conformal mapping based coordinate generation method for flows in periodic configurations abstract a conformal mapping based coordinate generation method for periodic configurations has been developed a channel of an arbitrary shape in the physical plane representing internal configurations is mapped into a straight channel in the computational plane and a wall of an arbitrary shape in the physical plane representing external configurations is mapped into a straight wall in the computational plane the parameters of the transformations have to be determined through a method of successive approximations a simple iteration scheme that converges quite rapidly even with a poor initial guess is presented solutions for different configurations are displayed to illustrate the capabilities of the method

dct domain watermarking techniques for still images detector performance analysis and a new structure a spread spectrum like discrete cosine transform dct domain watermarking technique for copyright protection of still digital images is analyzed the dct is applied in blocks of 8 spl times 8 pixels as in the jpeg algorithm the watermark can encode information to track illegal misuses for flexibility purposes the original image is not necessary during the ownership verification process so it must be modeled by noise two tests are involved in the ownership verification stage watermark decoding in which the message carried by the watermark is extracted and watermark detection which decides whether a given image contains a watermark generated with a certain key we apply generalized gaussian distributions to statistically model the dct coefficients of the original image and show how the resulting detector structures lead to considerable improvements in performance with respect to the correlation receiver which has been widely considered in the literature and makes use of the gaussian noise assumption as a result of our work analytical expressions for performance measures such as the probability of errors in watermark decoding and the probabilities of false alarms and of detection in watermark detection are derived and contrasted with experimental results

implicit spectrally accurate method for moving boundary problems using immersed boundary conditions concept a fully implicit spectral algorithm for the analysis of moving boundary problem is described the algorithm is based on the concept of immersed boundary conditions ibc i e the computational domain is fixed while the time dependent physical domain is submerged inside the computational domain and is described in the context of the diffusion type problems the physical conditions along the edges of the physical domain are treated as internal constraints the method eliminates the need for adaptive grid generation that follows evolution of the physical domain and provides sharp resolution of the location of the boundary various tests confirm the spectral accuracy in space and the first and second order accuracy in time the computational cost advantage of the ibc method as compared with the more traditional algorithm based on the mapping concept is demonstrated

chebyshev fourier spectral methods in bipolar coordinates bipolar coordinates provide an efficient cartography for a variety of geometries the exterior of two disks or cylinders a half plane containing a disk an eccentric annulus with a small disk offset from the center of an outer boundary that is a large circle and so on a pseudospectral method that employs a tensor product basis of fourier functions in the cyclic coordinate and chebyshev polynomials in the quasi radial coordinate gives easy to program spectral accuracy we show however that as the inner disk becomes more and more offset from the center of the outer boundary circle the grid is increasingly non uniform and the rate of exponential convergence increasingly slow one dimensional coordinate mappings significantly reduce the non uniformity in spite of this non uniformity the chebyshev fourier method is quite effective in an idealized model of the wind driven ocean circulation resolving both internal and boundary layers bipolar coordinates are also a good starting point for solving problems in a domain which is not one of the bipolar compatible domains listed above but is a sufficiently small perturbation of such this is illustrated by applying boundary collocation with bipolar harmonics to solve laplace s equation in a perturbed eccentric annulus in which the disk shaped island has been replaced by an island bounded by an ellipse similarly a perturbed bipolar domain can be mapped to an eccentric annulus by a smooth change of coordinates

three dimensional front tracking we describe a three dimensional front tracking algorithm discuss its numerical implementation and present studies to validate the correctness of this approach based on the results of the two dimensional computations we expect three dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontinuities in some cases for which the interface computations display considerable numerical sensitivity we expect a greatly enhanced capability

enumerating representations in finite wreath products abstract let be a group finite or infinite h a finite group and let rn denote the sequence h sn of symmetric wreath products as well as certain variants of it including in particular h an and wn the weyl group of type dn we compute the exponential generating function for the number hom rn of representations in rn and for some refinements of this sequence under very mild finiteness assumptions on always met for instance if is finitely generated this generalizes in a uniform way the connection between the problem of counting finite index subgroups in a group and the enumeration of actions on finite sets on the one hand and the recent results of chigira concerning solutions of the equation xm 1 in the groups h sn h an and wn on the other we also study the asymptotics of the function hom g h sn for arbitrary finite groups g and h

enhancement of speech coding in background noise for low rate speech coder a speech coding system employs measurements of robust features of speech frames whose distribution are not strongly affected by noise levels to make voicing decisions for input speech occurring in a noisy environment linear programing analysis of the robust features and respective weights are used to determine an optimum linear combination of these features the input speech vectors are matched to a vocabulary of codewords in order to select the corresponding optimally matching codeword adaptive vector quantization is used in which a vocabulary of words obtained in a quiet environment is updated based upon a noise estimate of a noisy environment in which the input speech occurs and the noisy vocabulary is then searched for the best match with an input speech vector the corresponding clean codeword index is then selected for transmission and for synthesis at the receiver end the results are better spectral reproduction and significant intelligibility enhancement over prior coding approaches robust features found to allow robust voicing decisions include low band energy zero crossing counts adapted for noise level amdf ratio speech periodicity measure low pass filtered backward correlation low pass filtered forward correlation inverse filtered backward correlation and inverse filtered pitch prediction gain measure

