relation of signal set choice to the performance of optimal non gaussian detectors the optimal procedure for detecting the presence of discrete time signals in additive noise can be derived from the likelihood ratio test when the noise has statistically independent identically distributed components the dependence of the detector s performance on signal characteristics can be related to the kullback leibler kl distance between the distributions governing the hypotheses performance predictions based on the central limit theorem are shown to be poor approximations to the true performance performance of the optimal detector has long been known to increase exponentially with increasing kl distance symmetric noise amplitude distributions yield a symmetric dependence on the difference between the signals amplitudes at each time index small signal locally optimal detection performance is shown to depend on signal energy whereas large signal performance depends on the signal waveform when a distance measure can be defined performance depends on a different measure than that used in the detector with one exception the gaussian

a polynomial approach to robust estimation of uncertain discrete time systems the robust estimation problem for uncertain discrete time systems is treated in this paper considering parametric uncertainties in the polynomial framework the estimator is the minimiser of a cost function written in a epsilon contaminated form uncertainties are not formally modelled it is shown that in the present context the proposed approach can be connected to stochastic modelling of uncertainties the optimal robust estimator is obtained by computing a spectral factorisation and by solving a single diophantine equation an example shows the efficiency of the proposed method

impedance profile inversion via the first transport equation abstract the subject of this paper is the inverse reflection problem for a stratified elastic half space that is a linear elastic medium whose elastic properties depend only on depth from a planar free surface is stimulated at t 0 by a plane wave impulsive source the motion of a typical surface element is recorded for 0 t 2t it is shown that this surface trace determines the acoustic impedance of the medium as a function of travel time to travel time depth t moreover we give a precise characterization of those functions which may appear as surface traces and show uniqueness existence and continuous dependence of the logarithm of the impedance as a function of the surface trace in the sobolev h1 topology

on the relationship between measures of discrimination and the performance of suboptimal detectors the problem of designing and analyzing suboptimal detectors via statistical distance measures is considered as a preliminary result we show that only the minimum and maximum probability of error are valid measures of discrimination between the input statistics this result would seem then to imply that the use of distance measures in this context can be inappropriate however to overcome this apparent obstacle we demonstrate explicit relationships between various f divergences and the loss in performance of an arbitrary detector relative to the optimal detector in particular we establish both upper and lower bounds on the performance loss of a suboptimal detector in terms of the distance between the pertinent statistics of both the optimal and suboptimal detectors while designing detectors by minimizing these upper bounds can be an elusive task in many practical cases the lower bound presented herein holds with equality in this case minimizing the separation of the output statistics of the detector with respect to a particular f divergence equivalently minimizes the resulting probability of error of the detector to facilitate design other researchers have established conditions under which one may design arbitrary detection strategies with respect to a specific f divergence kullback leibler distance being a principal example we extend this approach by deriving necessary and sufficient conditions under which one may design detection strategies with respect to an arbitrarily chosen f divergence thus when these conditions are met one may optimize a detector with respect to the most analytically tractable distance measure to obtain the minimum probability of error detector over a selected class of detection strategies examples demonstrating the utility of this theory for the problem of designing optimal linear detectors and optimal signal sets are presented

the electromagnetic scattering problem in the time domain for a dissipative slab and a point source using invariant imbedding a vertical magnetic dipole source above an inhomogeneous slab is considered where the permittivity e e z and conductivity z vary with the depth z using the axial symmetry of the problem a hankel transform is introduced besides physical scattering kernels nonphysical scattering kernels are introduced and the direct and inverse transformed problem is solved by means of wave splitting in an invariant imbedding approach the imbedding equations for the nonphysical scattering kernels are simpler than the corresponding equations for the physical kernels and they are solved using existing techniques for the imbedding equations for normally incident plane waves the solution for the physical kernels is obtained by establishing relations between the two sets of kernels these relations are given by volterra equations of the second kind and thus are very easy to solve numerically some applications and extensions of the results derived in the paper are discussed

