explicit solvability of a class of maliuzhinets equations with matrix coefficients a coupled system of maliuzhinets functional equations for a pair of unknown functions is studied it is shown that the system can be solved in an explicit form for a specific but non trivial class of its matrix coefficients two examples arising in electromagnetic diffraction theory in a wedge shaped region are briefly discussed

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

diffraction at skew incidence by an anisotropic impedance wedge in electromagnetism theory a new class of canonical cases an original mathematical approach for the diffraction of an electromagnetic skew incident wave by a wedge allows us to reduce such a problem to new elementary functional equations using this method we present an exact analytical solution with closed form expressions for a class of wedge of any angle with a certain type of anisotropic boundary condition which does not require any field component to vanish on the faces we thereby consider the important case where the principal axes of anisotropy are along and normal to the edge the relative impedance matrix attached to each face being diagonal with its determinant equal to unity

transformation techniques towards the factorization of non rational 2 2 matrix functions abstract for the wiener hopf factorization of 2 2 matrix functions g defined on a closed carleson curve transformations g ugv where u and v are invertible rational 2 2 matrix functions are important in the first part of this paper we establish a classification scheme for 2 2 matrix functions which is based on such transformations we determine invariants under these transformations and describe those matrix functions which can be transformed to triangular or daniele khrapkov form in the second part we consider special rational transformations and study the same problem for instance we consider transformations where u and v are rational matrix functions that are analytic and invertible on an open neighborhood of in the more complicated but for factorization theory important case where u and v are rational matrix functions that are analytic and invertible on an open neighborhood of the closure of the domain inside of or outside of respectively the answer is slightly different

indexing the output points of an lbvq used for image transform coding a new method for indexing the points of a lattice based vector quantizer lbvq used to quantize the dct coefficients of images is presented with this method a large number of lattice points can be selected as codewords as a result the quality of the compressed data can be very high the problem is that the large number of points results in a high bit rate to reduce the bit rate a shorter representation is assigned to the more frequently used lattice points these points are grouped and a prefix code is used to index these lattice points our method outperforms jpeg particularly in the case of images with high frequency components

a fast encoding method for lattice codes and quantizers in an earlier paper the authors described a very fast method which for the root lattices a n d n e n their duals and certain other lattices finds the closest lattice point to an arbitrary point of the underlying space if the lattices are used as codes for a gaussian channel the algorithm provides a fast decoding procedure or if they are used as vector quantizers the algorithm performs the analog to digital conversion efficiently the present paper offers a solution to the inverse problem for the same lattices the encoding problem for channel codes or the digital to analog part of quantizing namely given an integer k to find the kth code vector and to the closely related problem of finding the index k of a given code vector

an entropy coded lattice vector quantizer for transform and subband image coding a lattice based vector quantizer vq and noiseless code are proposed for transform and subband image coding the quantization is simple to implement and no vector codebooks need to be stored the noiseless code enumerates lattice codevectors based on their weighted l sub 1 norm a software implementation is able to handle lattice codebooks of size 2 sup 256 the image coding performance is shown to be comparable or superior to the best encoding methods reported in the literature

spitzer identity wiener hopf factorization and pricing of discretely monitored exotic options the wiener hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability finance insurance queuing theory radio engineering and fluid mechanics the factorization fully characterizes the distribution of functionals of a random walk or a levy process such as the maximum the minimum and hitting times here we propose a constructive procedure for the computation of the wiener hopf factors valid for both single and double barriers based on the combined use of the hilbert and the z transform the numerical implementation can be simply performed via the fast fourier transform and the euler summation given that the information in the wiener hopf factors is strictly related to the distributions of the first passage times as a concrete application in mathematical finance we consider the pricing of discretely monitored exotic options such as lookback and barrier options when the underlying price evolves according to an exponential levy process we show that the computational cost of our procedure is independent of the number of monitoring dates and the error decays exponentially with the number of grid points

image coding with uniform and piecewise uniform vector quantizers new lattice vector quantizer design procedures for nonuniform sources that yield excellent performance while retaining the structure required for fast quantization are described analytical methods for truncating and scaling lattices to be used in vector quantization are given and an analytical technique for piecewise linear multidimensional companding is presented the uniform and piecewise uniform lattice vector quantizers are then used to quantize the discrete cosine transform coefficients of images and their objective and subjective performance and complexity are contrasted with other lattice vector quantizers and with lbg training mode designs