enumerating representations in finite wreath products ii explicit formulae abstract we present several contributions to the enumerative theory of wreath product representations developed in a previous paper by the first named author adv in math 153 2000 118 154 theorem 3 1 of the present paper establishes an explicit formula for one of the key ingredients in the description of the corresponding generating functions given in muller 2000 the exterior function building on theorem 1 in muller 2000 and the latter result we derive explicit formulae for the exponential generating function of the series hom r n in the case where is dihedral or a finite abelian group and the representation sequence r n is any of h sn or h an with a fixed finite group h or the sequence hom g wn moreover we verify a conjecture concerning the asymptotic behaviour of the sequence hom g wn for finite groups g made in muller 2000 in the case when g is dihedral or abelian

the spatial relationship of dct coefficients between a block and its sub blocks at present almost all digital images are stored and transferred in their compressed format in which discrete cosine transform dct based compression remains one of the most important data compression techniques due to the efforts from jpeg in order to save the computation and memory cost it is desirable to have image processing operations such as feature extraction image indexing and pattern classifications implemented directly in the dct domain to this end we present in this paper a generalized analysis of spatial relationships between the dcts of any block and its sub blocks the results reveal that dct coefficients of any block can be directly obtained from the dct coefficients of its sub blocks and that the interblock relationship remains linear it is useful in extracting global features in the compressed domain for general image processing tasks such as those widely used in pyramid algorithms and image indexing in addition due to the fact that the corresponding coefficient matrix of the linear combination is sparse the computational complexity of the proposed algorithms is significantly lower than that of the existing methods

fast computation of transform coefficients for a subadjacent block for a transform family the authors examine several different kinds of subadjacent blocks and consider fast computation for a transform family including the walsh hadamard transform and the rh transform as special cases the approach proposed here provides a direct frequency frequency procedure results indicate that for this transform family a reduction of the number of multiplications and additions is achieved by a factor of two thirds an example for the rh transform shows that further reduction of arithmetic operations is also possible the results of this method are even better for the walsh hadamard transform the new algorithms can reduce the number of additions from the level o n log sub 2 n to the level o n as compared to the traditional method

vector adaptive vector quantization with application to speech coding a vector adaptive vector quantization vavq scheme which may be viewed as a generalization of gain adaptive vector quantization is described the proposed scheme adjusts each component of the encoding signal vector according to a statistical estimate of the signal characteristics the vavq scheme can cope with large input dynamic ranges it can be used in either the time domain or the transform domain and exhibits approximately 4 db improvement in segmental signal to noise ratio snr over the fixed vq

fast algorithm for computing discrete cosine transform an efficient method for computing the discrete cosine transform dct is proposed based on direct decomposition of the dct the recursive properties of the dct for an even length input sequence is derived which is a generalization of the radix 2 dct algorithm based on the recursive property a new dct algorithm for an even length sequence is obtained the proposed algorithm is very structural and requires fewer computations when compared with others the regular structure of the proposed algorithm is suitable for fast parallel algorithm and vlsi implementation

over determined formulation of the immersed boundary conditions method abstract the over determined formulation of the immersed boundary conditions ibc method is proposed the method relies on the fourier expansions in the periodic direction and chebyshev expansions in the transverse direction the boundaries of the physical domain are immersed inside a regular computational domain and the boundary conditions enter the algorithm in the form of constraints construction of these constraints provides degrees of freedom in excess of that required to formulate a closed system of algebraic equations use of the additional degrees of freedom that leads to an over determined system is explored in order to improve the accuracy of the ibc method and to expand its applicability to more extreme geometries the over constraint formulation has been tested on three model problems that lead to the laplace biharmonic and navier stokes equations and thus cover the most commonly encountered types of operators in all cases tested the over determined formulation was found to improve the performance of the ibc method

multiplication free approximate algorithms for compressed domain linear operations on images we propose a method for devising approximate multiplication free algorithms for compressed domain linear operations on images e g downsampling translation filtering etc we demonstrate that the approximate algorithms give output images that are perceptually nearly equivalent to those of the exact processing while the computational complexity is significantly reduced

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

a fast recursive algorithm for computing the discrete cosine transform the discrete cosine transform dct is widely applied in various fields including image data compression because it operates like the karhunen loeve transform for stationary random data this paper presents a recursive algorithm for dct with a structure that allows the generation of the next higher order dct from two identical lower order dct s as a result the method for implementing this recursive dct requires fewer multipliers and adders than other dct algorithms

a direct spectral method for determination of flows over corrugated boundaries a completely spectral algorithm for analysis of flows over corrugated boundaries is proposed the algorithm treats the flow problem as an internal rather then a boundary value problem where the flow conditions are specified along a line in the interior of the computational domain the method eliminates the need for a coordinate generation and or premapping required for regularization of the computational domain in standard implementations of spectral discretizations various tests confirm the spectral accuracy of the algorithm

a fused cp factorization method for incomplete tensors low rank tensor completion methods have been advanced recently for modeling sparsely observed data with a multimode structure however low rank priors may fail to interpret the model factors of general tensor objects the most common method to address this drawback is to use regularizations together with the low rank priors however due to the complex nature and diverse characteristics of real world multiway data the use of a single or a few regularizations remains far from efficient and there are limited systematic experimental reports on the advantages of these regularizations for tensor completion to fill these gaps we propose a modified cp tensor factorization framework that fuses the l 2 norm constraint sparseness l 1 norm manifold and smooth information simultaneously the factorization problem is addressed through a combination of nesterov s optimal gradient descent method and block coordinate descent here we construct a smooth approximation to the l 1 norm and tv norm regularizations and then the tensor factor is updated using the projected gradient method where the step size is determined by the lipschitz constant extensive experiments on simulation data visual data completion intelligent transportation systems and gps data of user involvement are conducted and the efficiency of our method is confirmed by the results moreover the obtained results reveal the characteristics of these commonly used regularizations for tensor completion in a certain sense and give experimental guidance concerning how to use them