exact and operator rational approximate solutions of the helmholtz weyl composition equation in underwater acoustics the quadratic profile the application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one way helmholtz equation is briefly reviewed the role of operator symbols is stressed and their properties briefly discussed the construction of the operator symbol requires the exact or approximate solution of the helmholtz weyl composition equation in the weyl pseudodifferential operator calculus the exact symbols for several quadratic profiles are presented and briefly analyzed the symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case these results are used to illustrate several points pertinent to wide angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics

wave splitting and the reflection operator for the wave equation in r3 the problem of wave splitting in a nonhomogeneous medium in r3 is considered previous results for wave splitting in a planar stratified medium can be generalized to a general nonhomogeneous medium with sufficiently smooth velocity the wave equation is factorized into an up and down going wave system using certain integral and integral differential operators the equation for the reflection operator which relates the up going wave to a down going wave is then obtained and certain properties of the reflection operator are deduced

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

sensitivity penalization based robust state estimation for uncertain linear systems this technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state space model based on a simultaneous minimization of nominal estimation errors and their sensitivities an analytic solution is derived for the optimal estimator which can be recursively realized this estimator has a form similar to the robust estimator of and its computational complexity is comparable to the kalman filter under certain conditions this robust estimator is proved to converge to a stable system its estimation errors have a bounded covariance matrix and the estimate is asymptotically unbiased numerical simulations show that the obtained estimator has nice estimation performances

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

on the rate distortion function of sources with incomplete statistics maximization of the rate distortion function rdf of a class of memoryless sources constrained by moments is transformed to a minimax problem kuhn tucker conditions for determining channel capacity and an rdf are solved simultaneously by a linear program special cases include the maximum entropy method gaussian densities and spherical invariance

parameters estimation for a new anomalous thermal diffusion model in layered media in this paper we study an inverse problem of parameters estimation for a new time fractional heat conduction model in multilayered medium in the anomalous thermal diffusion model we consider the fractional derivative boundary conditions and the conduction obeys modified fourier law with riemannliouville fractional operator of different order in each layer for the direct problem we construct an effective finite difference scheme by using the balance method to deal with the discontinuity interface for the inverse problem we apply the nonlinear conjugate gradient ncg method with different conjugated coefficients to simultaneously identify the fractional exponent in each layer finally we use experimental data to verify the effectiveness of the proposed technique in which the jacobian matrix is achieved by a derivative free approach we analyze the sensitivity coefficients and the convergence behaviors of the ncg algorithm the simulation results confirm that the fractional heat conduction model with estimated parameters gives a more accurate fitting than the classical counterpart and the ncg method is a feasible and effective technique for the inverse problem of parameters estimation in fractional model

a game theory approach to robust discrete time h sub spl infin estimation the deterministic robust estimation problem is formulated in the discrete time case as a zero sum two person difference game in which a statistician plays against nature the statistician tries to estimate a linear combination of the states of an uncertain linear system which is driven by nature saddle point strategies for the statistician in the above game are difficult to find a suboptimal strategy is therefore considered which guarantees an h sub spl infin performance bound on the estimation error different patterns of the information that is available to the statistician are treated and the corresponding fixed point fixed lag and fixed interval smoothing strategies are derived

full waveform inversion of plane wave seismograms in stratified acoustic media theory and feasibility we have implemented an inversion procedure for obtaining velocity and density profiles from multioffset data in a layered acoustic medium using an iterative modeling technique and the p representation the procedure is derived from the nonlinear least squares formalism of tarantola and valette the feasibility of this method depends upon obtaining frechet derivatives during the modeling process and on vectorizing the thompson haskell reflectivity algorithm test data sets for this study are gathers of two to four plane wave synthetic seismograms which may contain both precritical and postcritical arrivals generated by a seismic wavelet these examples demonstrate convergence to the correct velocity and density profiles with reasonable accuracy

robust spl hscr sub spl infin filtering for discrete time linear systems with uncertain time varying parameters this paper deals with the problem of robust spl hscr sub spl infin filtering for linear discrete time state space models with uncertain time varying parameters the parameters enter affinely into the state space model matrices and their admissible values and variations are assumed to belong to given intervals a method is derived for designing a linear stationary asymptotically stable filter with a prescribed spl hscr sub spl infin performance in spite of large parameter uncertainty the proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a lyapunov function with quadratic dependence on the parameters the filter design is given in terms of linear matrix inequalities

