quantal problems with partial algebraization of the spectrum we discuss a new class of spectral problems discovered recently which occupies an intermediate position between the exactly solvable problems e g harmonic oscillator and all others the problems belonging to this class are distinguished by the fact that a part of the eigenvalues and eigenfunctions can be found algebraically but not the whole spectrum the reason explaining the existence of the quasi exactly solvable problems is a hidden dynamical symmetry present in the hamiltonian for one dimensional motion this hidden symmetry issl 2 r it is shown that other groups lead to a partial algebraization in multidimensional quantal problems in particular sl 2 r sl 2 r so 3 andsl 3 r are relevant to two dimensional motion inducing a class of quasi exactly solvable two dimensional hamiltonians typically they correspond to systems in a curved space but sometimes the curvature turns out to be zero graded algebras open the possibility of constructing quasi exactlysolvable hamiltonians acting on multicomponent wave functions for example with a non minimal superextension ofsl 2 r we get a hamiltonian describing the motion of a spinor particle

burst erasures and the mean square error for cyclic parseval frames this paper investigates the performance of frames for the linear redundant encoding of vectors when consecutive frame coefficients are lost due to the occurrence of random burst errors we assume that the distribution of bursts is invariant under cyclic shifts and that the burst length statistics are known in analogy with rate distortion theory we wish to find frames of a given size which minimize the mean square reconstruction error for the encoding of vectors in a complex finite dimensional hilbert space we obtain an upper bound for the mean square reconstruction error for a given parseval frame and in the case of cyclic parseval frames we find a family of frames which minimizes this upper bound under certain conditions these minimizers are identical to complex bose chaudhuri hocquenghem codes discussed in the literature the accuracy of our upper bounds for the mean square error is substantiated by complementary lower bounds all estimates are based on convexity arguments and a discrete rearrangement inequality

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

joint source channel coding using real bch codes for robust image transmission in this paper a new still image coding scheme is presented in contrast with standard tandem coding schemes where the redundancy is introduced after source coding it is introduced before source coding using real bch codes a joint channel model is first presented the model corresponds to a memoryless mixture of gaussian and bernoulli gaussian noise it may represent the source coder the channel coder the physical channel and their corresponding decoder decoding algorithms are derived from this channel model and compared to a state of art real bch decoding scheme a further comparison with two reference tandem coding schemes and the proposed joint coding scheme for the robust transmission of still images has been presented when the tandem scheme is not accurately tuned the joint coding scheme outperforms the tandem scheme in all situations compared to a tandem scheme well tuned for a given channel situation the joint coding scheme shows an increased robustness as the channel conditions worsen the soft performance degradation observed when the channel worsens gives an additional advantage to the joint source channel coding scheme for fading channels since a reconstruction with moderate quality may be still possible even if the channel is in a deep fade

saddle point principles and numerical integration methods for second order hyperbolic equations abstract this work describes a family of functionals whose stationarity often saddle point condition leads to well known so called variational formulations for structural dynamics such as the weak hamilton ritz formulation and the continuous discontinuous galerkin formulation and in turn to methods for the numerical integration of the equations of motion it is shown that all the time integration methods based on variational formulations do descend from such functionals moreover starting from the described family of functionals it is possible to construct new families of time integration methods which might exhibit computational advantages over the corresponding ones derived from variational formulations only

quasi exactly solvable lie algebras of differential operators in two complex variables the authors completely classify all quasi exactly solvable lie algebras of first order differential operators in two complex variables applications to quasi exactly solvable quantum problems are indicated

