subordination approach to multi term time fractional diffusion wave equations abstract this paper is concerned with the fractional evolution equation with a discrete distribution of caputo time derivatives such that the largest and the smallest orders and m satisfy the conditions 1 2 and m 1 first based on a study of the related propagation function the nonnegativity of the fundamental solutions to the spatially one dimensional cauchy and signaling problems is proven and propagation speed of a disturbance is discussed next we study the equation with a general linear spatial differential operator defined in a banach space and suppose it generates a cosine family a subordination principle is established which implies the existence of a unique solution and gives an integral representation of the solution operator in terms of the corresponding cosine family and a probability density function explicit representation of the probability density function is derived the subordination principle is applied for obtaining regularity results the analytical findings are supported by numerical work

retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations we propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena whose diffusion exponent varies with time and which correspondingly cannot be viewed as self affine random processes possessing a unique hurst exponent we prove the positivity of the solutions of the proposed equations and establish their relation to the continuous time random walk theory we show that the distributed order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the wiener process and whose diffusion exponent decreases in time retarding subdiffusion this process may lead to superslow diffusion with the mean square displacement growing logarithmically in time we also demonstrate that the distributed order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time accelerating superdiffusion

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

a diffusion wave equation with two fractional derivatives of different order we analyse a diffusion wave equation with two fractional derivatives of different order on bounded and unbounded spatial domains thus our model represents a generalized telegraph equation solutions to signalling and cauchy problems in terms of a series and integral representation are given classical wave and heat conduction equations are obtained as limiting cases

wright functions as scale invariant solutions of the diffusion wave equation the time fractional diffusion wave equation is obtained from the classical diffusion or wave equation by replacing the first or second order time derivative by a fractional derivative of order 0 2 using the similarity method and the method of the laplace transform it is shown that the scale invariant solutions of the mixed problem of signalling type for the time fractional diffusion wave equation are given in terms of the wright function in the case 0 1 and in terms of the generalized wright function in the case 1 2 the reduced equation for the scale invariant solutions is given in terms of the caputo type modification of the

anomalous diffusion without scale invariance asymptotic behaviour of a new class of anomalous diffusion equations for subdiffusive transport defined in terms of generalized distributed fractional order time derivatives is considered the effect of slowly varying factors on the scaling function of asymptotic solutions is demonstrated the origin of slowly varying scaling factors in the ctrw models is discussed

theoretical issues on lti systems that preserve signal richness in this paper theoretical issues about linear time invariant lti systems that preserve signal richness are explored this paper considers two particular definitions of signal richness and finds the necessary and sufficient conditions under which an lti system preserves the richness property several examples are presented to clarify the issues involved in the problem paraunitary pu and unimodular matrices can be shown not to preserve richness unless they are constant matrices or a delayed version in the pu case some richness preserving properties of cascaded systems are also investigated a structured proof of the necessary and sufficient conditions is presented the relationship between persistent excitation pe and the proposed definitions of richness is also described

an alternating direction implicit galerkin finite element method for the distributed order time fractional mobile immobile equation in two dimensions abstract in this paper we shall present the alternating direction implicit adi galerkin finite element method fem for solving the distributed order time fractional mobile immobile equation in two dimensions in the time direction the backward euler method is used to deal with the temporal first order derivative and the weighted and shifted grunwald formula is employed to discretize the distributed order time fractional derivative galerkin fem is used for discretization of the spatial direction and then an adi galerkin finite element scheme is constructed the stability and l 2 norm convergence are proved several numerical experiments are provided to verify our theoretical analysis

space time fractional zener wave equation the space time fractional zener wave equation describing viscoelastic materials obeying the time fractional zener model and the space fractional strain measure is derived and analysed this model includes waves with finite speed as well as non propagating disturbances the existence and the uniqueness of the solution to the generalized cauchy problem are proved special cases are investigated and numerical examples are presented

fractional langevin equations of distributed order distributed order fractional langevin like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent it is shown that these fractional langevin equations of distributed order can be used to model the kinetics of retarding subdiffusion whose scaling exponent decreases with time and the strongly anomalous ultraslow diffusion with mean square displacement which varies asymptotically as a power of logarithm of time

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

antipodal paraunitary matrices and their application to ofdm systems paraunitary pu matrices and filterbanks have played an important role in many applications this paper studies a special class of pu matrices called antipodal paraunitary apu matrices apu matrices are pu matrices whose coefficient matrices consist of spl plusmn 1 only several new methods will be introduced for the construction of apu matrices in particular a new method based on the butterfly structure that has a low cost implementation is proposed moreover one application of apu matrices in precoded orthogonal frequency division multiplexing ofdm systems will be considered by using an apu precoding matrix the complexity will be very low and experiments show that the use of apu matrices can greatly enhance the performance

time distributed order diffusion wave equation ii applications of laplace and fourier transformations a cauchy problem for a time distributed order multi dimensional diffusion wave equation containing a forcing term is reinterpreted in the space of tempered distributions and a distributional diffusion wave equation is obtained the distributional equation is solved in the general case of weight function or distribution solutions are given in terms of solution kernels green s functions which are studied separately for two cases the first case is when the order of the fractional derivative is in the interval 0 1 while in the second case the order of the fractional derivative is in the interval 0 2 solutions of fractional diffusionwave and fractional telegraph equations are obtained as special cases numerical experiments are also performed an analogue of the maximum principle is also presented