generalized divergences from generalized entropies abstract several quantifiers of information also known as entropies have been introduced in different contexts and from different motivations for almost each one of these entropies a measure of the loss or gain of information has been introduced in this work we introduce generalized weighted divergences associated with an arbitrary entropy the resulting measures are closely related to bregman divergences we study the main formal properties of the resulting divergences we extend them to weighted probability distributions and we apply some of them to the analysis of simulated and real time series

factorization of the wave equation in higher dimensions the factorization of the wave equation into a coupled system involving up and down going wave components is obtained for the case where the field quantities are multivariate functions of spatial variables but the velocity c is a function of the z variable only the form of the reflection operator is derived and the quadratic differential integral equation satisfied by its kernel is obtained

robust memoryless quantization for minimum signal distortion robust quantizers are designed for situations where there is only an incomplete statistical description of the quantizer input the goal of the design is to closely approximate quantizer inputs by quantizer outputs without using more than a specified number of quantization levels the exact probability distribution of the input is unknown but this distribution is known to belong to some set c the primary set c considered is the set of all unimodal probability distributions which satisfy generalized moment constraint e g mean square value less than or equal to a constant a quantizer is derived which minimizes over all quantizers the maximum distortion over all distributions in c this robust quantizer guarantees a significanfiy lower worst case distortion than the classical gaussian optimal quantizer while performing nearly as well as the gaussian optimal quantizer when the input is in fact gaussian

analytical solutions to time fractional partial differential equations in a two dimensional multilayer annulus abstract in this paper analytical solutions to time fractional partial differential equations in a multi layer annulus are presented the final solutions are obtained in terms of mittag leffler function by using the finite integral transform technique and laplace transform technique in addition the classical diffusion equation 1 the helmholtz equation 0 and the wave equation 2 are discussed as special cases finally an illustrative example problem for the three layer semi circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative

a parametric approach to suboptimal signal detection in alpha stable noise this paper deals with the detection of a known deterministic signal embedded in alpha stable noise the implementation of the optimal receiver requires the explicit expression of the probability density function pdf of the noise unfortunately since there exists no closed form for the pdf of alpha stable distributed random variables numerical integrations are required to avoid such numerical approximations we suggest a low complexity parametric suboptimal detector well matched to essential properties of alpha stable noises this receiver does not require the explicit expression of the noise pdf in addition parameter optimization is fast for several optimization criteria and the selected receiver allows retrieval of the optimal gaussian detector matched filter as well as the locally optimal detector in the cauchy context the performance of the detector is studied and a comparison with the optimal solution along with a variety of classical detectors is given the robustness of the detector against the signal amplitude and the stability index alpha of the noise is discussed

robust quantization of e contaminated data the problem of robust quantization of data with uncertain statistical properties is considered uncertainty in the statistics of the data is modeled by assuming that the data have a probability density function of the e contaminated form and a minimax approach to robust design is adopted an approximation is developed for the asymptotic worst case distortion over the e contaminated class produced by an arbitrary companded quantizer and the quantizer design which minimizes this worst case distortion is derived the robustness of the resulting design is verified numerically for the particular problem of quantizing e contaminated gaussian data

recovery of the acoustic impedance from reflection seismograms this paper examines the problem of recovering the acoustic impedance from a band limited normal incidence reflection seismogram the convolutional model for the seismogram is adopted at the outset and it is therefore required that initial processing has removed multiples and recovered true amplitudes as well as possible in the first portion of the paper we investigate the effect of substituting the deconvolved seismic trace that is the band limited version of the reflectivity function into the standard recursion formula for the acoustic impedance the formalism of linear inverse theory is used to show that the logarithm of the normalized acoustic impedance estimated from the deconvolved seismogram is approximately an average of the true logarithm of the impedance moreover the averaging function is identical to that used in deconvolving the initial seismogram the advantage of these averages is that they are unique their disadvantage is that low frequency information which is crucial to making a g