repetitive learning control for a class of partially linearizable uncertain nonlinear systems the repetitive learning control for a class of partially feedback linearizable systems is considered the signal to be tracked is a general periodic function with known period the considered system especially the unlinearizable subsystem of it contains unknown functions only the desired state variables of the linearizable subsystem can be used in control law design first some system constants related to the desired system and error system are presented then based on these system constants a state feedback repetitive control algorithm is proposed which guarantees that all the signals in the closed loop systems are bounded and the tracking error converges to zero asymptotically a simulation example is presented to show the utility of the proposed control algorithm

distributions of the two dimensional dct coefficients for images for a two dimensional discrete cosine transform dct image coding system there have been different assumptions concerning the distributions of the transform coefficients this paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a gaussian distribution for the dc coefficient and a laplacian distribution for the other coefficients furthermore from a simulation of the dct coding system it is shown that the assumption that the coefficients are laplacian yields a higher actual output signal to noise ratio and a much better agreement between theory and simulation than the gaussian assumption

adaptive iterative learning control for nonlinearly parameterised systems with unknown time varying delays and input saturations in this work an adaptive iterative learning control ailc scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time varying delays and input saturations by incorporating a saturation function a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain which is used to estimate the unknown time varying system uncertainty a new time weighted lyapunov krasovskii like composite energy function lkl cef is designed for the convergence analysis where time weighted inputs states and estimates of system uncertainty are all considered despite the existence of time varying parametric uncertainties time varying delays input saturations and local lipschitz nonlinearities the learning convergence is guaranteed with rigorous mathematical analysis simulation results verify the correctness and effectiveness of the proposed method further

a contribution to the quarter plane problem in diffraction theory abstract the three dimensional analog of sommerfeld s famous half plane problem for a screen 1 x1 0 x2 0 x3 0 is treated by an operator theoretic approach this paper shows that the dirichlet problem is well posed for any complex wave number k r if we look for a solution u h1 r3 of the helmholtz equation k2 u 0 in e 7mid 1 g h 1 2 1 with u 1 g h 1 2 1 an explicit representation formula for the solution is established by use of general wiener hopf operator theory sobolev space properties and hilbert space methods the corresponding neumann problem can be solved by analogy

commutative wiener hopf factorization of a matrix a class of n x n matrices is given for which commutative wiener hopf factorization is possible and the explicit factors are obtained it is also shown that there are no other matrices with factors which commute if the factors possess distinct eigenvalues

wiener hopf splitting of a 2 x 2 matrix explicit expressions for the wiener hopf factors of a 2 x 2 matrix are determined in terms of a single scalar examples of the application to various matrices are given

stable adaptive control of a class of first order nonlinearly parameterized plants stable adaptive control algorithms are designed for a class of first order nonlinearly parameterized plants containing nonlinearities similar to those arising in fermentation process models when the plant nonlinearity is conveniently parameterized and when the controller parameters are adjusted adaptively the output error is shown to converge to zero stability of the overall system is proved using the lyapunov function with a suitably chosen cubic term

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

an algorithm for uniform vector quantizer design a vector quantizer maps a k dimensional vector into one of a finite set of output vectors or points although certain lattices have been shown to have desirable properties for vector quantization applications there are as yet no algorithms available in the quantization literature for building quantizers based on these lattices an algorithm for designing vector quantizers based on the root lattices a n d n and e n and their duals is presented also a coding scheme that has general applicability to all vector quantizers is presented a four dimensional uniform vector quantizer is used to encode laplacian and gamma distributed sources at entropy rates of one and two bits sample and is demonstrated to achieve performance that compares favorably with the rate distortion bound and other scalar and vector quantizers finally an application using uniform four and eight dimensional vector quantizers for encoding the discrete cosine transform coefficients of an image at 0 5 bit pel is presented which visibly illustrates the performance advantage of vector quantization over scalar quantization