numerical simulation of unsteady nonisothermal capillary interfaces a family of algorithms for simulation of unsteady nonisothermal capillary interfaces has been developed the algorithms are based on a coordinate transformation method the time dependent unknown physical domain is mapped onto a rectangular computational domain with the explicit form of the mapping function not being known four types of temporal discretization are used leading to the first order accurate one step implicit method second order accurate crank nicolson and trapezoidal methods and second order accurate two step implicit method in all cases second order finite difference approximations were used for spatial discretizations various tests demonstrated that the algorithms deliver theoretically predicted accuracy even for very large interfacial distortions the crank nicolson and trapezoidal methods have been found to be conditionally stable and thus are not recommended

the enumeration of coverings of closed orientable euclidean manifolds g3 and g5 abstract there are only 10 euclidean forms that is flat closed three dimensional manifolds six are orientable and four are non orientable the aim of this paper is to describe all types of n fold coverings over the orientable euclidean manifolds g 3 and g 5 and calculate the numbers of non equivalent coverings of each type the manifolds g 3 and g 5 are uniquely determined among other forms by their homology groups h 1 g 3 z 3 z and h 1 g 5 z we classify subgroups in the fundamental groups 1 g 3 and 1 g 5 up to isomorphism given index n we calculate the numbers of subgroups and the numbers of conjugacy classes of subgroups for each isomorphism type and provide the dirichlet generating functions for the above sequences

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

subband coded image reconstruction for lossy packet networks transmission of digital subband coded images over lossy packet networks presents a reconstruction problem at the decoder this paper presents two techniques for reconstruction of lost subband coefficients one for low frequency coefficients and one for high frequency coefficients the low frequency reconstruction algorithm is based on inherent properties of the hierarchical subband decomposition to maintain smoothness and exploit the high intraband correlation a cubic interpolative surface is fit to known coefficients to interpolate lost coefficients accurate edge placement crucial for visual quality is achieved by adapting the interpolation grid in both the horizontal and vertical directions as determined by the edges present an edge model is used to characterize the adaptation and a quantitative analysis of this model demonstrates that edges can be identified by simply examining the high frequency bands without requiring any additional processing of the low frequency band high frequency reconstruction is performed using linear interpolation which provides good visual performance as well as maintains properties required for edge placement in the low frequency reconstruction algorithm the complete algorithm performs well on loss of single coefficients vectors and small blocks and is therefore applicable to a variety of source coding techniques

frequency domain motion estimation using a complex lapped transform a frequency domain algorithm for motion estimation based on overlapped transforms of the image data is developed as an alternative to block matching methods the complex lapped transform clt is first defined by extending the lapped orthogonal transform lot to have complex basis functions the clt basis functions decay smoothly to zero at their end points and overlap by 2 1 when a data sequence is transformed a method for estimating cross correlation functions in the clt domain is developed this forms the basis of a motion estimation algorithm that calculates vectors for overlapping windowed regions of data the overlapping data window used has no block edge discontinuities and results in smoother motion fields furthermore when motion compensation is performed using similar overlapping regions the algorithm gives comparable or smaller prediction errors than standard models using exhaustive search block matching and computational load is lower for larger displacement ranges and block sizes

categorical aspects of generating functions i exponential formulas and krull schmidt categories abstract in this paper we study formal power series with exponents in a category for example the generating function of a category e with finite hom sets is defined by e t tx aut x where the summation is taken over all isomorphism classes of objects of e we can use such power series to enumerate the number of e structures along a faithful functor theorem 4 6 our theory is closely related to the theory of species joyal 1981 a species can be identified with a faithful functor from a groupoid to the category of finite sets theorem 3 6 we use mainly the concept of faithful functors with finite fibers instead of species so that we can separate the roles categories and functors play for example the exponential formula e t exp con e t means the unique coproduct decomposition property theorem 5 8 in the final section we give some applications of our theory to rather classical enumerations

fuchsian groups finite simple groups and representation varieties let be a fuchsian group of genus at least 2 at least 3 if is non oriented we study the spaces of homomorphisms from to finite simple groups g and derive a number of applications concerning random generation and representation varieties precise asymptotic estimates for hom g are given implying in particular that as the rank of g tends to infinity this is of the form g 1 o 1 where is the measure of we then prove that a randomly chosen homomorphism from to g is surjective with probability tending to 1 as g combining our results with lang weil estimates from algebraic geometry we obtain the dimensions of the representation varieties text hom gamma bar g where bar g is gl n k or a simple algebraic group over k an algebraically closed field of arbitrary characteristic a key ingredient of our approach is character theory involving the study of the zeta function g s 1 s where the sum is over all irreducible complex characters of g