design of quantizers from histograms the design of signal quantizers when the statistical description of the source is a histogram on a finite domain is considered minimum mean and minimax error criteria are discussed both leading to the design of piecewise linear compressor functions the problem of allocating the histogram intervals in the symmetric source density case is addressed through the use of chebyshev probability inequalities finally an adaptive implementation of the proposed system is described

robust quantization of memoryless sources using dispersive fir filters an approach to quantizing discrete time memoryless sources is presented an important feature is that its performance is largely insensitive to errors in modeling the input pdf the method involves changing the amplitude distribution of the source to be approximately gaussian by all pass filtering then applying a lloyd max quantizer designed for a gaussian source after quantization the samples are passed through another all pass filter which is an approximate inverse of the first filter the mean square error mse for the overall process is roughly equal to the quantization mse for the intermediate gaussian signal independent of the source statistics for some sources this is actually an improvement over direct correct model lloyd max quantization the cost of this technique is some delay due to filtering

the time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems abstract in this paper a time fractional fourier law is obtained from fractional calculus according to the fractional fourier law a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built the fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases in addition we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized h function using integral transformation methods the fractional heat conduction equation in the case 0 1 interpolates the standard heat conduction equation 1 and the localized heat conduction equation 0 finally numerical results are presented graphically for various values of order of fractional derivative

the fractional fick s law for non local transport processes fick s law is extensively adopted as a model for standard diffusion processes however requiring separation of scales it is not suitable for describing non local transport processes we discuss a generalized non local fick s law derived from the space fractional diffusion equation generating the levy feller statistics this means that the fundamental solutions can be interpreted as levy stable probability densities in the feller parameterization with index 1 2 and skewness 2 we explore the possibility of defining an equivalent local diffusivity by displaying a few numerical case studies concerning the relevant quantities flux and gradient it turns out that the presence of asymmetry 0 plays a fundamental role it produces shift of the maximum location of the probability density function and gives raise to phenomena of counter gradient transport

robust filter design for uncertain systems defined by both hard and soft bounds a new approach to robust linear filter design is described that attempts to combine the advantages of h sub spl infin robust linear synthesis with a probabilistic method of system and noise modeling the signal and measurement noise model parameters are assumed to be subject to perturbations represented by random variables with known covariances the system is represented in polynomial form and the uncertainty can be described by both soft and hard bounds an h sub spl infin cost function is minimized and averaged with respect to model errors in signal and noise descriptions the polynomial solution is no more complicated than the usual h sub spl infin optimal filter and involves averaged spectral factorizations and linear equations both usual and deconvolution filtering problems are considered

a class of lower bounds on the bayesian probability of error abstract in this paper a class of lower bounds is considered which unifies and extends some well known bounds on the bayesian probability of error this class is obtained by considering the divergence between two hypotheses both the symmetric and the nonsymmetric case are studied

analysis of the green s function approach to one dimensional inverse problems i one parameter reconstruction an analysis of a green s function approach based on wave splitting to the one dimensional electromagnetic inverse problem is given the green s functions refer to split components of the fundamental solution the linear system of equations for the green s functions is shown to be well posed for the inverse problem and stability estimates theorems on existence uniqueness local correctness and convergence are given

fundamental solutions to advection diffusion equation with time fractional caputo fabrizio derivative abstract the advection diffusion equation with time fractional derivatives without singular kernel and two space variables is considered the fundamental solutions in a half plane are obtained by using the laplace transform with respect to temporal variable t and fourier transform with respect to the space coordinates x and y the dirichlet problem and the source problem are investigated the general solution for the fractional case is particularized for the ordinary case of the normal advection diffusion phenomena and for the fractional normal diffusion process it should be noted that it is more advantageous to use the time fractional derivative without singular kernel caputo fabrizio time fractional derivative instead of caputo time fractional derivative the advantages are reflected both in the handling of computations but especially in expressing convenient of solutions some numerical calculations are carried out and the results are discussed and illustrated graphically