distributed order calculus and equations of ultraslow diffusion abstract we consider equations of the form d u t x u t x f t x t 0 x r n where d is a distributed order derivative that is d t 0 1 d t d d is the caputo dzhrbashyan fractional derivative of order is a positive weight function the above equation is used in physical literature for modeling diffusion with a logarithmic growth of the mean square displacement in this work we develop a mathematical theory of such equations study the derivatives and integrals of distributed order

unified fluid flow model for pressure transient analysis in naturally fractured media naturally fractured reservoirs present special challenges for flow modeling with regards to their internal geometrical structure the shape and distribution of matrix porous blocks and the geometry of fractures play key roles in the formulation of transient interporosity flow models although these models have been formulated for several typical geometries of the fracture networks they appeared to be very dissimilar for different shapes of matrix blocks and their analysis presents many technical challenges the aim of this paper is to derive and analyze a unified approach to transient interporosity flow models for slightly compressible fluids that can be used for any matrix geometry and fracture network a unified fractional differential transient interporosity flow model is derived using asymptotic analysis for singularly perturbed problems with small parameters arising from the assumption of a much smaller permeability of the matrix blocks compared to that of the fractures this methodology allowed us to unify existing transient interporosity flow models formulated for different shapes of matrix blocks including bounded matrix blocks unbounded matrix cylinders with any orthogonal crossection and matrix slabs the model is formulated using a fractional order diffusion equation for fluid pressure that involves caputo derivative of order 1 2 with respect to time analysis of the unified fractional derivative model revealed that the surface area to volume ratio is the key parameter in the description of the flow through naturally fractured media expressions of this parameter are presented for matrix blocks of the same geometrical shape as well as combinations of different shapes with constant and random sizes numerical comparisons between the predictions of the unified model and those obtained

time distributed order diffusion wave equation i volterra type equation a single order time fractional diffusion wave equation is generalized by introducing a time distributed order fractional derivative and forcing term while a laplacian is replaced by a general linear multi dimensional spatial differential operator the obtained equation is in the case of the laplacian called a time distributed order diffusion wave equation we analyse a cauchy problem for such an equation by means of the theory of an abstract volterra equation the weight distribution occurring in the distributed order fractional derivative is specified as the sum of the dirac distributions and the existence and uniqueness of solutions to the cauchy problem and the corresponding volterra type equation were proven for a general linear spatial differential operator as well as in the special case when the operator is laplacian

multi dimensional solutions of space time fractional diffusion equations green9s functions and propagators for the multi dimensional anisotropic space time fractional diffusion equation are obtained in integral form uniqueness of the solutions is studied in the framework of abstract volterra equations unimodality of propagator functions is demonstrated in the centrally symmetric case the transition from diffusion to wave propagation is discussed numerical examples are constructed

totally blind channel identification by exploiting guard intervals blind identification techniques estimate the impulse response of a channel by exploiting known finite alphabet or statistical properties of the transmitted symbols alternatively oversampling the output is known to introduce dependencies also exploitable for channel identification this paper proves the feasibility of estimating the channel by relying instead on the short sequences of zeros known as guard intervals or zero padding introduced between transmitted blocks by a number of communication protocols since no property of the transmitted information symbols is assumed the method is called totally blind channel identification it is proved that totally blind channel identification requires only two received blocks to estimate the channel

semilinear ordinary differential equation coupled with distributed order fractional differential equation abstract the system d 2 y t z t f t y 0 2 1 d y t d 0 2 2 d z t d t 0 where d 0 2 are operators of fractional differentiation is investigated and the existence of a mild and classical solution is proven also a necessary and sufficient condition for the existence and uniqueness of a solution to a general linear fractional differential equation i 1 k a i d i z g i r i 1 k in s is given

waves in fractional zener type viscoelastic media classical wave equation is generalized for the case of viscoelastic materials obeying fractional zener model instead of hooke s law cauchy problem for such an equation is studied existence and uniqueness of the fundamental solution is proven and solution is calculated

generalized signal richness preservation problem and vandermonde form preserving matrices in this paper a theoretical problem arising in digital communications namely the generalized signal richness preservation problem is addressed and studied in order to solve the problem a special class of square matrices namely the vandermonde form preserving vfp matrices is introduced and found to be highly relevant to the problem several properties of vfp matrices are studied in detail the necessary and sufficient conditions of the problem have been found and a systematic proof is also presented

superconvergent extraction of flux intensity factors and first derivatives from finite element solutions a superconvergent method for the computation of the derivatives of the solution and the coefficients of the asymptotic expansion at singular points is presented for the laplace problem in two dimensions the algorithm utilizes the complementary weak form on a localized small domain mathematical analysis demonstrates the superconvergent behavior and numerical experiments support our analysis this method is well suited for anisotropic multi material singular interface problems