transform domain filtering based on pipelining structure the concept of transform domain filtering tdf is defined and a pipelining structure is proposed as a means to implement it tdf refers to filtering applied directly to transform domain data the proposed structure consists of product blocks and an array of m adders where m is the transform block length the tdf output data can be obtained by summing the outputs of each product block the product block in the proposed structure performs the product operation between an m m matrix and an m vector which can be effectively implemented by using a distributed arithmetic structure of a systolic array structure the proposed structure is simple with localized interconnections and is therefore suitable for vlsi implementations

upper bound on the characters of the symmetric groups let c be a conjugacy class in the symmetric group s n and be a partition of n let f be the degree of the irreducible representation s c the character of s at c and r c the normalized character c f we prove that there exist constants b 0 and 1 q 0 such that for n 4 for every conjugacy class c in s n and every irreducible representation s of s n r c max q 1 n 1 n b supp c where supp c is the number of non fixed digits under the action of a permutation in c 1 is the size of the largest part in and 1 is the number of parts in the proof is obtained by enumeration of rim hook tableaux the hook formula and probabilistic arguments combinatorial algebraic and statistical applications follow this result in particular we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes

fast dct domain filtering using the dct and the dst a method for efficient spatial domain filtering directly in the discrete cosine transform dct domain is developed and proposed it consists of using the discrete sine transform dst and the dct for transform domain processing on the in jpeg basis of the previously derived convolution multiplication properties of discrete trigonometric transforms the proposed scheme requires neither zero padding of the input data nor kernel symmetry it is demonstrated that in typical applications the proposed algorithm is significantly more efficient than the conventional filtered spatial domain and earlier proposed dct domain methods the proposed method is applicable to any dct based image compression standard such as jpeg mpeg and h 261

a fast 4 4 dct algorithm for the recursive 2 d dct the authors present an efficient algorithm for the computation of the 4 4 discrete cosine transform dct the algorithm is based on the decomposition of the 4 4 dct into four 4 point 1 d dcts thus only 1 d transformations and some additions are required it is shown that the proposed algorithm requires only 16 multiplications which is half the number needed for the conventional row column method since the 2 sup m 2 sup m dct can be computed using the 4 4 dct recursively for any m the proposed algorithm leads to a fast algorithm for the computation of the 2 d dct

on the spectral accuracy of a fictitious domain method for elliptic operators in multi dimensions this work is a continuation of the authors efforts to develop high order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach in a previous paper a new method was proposed based on the use of smooth forcing functions with identical shapes mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of lagrange multipliers in relation to a discrete set of boundary constraints for one dimensional elliptic problems this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth order algebraic convergence rate in this paper a spectrally accurate formulation is presented for multi dimensional applications instead of being specified locally the forcing function is defined as a convolution of a mollifier smooth bump function and a lagrange multiplier function the amplitude of the bump the multiplier function is then approximated by fourier series using a fourier galerkin approximation the spectral accuracy is demonstrated on a two dimensional laplacian problem and on a stokes flow around a periodic array of cylinders in the latter the numerical solution achieves the same high order accuracy as a stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom

classification and statistics of finite index subgroups in free products abstract the principal theme of this paper is the enumeration of finite index subgroups in a free product of finite groups under various restrictions on the isomorphism type of in particular we completely resolve the realization asymptotic and distribution problems for free products of cyclic groups of prime order prior to this work these questions were wide open even in the case of the classical modular group this complex of problems usually referred to as poincare klein problem originally arose around 1880 out of the work of klein and poincare on automorphic functions and related number theory but has also grown roots in geometric function theory and more recently in the theory of subgroup growth ideas and techniques from the theory of generalized permutation representations an enumerative theory of wreath product representations recently developed by the first named author play a fundamental role here other tools come from analytic number theory combinatorics and probability theory

low complexity multidimensional dct approximations for high order tensor data decorrelation in this paper we introduce low complexity multidimensional discrete cosine transform dct approximations 3d dct approximations are formalized in terms of high order tensor theory the formulation is extended to higher dimensions with arbitrary lengths several multiplierless 8 times 8 times 8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case the proposed methods complexity cost was assessed presenting considerably lower arithmetic operations when compared with the exact 3d dct the proposed approximations were embedded into 3d dct based video coding scheme and a modified quantization step was introduced the simulation results showed that the approximate 3d dct coding methods offer almost identical output visual quality when compared with exact 3d dct scheme the proposed 3d approximations were also employed as a tool for visual tracking the approximate 3d dct based proposed system performs similarly to the original exact 3d dct based method in general the suggested methods showed competitive performance at a considerably lower computational cost

a fast algorithm for computing multidimensional dct on certain small sizes this paper presents a new algorithm for the fast computation of multidimensional m d discrete cosine transform dct with size n sub 1 spl times n sub 2 spl times spl middot spl middot spl middot spl times n sub m where n sub i is a power of 2 and n sub i spl les 256 by using the tensor product decomposition of the transform matrix it is shown that the m d dct or inverse discrete cosine transform idct on these small sizes can be computed using only one dimensional 1 d dcts and additions and shifts if all the dimensional sizes are the same the total number of multiplications required for the algorithm is only 1 m times of that required for the conventional row column method we also introduce approaches for computing scaled dcts in which the number of multiplications is considerably reduced

the relationship of transform coefficients for differing transforms and or differing subblock sizes jiang and feng have developed a relationship between the discrete cosine transform dct coefficients of a block and those of its subblocks their derivation of this result can be significantly simplified the new derivation also generalizes to all linear invertible transforms and any separable subblock geometry