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

postintegration methods for numerical integration of non linear dynamic equations of motion the paper presents a family of methods with postintegration for numerical integration of non linear dynamic equations of motion of discrete systems both explicit and implicit algorithms of these methods are conditionally stable but can give solutions of accuracy of a few orders higher than the known methods with preintegration corresponding to them a general analysis of stability and accuracy of single step methods is carried out the postintegration methods have been tested on a single degree of freedom non linear system

new quasi exactly solvable hamiltonians in two dimensions quasi exactly solvable schrodinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods such operators lie in the enveloping algebra of a finite dimensional lie algebra of first order differential operators the hidden symmetry algebra in this paper we develop some general techniques for constructing quasi exactly solvable operators our methods are applied to provide a wide variety of new explicit two dimensional examples on both flat and curved spaces of quasi exactly solvable hamiltonians corresponding to both semisimple and more general classes of lie algebras

complex field coding for ofdm over fading wireless channels orthogonal frequency division multiplexing ofdm converts a time dispersive channel into parallel subchannels and thus facilitates equalization and de coding but when the channel has nulls close to or on the fast fourier transform fft grid uncoded ofdm faces serious symbol recovery problems as an alternative to various error control coding techniques that have been proposed to ameliorate the problem we perform complex field coding cfc before the symbols are multiplexed we quantify the maximum achievable diversity order for independent and identically distributed i i d or correlated rayleigh fading channels and also provide design rules for achieving the maximum diversity order the maximum coding gain is given and the encoder enabling the maximum coding gain is also found simulated performance comparisons of cfc ofdm with existing block and convolutionally coded ofdm alternatives favor cfc ofdm for the code rates used in a hiperlan2 experiment

a unified set of single step algorithms part 3 the beta m method a generalization of the newmark scheme introduced herein is a generalization of newmark s time marching integration scheme called the m method like the sspj method introduced in parts 1 and 2 of this series the m method provides a gcneral single step scheme applicable to any set of initial value problems the method is specialized by specifying the method order m along with rn integration parameters 0 1 m 1 for a particular choice of m the integration parameters provide a subfamily of methods which control accuracy and stability as well as offering options for explicit or implicit algorithms for the most part attention is focused on the application to structural dynamic equations most well known methods e g newmark wilson houbolt etc are shown to be special cases within the m family hence one computationally efficient and surprisingly simple algorithm unifies old and new methods stability and accuracy analyses are presented for method orders m 2 3 and 4 to determine optimal parameters for implicit and explicit schemes along with numerical verification

consistent use of finite elements in time and the performance of various recurrence schemes for the heat diffusion equation the use of the finite element concept in the time domain has resulted in a reinterpretation of many previously recorded recurrence formulae and the discovery of new ones an important new feature common to all such schemes is the fact that a weighted forcing term is used this precludes the application of unrealistic forcing terms resulting in a direct finite difference derivation and smooths oscillation due to sudden changes of boundary condition this problem is discussed in the context of various two and three level time schemes

variable order variable step algorithms for second order systems part 2 the codes we develop a new class of multistage algorithms for second order systems of ordinary differential equations ode s based on methods by zienkiewicz et al 13 our new methods are designed to provide a set of efficient methods which can be used with local error estimators based on embedding techniques in a companion paper we provide a set of subroutines implementing the algorithms derived and a discussion of numerical experience with the resulting codes

error estimation and adaptivity in elastodynamics abstract the paper discusses adaptive procedures for elastodynamic problems using semi discrete finite elements the adaptivity in space may be done by mesh refinement h version by increase of order of the approximation polynomials p version or a combination of these hp version in time the integration is either made by mode superposition of characteristic functions or by direct integration the adaptation in time may either be made by change of the global time step h version or increase of the order of approximation polynomials p version crucial parts of the analysis are the error estimator and the error indicator which are based either on interpolation theory or on total energy obtained from postprocessed stresses for the mesh generation and regeneration an isoline technique is utilized by which the mesh can be smoothed by interpolation theory the isolines are created for some characteristic scalar function for time discretization a new simple a posteriori local error estimator for the newmark scheme is described it is derived by a post processing technique without solving new equations so the additional computational cost is small and the implementation is convenient the paper also describes a sequence of nested time integration methods for dynamic problems formulated as two first order equations in time these nested integration methods in time based on a hierarchical formulation in time are a stable schemes of order 2k and l stable schemes of order 2k 1 a considerable improvement in terms of accuracy as well as effectiveness is obtained compared to currently available methods