approximate solution of nonlinear quadratic integral equations of fractional order via piecewise linear functions abstract in this paper the main objective is to describe an approximate scheme for solving nonlinear quadratic integral equations nqies of fractional order the method is based on piecewise linear functions that are called hat functions hfs by applying the hfs approximation their properties and operational matrices nonlinear equation becomes to a nonlinear system of equations which can be solved by using simple arithmetic methods also the error analysis of hfs method and convergence analysis of proposed model are given at the end two nonlinear examples are presented to illustrate the validity and applicability of the explained approach

weiner and kalman filters for systems with random parameters a linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known unknown plant parameters in the plant model such as gains and time constants are treated as random variables with specified means and variances generalized wiener and kalman bucy filters are derived on the basis of transfer function matrix or state space representations of the plant respectively an application of the generalized filter to the linear quadratic optimal control of plants with unknown disturbances is also described and a certainty equivalence principle is shown to apply

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

new results on robust quantization in this paper we consider the design of robust block quantizers when the number of quantization levels is large the r th power distortion measure is utilized through the convenient expression developed by bennett and gersho the robust design is formulated as a two person game and it is shown that for convex families of signal probability density functions there is a saddle point solution the evaluation of the robust solution amounts to determining the maximum s norm element in the class of signal densities we then develop specific solutions for three classes of pdf a the class specified by generalized moment contraints b the class of econtaminated densities which has been a popular model in robust signal detection and c the class specified by upper and lower bounds to the probability density function of the signal for high quality quantization under fixed output entropy the quantizer is uniform and the resulting distortion is an increasing function of the source entropy the least favorable distribution is then the one having maximum entropy for the e contaminated family and the banded family c we derive the maxentropic distributions

wiener filter design using polynomial equations a simplified way of deriving realizable and explicit wiener filters is presented discrete time problems are discussed in a polynomial equation framework optimal filters predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations a tool for obtaining these equations for a given problem structure is described it is based on the evaluation of orthogonality in the frequency domain by means of canceling stable poles with zeros comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical wiener solution the simplicity of the proposed derivation method is particularly evident in multistage filtering problems to illustrate two examples are discussed a filtering and a generalized deconvolution problem a new solvability condition for linear polynomial equation appearing in scalar problems is also presented

on a system of differential equations with fractional derivatives arising in rod theory we study a system of equations with fractional derivatives that arises in the analysis of the lateral motion of an elastic column fixed at one end and loaded by a concentrated follower force at the other end we assume that the column is positioned on a viscoelastic foundation described by a constitutive equation of fractional derivative type the stability boundary is determined it is shown that as in the case of an elastic winkler type of foundation the stability boundary remains the same as for the column without a foundation thus with the solution analysed here the column exhibits the so called hermann smith paradox

fractional diffusion equation and green function approach exact solutions abstract we investigate the solutions of a fractional diffusion equation with radial symmetry by using the green function approach and by taking the n dimensional case into account in our analysis a spatial time dependent diffusion coefficient is considered i e d r t d t 1 r the presence of external forces f r k r e with e 1 and f r kr k r e is also taken into account in particular we discuss the results obtained by employing boundary conditions defined on a finite interval and afterwards the analysis is extended to a semi infinite interval finally we also discuss a rich class of diffusive processes that can be obtained from the results presented in this work

closed form solution for the transient reflected pressure for a point source above an acoustic half space with an exponentially stratified density the reflection problem for a transient point source over an acoustic half space with an exponentially stratified density is considered a spatial hankel transform is used to obtain a one dimensional wave equation the transient reflected pressure on the surface in the hankel transformed space is expressed by a convolution of a reflection kernel and the transformed incident pressure and the exact expression for the reflection kernel is obtained by means of a laplace transform closed form solution of the transient reflected pressure in physical space is obtained through an inverse hankel transform closed form solution for a generalization of the exponential density profile is also given numerical examples are given to illustrate these closed form solutions

an ill posed problem of the continuation of transient data for a hyperbolic equation in a three dimensional inhomogeneous half space a time domain data continuation problem for a second order hyperbolic equation in a three dimensional inhomogeneous half space which is a common problem in time domain layer stripping is considered two different approaches namely the local continuation approach and the wave splitting approach are used to propagate the surface data the dirichlet and neumann data to the data at deeper planes the local continuation approach requires a regularization in order to obtain a stable numerical result the wave splitting approach uses larger transverse spatial domain of dependence and gives reasonably stable results even without any additional smoothing process