modeling of multichannel time series and extrapolation of matrix valued autocorrelation sequences this paper deals with multichannel time series and extends the autocorrelation method for fitting the time series from the nondegenerate case to the general case we shall show that the ar model obtained by solving the normal equations is always stable even in the degenerate case the multichannel levinson algorithm for solving the normal equations is extended from the nondegenerate case to the general case in the nondegenerate case the first n 1 values of the auto correlation sequence of the obtained ar model of order n are identical with those of the original data the next considered is the extrapolation problem of an autocorrelation sequence that is given data r 0 r 1 r n it is to construct a model whose first n 1 values of the autocorrelation sequence are identical with these data we shall show that even in the degenerate case when the given data r 0 r 1 r n are taken from the autocorrelation sequence of a purely nondeterministic time series they are identical with the first n 1 values of the autocorrelation sequence of the ar model of order n

diameters of finite simple groups sharp bounds and applications let g be a finite simple group and let s be a normal subset of g we determine the diameter of the cayley graph r g s associated with g and s up to a multiplicative constant many applications follow for example we deduce that there is a constant c such that every element of g is a product of c involutions and we generalize this to elements of arbitrary order we also show that for any word w w xl xd there is a constant c c w such that for any simple group g on which w does not vanish every element of g is a product of c values of w from this we deduce that every verbal subgroup of a semisimple profinite group is closed other applications concern covering numbers expanders and random walks on finite simple groups

gridless spectral algorithm for stokes flow with moving boundaries a gridless spectrally accurate algorithm for the stokes flow with moving boundaries is presented the algorithm uses fixed computational domain with boundaries of the flow domain moving inside the computational domain the spatial discretization is based on the fourier expansions in the streamwise direction and the chebyshev expansions in the transverse direction temporal discretization uses one and two steps implicit formulations the boundary conditions on the moving boundaries are imposed using the immersed boundary conditions concept numerical tests confirm the spectral accuracy in space and theoretically predicted accuracy in time different variants of the solution procedure are presented and their relative advantages are discussed

spectrally accurate algorithm for the analysis of flows in two dimensional vibrating channels a spectral algorithm based on the immersed boundary conditions ibc concept has been developed for the analysis of flows in channels bounded by vibrating walls the vibrations take the form of travelling waves of arbitrary profile the algorithm uses a fixed computational domain with the flow domain immersed in its interior boundary conditions enter the algorithm in the form of constraints the spatial discretization uses a fourier expansion in the stream wise direction and a chebyshev expansion in the wall normal direction use of the galileo transformation converts the unsteady problem into a steady one an efficient solver which takes advantage of the structure of the coefficient matrix has been used it is demonstrated that the method can be extended to more extreme geometries using the overdetermined formulation various tests confirm the spectral accuracy of the algorithm

multiple local optima in vector quantizers corresp two results are presented on vector quantizers meeting necessary conditions for optimality first a simple generalization of well known centroid and moment properties of the squared error distortion measure to a weighted quadratic distortion measure with an input dependent weighting is presented the second result is an application of the squared error special case of the first result to a simulation study of the design of 1 bit per sample two and three dimensional quantizers for a memoryless gaussian source using the generalized lloyd technique the existence of multiple distinct local optima is demonstrated thereby showing that sufficient conditions for unique local optima do not exist for this simple common case it is also shown that at least three dimensions are required for a vector quantizer to outperform a scalar quantizer for this source

on wohlfahrt series and wreath products abstract suppose that a group a contains only a finite number of subgroups of index d for each positive integer d let g s n be the wreath product of a finite group g with the symmetric group s n on 1 n for each positive integer n let k n be a subgroup of g s n containing the commutator subgroup of g s n if the sequence k n 0 satisfies a certain compatible condition then the exponential generating function n 0 hom a k n x n g n n of the sequence hom a k n 0 takes the form of a sum of exponential functions

multiple burnside rings and brauer induction formulae abstract let g be a finite group and suppose that g is an operator group of a finite group a define s g a h h s g and z 1 h a where s g is the set of subgroups of g and z 1 h a is the set of crossed homomorphisms from h to a we view g as an operator group of the opposite group a of a and make s g a into a left a g set the ring g a is defined to be a commutative ring consisting of all formal z linear combinations of a g orbits in s g a idempotent formulae for q z g a not only imply a generalization of dress induction theorem but bring in the case where z 1 g a is the set of linear c characters of g boltje s explicit formula for brauer s induction theorem and its hyperelementary version

spectrally accurate algorithm for analysis of convection in corrugated conduits abstract an algorithm suitable for analysis of convection problems in corrugated conduits has been developed the algorithm uses the immersed boundary conditions ibc concept to capture the effects of corrugated walls the field equations are discretized on a regular domain surrounding the flow domain using fourier expansions in the stream wise direction and chebyshev expansions in the wall normal direction the boundary conditions are expressed in the form of constraints and the spectrally accurate discretization of these constraints is discussed the solution is carried out using the fix flow rate constraint discretization as well as a method for the direct inclusion of this constraint in the flow solver is presented several tests are used to demonstrate the spectral accuracy of the solution the solution process relies on iterations with an efficient solver taking advantage of the structure of the coefficient matrix used to solve the linear system the limitations of the algorithm are discussed and gains associated with the over determined formulation are presented