conservation properties of a time fe method part i time stepping schemes forn body problems in the present paper one step implicit integration algorithms for the n body problem are developed the time stepping schemes are based on a petrov galerkin finite element method applied to the hamiltonian formulation of the n body problem the approach furnishes algorithmic energy conservation in a natural way the proposed time finite element method facilitates a systematic implementation of a family of time stepping schemes a particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals the influence of various standard as well as non standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements copyright 2000 john wiley sons ltd

generalized and extended subspace algorithms for error correction with quantized dft codes discrete fourier transform dft codes have been used to provide robustness against errors and erasures in various applications this paper focuses on improving error localization of the bose chaudhuri hocquenghem bch dft codes first we analyze how the subspace based error localization outperforms the coding theoretic one then we propose an extension of the subspace based error localization based on additional syndrome that improves the existing one and is naturally suitable for rate adaptive distributed source coding dsc further we propose a new generic subspace based algorithm to decode bch dft codes the proposed approach generalizes the encoding and decoding of this important class of dft codes it introduces many different decoding matrices for a dft code this diversity is then used to diminish the effect of the quantization noise and thus to improve the decoding finally the extended and generalized approaches are combined to maximize the decoding gain simulation results demonstrate the capability of the proposed algorithms to perform significantly better than the existing subspace based error localization in the presence of quantization noise

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

a further look at newmark houbolt etc time stepping formulae this paper looks at some well known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved new forms are given of the general three parameter method introduced by zienkiewicz 1 some new one step methods are introduced these are of great practical importance because of the ease with which the size of time step can be changed

normalizability of one dimensional quasi exactly solvable schrodinger operators we completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi exactly solvable schrodinger operator on the line methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi exactly solvable hamiltonians and explicit normalizability conditions in general coordinate systems

subspace algorithms for error localization with quantized dft codes recently a class of real number bose chaudhuri hocquengem codes known as discrete fourier transform dft codes have been considered as joint source and channel codes for providing robustness to erasures and errors over wireless networks we propose three subspace algorithms for error localization with quantized dft codes the algorithms are similar to the music the minimum norm and the esprit algorithms used in array signal processing for direction of arrival estimation they provide different but related formulations of the error localizations by first partitioning a vector space into the channel error subspace and its orthogonal complement the noise subspace the locations of the errors are determined from either the error subspace eigenvectors or the noise subspace eigenvectors we also present a brief performance analysis of the localization error in terms of the perturbation of the error subspace due to quantization simulation results show that their localization performances are similar and they perform better than the coding theoretic approach over a broad range of channel error to quantization noise ratios

computational algorithms for transient analysis the burden of weight and consequences towards formalizing discrete numerically assigned dna algorithmic markers wp family abstract different from the way we have been looking in the past at developments encompassing modal type and a wide class of step by step time stepping approaches for transient and dynamic field problems and significantly different from the way these have been developed and described in standard text books over the years this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems it is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi discretized equation system subsequently the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of exact integral operators approximate integral operators and a wide class of integration operators thus the present developments not only serve as a prelude towards the formal developments for exact integral operators but also demonstrate that the resulting approximate integral operators and a wide class of integration operators and known methods are simply subsets of the generalizations of a standardized w p family and emanate from the principles presented herein the burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned dna algorimmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems respectively

dynamic analysis of two dimensional frictional contact by linear complementarity problem formulation two dimensional dynamic contact is formulated as a linear complementarity problem using contact compatibility conditions and the coulomb friction law for the time integration of dynamic response displacements are approximated as second order polynomials and a new scheme of considering velocity discontinuities is presented the efficiency of the method is shown with three numerical examples

a unified set of single step algorithms part 4 backward error analysis applied to the solution of the dynamic vibration equation this paper applies the method of backward error analysis to the numerical solution of the dynamic vibration equation by the single step algorithms proposed in references 1 3 and obtains some general rules to help with the choice of parameters

dynamic transient analysis by a mixed iterative method summary mixed methods solved by an iterative process have been shown to provide an inexpensive procedure for improving the results of standard displacement analysis this paper shows the possibilities present in their application to dynamic problems where again accuracy improvement is achieved at small additional expense the advantages of the formulation presented are particularly noteworthy in explicit forms where the difficulties of hour glass modes associated with minimal integration rules ae avoided without cost increase