adaptive control of continuous time systems with convex concave parametrization this paper deals with adaptive control of a class of nonlinear dynamic systems with nonlinear parametrization in this class the state variables are assumed to be accessible and the nonlinearity in the parameters is assumed to be either convex or concave by introducing a tuning function and an adaptive law based on a min max strategy it is shown that such a class of dynamic systems can be adaptively controlled in a stable manner global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller the proposed controller is applied to a precise positioning problem in the presence of nonlinearly parametrized friction dynamics it is shown that the controller leads to position errors and friction compensation that are orders of magnitude better than those based on estimation of linear parametrizations the fact that the new parameter estimation strategy used is distinct from the traditionally used gradient schemes permits the expansion of the scope of adaptive control which has been restricted hitherto in most cases to systems with linear parametrization

the root lattices as low bit rate vector quantizers vector quantizers based on the a and d lattices are explored using the mean square error mse fidelity criterion for independent identically distributed sources with normal laplacian and gamma probability density functions code books are studied for uniform coding rates of up to 2 b sample and two and four dimensions the expected mse performance of the quantizers is better than that of optimal nonuniform lloyd max quantizers while the design algorithm presented offers only modest improvements in mse performance for a normally distributed source improvement gains of up to several decibels can be achieved when coding laplacian and gamma sources

enumeration encoding and decoding algorithms for pyramid cubic lattice and trellis codes a pyramid source code is a code that assigns equal length binary strings to all reproduction codevectors of equal weighted spl epsiv sub 1 norm a pyramid source encoding is partitioned into two concatenated mappings the first from source word to reproduction codeword within a codebook the second from the reproduction codevector to a binary string the first mapping allows distortion and is accomplished using lattice quantization or trellis coded quantization the second mapping is noiseless and is denoted as enumeration efficient pyramid enumeration encoding and decoding algorithms are presented for use with fixed rate or variable rate pyramid lattice and trellis codes

error resilient pyramid vector quantization for image compression pyramid vector quantization pvq uses the lattice points of a pyramidal shape in multidimensional space as the quantizer codebook it is a fixed rate quantization technique that can be used for the compression of laplacian like sources arising from transform and subband image coding where its performance approaches the optimal entropy coded scalar quantizer without the necessity of variable length codes in this paper we investigate the use of pvq for compressed image transmission over noisy channels where the fixed rate quantization reduces the susceptibility to bit error corruption we propose a new method of deriving the indices of the lattice points of the multidimensional pyramid and describe how these techniques can also improve the channel noise immunity of general symmetric lattice quantizers our new indexing scheme improves channel robustness by up to 3 db over previous indexing methods and can be performed with similar computational cost the final fixed rate coding algorithm surpasses the performance of typical joint photographic experts group jpeg implementations and exhibits much greater error resilience

mode conversion corner singularities and matrix wiener hopf factorization in diffraction theory the diffraction of acoustic electromagnetic and elastic waves by an edge is a subject of continuing mathematical and physical importance the physical motivation for research is the vast number of technological and geophysical applications of the fundamental models of linear wave propagation in continuous media while the mathematical drive is to understand and devise new analytical and numerical techniques for their quantification this paper is concerned with certain physical aspects of diffraction which have proven to give the most troublesome of mathematical difficulties these are mode conversion that is when the incident wave is scattered among different modes supported by the propagating medium and edge or corner singularities when the diffracting obstacle creates a stress singularity it is shown by way of a particular example that the exact solution of diffraction problems involving these phenomena will in general give rise to a vector wiener hopf equation with a matrix kernel whose factorization is non commutative the main result of this paper is a new procedure motivated by a precise treatment of both the corner singularity and mode conversion for determining the factors in this case

mixed boundary value problems of the type of sommerfeld s half plane problem on etudie des modifications du probleme de demi plan de sommerfeld gouverne par deux equations elliptiques propres dans des demi espaces complementaires de r 3 et on pose des conditions aux limites et de transmission sur les deux demi plans qui ensemble forment la frontiere commune de

on the modeling of dct and subband image data for compression image subband and discrete cosine transform coefficients are modeled for efficient quantization and noiseless coding quantizers and codes are selected based on laplacian fixed generalized gaussian and adaptive generalized gaussian models the quantizers and codes based on the adaptive generalized gaussian models are always superior in mean squared error distortion performance but generally by no more than 0 08 bit pixel compared with the much simpler laplacian model based quantizers and noiseless codes this provides strong motivation for the selection of pyramid codes for transform and subband image coding