fast algorithms for multidimensional dct to dct computation between a block and its associated subblocks in this paper we first propose an efficient algorithm for computing one dimensional 1 d discrete cosine transform dct for a signal block given its two adjacent subblocks in the dct domain and then introduce several algorithms for the fast computation of multidimensional m d dct with size n sub 1 spl times n sub 2 spl times spl times n sub m given 2 sup m subblocks of dct coefficients with size n sub 1 2 spl times n sub 2 2 spl times spl times n sub m 2 where n sub i i 1 2 m are powers of 2 obviously the row column method which employs the most efficient algorithms along each dimension reduces the computational complexity considerably compared with the traditional method which employs only the one dimensional 1 d fast dct and inverse dct idct algorithms however when m spl ges 2 the traditional method which employs the most efficient multidimensional dct idct algorithms has lower computational complexity than the row column method besides we propose a direct method by dividing the data into 2 sup m parts for independent fast computation in which only two steps of r dimensional r 1 2 m idct and additional multiplications and additions are required if all the dimensional sizes are the same the number of multiplications required for the direct method is only 2 sup m 1 m2 sup m 1 times of that required for the row column method and if n spl ges 2 sup 2m 1 the computational efficiency of the direct method is surely superior to that of the traditional method which employs the most efficient multidimensional dct idct algorithms

enhancing poisson s equation based approach for dct prediction yamatani and saito recently published an interesting method for predicting discrete cosine transform dct coefficients of an image block which uses partial derivatives of the image at the block boundary points it estimates partial derivatives the same way for all four side boundary points in this correspondence we improve their estimation method for the left and top side boundary points by observing that the decoder can use 1 d dct of the rightmost column of pixels of the block on the left side and bottom row pixels of the block on the top side instead of using just the dc of these two blocks it led us to revise their prediction equations experimental results show that the cumulative reduction in the size of the first five ac coefficients obtained using their equations is 15 1 and the same using our equations is 24 6

fast algorithms for the discrete cosine transform several fast algorithms for computing discrete cosine transforms dcts and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced because the 1 d 8 point dct and the 2 d 8 8 point dct are so widely used they are discussed in detail algorithms for computing scaled dcts and their inverses are also presented these have applications in compression of continuous tone image data where the dct is generally followed by scaling and quantization

enhancement of color images by scaling the dct coefficients this paper presents a new technique for color enhancement in the compressed domain the proposed technique is simple but more effective than some of the existing techniques reported earlier the novelty lies in this case in its treatment of the chromatic components while previous techniques treated only the luminance component the results of all previous techniques along with that of the proposed one are compared with respect to those obtained by applying a spatial domain color enhancement technique that appears to provide very good enhancement the proposed technique computationally more efficient than the spatial domain based method is found to provide better enhancement compared to other compressed domain based approaches

diagonalizing properties of the discrete cosine transforms since its introduction in 1974 by ahmed et al the discrete cosine transform dct has become a significant tool in many areas of digital signal processing especially in signal compression there exist eight types of discrete cosine transforms dcts we obtain the eight types of dcts as the complete orthonormal set of eigenvectors generated by a general form of matrices in the same way as the discrete fourier transform dft can be obtained as the eigenvectors of an arbitrary circulant matrix these matrices can be decomposed as the sum of a symmetric toeplitz matrix plus a hankel or close to hankel matrix scaled by some constant factors we also show that all the previously proposed generating matrices for the dcts are simply particular cases of these general matrix forms using these matrices we obtain for each dct a class of stationary processes verifying certain conditions with respect to which the corresponding dct has a good asymptotic behavior in the sense that it approaches karhunen loeve transform performance as the block size n tends to infinity as a particular result we prove that the eight types of dcts are asymptotically optimal for all finite order markov processes we finally study the decorrelating power of the dcts obtaining expressions that show the decorrelating behavior of each dct with respect to any stationary processes

some identities and asymptotics for characters of the symmetric group w this paper is motivated by the problem arising from quantum gravity 9 x 2 of counting combinatorial types of triangulations s of a riemann surface x with given degrees of vertices let us color 2 simplexes of the barycentric subdivision s9 in black and white so that adjacent simplexes are of different color and consider a mapping p x a p onto the riemann sphere p which send white simplexes onto the northern hemisphere black simplexes onto the southern hemisphere and centers k simplexes of s into an equatorial point y k s 0 1 2 then deg p s 3n n is k the number of 2 simplexes in s and p is unramified outside y y y it 0 1 2 is easy to see that points of x over y and y have ramification index 2 1 2 respectively 3 while rmaification indices of points over y are just 0 degrees of vertices of s so the problem of counting triangulations reduces to the problem of counting ramified coverings p x a y of riemann surfaces with given ramification indices in section 2 we recall a connection between ramified coverings p x a y of a riemann surface y of genus g and irreducible characters x of the y symmetric group s n s deg p the starting point is the following forn w x w x mula essentially owing to hurwitz 6 see also 10 4 2

alternating groups as quotients of two generator groups abstract graham higman has proved that for sufficiently large n the group a n is a homomorphic image of the triangle group 2 3 l where l 7 later his result was generalized by proving it for all l 7 in this paper we have shown that for sufficiently large n the group a n is a homomorphic image of 2 k l where l 5 k 3 and k 6 is even

