neumann boundary value problems for a time fractional diffusion wave equation in a half plane the time fractional diffusion wave equation with the caputo derivative of the order 0 a 2 is considered in a half plane two types of neumann boundary condition are examined the mathematical condition with the prescribed boundary value of the normal derivative and the physical one with the prescribed boundary value of the matter flux

wold decomposition prediction and parameterization of stationary processes with infinite variance a discrete time stochastic process t is said to be a p stationary process 1 p 2 if e left sum limits k 1 n b k x tk h right p e left sum limits k 1 n b k x tk right p for all integers n 1 t 1 t n h and scalars b 1 b n the class of p stationary processes includes the class of second order weakly stationary stochastic processes harmonizable stable processes of order 1 2 and p thorder strictly stationary processes for any nondeterministic process in this class a finite wold decomposition moving average representation and a finite predictive decomposition autoregressive representation are given without alluding to any notion of covariance or spectrum these decompositions produce two unique interrelated sequences of scalar which are used as parameters of the process t it is shown that the finite wold and predictive decomposition are all that one needs in developing a kolmogorov wiener type prediction theory for such processes

some results in the theory of crosstalk free transmultiplexers the crosstalk free transmultiplexer cf tmux focuses on crosstalk cancellation cc rather than on suppressing it the authors present an analysis of the cf tmux based on the polyphase component matrices of the filter banks used in tdm to fdm and fdm to tdm conversions respectively thus a necessary and sufficient condition for complete cc is obtained it is shown that the filters for a cf tmux are the same as the filters for a 1 skewed alias free qmf bank in addition if the qmf bank satisfies the perfect reconstruction pr property then the tmux also satisfies pr the relation between cf tmux filters and alias free qmf banks is used to obtain a direct design procedure for cf tmux filters both fir and iir it is also shown that approximately crosstalk free tmux filters can be obtained from any approximately alias free qmc bank design examples and comparison tables are included

existence theory for anti periodic boundary value problems of fractional differential equations and inclusions this paper studies the existence of solutions for nonlinear fractional differential equations and inclusions of order email protected 3 4 with anti periodic boundary conditions in the case of inclusion problem the existence results are established for convex as well as nonconvex multivalued maps our results are based on some fixed point theorems leray schauder degree theory and nonlinear alternative of leray schauder type some illustrative examples are discussed

mathematical modeling of different types of instabilities in time fractional reaction diffusion systems abstract in this article we investigate possible scenarios of pattern formations in reaction diffusion systems with time fractional derivatives linear stability analysis is performed for different values of derivative orders results of qualitative analysis are confirmed by numerical simulations of specific partial differential equations most attention is paid to two models a fractional order reaction diffusion system with bonhoeffer van der pol kinetics and to the brusselator model

nonuniform directional filter banks with arbitrary frequency partitioning directional filter banks dfbs are highly desired in directional representation of images in this correspondence we propose a 2 d nonsubsampled nonuniform directional filter bank nudfb and its design method the proposed nudfb has nonuniform wedge shaped subbands and allows arbitrary frequency partitioning schemes it can extract directional information according to the directional distribution of images this attractive advantage cannot be achieved by the existing directional transforms the design method of the proposed nudfb is based upon the pseudopolar fourier transform by utilizing the geometry property of the pseudopolar grid we employ a 1 d nonsubsampled nonuniform filter bank to obtain a set of nonuniform wedge shaped subbands during the design process only 1 d operations are involved and thus the difficulty encountered in the design of 2 d fan filters is avoided to demonstrate the potential of the proposed nudfb an example on image directional decomposition is given

pattern formation in a fractional reaction diffusion system abstract we investigate pattern formation in a fractional reaction diffusion system by the method of computer simulation of the model of excitable media with cubic nonlinearity we are able to show structure formation in the system with time and space fractional derivatives we further compare the patterns obtained by computer simulation with those obtained by simulation of the similar system without fractional derivatives as a result we are able to show that nonlinearity plays the main role in structure formation and fractional derivative terms change the transient dynamics so when the order of time derivative increases and approaches the value of 1 5 the special structure formation switches to homogeneous oscillations in the case of space fractional derivatives the decrease of the order of these derivatives leads to more contrast dissipative structures the variational principle is used to find the approximate solution of such fractional reaction diffusion model in addition we provide a detailed analysis of the characteristic dissipative structures in the system under consideration

some boundary value problems of fractional differential equations and inclusions in this paper we study the existence of solutions for nonlinear fractional differential equations and inclusions of order q 1 2 with families of mixed and closed boundary conditions in case of inclusion problems the existence results are established for convex as well as nonconvex multivalued maps our results are based on leray schauder degree theory nonlinear alternative of leray schauder type and some fixed point theorems for multivalued maps some interesting special cases are also discussed

transition to chaos in discrete nonlinear schrodinger equation with long range interaction discrete nonlinear schrodinger dnls equation describes a chain of oscillators with nearest neighbor interactions and a specific nonlinear term we consider its modification with long range interaction through a potential proportional to 1 l1 with fractional 2 and l as a distance between oscillators this model is called dnls it exhibits competition between the nonlinearity and a level of correlation between interacting far distanced oscillators that is defined by the value of we consider transition to chaos in this system as a function of and nonlinearity it is shown that decreasing of with respect to nonlinearity stabilize the system connection of the model to the fractional generalization of the nls called fnls in the long wave approximation is also discussed and some of the results obtained for dnls can be correspondingly extended to the fnls

optimal design of nonuniform fir transmultiplexer using semi infinite programming this correspondence considers an optimum nonuniform finite impulse response fir transmultiplexer design problem subject to specifications in the frequency domain our objective is to minimize the sum of the ripple energy for all the individual filters subject to the specifications on amplitude and aliasing distortions and to the passband and stopband specifications for the individual filters this optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi infinite programming problem the dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem if the lengths of the filters are sufficiently long and the set of decimation integers is compatible then a solution exists since the problem is formulated as a convex problem if a solution exists then the solution obtained is unique and the local solution is a global minimum

generalized taylor s formula abstract in this paper a new generalized taylor s formula of the kind f x j 0 n a j x a j r n x where a j r x a 0 1 is established such an expression is precisely the classical taylor s formula in case of 1 in addition detailed expressions for r n x and a j that involving caputo fractional derivatives are well constructed some applications including approximation of functions and solutions of fractional differential equations are also given

an inner outer factorization in lp with applications to arma processes abstract the following inner outer type factorization is obtained for the sequence space l p if the complex sequence f f 0 f 1 f 2 decays geometrically then for any p sufficiently close to 2 there exist j and g in l p such that f j g j is orthogonal in the birkhoff james sense to all of its forward shifts s j s 2 j s 3 j j and f generate the same s invariant subspace of l p and g is a cyclic vector for s on l p these ideas are used to show that an arma equation with characteristic roots inside and outside of the unit circle has symmetric stable solutions in which the process and the given white noise are expressed as causal moving averages of a related i i d s s white noise an autoregressive representation of the process is similarly obtained

approximate solution of space and time fractional higher order phase field equation abstract this paper is concerned with a class of space and time fractional partial differential equation stfde with riesz derivative in space and caputo in time the proposed stfde is considered as a generalization of a sixth order partial phase field equation we describe the application of the optimal homotopy analysis method oham to obtain an approximate solution for the suggested fractional initial value problem an averaged squared residual error function is defined and used to determine the optimal convergence control parameter two numerical examples are studied considering periodic and non periodic initial conditions to justify the efficiency and the accuracy of the adopted iterative approach the dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated

anomalous diffusion with linear reaction dynamics from continuous time random walks to fractional reaction diffusion equations we have revisited the problem of anomalously diffusing species modeled at the mesoscopic level using continuous time random walks to include linear reaction dynamics if a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term if the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term we have also developed further extensions of the ctrw model to include more general reaction dynamics

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

front propagation in hyperbolic fractional reaction diffusion equations from the continuous time random walk scheme and assuming a l evy waiting time distribution typical of subdiffusive transport processes we study a hyperbolic reaction diffusion equation involving time fractional derivatives the linear speed selection of wave fronts in this equation is analyzed when the reaction diffusion dimensionless number and the fractional index satisfy a certain condition we find fronts exhibiting an unphysical behavior they travel faster in the subdiffusive than in the diffusive regime

continuous time random walks with internal dynamics and subdiffusive reaction diffusion equations humboldt university newtonstr 15 d 12489 berlin germany dated september 8 2008 we formulate the generalized master equation for a class of continuous time random walks in thepresence of a prescribed deterministic evolution between successive transitions this formulation isexempli ed by means of an advection di usion and a jump di usion scheme based on this masterequation we also derive reaction di usion equations for subdi usive chemical species using a mean eld approximation

diffusive effects on dispersion in excitable media perturbation and numerical methods are used to study traveling and standing wave solutions for a system of reaction diffusion equations modeled after excitable media and the effect of variation of the diffusion coefficients it is shown that traveling waves and standing waves can coexist and that as a certain diffusion coefficient is varied a branch of traveling waves can bifurcate from a branch of standing waves providing a transition between only traveling solutions in one limit and only standing waves in the other limit key words traveling waves standing waves bifurcation dispersion reaction diffusion equations singular perturbation

innovations and wold decompositions of stable sequences for symmetric stable sequences notions of innovation and wold decomposition are introduced characterized and their ramifications in prediction theory are discussed as the usual covariance orthogonality is inapplicable the non symmetric james orthogonality is used this leads to right and left innovations and wold decompositions which are related to regression prediction and least pth moment prediction respectively independent innovations and wold decompositions are also characterized and several examples illustrating the various decompositions are presented

mathematical modeling of time fractional reaction diffusion systems we study a fractional reaction diffusion system with two types of variables activator and inhibitor the interactions between components are modeled by cubical nonlinearity linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives it is shown that by combining the fractional derivatives index with the ratio of characteristic times it is possible to find the marginal value of the index where the oscillatory instability arises the increase of the value of fractional derivative index leads to the time periodic solutions the domains of existing periodic solutions for different parameters of the problem are obtained a computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented for the fractional reaction diffusion systems it is established that there exists a set of stable spatio temporal structures of the one dimensional system under the neumann and periodic boundary conditions the characteristic features of these solutions consist of the transformation of the steady state dissipative structures to homogeneous oscillations or space temporary structures at a certain value of fractional index and the ratio of characteristic times of system

turing pattern formation in the brusselator model with superdiffusion the effect of superdiffusion on pattern formation and pattern selection in the brusselator model is studied our linear stability analysis shows in particular that unlike the case of normal diffusion the turing instability can occur even when diffusion of the inhibitor is slower than that of the initiator a weakly nonlinear analysis yields a system of amplitude equations analysis of which predicts parameter regimes where hexagons stripes and their coexistence are expected numerical computations of the original brusselator model near the stability boundaries confirm the results of the analysis in addition further from the stability boundaries we find a regime of self replicating spots

global existence and blow up of solutions of the cauchy problem for a time fractional diffusion system abstract we prove sharp blow up and global existence results for the cauchy problem of a time fractional diffusion system when initial values u 0 0 and v 0 0 the critical exponent of this problem is determined

duality of the weak parallelogram laws on banach spaces abstract this paper explores a family of weak parallelogram laws for banach spaces some basic properties of such spaces are obtained the main result is that a banach space satisfies a lower weak parallelogram law if and only if its dual satisfies an upper weak parallelogram law and vice versa connections are established between the weak parallelogram laws and the following subspaces quotient spaces cartesian products and the rademacher type and co type properties

shift invariant subspaces with arbitrary indices in lp spaces we construct right shift invariant subspaces of index n 1 n in lp spaces 2 p and in weighted lp spaces

design of interpolative sigma delta modulators via semi infinite programming this correspondence considers the optimized design of interpolative sigma delta modulators sdms the first optimization problem is to determine the denominator coefficients the objective of the optimization problem is to minimize the passband energy of the denominator of the loop filter transfer function excluding the dc poles subject to the continuous constraint of this function defined in the frequency domain the second optimization problem is to determine the numerator coefficients in which the cost function is to minimize the stopband ripple energy of the loop filter subject to the stability condition of the noise transfer function ntf and signal transfer function stf these two optimization problems are actually quadratic semi infinite programming sip problems by employing the dual parameterization method global optimal solutions that satisfy the corresponding continuous constraints are guaranteed if the filter length is long enough the advantages of this formulation are the guarantee of the stability of the transfer functions applicability to design of rational infinite impulse response iir filters without imposing specific filter structures and the avoidance of iterative design of numerator and denominator coefficients our simulation results show that this design yields a significant improvement in the signal to noise ratio snr and have a larger stability range compared with the existing designs

stability of the static spike autosolitons in the gray scott model we performed an asymptotic linear stability analysis of the static spike autosolitons ass self sustained solitary inhomogeneous states in the gray scott model of an autocatalytic chemical reaction we found that in one dimension these ass destabilize with respect to pulsations or the onset of traveling motion when the inhibitor is slow enough in higher dimensions the one dimensional static spike ass are always unstable with respect to corrugation and wriggling the higher dimensional radially symmetric static spike ass may destabilize with respect to the radially nonsymmetric fluctuations leading to their splitting when the inhibitor is fast or with respect to pulsations when the inhibitor is slow

anti periodic fractional boundary value problems we study a class of anti periodic boundary value problems of fractional differential equations some existence and uniqueness results are obtained by applying some standard fixed point principles several examples are given to illustrate the results

variational representation of the projection dynamics and random motion of highly dissipative systems we propose the method of investigation of highly dissipative systems which are based on the approximation of the attractor by some manifold the projection dynamic equations for the general form of such manifold of the dissipative dynamic system are obtained variational principles for the projection dynamics are considered on the basis of the projection dynamic equations we investigate the influence of the random forces on the behaviour of the system

fractional diffusion equations coupled by reaction terms we investigate the behavior for a set of fractional reaction diffusion equations that extend the usual ones by the presence of spatial fractional derivatives of distributed order in the diffusive term these equations are coupled via the reaction terms which may represent reversible or irreversible processes for these equations we find exact solutions and show that the spreading of the distributions is asymptotically governed by the same the long tailed distribution furthermore we observe that the coupling introduced by reaction terms creates an interplay between different diffusive regimes leading us to a rich class of behaviors related to anomalous diffusion

on the failure of canonical factorization in lap abstract it is shown by construction that for some values of p there exists a polynomial f l a p such that f fails to factorize as f j g where j is p inner and g is analytic and nonvanishing in the open unit disk d in this situation any p inner function j vanishing at the roots of f in d with multiplicities taken into account must also vanish at some other point of d it is shown that any such extra zeros of j must lie close to the boundary of the disk

design of multichannel nonuniform transmultiplexers using general building blocks the paper considers design of multichannel nonuniform band transmultiplexers it is well known that using traditional building blocks up and downsamplers and linear time invariant lti causal filters nonuniform transmultiplexers typically do not achieve perfect reconstruction to alleviate this we propose to build nonuniform transmultiplexers using general dual rate structures that provide more design freedom and hence perfect reconstruction can be achieved such general transmultiplexers have a new source of error called aliasing distortion in addition to the traditional cross talk magnitude and phase distortions we propose a composite error criterion that captures all four distortions in one using this error criterion as reconstruction performance measure we develop an optimal design procedure and apply it to a three channel nonuniform example yielding an fir transmultiplexer that has good frequency limiting properties in the synthesis end and is very close to perfect reconstruction