robust filtering for linear time invariant continuous systems the problem of robust filtering for linear time invariant lti continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations and then in the state space domain the basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv contaminated model the general solution to the problem is given in the transfer function representation while in the polynomial framework the causal estimator is obtained by means of a spectral factorization and a diophantine equation the state space realization of the causal estimator is discussed examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty

frequency wavenumber inversion of acoustic data we describe an inversion procedure for obtaining velocities densities and layer thicknesses from multioffset reflection seismograms generated by a point source excitation in a stratified acoustic medium the reference seismograms are decomposed into cylindrical waves in the frequency wavenumber domain where the inversion is performed by minimizing the difference between the reference data and modeled data using a least squares technique the modeling algorithm is based on the classical reflectivity method we include the effects of limited temporal and spatial apertures by applying a frequency and wavenumber dependent filter in the modeling process this inversion is suited for jacobian matrix methods where the first derivatives of the model generated data with respect to the model parameters are calculated from analytical expressions together with the modeling the numerical examples show that the inversion algorithm recovers with reasonable accuracy the parameters used to generate the reference data the low frequency trends of both the velocity and the density are restored the convergence of the iterative minimization algorithm is fast

decay of a potential vortex in a generalized oldroyd b fluid the velocity field and the adequate shear stress corresponding to the decay of a potential vortex in a generalized oldroyd b fluid are determined by means of hankel and laplace transforms the exact solutions written in terms of the generalized g and r functions are presented as a sum of the newtonian solutions and the adequate non newtonian contributions these solutions can be easy specialized to give the solutions for generalized maxwell fluids and ordinary oldroyd b or maxwell fluids performing the same motion the influence of the fractional parameters as well as that of the material parameters on the decay of the vortex is emphasized by graphical illustrations

direct and inverse scattering in the time domain via invariant imbedding equations this paper examines the implementation of a new approach to direct and inverse scattering problems in the time domain which is applied here to the case of a one dimensional lossless medium the method is based on an integro differential equation which is satisfied by the reflection kernel and has been derived elsewhere using invariant imbedding techniques an example of an exact solution to this equation is given numerical schemes for solving the direct and inverse problems are derived by discretizing this equation the behavior of the resulting algorithms is then tested on several examples the results suggest that the inversion method is stable in the presence of additive noise

reconstruction of the velocity and density in a stratified acoustic half space using a short pulse point source the reconstruction of the velocity and density in a stratified half space using the reflection data generated by a short pulse point source is considered transverse spatial hankel transform is applied to the transient reflected and incident pressures on the surface the reflection kernel in the hankel transformed space is obtained through a deconvolution the time domain green function approach based on the wave splitting is then used to reconstruct the parameters this time domain approach to the inverse problem is exact and noniterative numerical results for some synthetical examples are presented to illustrate the hankel transform deconvolution and the reconstruction the finite difference time domain method is used to generate the transient reflection data in the physical space in a numerical simulation the reconstruction using obliquely incident plane waves is also considered in an appendix

radial anomalous diffusion in an annulus abstract in this study time fractional radial diffusion has been modeled in cylindrical coordinates in order to analyze the anomalous diffusion in an annulus by using an integral transform technique the analytical solution of the concentration distribution formula is obtained the establishing of the concentration distribution is found to be controlled by the fractional derivative and the influences of on the concentration field the total amount diffused and the quantity of mass passing through the inner wall are presented graphically and studied in detail asymptotic expressions for the exact solutions are developed in order to explain the numerical results at small and large time respectively and the physical mechanism explanation for the paradoxical behavior shown in the numerical results is given

some results for a fractional diffusion equation with radial symmetry in a confined region abstract we investigate an n dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account i e d r t d t r with d t d t d t the equation is considered in a confined region and subjected to time dependent boundary conditions which may be related to inhomogeneous characteristics of the surfaces confining the system the results show an anomalous spreading of the solutions and an unusual behavior of the survival probability