l m fold image resizing in block dct domain using symmetric convolution image resizing is to change an image size by upsampling or downsampling of a digital image most still images and video frames on digital media are given in a compressed domain image resizing of a compressed image can be performed in the spatial domain via decompression and recompression in general resizing of a compressed image in a compressed domain is much faster than that in the spatial domain we propose a novel approach to resize images with l m resizing ratio in the discrete cosine transform dct domain which exploits the multiplication convolution property of dct multiplication in the spatial domain corresponds to symmetric convolution in the dct domain when an image is given in terms of its 8 spl times 8 block dct coefficients its resized image is also obtained in 8 spl times 8 block dct coefficients the proposed approach is computationally fast and produces visually fine images with high psnr

sharp interface cartesian grid method i an easily implemented technique for 3d moving boundary computations a cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three dimensional immersed boundaries the embedded boundaries are represented using level sets and treated in a sharp manner without the use of source terms to represent boundary effects the narrow band distance function field in the level set boundary representation facilitates implementation of the finite difference flow solver the resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second order accuracy the accuracy of the finite difference scheme is established and shown to be comparable to finite volume schemes that are considerably more difficult to implement moving boundaries are handled naturally the pressure solver is accelerated using an algebraic multigrid technique adapted to be effective in the presence of moving embedded boundaries benchmarking of the method is performed against available numerical as well as experimental results

symmetric convolution and the discrete sine and cosine transforms this paper discusses the use of symmetric convolution and the discrete sine and cosine transforms dsts and dcts for general digital signal processing the operation of symmetric convolution is a formalized approach to convolving symmetrically extended sequences the result is the same as that obtained by taking an inverse discrete trigonometric transform dtt of the product of the forward dtts of those two sequences there are 16 members in the family of dtts each provides a representation for a corresponding distinct type of symmetric periodic sequence the author defines symmetric convolution relates the dsts and dcts to symmetric periodic sequences and then use these principles to develop simple but powerful convolution multiplication properties for the entire family of dsts and dcts symmetric convolution can be used for discrete linear filtering when the filter is symmetric or antisymmetric the filtering will be efficient because fast algorithms exist for all versions of the dtts conventional linear convolution is possible if one first zero pad the input data symmetric convolution and its fast implementation using dtts are now an alternative to circular convolution and the dft

vector predictive coding of speech at 16 kbits s vector quantization in its simplest form may be regarded as a generalization of pcm independent quantization of each sample of a waveform to what might be called vector pcm where a block of consecutive samples a vector is simultaneously quantized as one unit in theory a performance arbitrarily close to the ultimate rate distortion limit is achievable with waveform vector quantization if the dimension of the vector k is large enough the main obstacle in effectively using vector quantization is complexity a vector quantizer of dimension k operating at a rate of r bits sample requires a number of computations on the order of k2 kr and a memory of the same order however a low dimensional vector quantizer dimensions 4 8 achieves a remarkable improvement over scalar quantization pcm consequently using the vector quantizer as a building block and imbedding it with other waveform data compression techniques may lead to the development of a new and powerful class of waveform coding systems this paper proposes and analyzes a waveform coding system adaptive vector predictive coding avpc in which a low dimensionality vector quantizer is used in an adaptive predictive coding scheme in the encoding process a locally generated prediction of the current input vector is subtracted from the current vector and the resulting error vector is coded by a vector quantizer each frame consisting of many vectors is classified into one of m statistical types this classification determines which one of m fixed predictors and of m vector quantizers will be used for encoding the current frame

gain adaptive vector quantization with application to speech coding the generalization of gain adaptation to vector quantization vq is explored in this paper and a comprehensive examination of alternative techniques is presented we introduce a class of adaptive vector quantizers that can dynamically adjust the gain or amplitude scale of code vectors according to the input signal level the encoder uses a gain estimator to determine a suitable normalization of each input vector prior to vq encoding the normalized vectors have reduced dynamic range and can then be more efficiently coded at the receiver the vq decoder output is multiplied by the estimated gain both forward and backward adaptation are considered and several different gain estimators are compared and evaluated gain adaptive vq can be used alone for vector pcm coding i e direct waveform vq or as a building block in other vector coding schemes the design algorithm for generating the appropriate gain normalized vq codebook is introduced when applied to speech coding gain adaptive vq achieves significant performance improvement over fixed vq with a negligible increase in complexity

alternating quotients of fuchsian groups abstract it is shown that any finitely generated non elementary fuchsian group has among its homomorphic images all but finitely many of the alternating groups a n this settles in the affirmative a long standing conjecture of graham higman

decomposable functors and the exponential principle abstract we develop a combinatorial theory for the operation of forming the logarithm of generating functions associated with covariant functors on the category of finite sets and bijective maps this leads to a rather general and flexible exponential principle for labeled combinatorial structures we also introduce the concept of a topos like category which turns out to be a convenient framework for the discussion of a wide range of applications a few of which are studied in detail

