lie bialgebroids and poisson groupoids lie bialgebras arise as infinitesimal invariants of poisson lie groups a lie bialgebra is a lie algebra g with a lie algebra structure on the dual g which is compatible with the lie algebra g in a certain sense for a poisson group g the multiplicative poisson structure induces a lie algebra structure on the lie algebra dual g which makes g g into a lie bialgebra in fact there is a one one correspondence between poisson lie groups and lie bialgebras if the lie groups are assumed to be simply connected 7 16 19 the importance of poisson lie groups themselves arises in part from their role as classical limits of quantum groups 8 and in part because they provide a class of poisson structures for which the realization problem is tractable 15 poisson groupoids were introduced by weinstein 24 as a generalization of both poisson lie groups and the symplectic groupoids which arise in the integration of arbitrary poisson manifolds 4 11 he noted that the lie algebroid dual a g of a poisson groupoid g itself has a lie algebroid structure but did not develop the infinitesimal structure further in this paper we introduce and study a natural infinitesimal invariant for poisson groupoids the lie bialgebroids of the title our ultimate purpose is to develop a lie theory for poisson groupoids parallel to that for poisson groups in this paper we are primarily concerned with the first half of this process that is with the construction of the lie bialgebroid of a poisson groupoid after the preliminary 2 in which we describe the generalization to arbitrary lie algebroids of the exterior calculus and schouten calculus in 3 we define a lie bialgebroid to be a lie algebroid a whose dual a is also equipped with a lie algebroid structure such that the coboundary operator d a a associated to a satisfies a cocycle equation with respect to a the lie algebra of sections of a this is clearly a straightforward extension of the concept of a lie bialgebra 16 but cannot be formalized in lie algebroid cohomological terms since there is no satisfactory adjoint representation for a general lie algebroid most of 3 is devoted to proving that this definition is self dual if a a is a lie bialgebroid then a a is also in 4 we briefly consider the special case of lie bialgebroids satisfying a triangularity condition which include some important examples such as the usual triangular lie bialgebras and lie bialgebroids associated to poisson manifolds the techniques used in 2 4 are similar to those known for lie bialgebras it would be possible by suitably generalizing the proof for poisson groups to prove

an image multiresolution representation for lossless and lossy compression we propose a new image multiresolution transform that is suited for both lossless reversible and lossy compression the new transformation is similar to the subband decomposition but can be computed with only integer addition and bit shift operations during its calculation the number of bits required to represent the transformed image is kept small through careful scaling and truncations numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity in addition we propose entropy coding methods that exploit the multiresolution structure and can efficiently compress the transformed image for progressive transmission up to exact recovery the lossless compression ratios are among the best in the literature and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods

classical solutions of the quantum yang baxter equation the classical analogue is developed here for part of the construction in which knot and link invariants are produced from representations of quantum groups whereas previous work begins with a quantum group obtained by deforming the multiplication of functions on a poisson lie group we work directly with a poisson lie groupg and its associated symplectic groupoid the classical analog of the quantumr matrix is a lagrangian submanifold open image in new window in the cartesian square of the symplectic groupoid for any symplectic leafs ing open image in new window induces a symplectic automorphism ofs s which satisfies the set theoretic yang baxter equation when combined with the flip map exchanging components and suitably implanted in each cartesian powers n generates a symplectic action of the braid groupb n ons n application of a symplectic trace formula to the fixed point set of the action of braids should lead to link invariants but work on this last step is still in progress

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

locally conformal dirac structures and infinitesimal automorphisms we study the main properties of locally conformal dirac bundles which include dirac structures on a manifold and locally conformal symplectic manifolds it is proven that certain locally conformal dirac bundles induce jacobi structures on quotient manifolds furthermore we show that given a locally conformal dirac bundle over a smooth manifold m there is a lie homomorphism between a subalgebra of the lie algebra of infinitesimal automorphisms and the lie algebra of admissible functions we also show that dirac manifolds can be obtained from locally conformal dirac bundles by using an appropriate covering map finally we extend locally conformal dirac bundles to the context of lie algebroids

reduction of courant algebroids and generalized complex structures we present a theory of reduction for courant algebroids as well as dirac structures generalized complex and generalized kahler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction the enhanced symmetry group of a courant algebroid leads us to define extended actions and a generalized notion of moment map key examples of generalized kahler reduced spaces include new explicit bi hermitian metrics on cp2

