on the design of multifilter banks and orthonormal multiwavelet bases several forms of parametric expressions for orthogonal multifilter banks are presented the explicit expressions for a group of orthogonal multifilter banks that generate symmetric antisymmetric scaling functions and orthonormal multiwavelets are obtained based on these parametric expressions for orthogonal multifilter banks orthonormal multiwavelet pairs with good time frequency localization are constructed and examples of optimal multifilter banks are provided

onset of chaos in differential delay equations abstract in the present paper we study the onset of chaos in the differential delay equation x dot t x t bx t 2 1 x 10 t 2 b 0 we develop a new numerical technique and apply it to study the global behavior of the flow on the attractor using this technique we find unstable periodic orbits connections between different periodic orbits transverse homoclinic orbits and try to explain the underlying reason for chaos

unbounded perturbation of the exponential dichotomy for evolution equations abstract in this paper we prove that the exponential dichotomy for evolution equations in banach spaces is not destroyed if we perturb the equation by small unbounded linear operator this is done by employing a skew product semiflow technique and a perturbation principle from linear operator theory finally we apply these results to partial parabolic equations and functional differential equations

he s variational iteration method for treating nonlinear singular boundary value problems this paper applies he s variational iteration method for solving nonlinear singular boundary value problems the solution process is illustrated and various physically relevant results are obtained comparison of the obtained results with exact solutions shows that the method used is an effective and highly promising method for treating various classes of both linear and nonlinear singular boundary value problems

transversal homoclinic orbits and chaos for partial functional differential equations abstract the persistence of degenerate homoclinic orbit is considered for parabolic functional differential equations with small periodic perturbations bifurcation functions constructed between two finite dimensional spaces are obtained the zeros of the function correspond to the existence of the homoclinic orbit for the perturbed systems some applicable conditions are given to ensure that the functions are solvable moreover we show that the homoclinic solution for the perturbed system is transversal and hence the perturbed system exhibits chaos

b spline solution of singular boundary value problems homogeneous and non homogenous singular boundary value problems special case are solved using b splines the original differential equation is modified at singular point then the boundary value problem is treated by using b spline approximation the method is tested on some model problems from the literature and the numerical results are compared with exact solution

the application of multiwavelet filterbanks to image processing multiwavelets are a new addition to the body of wavelet theory realizable as matrix valued filterbanks leading to wavelet bases multiwavelets offer simultaneous orthogonality symmetry and short support which is not possible with scalar two channel wavelet systems after reviewing this theory we examine the use of multiwavelets in a filterbank setting for discrete time signal and image processing multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank we describe two methods repeated row and approximation deapproximation for obtaining such a vector input stream from a one dimensional 1 d signal algorithms for symmetric extension of signals at boundaries are then developed and naturally integrated with approximation based preprocessing we describe an additional algorithm for multiwavelet processing of two dimensional 2 d signals two rows at a time and develop a new family of multiwavelets the constrained pairs that is well suited to this approach this suite of novel techniques is then applied to two basic signal processing problems denoising via wavelet shrinkage and data compression after developing the approach via model problems in one dimension we apply multiwavelet processing to images frequently obtaining performance superior to the comparable scalar wavelet transform

heteroclinic bifurcation and singularly perturbed boundary value problems abstract we study a singularly perturbed boundary value problem in r m n x f x y e e y g x y e b 1 x 0 y 0 e 0 b 2 x 0 y 0 e 0 given a candidate for the 0th order approximation which exhibits both boundary layers and interior layers we present a complete procedure to compute higher order expansions and a procedure to compute the real solution near a truncated asymptotic expansion assuming the hyperbolicity of the regular layers and some generic assumptions similar results concerning the existence of periodic solutions relaxation oscillations are also presented several ideas from dynamical systems theory are employed e g exponential dichotomies fredholm alternatives and heteroclinic bifurcations

b spline method for solving linear system of second order boundary value problems the b spline method is used for the numerical solution of a linear system of second order boundary value problems two examples are considered for the numerical illustration and the method is also compared with the method proposed by j lu j lu variational iteration method for solving a nonlinear system of second order boundary value problems comput math appl 54 2007 1133 1138 the comparison shows that the b spline method is a more efficient and effective tool and yields better results

the existence of transverse homoclinic solutions for higher order equations abstract differential equations are considered which contain a small parameter when the parameter is zero the equation is autonomous with a hyperbolic equilibrium and a homoclinic solution no restriction is placed on the dimension of the phase space or the dimension of intersection of the stable and unstable manifolds sufficient conditions on the perturbation terms for producing a transverse homoclinic solution and hence chaos are obtained the technique follows the work of palmer using exponential dichotomies and the method of lyapunov schmidt

melnikov functions and heteroclinic orbits in delay differential equations let c c r 01 r e 0 co be the banach space of continuous functions 4 r 0 r with the sup norm for any continuous function z r tr and per z e c is defined by means of z 0 z t e r 8 0 the main aim of this paper is to give sufficient conditions assuring the existence of bounded solutions to perturbed delay differential equations d d e of the following type

quintic b spline collocation method for fourth order partial integro differential equations with a weakly singular kernel quintic b spline collocation method for the numerical solution of fourth order partial integro differential equations is considered the scheme is based on the second order backward differential formula in the time direction and the quintic b spline method for the spatial derivative some numerical experiments are included to demonstrate the effectiveness of the discrete technique from the numerical experiments we can find that the present scheme possesses high accuracy and efficiency and the numerical results are in good agreement with the exact solutions

exponential dichotomies and homoclinic orbits in functional differential equations abstract suppose an autonomous functional differential equation has an orbit which is homoclinic to a hyperbolic equilibrium point the purpose of this paper is to give a procedure for determining the behavior of the solutions near of a functional differential equation which is a nonautonomous periodic perturbation of the original one the procedure uses exponential dichotomies and the fredholm alternative it is also shown that any smooth function p t defined on the reals which approaches zero monotonically as t is the solution of a scalar functional differential equation and generates an orbit homoclinic to zero examples illustrating the results are also given

numerical solution of singular boundary value problems with logarithmic singularities by pade approximation and collocation methods in this paper we present a method using quintic b spline and pade approximation for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficient we use the modified quintic b spline to approximate the first coefficients in the taylor expansion on which all the other coefficients depend moreover we introduce the superposed pade approximation the resulting perturbed initial value problem is then efficiently treated

properties of bounded solutions of linear and nonlinear evolution equations homoclinics of a beam equation abstract the objective of this work is to discuss the existence bifurcation and regularity with respect to time and parameters of bounded solutions of infinite dimensional equations the authors present an application of their results to the study of homoclinic solutions of a nonlinear forced beam equation they use the approach of alternative method and semigroup theory

heteroclinic orbits for retarded functional differential equations abstract suppose is a heteroclinic orbit of a ck functional differential equation x t x i with limit set and limit set being either hyperbolic equilibrium points or periodic orbits necessary and sufficient conditions are given for the existence of an ftf close to in ck with the property that x t tf x t has a heteroclinic orbit gg close to the orbits gg are obtained from the zeros of a finite number of bifurcation functions g f r d r d 1 transversality of is characterized by the nondegeneracy of the derivative d g it is also shown that the tf which have heteroclinic orbits near are on a ck submanifold of finite codimension max 0 ind or on the closure of it where ind is the index of

traveling waves in the nonlocal kpp fisher equation different roles of the right and the left interactions abstract we consider the nonlocal kpp fisher equation u t t x u x x t x u t x 1 k u t x which describes the evolution of population density u t x with respect to time t and location x the non locality is expressed in terms of the convolution of u t with kernel k 0 r k s d s 1 the restrictions k s s 0 and k s s 0 are responsible for interactions of an individual with his left and right neighbors respectively we show that these two parts of k play quite different roles as for the existence and uniqueness of traveling fronts to the kpp fisher equation in particular if the left interaction is dominant the uniqueness of fronts can be proved while the dominance of the right interaction can induce the co existence of monotone and oscillating fronts we also present a short proof of the existence of traveling waves without assuming various technical restrictions usually imposed on k

balanced multiwavelets with interpolatory property balanced multiwavelets with interpolatory property are discussed in this paper this kind of multiwavelets can have a sampling property like shannon s sampling theorem it has been shown that the corresponding matrix valued refinable mask has special structure and an orthogonal multifilter bank h z g z can be reduced to a scalar valued conjugate quadrature filter cqf a z but it does not mean that any scalar cqf can form a good multifilter bank which can generate a vector valued refinable function with some degree of smoothness in the context of balanced multiwavelets we give the definition of transferring balance order which a scalar cqf a z satisfies to guarantee that the multiwavelet generated is balanced on the basis of the parametrization of a scalar cqf with any length and conditions of transferring balance order parametrization of multifilter banks which can generate interpolatory multiwavelet and interpolatory scaling function is gotten moreover some balanced interpolatory multiwavelets have been constructed interpolatory analysis ready multiwavelets armlets are also discussed in this paper it is known that conditions of armlets are easy to validate compared with balanced multiwavelets but it will be present that if the corresponding scaling function is interpolatory the multiwavelet is balanced of order n if and only if it is an armlet of order n finally the application of balanced multiwavelets with interpolatory property in image processing is also discussed

vector subdivision schemes and multiple wavelets we consider solutions of a system of refinement equations written in the form formula math where the vector of functions 1 r t is in l p r r and a is a finitely supported sequence of r r matrices called the refinement mask associated with the mask a is a linear operator q a defined on l p r r by q a f z a f 2 this paper is concerned with the convergence of the subdivision scheme associated with a i e the convergence of the sequence q a n f n 1 2 in the l p norm our main result characterizes the convergence of a subdivision scheme associated with the mask a in terms of the joint spectral radius of two finite matrices derived from the mask along the way properties of the joint spectral radius and its relation to the subdivision scheme are discussed in particular the l 2 convergence of the subdivision scheme is characterized in terms of the spectral radius of the transition operator restricted to a certain invariant subspace we analyze convergence of the subdivision scheme explicitly for several interesting classes of vector refinement equations finally the theory of vector subdivision schemes is used to characterize orthonormality of multiple refinable functions this leads us to construct a class of continuous orthogonal double wavelets with symmetry

approximation by translates of refinable functions the functions f 1 x dots f r x are refinable if they are combinations of the rescaled and translated functions f i 2x k this is very common in scientific computing on a regular mesh the space v 0 of approximating functions with meshwidth h 1 is a subspace of v 1 with meshwidth h 1 2 these refinable spaces have refinable basis functions the accuracy of the computations depends on p the order of approximation which is determined by the degree of polynomials 1 x dots x p 1 that lie in v 0 most refinable functions such as scaling functions in the theory of wavelets have no simple formulas the functions f i x are known only through the coefficients c k in the refinement equation scalars in the traditional case r times r matrices for multiwavelets the scalar sum rules that determine p are well known we find the conditions on the matrices c k that yield approximation of order p from v 0 these are equivalent to the strang fix conditions on the fourier transforms hat f i omega but for refinable functions they can be explicitly verified from the c k

construction for a class of interpolation multiscaling functions with dilation factor a 3 this paper is devoted to construction interpolatory multiscaling functions with a general dilation factor a 3 we first show two scale matrix symbol associated with interpolatory multiscaling functions is reduced to a special form also a characterization on approximation order for the multiscaling functions is described in terms of elements of this special two scale matrix symbol then an algorithm is provided for constructing compactly supported interpolating multiscaling functions with dilation factor a 3 and higher approximation order finally the associated several families examples with one parameter or two parameters are explicitly presented the optimal parameter values which make multiscaling functions provide the highest regularity are also computed

stability of concatenated traveling waves alternate approaches abstract we consider a reaction diffusion equation in one space dimension whose initial condition is approximately a sequence of widely separated traveling waves with increasing velocity each of which is asymptotically stable as in 14 24 25 we show that the sequence of traveling waves is itself asymptotically stable as t the solution approaches the concatenated wave pattern with different shifts of each wave allowed our proof is similar to that of 14 in that it is based on spatial dynamics laplace transform and exponential dichotomies but it incorporates a number of modifications

interpolating multiwavelet bases and the sampling theorem this paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants as discussed by xia and zhang 1993 for an orthogonal scaling function to support such a sampling theorem the scaling function must be cardinal interpolating they also showed that the only orthogonal scaling function that is both cardinal and of compact support is the haar function which is not continuous this paper addresses the same question but in the multiwavelet context where the situation is different this paper presents the construction of compactly supported orthogonal multiscaling functions that are continuously differentiable and cardinal the scaling functions thereby support a shannon like sampling theorem such wavelet bases are appealing because the initialization of the discrete wavelet transform prefiltering is the identity operator

a quartic b spline for second order singular boundary value problems second order singular boundary value problems are treated using quartic fourth degree b spline approximations the values of the coefficients c i are chosen via optimization error analysis is discussed the efficiency of the method is illustrated with several problems from the literature

cubic spline for a class of singular two point boundary value problems in this paper we have presented a method based on cubic splines for solving a class of singular two point boundary value problems the original differential equation is modified at the singular point then the boundary value problem is treated by using cubic spline approximation the tridiagonal system resulting from the spline approximation is efficiently solved by thomas algorithm some model problems are solved and the numerical results are compared with exact solution

numerical approximation of connecting orbits with asymptotic rate in this paper we set up and analyze a numerical method for so called bf connecting orbits with asymptotic rate in parameterized dynamical systems a connecting orbit with asymptotic rate has its initial value in a given submanifold of the phase space or its cross product with parameter space and it converges with an exponential rate to a given orbit e g a steady state or a periodic orbit it is well known that orbits with asymptotic rate can be used to foliate stable or strong stable manifolds of invariant sets we show that the problem of determining a connecting orbit with asymptotic rate is well posed if a certain transversality condition is made and a specific relation between the number of stable dimensions and the number of parameters holds for the proof we employ the implicit function theorem in spaces of exponentially decaying functions using asymptotic boundary conditions we truncate the original problem to a finite interval and show that the error decays exponentially typically the asymptotic boundary conditions by themselves are the result of a boundary value problem e g if the limiting orbit is periodic thus it is expensive to calculate them in a parameter dependent way during the approximation procedure to avoid this we develop a boundary corrector method which turns out to be nearly optimal after very few steps

sampling theorem and irregular sampling theorem for multiwavelet subspaces we generalize the multiwavelet sampling theorem by reproducing a kernel that is easy to use multiscaling functions that have orthogonality regularity short compact support symmetry and high approximation order satisfy the conditions in the sampling theorem which is not possible in the case of the scalar wavelet we consider the general cases of the uniform noninteger and irregular sampling a reconstruction from more general sets of points is necessary since the measurements may not be made at uniform points finally we establish a general irregular sampling theorem for multiwavelet subspaces and derive an estimate for the perturbations of uniform noninteger sampling in shift invariant spaces

generalized rankine hugoniot condition and shock solutions for quasilinear hyperbolic systems abstract for a quasilinear hyperbolic system we use the method of vanishing viscosity to construct shock solutions the solution consists of two regular regions separated by a free boundary shock we use melnikov s integral to obtain a system of differential algebraic equations that governs the motion of the shock for lax shocks in conservation laws these equations are equivalent to the rankine hugoniot condition for under compressive shocks in conservation laws or shocks in non conservation systems the melnikov type integral obtained in this paper generalizes the rankine hugoniot condition under some generic conditions we show that the initial value problem of shock solutions can be solved as a free boundary problem by the method of characteristics

multiwavelet bases with extra approximation properties this paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order because multiwavelet bases normally lack important properties that traditional wavelet bases of equal approximation order possess the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step prefiltering this paper examines the properties and design of orthogonal multiwavelet bases with approximation order 1 that possess those properties that are normally absent for these balanced bases so named by lebrun and vetterli see proc ieee int conf acoust speech signal process icassp munich germany vol 3 p 2473 76 1997 and ibid vol 46 p 1119 24 1998 prefiltering can be avoided by reorganizing the multiwavelet filter bank the development in this paper draws from results regarding the approximation order of m band wavelet bases the main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by powers of z sup 2r 1 z sup 1 1 for traditional wavelets r 1 this specializes to the usual factor z 1 sup k

asymptotic expansion for layer solutions of a singularly perturbed reaction diffusion system for a singularly perturbed n dimensional system of reactiondiffusion equations assuming that the 0th order solutions possess boundary and internal layers and are stable in each regular and singular region we construct matched asymptotic expansions for formal solutions in all the regular boundary internal and initial layers to any desired order in e the formal solution shows that there is an invariant manifold of wave front like solutions that attracts other nearby solutions we also give conditions for the wave front like solutions to converge slowly to stationary solutions on that manifold

on the relationship between exponential dichotomies and the fredholm alternative the above fredholm alternative is very important in studying homoclinic and heteroclinic solutions of nonlinear differential equations using the liapunov schmidt method this was pointed out by chow hale and mallet paret in 3 3 and since then many results appeared even in the infinite dimensional case the last ones can be found in blasquez l hale and lin s lin 7 rodrigues and silveira lo and silveira 111 2

vector valued wavelets and vector filter banks in this paper we introduce vector valued multiresolution analysis and vector valued wavelets for vector valued signal spaces we construct vector valued wavelets by using paraunitary vector filter bank theory in particular we construct vector valued meyer wavelets that are band limited we classify and construct vector valued wavelets with sampling property as an application of vector valued wavelets multiwavelets can be constructed from vector valued wavelets we show that certain linear combinations of known scalar valued wavelets may yield multiwavelets we then present discrete vector wavelet transforms for discrete time vector valued or blocked signals which can be thought of as a family of unitary vector transforms

interpolatory orthogonal multiwavelets and refinable functions multiwavelet bases of l sub 2 consist of families of functions 2 sup j 2 spl psi sub 2 2 sup j x k by allowing more than one function spl psi sub 1 spl psi sub 2 multiwavelets provide some useful applications in signal processing and nice features such as symmetry and orthogonality the elementary structure for multiwavelets is the multiresolution analysis of multiplicity two v sub j generated by dilating the basic subspace v sub 0 this subspace v sub 0 is generated by a multiple refinable function spl phi spl phi sub 1 spl phi sub 2 sup t refinable vector of functions satisfying a vector refinement equation spl phi x spl sigma a k spl phi 2x k here each a k is a 2 spl times 2 matrix in this paper we investigate interpolatory orthogonal multiple refinable functions and multiwavelets the interpolatory property here means that spl phi sub 1 and spl phi sub 2 vanish at all integers and half integers except that spl phi sub 1 0 1 and spl phi sub 2 1 2 1 when spl phi is both interpolatory and orthogonal which is impossible for scalar refinable functions the coefficients in the multiresolution representation can be realized by sampling instead of inner products if f x spl sigma c sub 1 k spl phi sub 1 2 sup n x k c sub 2 k spl phi sub 2 2 sup n x k then c sub 1 k f k 2 sup n and c sub 2 k f k 2 sup n 1 2 sup n 1 for k spl isin z what is more the orthogonal multiwavelets we construct here are also interpolatory we show that the refinement mask for an interpolatory orthogonal multiple refinable function and multiwavelets filterbank is reduced to a scalar cqf the approximation order of interpolatory multiple refinable functions is described a complete characterization of interpolatory orthogonal multiple refinable functions is given in this paper however interpolatory orthogonal multiple refinable functions cannot be symmetric examples are presented to illustrate the general theory

multiple transverse homoclinic solutions near a degenerate homoclinic orbit consider an autonomous ordinary differential equation in r n that has a homoclinic solution asymptotic to a hyperbolic equilibrium the homoclinic solution is degenerate in the sense that the linear variational equation has 2 bounded linearly independent solutions we study bifurcation of the homoclinic solution under periodic perturbations using exponential dichotomies and lyapunov schmidt reduction we obtain general conditions under which the perturbed system can have transverse homoclinic solutions and nearby periodic or chaotic solutions published by elsevier inc

generalized interpolating refinable function vectors interpolating scalar refinable functions with compact support are of interest in several applications such as sampling theory signal processing computer graphics and numerical algorithms in this paper we shall generalize the notion of interpolating scalar refinable functions to compactly supported interpolating d refinable function vectors with any multiplicity r and dilation factor d more precisely we are interested in a d refinable function vector f f 1 f r t such that f is an rx1 column vector of compactly supported continuous functions with the following interpolation property f mr k email protected email protected 1 m email protected z m 0 r 1 1 r where d 0 1 and d k 0 for k 0 now for any function f email protected c the function f can be interpolated and approximated by email protected email protected email protected email protected email protected zf 1r k f k email protected email protected z f k f 1r k f r 1r k f k since f is interpolating email protected k r f k r for all email protected z that is email protected agrees with f on r 1z moreover for r 2 or d 2 such interpolating refinable function vectors can have the additional orthogonality property r email protected d k k for all k k z and 1

exponential dichotomies heteroclinic orbits and melnikov functions the interest in the behaviour of the solutions to perturbed autonomous systems with bounded perturbative term like

b spline interpolation compared with finite difference finite element and finite volume methods which applied to two point boundary value problems abstract this paper considers the b spline interpolation and compares this method with finite difference finite element and finite volume methods which applied to the two point boundary value problem d d x p x d u d x f x a x b u a u b 0

fifth degree b spline solution for a fourth order parabolic partial differential equations in this paper we find the numerical solution of a fourth order parabolic partial differential equation a family of b spline methods has been considered for the numerical solution of the problems the results show that the present method is an applicable technique and approximates the exact solution very well

the solution of a time dependent problem by the b spline method abstract in this paper we apply the b spline method for solving the boundary value problems involving non homogeneous heat convection diffusion wave and telegraph equations the accuracy of the method for the equation is o t h 2 several examples are given to verify the reliability and efficiency of the method

new cubic b spline approximation for solving third order emden flower type equations abstract in this article the typical cubic b spline collocation method equipped with new approximations for second and third order derivatives is employed to explore the numerical solution of a class of third order non linear singular boundary value problems the singularity is removed by means of l hospital s rule the taylor s series expansion of the error term reveals that our new scheme is fifth order accurate the proposed technique is tested on several third order emden flower type equations and the numerical results are compared with those found in the current literature it is found that our new approximation technique performs superior to the existing methods due to its simple implementation straight forward interpolation and very less computational cost

the existences of transverse homoclinic solutions and chaos for parabolic equations by using lyapunov schmidt reduction and exponential dichotomies the persistence of homoclinic orbit is considered for parabolic equations with small perturbations bifurcation functions h rd 1 r r rd are obtained where d is the dimension of the intersection of the stable and unstable manifolds the zeros of h correspond to the existence of the homoclinic orbit for the perturbed systems some applicable conditions are given to ensure that the functions are solvable moreover the homoclinic solution for the perturbed system is transversal under the applicable conditions and hence the perturbed system exhibits chaos the basic tools are shadowing lemma which was obtained by blazquez see c m blazquez transverse homoclinic orbits in periodically perturbed parabolic equations nonlinear anal 10 1986 1277 1291

exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders in applications solitary wave solutions of semilinear elliptic equations u g u u 0 x y r in infinite cylinders frequently arise as travelling waves of parabolic equations as such their bifurcations are an interesting issue interpreting elliptic equations on infinite cylinders as dynamical systems inxhas proved very useful still there are major obstacles in obtaining for instance bifurcation results similar to those for ordinary differential equations in this article persistence and continuation of exponential dichotomies for linear elliptic equations is proved with this technique at hands lyapunov schmidt reduction near solitary waves can be applied as an example existence of shift dynamics near solitary waves is shown if a perturbation h x u u periodic inxis added

stability of standing waves for monostable reaction convection equations in a large bounded domain with boundary conditions abstract it is well known that the standing wave u 0 for the kpp type convection diffusion equation is stable if the perturbations of the initial data are in the weighted function spaces proposed by sattinger we study boundary conditions so that in a large finite domain there is a stable standing wave u near u 0 the standing wave u may not be monotone and the stability is proved by pseudo exponential dichotomies that are weighted both in the spatial variable and in the dual variable s to the time t

a numerical method for singular two point boundary value problems via chebyshev economizition in this paper we present a numerical method for solving a two point boundary value problem in the interval 0 1 with regular singularity at x 0 by employing the chebyshev economizition on 0 d where d is near the singularity we first replace it by a regular problem on some interval d 1 the stable central difference method is then employed to solve the problem over the reduced interval some numerical results are presented to demonstrate the applicability of the method

the m band cardinal orthogonal scaling function the m band symmetric cardinal orthogonal scaling function with compact support is of interest in several applications such as sampling theory signal processing computer graphics and numerical algorithms in this paper we provide a complete mathematical analysis for the m band symmetric cardinal orthogonal scaling function firstly we generalize some results of the cardinal orthogonal scaling function from the special case m 2 to the most general case m 2 also we find some new results secondly we obtain the characterizations of the m band symmetric cardinal orthogonal scaling function and revisit some known examples to prove our theory

spatial spread of rabies revisited influence of age dependent diffusion on nonlinear dynamics we consider the spatio temporal patterns of disease spread involving structured populations we start with a general model framework in population biology and spatial ecology where the individual s spatial movement behaviors depend on its maturation status and we show how delayed reaction diffusion equations with nonlocal interactions arise naturally we then consider the impact of this delayed nonlocal interaction on the disease spread by revisiting the spatial spread of rabies in continental europe during the period between 1945 and 1985 we show how the distinction of territorial patterns between juvenile and adult foxes the main carriers of the rabies under consideration yields a class of partial differential equations involving delayed and nonlocal terms that are implicitly defined by a hyperbolic parabolic equation and we show how incorporating this distinction into the model leads to a formula describing the relation of the minimal wave speed and the maturation time of foxes we show how the ho

on sampling theorem wavelets and wavelet transforms the classical shannon sampling theorem has resulted in many applications and generalizations from a multiresolution point of view it provides the sine scaling function in this case for a band limited signal its wavelet series transform wst coefficients below a certain resolution level can be exactly obtained from the samples with a sampling rate higher than the nyquist rate the authors study the properties of cardinal orthogonal scaling functions cosf which provide the standard sampling theorem in multiresolution spaces with scaling functions as interpolants they show that cosf with compact support have and only have one possibility which is the haar pulse they present a family of cosf with exponential decay which are generalizations of the haar function with these cosf an application is the computation of wst coefficients of a signal by the mallat 1989 algorithm they present some numerical comparisons for different scaling functions to illustrate the advantage of cosf for signals which are not in multiresolution spaces they estimate the aliasing error in the sampling theorem by using uniform samples

an explicit time integration method for structural dynamics using septuple b spline functions in this paper an explicit time integration method with three parameters is proposed for structural dynamics using periodic septuple b spline interpolation polynomial functions in this way by use of septuple bsplines the authors have proceeded to solve the de of motion governing a single dof system and later the presented method has been generalized for a multiple dof system in the proposed method a direct recursive formula for response of the system was formulated on the basis of septuple b spline interpolation approximation in terms of the specific requirements of this proposed method two initialization approaches are given for initial calculation one is called direct initialization and the other is indirect initialization the stability analysis of the proposed method illustrates that by use of adjustable parameters a highfrequency response can be damped out without inducing excessive algorithmic damping in important low frequency modes the computational accuracy and efficiency of the proposed method is demonstrated with three numerical examples and the results from the proposed method are compared with those from some of the existent numerical methods such as the newmark and wilsonmethods the compared results show that the proposed method has high accuracy with low time consumption copyright 2013 john wiley sons ltd

multiple chaos arising from single parametric perturbation of a degenerate homoclinic orbit abstract in this paper we investigate multiple existence of homoclinic solutions for a periodically perturbed n dimensional autonomous differential equation with a degenerate homoclinic solution of degeneracy degree d known results were obtained with a functional perturbation which is regarded as an infinite dimensional parameter in this paper we consider a single parameter perturbation a special form of former s functional perturbation and prove that the single parameter is enough to unfold all possibilities of linearly independent homoclinic solutions bifurcated from the unperturbed degenerate homoclinic one which actually improves the known results furthermore we prove that those homoclinic solutions are all transversal showing co existence of multiple chaotic motions

lyapunov schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies abstract this article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits in addition tangencies in the intersection of un stable manifolds are allowed the main result is a reduction to algebraic equations of the problem to find all solutions that are close to the heteroclinic network for all time and their parameter values a leading order expansion is given in terms of the time spent near vertices and if applicable the location on the non trivial tangent directions the only difference between a periodic orbit and an equilibrium is that the time parameter is discrete for a periodic orbit the essential assumptions are hyperbolicity of the vertices and transversality of parameters using the result conjugacy to shift dynamics for a generic homoclinic orbit to a periodic orbit is proven finally equilibrium to periodic orbit heteroclinic cycles of various types are considered

homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit we analyze homoclinic orbits near codimension 1 and 2 heteroclinic cycles between an equilibrium and a periodic orbit for ordinary differential equations in three or higher dimensions the main motivation for this study is a self organized periodic replication process of travelling pulses which has been observed in reaction diffusion equations we establish conditions for existence and uniqueness of countably infinite families of curve segments of 1 homoclinic orbits which accumulate at codimension 1 or 2 heteroclinic cycles the main result shows the bifurcation of a number of curves of 1 homoclinic orbits from such codimension 2 heteroclinic cycles which depends on a winding number of the transverse set of heteroclinic points in addition a leading order expansion of the associated curves in parameter space is derived its coefficients are periodic with one frequency from the imaginary part of the leading stable floquet exponents of the periodic orbit and one from the winding number

solution of fifth order boundary value problems by using local polynomial regression abstract in this paper we present a novel method based on the local polynomial regression for solving of fifth order boundary value problems the method is tested on numerical example to demonstrate its usefulness the method presented in this paper is also compared with those developed by siddiqi and akram solution of fifth order boundary value problems using nonpolynomial spline technique appl math comput 175 2006 1575 1581 as well and is observed to be better

balanced multiwavelets theory and design this article deals with multiwavelets which are a generalization of wavelets in the context of time varying filter banks and with their applications to signal processing and especially compression by their inherent structure multiwavelets are fit for processing multichannel signals this is the main issue in which we are interested first we review material on multiwavelets and their links with multifilter banks and especially time varying filter banks then we have a close look at the problems encountered when using multiwavelets in applications and we propose new solutions for the design of multiwavelets filter banks by introducing the so called balanced multiwavelets