i e a complete scan through the relevant coupling parameters furthermore we demonstrate suppression and control of spatiotemporal chaos e g stabilizing the homogeneous steady state and spatially localized control as an application all model parameters of the ginzburg landau equation are estimated given only the local information of the system

antichains in weight posets associated with gradings of simple lie algebras for a reductive lie algebra mathfrak h and a simple finite dimensional mathfrak h module v the set of weights of v mathcal p v is equipped with a natural partial order we consider antichains in the weight poset mathcal p v and a certain operator mathfrak x acting on antichains eventually we impose stronger constraints on mathfrak h v and stick to the case in which mathfrak h mathfrak g 0 and v mathfrak g 1 for a mathbb z grading mathfrak g bigoplus i in mathbb z mathfrak g i of a simple lie algebra mathfrak g then v is a weight multiplicity free mathfrak h module and mathcal p v can be regarded as a subposet of delta where delta is the root system of mathfrak g our goal is to demonstrate that the weight posets associated with mathbb z gradings exhibit many good properties that are similar to those of delta that are observed earlier in panyushev eur j combin 30 2 586 594 2009

bifurcation and chaos in coupled ratchets exhibiting synchronized dynamics the bifurcation and chaotic behavior of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude a and frequency a classification of the various types of bifurcations likely to be encountered in this system was done by examining the stability of the steady state in linear response as well as constructing a two parameter phase diagram in the a plane numerical explorations revealed varieties of bifurcation sequences including quasiperiodic route to chaos besides the familiar perioddoubling and crises route to chaos exhibited by the one dimensional ratchet were also found in addition the coupled ratchets display symmetry breaking saddle nodes and bubbles of bifurcations chaotic behavior is characterized by using the lyapunov exponent spectrum while a perusal of the phase space projected in the poincare cross section confirms some of the striking features

transform and hybrid transform dpcm coding of images using pyramid vector quantization the transform and hybrid transform dpcm methods of image coding are generalized to allow pyramid vector quantization of the transform coefficients an asymptotic mean squared error performance expression is derived for the pyramid vector quantizer and used to determine the optimum rate assignment for encoding the various transform coefficients coding simulations for two images at average rates of 0 5 1 bit pixel demonstrate a 1 3 db improvement in signal to noise ratio for the vector quantization approach in the hybrid coding with more modest improvements in signal to noise ratio in the transform coding however this improvement is quite noticeable in image quality particularly in reducing blockiness in the low bit rate encoded images

rings with lexicographic straightening law the concept of a straightening law as a means of analyzing the structure of particular commutative algebras has appeared independently in the work of a number of authors the purpose of this paper is to introduce a systematic theory of algebras endowed with a structure of a lexicographic straightening law based on a partially ordered set or lexicographic ring for short much of the work in the literature dealing with such rings fits quite naturally in the context of our theory and we sketch some of this work moreover some of our later results in particular the betti number bound in section 6 may actually be new results even for the special cases of the known examples of lexicographic rings the concept of a lexicographic ring as an interesting area of study was suggested to this author by deconcini who conjectured that a lexicographic ring is cohen macaulay if the underlying partially ordered set is so we prove this result in two different ways it has recently come to our attention that this conjecture has also been proved by deconcini et al 131 using deformation theory methods the results of this paper are arranged in two parts the first part consisting of sections 2 through 4 is more elementary and uses the technique of combinatorial decompositions as developed by garsia and this author the second part sections 6 and 7 requires some knowledge of homological algebra methods in ring theory the intermediate section 5 discusses some of the known examples of lexicographic rings in this section we also sketch some of the ways that our theory may be extended to more general contexts the main result of the first part is the transfer theorem 4 3 which enables one to transfer combinatorial decompositions from the underlying partially ordered set or more precisely from the corresponding stanley reisner ring to the lexicographic ring as a result those concepts that are expressible in terms of combinatorial decompositions are also

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

richardson varieties and equivariant k theory we generalize standard monomial theory smt to intersections of schubert varieties and opposite schubert varieties such varieties are called richardson varieties the aim of this article is to get closer to a geometric interpretation of the standard monomial theory as constructed in p littelmann j amer math soc 11 1998 551 567 in fact the construction given here is very close to the ideas in p lakshmibai c s seshadri j algebra 100 1986 462 557 our methods show that in order to develop a smt for a certain class of subvarieties in g b which includes g b it suffices to have the following three ingredients a basis for h0 g b l compatibility of such a basis with the varieties in the class certain quadratic relations in the monomials in the basis elements an important tool as in p lakshmibai c s seshadri j algebra 100 1986 462 557 will be the construction of nice filtrations of the vanishing ideal of the boundary of the varieties above this provides a direct connection to the equivariant k theory products of classes of structure sheaves with classes of line bundles where the combinatorially defined notion of standardness gets a geometric interpretation

on tangent spaces to schubert varieties ii abstract we prove the results on the tangent spaces to schubert varieties announced in v lakshmibai math res lett 2 1995 473 477 for g classical we give two descriptions of the tangent space to a schubert variety at id the first description is in terms of the root system and the second one is in terms of multiplicities of certain weights in the fundamental representations of g