piecewise uniform vector quantizers the companding model for quantizer design and analysis has been widely applied in the scalar quantization case however if the signal to be quantized is a vector then the optimum companding system can be designed for only a limited number of distributions on the other hand multidimensional piecewise linear companders can be designed for any signal density generating quantizers that are uniform on each region of the compander these systems while not optimal can have asymptotic performance arbitrarily close to the optimum their analysis and implementation can be simpler than those of optimal systems piecewise linear companders for asymptotic multidimensional quantization are analyzed and a method for their design is suggested

partial period adaptive repetitive control by symmetry this paper presents a partial period adaptive repetitive control method for a class of periodically time varying nonlinear systems to reduce the size of memory usage the symmetric feature of periodic parameters is explored to form partial period adaptation mechanisms both half and quarter period adaptation strategies are proposed and characterized analytically the stability of the closed loop system with each repetitive control is established along with tracking error convergence to zero in addition the saturated adaptation is suggested for providing bounded estimation

uniform and piecewise uniform lattice vector quantization for memoryless gaussian and laplacian sources lattice vector quantizer design procedures for nonuniform sources are presented the procedures yield lattice vector quantizers with excellent performance and retaining the structure required for fast quantization analytical methods for truncating and scaling lattices to be used in vector quantizations are given and their utility is demonstrated for independent and identically distributed i i d gaussian and laplacian sources an analytical technique for piecewise linear multidimensional compandor designs is evaluated for i i d gaussian and laplacian sources by comparing its performance to that of the other vector quantizers

iterative learning control design based on composite energy function with input saturation in this work an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation the analysis of convergence in the iteration domain is based on composite energy function which consists of both input and state information along the time and iteration axes through rigorous analysis the learning convergence in the iteration domain can be guaranteed under the input saturation provided the desired trajectory is realizable within the saturation bound

computing the weight distribution of a set of points obtained by scaling shifting and truncating a lattice a method is developed to compute the weight distribution of a set of points obtained from a lattice the lattice is scaled with possibly nonequal factors along different dimensions is shifted to an arbitrary point and its lower dimensional subspaces are truncated within given shaping regions each branch in the lattice trellis diagram is labeled by the weight distribution of the corresponding coset incorporating the effects of scaling shifting and truncation the weight distribution is obtained by multiplying the weight distribution of the serial branches and then adding the result over parallel paths

technical communique a direct adaptive controller for dynamic systems with a class of nonlinear parameterizations in this note the adaptive control problem is considered for a class of nonlinearly parametrized systems by introducing a novel kind of lyapunov functions a direct adaptive controller is developed for achieving asymptotic tracking control the transient performance of the resulting closed loop system can be guaranteed by suitably choosing the lyapunov function to construct the controller the effectiveness of the proposed scheme is illustrated with two examples

adaptive stabilization of stochastic nonholonomic systems with nonlinear parameterization this paper investigates the problem of adaptive stabilization by state feedback for a class of stochastic nonholonomic systems in chained form with nonlinear parameterization a parameter separation technique is introduced to transform the nonlinear parameterized nonholonomic system into a linear like parameterized one then using input state scaling and backstepping techniques an adaptive state feedback controller is obtained based on switching strategy to eliminate the phenomenon of uncontrollability global asymptotic regulation in probability of the closed loop system states are guaranteed finally a simulation example is provided to illustrate the effectiveness of the proposed method

adaptive repetitive control for a class of nonlinearly parametrized systems in this note lyapunov based adaptive repetitive control is presented for a class of nonlinearly parametrized systems through the use of an integral lyapunov function the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control global stability of the adaptive system and asymptotic convergence of the tracking error are established and tracking error bounds are provided to quantify the control performance both partially and fully saturated learning laws are analyzed in detail and compared analytically

adaptive rejection of multi periodic disturbances for a class of linear systems abstractthis paper deals with adaptive rejection of general multi periodic disturbances for a class of linear systems via output feedback the multi periodic disturbance is a superposition of several general periodic disturbances assume that all periods of the multi periodic disturbance are known a method of estimating the multi periodic disturbance and its derivatives is presented which can ensure these estimate errors converge to zero based on these estimation methods we present a new adaptive control method for disturbance rejection which guarantees that in the closed loop system all the signals are bounded and the output converges to zero a simulation example is presented to verify the effectiveness of the control scheme