constrained controllability of perturbed discrete time systems in this paper we study the global null controllability with bounded controls of perturbed linear discrete time systems in rn more explicitly a globally null controllable autonomous discrete time system is perturbed by suitably small terms v k and b k to obtain a system of the form x k 1 a v k x k b b k u k and sufficient conditions are given to ensure the global null controllability of the resulting perturbed system

the lifting factorization of 2d 4 channel nonseparable wavelet transforms abstract one dimensional 1d wavelet transform was lifted successfully using the division with remainder of univariate laurent polynomials however division with remainder does not exist in the case of a bivariate polynomial thus it makes sense that the polyphase matrix of a two dimensional 2d nonseparable wavelet transform cannot be decomposed into the lifting format using the same solution as that of the 1d wavelet transform in this research we present a new lifting factorization method of two dimensional four channel 2d 4 channel nonseparable wavelet filter banks according to the uniform constructing format of high dimensional multivariate wavelet filter banks the general form of 2d 4 channel nonseparable wavelet filter bank is given with these filter banks the polyphase matrix of 2d 4 channel nonseparable wavelet transform is found and proven then we present the lifting factorization of the polyphase matrix and some examples are demonstrated in the factorization procedures finally the lifting performances of the proposed method are analyzed this lifting method factorizes the polyphase matrix into the product of a series of unit lower left triangular numerical matrices unit upper right triangular numerical matrices diagonal numerical matrices and diagonal polynomial matrices whose elements on the diagonal line are 1 x y and xy the original filter banks that all leading principal minors of the numerical matrices are not equal to zero can be factorized into lifting format the proposed method transforms the lifting factorization of the polyphase matrix into the decompositions of the numerical matrices without euclidian division thereby only multiplication and addition operations are performed with no fourier transformation involved when compared with the lifting method of the tensor product lifting wavelet transform and the contourlet transform the proposed lifting method can extract more edge information of images the computational complexity of the original 2d 4 channel nonseparable wavelet transform for image decomposition is n 1 times as much as that of the proposed lifting factorization method and the original wavelet transform is accelerated furthermore the proposed lifting factorization method is faster than the conventional 2d 4 channel nonseparable wavelet transform based on fourier transformation theory and convolution operation when the size of each filter in the latter is greater than 4 n 1 the proposed lifting factorization has better sparsity than that of its original 2d 4 channel nonseparable wavelet transform and other typical 2d 4 channel nonseparable wavelet transforms

reversible intraframe compression of medical images the performance of several reversible intraframe compression methods is compared by applying them to angiographic and magnetic resonance mr images reversible data compression involves two consecutive steps decorrelation and coding the result of the decorrelation step is presented in terms of entropy because huffman coding generally approximates these entropy measures within a few percent coding has not been investigated separately it appears that a hierarchical decorrelation method based on interpolation hint outperforms all other methods considered the compression ratio is around 3 for angiographic images of 8 9 b pixel but is considerably less for mr images whose noise level is substantially higher

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

dirac structures and poisson homogeneous spaces poisson homogeneous spaces for poisson groupoids are classified in terms of dirac structures for the corresponding lie bialgebroids applications include drinfel d s classification in the case of poisson groups and a description of leaf spaces of foliations as homogeneous spaces of pair groupoids

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

global numerical approach to nonlinear discrete time control interval analysis is used to characterize the set of all input sequences with a given length that drive a nonlinear discrete time state space system from a given initial state to a given set of terminal states no requirement other than computability i e ability to be evaluated by a finite algorithm is put on the nature of the state equations the method is based on an algorithm for set inversion and approximates the solution set in a guaranteed way

nambu dirac manifolds we present a generalization of the dirac structure in the direction of the nambu poisson structure it is shown that with every integrable nambu dirac structure there is associated a leibniz algebroid which yields a singular foliation endowed with a closed form the examples of nambu dirac manifolds are dirac manifolds nambu poisson manifolds and manifolds with closed forms a different leibniz algebroid structure associated with a nambu poisson structure is adopted for this generalization