quasi exactly solvable lie superalgebras of differential operators in this paper we study lie superalgebras of matrix valued first order differential operators on the complex line we first completely classify all such superalgebras of finite dimension among the finite dimensional superalgebras whose odd subspace is non trivial we find those admitting a finite dimensional invariant module of smooth vector valued functions and classify all the resulting finite dimensional modules the latter lie superalgebras and their modules are the building blocks in the construction of quasi exactly solvable quantum mechanical models for spin particles in one dimension

constitutive relation error estimator for transient finite element analysis the concept of error in the constitutive relation allows defining a consistent error measurement for dynamic finite element simulations a solution which satisfies exactly the kinematic constraints the initial conditions and the equilibrium equation is built from the solution to the discretised problem this construction utilizes as best as possible the properties of the integration scheme used to obtain a satisfactory effectivity index the quality of the numerical solution is assessed by the way in which the constitutive relations are satisfied results from various tests conducted on a one degree of freedom problem and on a 1d example display the estimator s good behaviour the effectivity index remains at a reasonable value and on the basis of the first test a comparison of the error in the constitutive relation with different estimators drawn from the literature is presented

frame theoretic analysis of dft codes with erasures discrete fourier transform dft codes have been used as joint source channel codes in order to provide robustness against channel errors and erasures this paper presents a frame theoretic analysis of lowpass dft codes with erasures first it is shown that such codes make a special class of frames then the message reconstructions by the frame theoretic signal space projection and coding theoretic syndrome decoding of erasures are analyzed and their equivalence is proved the error performance of lowpass dft codes is analyzed using the frame theory the analysis helps in classifying the subframes of a dft frame into several classes this classification leads to the development of packetization criteria in order to guarantee minimum mean square reconstruction error and thus to minimize the effect of the quantization error simulation results substantiate the presented theory and the proposed packetization schemes

generalized midpoint finite element dynamic analysis of elastoplastic systems the application of a four parameter generalized midpoint integration method to small displacement elastoplastic dynamic problems is considered the integration of the governing relations over a time step is formulated as a non linear algebraic problem finite step problem by making use of generalized variables finite element modelling uniqueness and an extremum characterization of the solution of the finite step problem are discussed sufficient conditions for convergence of various iterative algorithms including newton raphson are given the b stability of the proposed procedure is assessed

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

systematic dft frames principle eigenvalues structure and applications motivated by a host of recent applications requiring some amount of redundancy frames are becoming a standard tool in the signal processing toolbox in this paper we study a specific class of frames known as discrete fourier transform dft codes and introduce the notion of systematic frames for this class this is encouraged by a new application of frames namely distributed source coding that uses dft codes for compression studying their extreme eigenvalues we show that unlike dft frames systematic dft frames are not necessarily tight then we come up with conditions for which these frames can be tight in either case the best and worst systematic frames are established in the minimum mean squared reconstruction error sense eigenvalues of dft frames and their subframes play a pivotal role in this work particularly we derive some bounds on the extreme eigenvalues dft subframes which are used to prove most of the results these bounds are valuable independently

correcting dct codes with laurent euclidean algorithm and syndrome extension real number block codes derived from the discrete cosine transform dct are corrupted by a few large errors along with low level noise checking syndromes are encapsulated in laurent polynomials and a special euclidean algorithm determines the locations of large errors these locations are adjusted properly to give an error modeling polynomial that is used to extend syndromes which are in turn transformed to codeword error values a probabilistic analysis describes the effects of the low level noise on corrected values after they pass through the syndrome extension process simulations yield probability of codeword errors mean squared decoding errors and sample means and variances of low level noise effects

iterative method for constrained and mixed approximation an inexpensive improvement of f e m performance a general iterative procedure for solving mixed lagrangian finite element equations is introduced the method allows a dramatic improvement in accuracy of simple irreducible formulations to be achieved in a few resolutions applications to incompressible flow stress analysis and metal forming problems are given the procedures can be easily implemented into standard programs