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

counting conjugacy classes of subgroups in a finitely generated group abstract a new general formula is obtained for the number of conjugacy classes of subgroups of given index in an arbitrary finitely generated group

fuchsian groups coverings of riemann surfaces subgroup growth random quotients and random walks abstract fuchsian groups acting as isometries of the hyperbolic plane occur naturally in geometry combinatorial group theory and other contexts we use character theoretic and probabilistic methods to study the spaces of homomorphisms from fuchsian groups to symmetric groups we obtain a wide variety of applications ranging from counting branched coverings of riemann surfaces to subgroup growth and random finite quotients of fuchsian groups as well as random walks on symmetric groups in particular we show that in some sense almost all homomorphisms from a fuchsian group to alternating groups an are surjective and this implies higman s conjecture that every fuchsian group surjects onto all large enough alternating groups as a very special case we obtain a random hurwitz generation of an namely random generation by two elements of orders 2 and 3 whose product has order 7 we also establish the analogue of higman s conjecture for symmetric groups we apply these results to branched coverings of riemann surfaces showing that under some assumptions on the ramification types their monodromy group is almost always sn or an another application concerns subgroup growth we show that a fuchsian group has n o 1 index n subgroups where is the measure of and derive similar estimates for so called eisenstein numbers of coverings of riemann surfaces a final application concerns random walks on alternating and symmetric groups we give necessary and sufficient conditions for a collection of almost homogeneous conjugacy classes in an to have product equal to an almost uniformly pointwise our methods involve some new asymptotic results for degrees and values of irreducible characters of symmetric groups

generating functions for permutation representations abstract we discuss the categorical approach to representations in wreath products and generalize the wohlfahrt formula of the exponential generating function for the number of permutation representations

an improvement of the minimum distortion encoding algorithm for vector quantization in this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords and about 25 40 percent for a tree search vector quantizer similar improvement can be achieved in other vector quantization systems

schwarz christoffel methods for conformal mapping of regions with a periodic boundary abstract numerical conformal mapping methods for regions with a periodic boundary have been developed these methods are based on the generalized schwarz christoffel equation and can deal with boundary curves of arbitrary forms i e made up of one or more rectifiable jordan curves high order quadrature rules have been implemented in order to increase accuracy of the mapping this is of particular relevance to highly accurate grid generation techniques required by for example implementation of high order compact finite difference discretization schemes

schwarz christoffel mappings a general approach abstract a general method is developed for constructing equations of the schwarz christoffel type these equations define conformal transformations between regions of the complex plane each of whose boundaries may consist of straight or continuously curved line segments and corners the more familiar types of schwarz christoffel equations are rederived and some new types are obtained

spectrally accurate algorithm for moving boundary problems for the navier stokes equations a spectral algorithm based on the immersed boundary conditions ibc concept is developed for simulations of viscous flows with moving boundaries the algorithm uses a fixed computational domain with flow domain immersed inside the computational domain boundary conditions along the edges of the time dependent flow domain enter the algorithm in the form of internal constraints spectral spatial discretization uses fourier expansions in the stream wise direction and chebyshev expansions in the normal to the wall direction up to fourth order implicit temporal discretization methods have been implemented it has been demonstrated that the algorithm delivers the theoretically predicted accuracy in both time and space performances of various linear solvers employed in the solution process have been evaluated and a new class of solver that takes advantage of the structure of the coefficient matrix has been proposed the new solver results in a significant acceleration of computations as well as in a substantial reduction in memory requirements

the immersed boundary method a projection approach a new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion like previous methods a boundary force is applied at the immersed surface to satisfy the no slip constraint this extra constraint can be added to the incompressible navier stokes equations by introducing regularization and interpolation operators the current method gives prominence to the role of the boundary force acting as a lagrange multiplier to satisfy the no slip condition this role is analogous to the effect of pressure on the momentum equation to satisfy the divergence free constraint the current immersed boundary method removes slip and non divergence free components of the velocity field through a projection the boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger cfl numbers compared to some past methods symmetry and positive definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field examples show that the current formulation achieves second order temporal accuracy and better than first order spatial accuracy in l 2 norms for one and two dimensional test problems results from two dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies

new polynomial transform algorithm for multidimensional dct a new algorithm for the type ii multidimensional discrete cosine transform md dct is proposed based on the polynomial transform the rd dct with size n sub 1 spl times n sub 2 spl times spl middot spl middot spl middot spl times n sub r where n sub i is a power of 2 can be converted into a series of one dimensional 1 d discrete cosine transforms dcts the algorithm achieves considerable savings on the number of operations compared with the row column method for example the number of multiplications for computing an r dimensional dct is only 1 r times that needed by the row column method and the number of additions is also reduced compared with other known polynomial transform algorithms for md dct and the most recently presented algorithm for md dct the proposed one uses about the same number of operations however advantages such as better computational structure and flexibility in the choice of dimensional sizes can be achieved

adaptive cosine transform coding of images in perceptual domain an adaptive cosine transform coding scheme for color images which incorporates human visual properties into the coding scheme is described it employs adaptive quantization to exploit the statistical nature of the coefficients and adaptive block distortion equalization to reduce the block edge structures inherent in block transform coding schemes results show that the subjective quality of the reconstructed images at a bit rate of 0 4 bit pixel or a compression ratio of 60 1 is very good

classical groups probabilistic methods and the 2 3 generation problem we study the probability that randomly chosen elements of prescribed type in a finite simple classical group g generate g in particular we prove a conjecture of kantor and lubotzky in this area the probabilistic approach is then used to determine the finite simple classical quotients of the modular group psl2 z up to finitely many exceptions

a direct computation of dct coefficients for a signal block taken from two adjacent blocks a direct computational algorithm for obtaining the dct discrete cosine transform coefficients of a signal block taken from two adjacent blocks is proposed this algorithm reduces the number of both multiplications and additions subtractions compared to the traditional method which requires inverse transforms of two received coefficient blocks followed by a forward transform the proposed algorithm is efficient and useful for speech coding and image processing especially for real time applications