a new class of biorthogonal wavelet systems for image transform coding we construct general biorthogonal coifman wavelet systems a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair a time domain design method is employed and closed form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived the resulting filter coefficients are all dyadic fractions which is an attractive feature in the realization of multiplication free discrete wavelet transform even ordered systems in this family are symmetric which correspond to linear phase dual filters in particular three filterbanks fbs in this family are systematically verified to have competitive compression potential to the 9 7 tap biorthogonal wavelet fb by cohen et al 1992 which is currently the most widely used one in the field of wavelet transform coding in addition the proposed fb s have much smaller computational complexity in terms of floating point operations required in transformation and therefore indicate a better tradeoff between compression performance and computational complexity

on the relationship between the overlapping rounding transform and lifting frameworks for reversible subband transforms a new framework for reversible subband transforms based on the overlapping rounding transform ort has been proposed as an alternative to the lifting framework in this article we show that the ort framework is in fact a special case of the lifting framework with only trivial extensions

reachable controllable sets and stabilizing control of constrained linear systems we consider discrete time linear systems with constrained controls we present an algorithm for computing an external representation of the n step reachable set and controllable set it is an improvement of previous methods in particular it is shown that for constructing the set of initial states that can be driven to the origin asymptotically one can restrict the search to a polyhedral set in the unstable subspace of the autonomous system which yields a drastic reduction in the computational burden application to the synthesis of stabilizing feedback controllers is discussed

on the least asymmetric wavelets the asymmetry of daubechies 1988 1992 scaling functions and wavelets can be diminished by minimizing a special second moment in time for the wavelet generating discrete time filter the moment is involved in an uncertainty relation for discrete time signals other measures of asymmetry are addressed as well and corresponding results are compared

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

algebraic constructions in the category of lie algebroids the aim of this paper is to give the first general and abstract treatment of the algebraic properties of lie algebroids the concept of lie algebroid was introduced in 1967 by pradines ls as the basic infinitesimal invariant of a differentiable groupoid the construction of the lie algebroid of a differentiable groupoid is a direct generalization of the construction of the lie algebra of a lie group and 183 described a full lie theory for differentiable groupoids and lie algebroids encompassing many phenomena in the foundations of differential geometry a more detailed account and further references are given in 13 however at this stage the algebraic properties of lie algebroids were not pursued in 13 iii section 2 iv section 11 one of us gave a fairly detailed account of the abstract algebra of lie algebroids over a fixed base lie algebroids are vector bundles with several additional structures and a category of lie algebroids on a given base and morphisms which preserve that base has properties similar to those of the category of lie algebras using this algebra it was demonstrated in 13 that the lie theory of a category of locally trivial differentiable lie groupoids over a fixed base and the corresponding category of transitive lie algebroids over that base is coextensive with the standard theory of connections in principal bundles we now propose to show that the lie functor from the category of all differentiable groupoids over arbitrary bases and arbitrary smooth morphisms to the category of all lie algebroids preserves the basic algebraic constructions known to be possible in the category of differentiable groupoids the main work is to give abstract formulations of the corresponding lie algebroid concepts the groupoid results with which we

rozansky witten type invariants from symplectic lie pairs we introduce symplectic structures on lie pairs of real or complex lie algebroids as studied by chen et al from atiyah classes to homotopy leibniz algebras arxiv 1204 1075 2012 encompassing homogeneous symplectic spaces symplectic manifolds with a mathfrak g action and holomorphic symplectic manifolds we show that to each such symplectic lie pair are associated rozansky witten type invariants of three manifolds and knots given respectively by weight systems on trivalent and chord diagrams

a complete characterization of reachable sets for constrained linear time varying systems we consider linear time varying systems with linear constraints on both control and state variables the reachable set is a convex polyhedron that we completely characterize in terms of its boundary hyperplanes

lossless subband coding system based on rounding transform we propose a new rounding transform called the overlapping rounding transform ort it is defined as a two port input two port output fir filtering system with a pair of rounding operations the ort is applied to develop lossless subband coding systems the ort approach has both a simpler representation and more possibilities for lossless subband implementation than the lifting scheme

null controllability of systems with control constraints and state saturation abstract sufficient conditions for the null controllability of discrete time systems with control constraints and state saturation are presented this is accomplished in two stages first we establish a result for the asymptotic stability of such systems under zero input conditions next we utilize this stability result to obtain a condition for the null controllability of such systems we include specific examples to demonstrate the applicability of the present results

lie algebroid foliations and script e1 m dirac structures we prove some general results about the relation between the 1 cocycles of an arbitrary lie algebroid a over m and the leaves of the lie algebroid foliation on m associated with a using these results we show that a 1 m dirac structure l induces on every leaf f of its characteristic foliation a 1 f dirac structure lf which comes from a precontact structure or from a locally conformal presymplectic structure on f in addition we prove that a dirac structure on m can be obtained from l and we discuss the relation between the leaves of the characteristic foliations of l and

infinity norm rotation transforms a new general paradigm of dynamic range preserving one to one mapping infinity norm rotations analogous to the general 2 norm rotations are proposed in this paper analogous to the well known discrete cosine transforms the linear 2 norm rotation transforms which preserve the 2 norm of the rotated vectors the proposed infinity norm rotation transforms are piecewise linear transforms which preserve the infinity norm of vectors besides the advantages of perfect reversibility in place calculation and dynamic range preservation the infinity norm rotation transforms also have good energy compact ability which is suitable for signal compression and analysis it can be implemented by shear transforms based on the 2 d rotation factorization of similar orthogonal transform matrices such as dct matrices the performance of the new transforms is illustrated with 2 d patterns and histograms its good performance in lossy and lossless image compression compared with other integer reversible transforms is demonstrated in the experiments

manin triples for lie bialgebroids in his study of dirac structures a notion which includes both poisson structures and closed 2 forms t courant introduced a bracket on the direct sum of vector fields and 1 forms this bracket does not satisfy the jacobi identity except on certain subspaces in this paper we systematize the properties of this bracket in the definition of a courant algebroid this structure on a vector bundle e rightarrow m consists of an antisymmetric bracket on the sections of e whose jacobi anomaly has an explicit expression in terms of a bundle map e rightarrow tm and a field of symmetric bilinear forms on e when m is a point the definition reduces to that of a lie algebra carrying an invariant nondegenerate symmetric bilinear form for any lie bialgebroid a a over m a notion defined by mackenzie and xu there is a natural courant algebroid structure on a oplus a which is the drinfel d double of a lie bialgebra when m is a point conversely if a and a are complementary isotropic subbundles of a courant algebroid e closed under the bracket such a bundle with dimension half that of e is called a dirac structure there is a natural lie bialgebroid structure on a a whose double is isomorphic to e the theory of manin triples is thereby extended from lie algebras to lie algebroids our work gives a new approach to bihamiltonian structures and a new way of combining two poisson structures to obtain a third one we also take some tentative steps toward generalizing drinfel d s theory of poisson homogeneous spaces from groups to groupoids

wavelet based linear system modeling and adaptive filtering it is shown how linear time varying systems can be modeled in several different ways by discrete time wavelets or more generally by some set of functions interpretation of physical meanings possible efficiency and other characteristics of the modeling are considered system identification minimizing the mean square output error is studied optimal coefficients and the corresponding minimum mean square error are found and they are in general time varying least mean square adaptive filtering algorithms are derived for on line filtering and system identification theoretically and by simulations the advantages of using wavelet based filtering are shown separation of adaptation effects from unknown time varying system behavior and fast convergence adaptive coefficients estimated by a recursive least square algorithm can tend toward constants even in the case of time varying systems time invariant system identification and adaptive filtering is given as a special case of the general time varying setting

3 d mesh sequence compression using wavelet based multi resolution analysis in this paper we present two compression methods for irregular three dimensional 3 d mesh sequences with constant connectivity the proposed methods mainly use an exact integer spatial wavelet analysis swa technique to efficiently decorrelate the spatial coherence of each mesh frame and also to adaptively transmit mesh frames with various spatial resolutions to reduce the temporal redundancy the first proposed method applies multi order differential coding mdc to the temporal sequences obtained from swa mdc determines the optimal order of the differential coder by analyzing the variance of prediction errors comparing with the first order differential coding fdc scheme the method can improve the compression performance the second proposed method applies temporal wavelet analysis twa to the temporal sequences in particular this method offers spatio temporal multi resolution coding through simulations we prove that our methods enable efficient lossy to lossless compression for 3 d mesh sequences in a single frame work

reversible resampling of integer signals except some extremely special cases signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation in this paper we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals i e the original signal can be reconstructed losslessly from the resampled data by using matrix factorization we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling the new factorization yields three elementary integer reversible matrices the method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices it can be applied to integer signals by in place integer reversible computation which needs no auxiliary memory to keep the original sample data for the transformation during the process or for ldquoundordquo recovery after the process some examples of low order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

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

technical communique null controllable region of lti discrete time systems with input saturation we present a formula for the extremes of the null controllable region of a general lti discrete time system with bounded inputs for an nth order system with only real poles not necessarily distinct the formula is simplified to an elementary matrix function which in turn shows that the set of the extremes coincides with a set of trajectories of the time reversed system under bang bang controls with n 2 or less switches

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

phase space localization theorem for ondelettes it is proven that an orthonormal basis of ondelettes can never have exponential localization in both position space and momentum space

ondelettes and phase cell cluster expansions a vindication y meyer has recently developed a particularly useful o n basis forl2 r d expansions using this basis i e expansions into ondelettes or wavelets have yielded important new results in soft and hard analysis the expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions a formalism already developed by the authors using other related bases adoption of ondelettes expansions into the phase cell program gives improvements of some extant results and excises an early error

heuristically enhanced feedback control of constrained discrete time linear systems recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on line minimization for the control of constrained linear systems still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms several ad hoc techniques have been proposed but their applicability is restricted by the lack of supporting theory in this paper we present a theoretical framework to analyze the stability of the closed loop system resulting from the use of on line optimization in the feedback loop using these results we show that a suboptimal algorithm based upon the use of heuristic search techniques yields asymptotically stable systems provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original the controller presented in this paper is valuable for situations where the customary approaches of using pontryagin s minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available

controllability results for systems with a nonconvex target this paper considers the problem of steering the state x t of the system dot x t a t x t f t u t to a prescribed target x the input u t is restricted to lie in a prespecified set which is assumed compact unlike the results of previous authors we allow x to be any set and do not require x to be convex or closed necessary conditions and sufficient conditions for the existence of a control which steers the system to the target from a specified initial condition are given conditions for global controllability to the target are also derived an additional concept of controllability that we investigate is that of complete controllability complete controllability is concerned with the ability to steer the system from any initial point to any final point one of the most important results of this paper is that we develop a technique for constructing a steering control previous work on the constrained controllability problem has dealt with methods for determining a steering control in only a limited way finally numerical techniques for checking controllability and for constructing a steering control are described and the results obtained from the application of our algorithm to several examples are presented

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

constrained controllability of discrete time systems the constrained controllability of the discrete time system xk 1 a k xk b k u k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state conditions for checking constrained controllability to a given target set from a specified initial state are presented these conditions involve solving finite dimensional optimization problems and can be checked via numerical computation in addition conditions for checking global constrained controllability to a given target set are presented a system is globally constrained controllable if for every initial state there exists an admissible control that steers the system to the target if a given discrete time system is constrained controllable it may be desirable to obtain an admissible control that steers the system to the target from a specified initial s

rounding transform and its application for lossless pyramid structured coding a new transform called the rounding transform rt is introduced in this paper this transform maps an integer vector onto another integer vector by using weighted average and difference filters followed by a rounding operation the rt can be applied to lossless pyramid structured coding with various elementary block sizes and filters in addition it generalizes other mean based lossless pyramid structured coding schemes

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

numerical methods for the generalized zakharov system we present two numerical methods for the approximation of the generalized zakharov system zs the first one is the time splitting spectral tssp method which is explicit time reversible and time transverse in variant if the generalized zs is keeps the same decay rate of the wave energy as that in the generalized zs gives exact results for the plane wave solution and is of spectral order accuracy in space and second order accuracy in time the second one is to use a local spectral method the discrete singular convolution dsc for spatial derivatives and the fourth order runge kutta rk4 for time integration which is of high the same as spectral order accuracy in space and can be applied to deal with general boundary conditions in order to test accuracy and stability we compare these two methods with other existing methods fourier pseudospectral method fps and wavelet galerkin method wg for spatial derivatives combining with the rk4 for time integration as well as the standard finite difference method fd for solving the zs with a solitary wave solution furthermore extensive numerical tests are presented for plane waves solitary wave collisions in 1d as well as a 2d problem of the generalized zs numerical results show that tssp and dsc are spectralorder accuracy in space and much more accurate than fd and for stability tssp requires k o h dsc rk4 requires k o h2 for fixed acoustic speed where k is the time step and h is the spatial mesh size