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

on the construction of quasi exactly solvable schrodinger operators on homogeneous spaces the closure conditions for a quasi exactly solvable operator is the requirement that a second order lie algebraic differential operator be equivalent up to scale change to a schrodinger operator on curved space the present work begins with an invariant characterization of the closure conditions and after a series of steps gives a reformulation of the closure conditions in terms of finite dimensional representations of the underlying lie algebra these techniques are used to give a complete solution to the closure condition for two different planar realizations of sl 2 along the way two theorems about homogeneous solutions to the closure conditions are introduced and proved also introduced is the class of abelian solutions to the closure conditions such solutions appear on flat spaces and give rise to a schrodinger operator with zero potential the concluding remarks highlight remaining questions and give references to research that address said questions

truncation error and stability analysis of iterative and non iterative thomas gladwell methods for first order non linear differential equations the consistency and stability of a thomas gladwell family of multistage time stepping schemes for the solution of first order non linear differential equations are examined it is shown that the consistency and stability conditions are less stringent than those derived for second order governing equations second order accuracy is achieved by approximating the solution and its derivative at the same location within the time step useful flexibility is available in the evaluation of the non linear coefficients and is exploited to develop a new non iterative modification of the thomas gladwell method that is second order accurate and unconditionally stable a case study from applied hydrogeology using the non linear richards equation confirms the analytic convergence assessment and demonstrates the efficiency of the non iterative formulation

application of the generalized α method to the time integration of the cable dynamics equations abstract the box method is a popular finite difference scheme for solving the cable dynamics equations in ocean engineering applications in this paper we analyze the shortcomings of the temporal integration defined by the box method and propose a new procedure that retains the box method s spatial discretization but employs the generalized method for temporal discretization the stability and accuracy of the generalized method as applied to the cable dynamics equations are developed this analysis procedure demonstrates the formulation of the semi discrete governing equations using spatial finite differences and the applicability of amplification matrix stability analysis to finite difference problems an example is presented that demonstrates the robustness of the new approach

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

improved coding theoretic and subspace based decoding algorithms for a wider class of dct and dst codes the decoding of a class of discrete cosine transform dct and discrete sine transform dst codes that are maximum distance separable codes mds is considered in this paper these class of codes are considered for error correction over real fields all the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes which can be characterized into the bose chaudhuri hocquenghem bch form and fails to decode the remaining even though they are mds in this paper we propose a new generic algorithm along the lines of coding theoretic and subspace methods to decode the entire class of mds dct and dst codes the proposed subspace approaches are similar to popular esprit and music algorithms the proposed algorithms also perform significantly better than the existing algorithms on the bch like subclass a perturbation analysis is also presented to study the effect of various parameters on the error localization due to the quantization noise simulation results are presented to demonstrate the capability of proposed algorithms to decode the entire class and to perform significantly better on the bch like subclass than the existing algorithm under the influence of quantization noise

quasi exactly solvable problems and sl 2 algebra recently discovered quasi exactly solvable problems of quantum mechanics are shown to be related to the existence of the finite dimensional representations of the groupsl 2 q whereq r c it is proven that the bilinear formh a j j b j stand for the generators allows one to generate a set of quasi exactly solvable problems of different types including those that are already known we get in particular problems in which the spectral riemannian surface containing an infinite number of sheets is split off one or two finite sheet pieces in the general case the transitionh h d2 dx2 v x is realized with the aim of the elliptic functions all known exactly solvable quantum problems with known spectrum and factorized riemannian surface can be obtained in this approach

time finite element methods for structural dynamics summary time finite element methods are developed for the equations of structural dynamics the approach employs the time discontinuous galerkin method and incorporates stabilizing terms having least squares form these enable a general convergence theorem to be proved in a norm stronger than the energy norm results are presented from finite difference analyses of the time discontinuous galerkin and least squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics these results show that for particular interpolations the time finite element method exhibits improved accuracy and stability

a new approach in non linear mechanics the large time increment method a new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non linearities and is tested on some examples in elastoplasticity the method considerably reduces the number of transfers between local and global levels hence the numerical cost of calculation is also diminished