a partial order on the regions of ⁿ dissected by hyperplanes we study a partial order on the regions of r dissected by hyperplanes this includes a computation of the mobius function and in some cases of the homotopy type applications are presented to zonotopes the weak bruhat order on weyl groups and acyclic orientations of graphs 0 introduction let cc h h2 hk be a set of hyperplanes in rw then the components of rw uheh form a set i of open n cells we will call regions traditionally i has been studied in terms of enumeration for instance counting the number of regions and the number of intersections of various dimensions among the hyperplanes in c for a thorough discussion of this problem see zaslavsky s monograph zi and the references therein see also os and te in this paper we will study i from a different perspective our concern will be the way in which one can move from one region to another by walking through one hyperplane at a time to analyze this situation we define a partial order on j relative to a base region where the cover relations correspond to walking through a hyperplane and moving further away from the base the paper is organized as follows in 1 we define the partial order on rfl and begin to study its structure this culminates in theorem 1 11 where an explicit computation of its mbbius function is performed in 11 we examine the special case where all the hyperplanes go through the origin in certain cases we are able to compute the homotopy type of these posets the next three sections are devoted to applications 111 applies our work to a partial order on a zonotope iv deals with the weak bruhat order of a weyl group as a special case of our posets as a corollary we show that the homotopy type of the weak bruhat order is that of a sphere finally v applies our results to a partial order on the acyclic orientations of a graph some of the relationships used in iii iv and v appear in an enumerative context in the excellent article of greene and zaslavsky gz most of our poset notation is standard and can be found in a when more than one partial order is being used we will sometimes use subscripts to indicate where the relation is i e x py means that x is less than or equal to y in the poset p by l p we mean the simplicial complex of chains totally ordered sets in p we will think of p as its geometric realization by p we mean the order dual of p i e received by the editors july 13 1982 and in revised form may 15 1983 1980 mathematics subject classification primary 06a10 51m20 1984 american mathematical society 0002 9947 84 1 00 25 per page

bifurcation analysis of two coupled periodically driven duffing oscillators bifurcation diagrams and phase diagrams of two coupled periodically driven identical duffing oscillators are presented it is shown that the global pattern of bifurcation curves in parameter space consists of repeated subpatterns similar to the superstructure observed for single periodically driven strictly dissipative oscillators the subpattern itself however is different from that of a single duffing oscillator due in particular to hopf bifurcations that are newly added to the bifurcation scenario

on the stability of thek1 functor for chevalley groups of type e7 abstract this paper is devoted to the study of the surjective stability of the k 1 functor for chevalley groups of type e 7 this is a particular case of the stability problem for chevalley groups which was posed by h bass in this paper surjective stability of the k 1 functor is proved under natural conditions on the dimension of the maximal spectrum of a ring and independently under a special condition which is meaningful from the point of view of equations defining a chevalley group

polytopes associated to demazure modules of symmetrizable kac moody algebras of rank two let 1 2 be the two fundamental weights of a symmetrizable kac moody algebra g of rank two hence necessarily affine or finite and an element of the weyl group in this paper we construct polytopes p 1 p 2 rl and a linear map rl h such that for any dominant weight k1 1 k2 2 we have char e e e x where the sum is over all the integral points x of the polytope k1p 1 k2p 2 furthermore we show that there exists a flat deformation of the schubert variety s into the toric variety defined by p 1 p 2

sharing and hiding secret images with size constraint this paper presents a method for sharing and hiding secret images the method is modified from the t n threshold scheme comput graph 26 5 2002 765 the given secret image is shared and n shadow images are thus generated each shadow image is hidden in an ordinary image so as not to attract an attacker s attention any t of the n hidden shadows can be used to recover the secret image the size of each stego image in which a shadow image is hidden is about 1 t of that of the secret image avoiding the need for much storage space and transmission time in the sense that the total size of t stego images is about the size of the secret image experimental results indicate that the qualities of both the recovered secret image and the stego images that contain the hidden shadows are acceptable the photographers who work in enemy areas can use this system to transmit photographs

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

arithmetic cohen macaulayness and arithmetic normality for schubert varieties let g be a semisimple simply connected chevalley group over a field k let t be a maximal torus b a borel subgroup d t and w the weyl group of g relative to t let p be a maximal parabolic subgroup of classical type cf 7 8 i e a maximal parabolic subgroup such that if w is the associated fundamental weight then i w av i 1 2 w c a is 2 for all roots ae being a w invariant scalar product on x t q where x t character group of t for t e w wp let x t denote the schubert variety in g p associated to t namely x t is the zariski closure btp mod p in g p of the bruhat cell endowed with the canonical reduced structure for the canonical projective embedding g p in p h g p l let rt denote the homogeneous co ordinate ring of x t then the main result of this paper is given by

shellability in reductive monoids the purpose of this paper is to extend to monoids the work of bjorner wachs and proctor on the shellability of the bruhat chevalley order on weyl groups let m be a reductive monoid with unit group g borel subgroup b and weyl group w we study the partially ordered set of b x b orbits with respect to zariski closure inclusion within a g x g orbit of m this is the same as studying a w x w orbit in the renner monoid r such an orbit is the retract of a universal orbit which is shown to be lexicograhically shellable in the sense of bjorner and wachs

identities for classical group characters of nearly rectangular shape abstract we derive several identities that feature irreducible characters of the general linear the symplectic the orthogonal and the special orthogonal groups all of the identities feature characters that are indexed by shapes that are nearly rectangular by which we mean that the shapes are rectangles except for one row or column that might be shorter than the others as applications we prove new results in plane partitions and tableaux enumeration including new refinements of the bender knuth and macmahon ex conjectures

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques