the application of multiwavelet filterbanks to image processing multiwavelets are a new addition to the body of wavelet theory realizable as matrix valued filterbanks leading to wavelet bases multiwavelets offer simultaneous orthogonality symmetry and short support which is not possible with scalar two channel wavelet systems after reviewing this theory we examine the use of multiwavelets in a filterbank setting for discrete time signal and image processing multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank we describe two methods repeated row and approximation deapproximation for obtaining such a vector input stream from a one dimensional 1 d signal algorithms for symmetric extension of signals at boundaries are then developed and naturally integrated with approximation based preprocessing we describe an additional algorithm for multiwavelet processing of two dimensional 2 d signals two rows at a time and develop a new family of multiwavelets the constrained pairs that is well suited to this approach this suite of novel techniques is then applied to two basic signal processing problems denoising via wavelet shrinkage and data compression after developing the approach via model problems in one dimension we apply multiwavelet processing to images frequently obtaining performance superior to the comparable scalar wavelet transform

heuristic solution methods for the stochastic flow shop problem we investigate the stochastic flow shop problem with m machines and general distributions for processing times no analytic method exists for solving this problem so we looked instead at heuristic methods we devised three constructive procedures with modest computational requirements each based on approaches that have been successful at solving the deterministic counterpart we compared the performance of these procedures experimentally on a set of test problems and found that all of them achieve near optimal performance

stochastically minimizing the makespan in two machine flow shops without blocking abstract this paper deals with a two machine stochastic flow shop with an infinite storage between the machines we present a new sufficient condition on the job processing time distributions that implies that the makespan becomes stochastically smaller when two jobs in a given job sequence are interchanged this condition is weaker than that given by ku and niu p s ku s c niu on johnson s two machine flow shop with random processing times opns res 34 1986 130 136 and is not restricted to adjacent jobs it is claimed that all optimal scheduling rules for minimizing the makespan that have been identified so far in the literature can be derived from the new condition examples and generalizations of known results are presented

a comprehensive review and evaluation of permutation flowshop heuristics in this work we present a review and comparative evaluation of heuristics and metaheuristics for the well known permutation flowshop problem with the makespan criterion a number of reviews and evaluations have already been proposed however the evaluations do not include the latest heuristics available and there is still no comparison of metaheuristics furthermore since no common benchmarks and computing platforms are used the results cannot be generalised we propose a comparison of 25 methods ranging from the classical johnson s algorithm or dispatching rules to the most recent metaheuristics including tabu search simulated annealing genetic algorithms iterated local search and hybrid techniques for the evaluation we use the standard test of taillard eur j operation res 64 1993 278 composed of 120 instances of different sizes in the evaluations we use the experimental design approach to obtain valid conclusions on the effectiveness and efficiency of the different methods tested

construction of a class of compactly supported symmetric and balanced refinable function vector by gtst the concept of general two scale similarity transform gtst is introduced by applying gtst we present an algorithm of constructing a class of balanced refinable function vector by balancing already existing nonbalanced refinable function vector in addition we discuss an especial setting that is if given refinable function vector x is symmetric then by gtst new refinable function vector x is not only balanced but also preserve symmetry finally two construction examples are given

dynamics and approximations of a velocity tracking problem for the navier stokes flows with piecewise distributed controls we study the dynamics of a piecewise in time distributed optimal control problem for the navier stokes equations which models velocity tracking over time we also study the dynamics of semidiscrete and fully discrete approximations of this velocity tracking problem we prove that the rates of velocity tracking are exponential some computational results are presented which reinforces the theoretical results derived

on a family of biorthogonal armlets with prescribed properties abstract the notion of armlets analysis ready multiwavelets was introduced and studied by jian ao lian most recently as a precise formulation of orthonormal multiwavelets that guarantee wavelet decomposition with highpass output not being effected by polynomial perturbation of the input in this paper we first extend this concept to the biorthogonal setting and then we concern ourselves about a particular construction of biorthogonal multiscaling function and multiwavelets with multiplicity r 2 in particular we consider the two pairs of lowpass filters are flipped and the two pairs of highpass filters are linearphase respectively and we also give several equivalent forms of flipping property in terms of symbols and filters associated with multiscaling functions and multiwavelets by requiring flipping property we can represent all the entries of the matrix symbols p z q z p z q z of a biorthogonal multiwavelet using p11 z and p 11 z which are the first row and first column entries of p z and p z respectively these results will lead to a procedure for the construction of biorthogonal armlets with prescribed properties consequently a family of biorthogonal multiscaling functions which are mirrored copies each other and biorthogonal multiwavelets which are armlets of higher order with symmetry and antisymmetry are constructed explicitly

multiwavelet prefilters ii optimal orthogonal prefilters for pt i see ieee trans circuits syst ii vol 45 p 1106 12 1998 prefiltering a given discrete signal has been shown to be an essential and necessary step in applications using unbalanced multiwavelets in this paper we develop two methods to obtain optimal second order approximation preserving prefilters for a given orthogonal multiwavelet basis these procedures use the prefilter construction introduced in hardin and roach 1998 the first prefilter optimization scheme exploits the taylor series expansion of the prefilter combined with the multiwavelet the second one is achieved by minimizing the energy compaction ratio ecr of the wavelet coefficients for an experimentally determined average input spectrum we use both methods to find prefilters for the cases of the dghm and chui lian cl multiwavelets we then compare experimental results using these filters in an image compression scheme additionally using the dghm multiwavelet with the optimal prefilters from the first scheme we find that quadratic input signals are annihilated by the high pass portion of the filter bank at the first level of decomposition

multiwavelet bases with extra approximation properties this paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order because multiwavelet bases normally lack important properties that traditional wavelet bases of equal approximation order possess the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step prefiltering this paper examines the properties and design of orthogonal multiwavelet bases with approximation order 1 that possess those properties that are normally absent for these balanced bases so named by lebrun and vetterli see proc ieee int conf acoust speech signal process icassp munich germany vol 3 p 2473 76 1997 and ibid vol 46 p 1119 24 1998 prefiltering can be avoided by reorganizing the multiwavelet filter bank the development in this paper draws from results regarding the approximation order of m band wavelet bases the main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by powers of z sup 2r 1 z sup 1 1 for traditional wavelets r 1 this specializes to the usual factor z 1 sup k

balanced multiwavelet bases based on symmetric fir filters this paper describes a basic difference between multiwavelets and scalar wavelets that explains without using zero moment properties why certain complications arise in the implementation of discrete multiwavelet transforms assuming we wish to avoid the use of prefilters in implementing the discrete multiwavelet transform it is suggested that the behavior of the iterated filter bank associated with a multiwavelet basis of multiplicity r is more fully revealed by an expanded set of r sup 2 scaling functions spl phi sub i j this paper also introduces new k balanced orthogonal multiwavelet bases based on symmetric fir filters the nonlinear design equations arising in this work are solved using the grobner basis the minimal length k balanced multiwavelet bases based on even length symmetric fir filters are better behaved than those based on odd length symmetric fir filters as illustrated by special relations they satisfy and by examples constructed

a new heuristic method for the flow shop sequencing problem abstract a new heuristic method is presented for solving the m machine n job flow shop scheduling problem this method named spirit is composed of two phases the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques the results of the heuristic are compared with those from other well known methods

a heuristic for minimizing the expected makespan in two machine flow shops with consistent coefficients of variation abstract the paper deals with the classical problem of minimizing the makespan in a two machine flow shop when the job processing times are deterministic the optimal job sequence can be determined by applying johnson s rule when they are independent and exponential random variables talwar s rule yields a job sequence that minimizes the makespan stochastically assuming that the job processing times are independently and weibull distributed random variables we present a new job sequencing rule that includes both johnson s and talwar s rules as special cases the proposed rule is applicable as a heuristic whenever the job processing times are characterized by their means and the same coefficient of variation simulation results show that it leads to very encouraging results when the expected makespan is minimized

the structure of balanced multivariate biorthogonal multiwavelets and dual multiframelets multiwavelets and multiframelets are of interest in several applications such as numerical algorithms and signal processing due to their desirable properties such as high smoothness and vanishing moments with relatively small supports of their generating functions and masks in order to process and represent vector valued discrete data efficiently and sparsely by a multiwavelet transform a multiwavelet has to be prefiltered or balanced balanced orthonormal univariate multiwavelets and multivariate biorthogonal multiwavelets have been studied and constructed in the literature dual multiframelets include bi orthogonal multiwavelets as special cases but their fundamental prefiltering and balancing property has not yet been investigated in the literature in this paper we shall study the balancing property of multivariate multiframelets from the point of view of the discrete multiframelet transform this approach to our best knowledge has not been considered so far in the literature even for multiwavelets but it reveals the essential structure of prefiltering and the balancing property of multiwavelets and multiframelets we prove that every biorthogonal multiwavelet can be prefiltered with the balancing order matching the order of its vanishing moments that is from every given compactly supported multivariate biorthogonal multiwavelet one can always build another essentially equivalent compactly supported biorthogonal multiwavelets with its balancing order matching the order of the vanishing moments of the original one more generally we show that if a dual multiframelet can be prefiltered then it can be equivalently transformed into a balanced dual multiframelet with the same balancing order however we notice that most available dual multiframelets in the literature cannot be simply prefiltered with its balancing order matching its order of vanishing moments and they must be designed to possess high balancing orders the key ingredient of our approach is based on investigating some properties of the subdivision and transition operators acting on discrete vector polynomial sequences which play a central role in a discrete multiframelet transform and are of interest in their own right we also establish a new canonical form of a matrix mask which greatly facilitates the investigation and construction of multiwavelets and multiframelets in this paper we obtain a complete criterion and the essential structure for balanced or prefiltered dual multiframelets in the most general setting our investigation of the balancing property of a multiframelet deepens our understanding of the multiframelet transform in signal processing and scientific computation

design of prefilters for discrete multiwavelet transforms the pyramid algorithm for computing single wavelet transform coefficients is well known the pyramid algorithm can be implemented by using tree structured multirate filter banks the authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets the proposed algorithm can be thought of as a discrete vector valued wavelet transform for certain discrete time vector valued signals the proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete time signals the authors then present some numerical experiments to illustrate the performance of the algorithm which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms

eigenvalues of spl darr 2 h and convergence of the cascade algorithm this paper is about the eigenvalues and eigenvectors of spl darr 2 h the ordinary fir filter h is a convolution with a vector h h o h n which is the impulse response the operator spl darr 2 downsamples the output y h x keeping the even numbered components y 2n where h is represented by a constant diagonal matrix this is a toeplitz matrix with h k on its kth diagonal the odd numbered rows are removed in spl darr 2 h the result is a double shift between rows yielding a block toeplitz matrix with 1 spl times 2 blocks iteration of the filter is governed by the eigenvalues if the transfer function h z spl sigma h k z sup k has a zero of order p at z 1 corresponding to spl omega spl pi then spl darr 2 h has p special eigenvalues 1 2 1 4 1 2 sup p we show how each additional zero at spl pi divides all eigenvalues by 2 and creates a new eigenvector for spl lambda 1 2 this eigenvector solves the dilation equation spl phi t 2 spl sigma h k spl phi 2t k at the integers t n the left eigenvectors show how 1 t t sup p 1 can be produced as combinations of spl phi t k the dilation equation is solved by the cascade algorithm which is an infinite iteration of m spl darr 2 2h convergence in l sup 2 is governed by the eigenvalues of t spl darr 2 2hh sup t corresponding to the response 2h z h z sup 1 we find a simple proof of the necessary and sufficient condition for convergence

multivariate matrix refinable functions with arbitrary matrix dilation characterizations of the stability and orthonormality of a multivariate matrix refinable function d with arbitrary matrix dilation m are provided in terms of the eigenvalue and 1 eigenvector properties of the restricted transition operator under mild conditions it is shown that the approximation order of d is equivalent to the order of the vanishing moment conditions of the matrix refinement mask pa the restricted transition operator associated with the matrix refinement mask pa is represented by a finite matrix ami j i j with a idet m i 1 e p j q3 p e and p j q3 p being the kronecker product of matrices p j and p the spectral properties of the transition operator are studied the sobolev regularity estimate of a matrix refinable function 4 is given in terms of the spectral radius of the restricted transition operator to an invariant subspace this estimate is analyzed in an example

rearrangement majorization and stochastic scheduling rearrangement inequalities such as the classical hardy littlewood polya inequality and the more general day s inequality and related majorization results are often useful in solving scheduling problems among other things they are essential for pairwise interchange arguments motivated by solving stochastic scheduling problems we develop stochastic versions of day s inequality over both unrestricted and restricted specifically one cycle permutations these lead to a general and unified approach which we apply to solve the stochastic versions of several classical deterministic scheduling problems in most cases the approach leads to new or stronger results in other cases it recovers known results with new insight the approach is built upon recent developments in stochastic majorization and multivariate characterization of stochastic order relations

some efficient heuristic methods for the flow shop sequencing problem abstract in this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one next this problem is applied to taboo search a new technique to solve combinatorial optimization problems and computational experiments are reported finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed up

on heuristic solutions for the stochastic flowshop scheduling problem abstract we address the problem of scheduling jobs in a permutation flowshop when their processing times adopt a given distribution stochastic flowshop scheduling problem with the objective of minimization of the expected makespan for this problem optimal solutions exist only for very specific cases consequently some heuristics have been proposed in the literature all of them with similar performance in our paper we first focus on the critical issue of estimating the expected makespan of a sequence and found that for instances with a medium large variability expressed as the coefficient of variation of the processing times of the jobs the number of samples or simulation runs usually employed in the literature may not be sufficient to derive robust conclusions with respect to the performance of the different heuristics we thus propose a procedure with a variable number of iterations that ensures that the percentage error in the estimation of the expected makespan is bounded with a very high probability using this procedure we test the main heuristics proposed in the literature and find significant differences in their performance in contrast with existing studies we also find that the deterministic counterpart of the most efficient heuristic for the stochastic problem performs extremely well for most settings which indicates that in some cases solving the deterministic version of the problem may produce competitive solutions for the stochastic counterpart

dynamics for controlled navier stokes systems with distributed controls the long time behavior of solutions for an optimal distributed control problem associated with the navier stokes equations is studied first a linear feedback solution for the navier stokes equations is constructed this feedback solution possesses decay in time properties then some preliminary estimates for the long time behavior of all solutions of the navier stokes equations are derived next the existence of a solution for the optimal control problem is proved finally the long time decay properties for the optimal solutions are established

dynamics for controlled 2 d boussinesq systems with distributed controls the long time behavior of solutions for an optimal distributed control problem associated with the boussinesq equations is studied first a quasi optimal solution for the boussinesq equations is constructed this quasi optimal solution possesses the decay in time properties then some preliminary estimates for the long time behavior of all solutions of the boussinesq equations are derived next the existence of a solution for the optimal control problem is proved finally the long time decay properties for the optimal solutions is established

balanced multi wavelets in ℝ the notion of k balancing was introduced a few years ago as a condition for the construction of orthonormal scaling function vectors and multi wavelets to ensure the property of preservation annihilation of scalarvalued discrete polynomial data of order k or degree k 1 when decomposed by the corresponding matrix valued low pass high pass filters while this condition is indeed precise to the best of our knowledge only the proof for k 1 is known in addition the formulation of the k balancing condition for k 2 is so prohibitively difficult to satisfy that only a very few examples for k 2 and vector dimension 2 have been constructed in the open literature the objective of this paper is to derive various characterizations of the k balancing condition that include the polynomial preservation property as well as equivalent formulations that facilitate the development of methods for the construction purpose these results are established in the general multivariate and bi orthogonal settings for any k 1

componentwise bounds for nearly completely decomposable markov chains using stochastic comparison and reordering this paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable markov chains and on an application it provides the first numerical results with the type of algorithm discussed the given two level algorithm uses aggregation and stochastic comparison with the strong stochastic st order in order to improve accuracy it employs reordering of states and a better componentwise probability bounding algorithm given st upper and lower bounding probability vectors results in sparse storage show that there are cases in which the given algorithm proves to be useful

balanced multiwavelets theory and design this article deals with multiwavelets which are a generalization of wavelets in the context of time varying filter banks and with their applications to signal processing and especially compression by their inherent structure multiwavelets are fit for processing multichannel signals this is the main issue in which we are interested first we review material on multiwavelets and their links with multifilter banks and especially time varying filter banks then we have a close look at the problems encountered when using multiwavelets in applications and we propose new solutions for the design of multiwavelets filter banks by introducing the so called balanced multiwavelets