some remarks on the structure of the solution set for differential inclusions in banach spaces abstract in this paper we show the general scheme of the proof the solution set of differential inclusions is r in general only if it is nonempty and compact new results are also obtained

neumann problems with time singularities in this paper we study the existence and uniqueness of solutions to a nonlinear neumann problem for a scalar second order ordinary differential equation u atu f t u u where a 0 and f t x y satisfies the local caratheodory conditions on 0 t xrxr

efficient tau p hyperbolic velocity filtering time and offset varying velocity filtering can be achieved by limiting the data input to forward tau p transforms this limiting procedure called hyperbolic velocity filtering hvf suppresses transform related artifacts as well as coherent and noncoherent noise while retaining elliptical reflection events we show that hvf can be viewed as a muting process in the slant stack domain based on this simple but physical interpretation of hvf a more efficient computer implementation is proposed we further examine possible applications of hvf for processing seismic reflection data and illustrate the results using both synthetic and real data examples

an algorithm for the numerical evaluation of the hankel and abel transforms a procedure for the efficient numerical evaluation of the hankel and abel transforms is proposed the abel transform is reduced to a convolution which is evaluated in part analytically and in part with an fft the hankel transform is obtained by following the abel transform with an fft

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

calculus of variations in mean and convex lagrangians si est l operateur symplectique standard dans r n r n si h c 2 r n r n r alors les orbites quasi periodiques du systeme hamiltonien sr z h z sont exactement les points critiques de la fonctionnelle j definie par j z 7b m z z 2 h z

a method for computing bessel function integrals abstract a method for numerical calculation of integrals containing bessel functions of integer or integer plus one half order is described the calculation involves first a one dimensional fourier sine or cosine transform followed by evaluation of the coefficient of the chebyshev series of the fourier transformed function in the case of the bessel function and evaluation of the legendre expansion coefficient in the case of the spherical bessel function a generalization of the method for the computation of an integral involving the bessel function of arbitrary real order v is presented as well

periodic solutions for coupled first order nonlinear differential systems of hamiltonian type soient f g 0 t r r r et p q 0 t r des fonctions continues donnees telles que f 0 x y f t x y g 0 x y g t x y x y er p o p t q o q t et 0 t p t dt s 0 t q t dt 0 on considere l existence des solutions periodiques pour les systemes differentiels non lineaires d ordre 1 couples de type hamiltonien x f t x y p t g t x y q t t d t x o x t g o y t 0

free boundary problems and the set valued mappings we have pointed out that many free boundary problems may be reduced to find the fixed points of certain set valued mappings and have solved the free boundary problem arising in the plasma physics 7 and the free boundary problem of the water cone in an oil reservoir with bottom water 111 as examples it is the purpose of this paper to develop the idea more extensively in this paper some typical free boundary problems such as the obstacle problem the seepage surface problem the stefan problem the elenbaas equation etc are all picked up into our scheme although most of them have been attacked by other methods there are still some new things in our approach especially the multiplicity of the solutions of the elenbaas equation is interesting we prove that there are l 1 and two distinct positive solutions of the equation

friedman versus abel equations a connection unraveled we present an interesting connection between einstein friedmann equations for the models of universe filled with scalar field and the special form of abel equation of the first kind this connection works in both ways first we show how knowing the general solution of the abel equation corresponding to the given scalar field potential one can obtain the general solution of the friedman equation and use the former for studying such problems as the existence of inflation with exit for particular models on the other hand one can invert the procedure and construct the backlund autotransformations for the abel equation

periodic solutions for damped differential equations with a weak repulsive singularity abstract this paper deals with the existence of positive t periodic solutions for the following damped differential equation x p t x q t x f t x c t where p q c l 1 r are t periodic functions and f car r r r is t periodic in the first variable we will prove that a weak repulsive singularity enables the achievement of new existence criteria through a basic application of schauder s fixed point theorem

why don t we measure seismic signatures there are three related problems with our approach to signature deconvolution first there is a confusion among geophysicists about the basis of the convolutional model itself which leads to doubts about the value of measurements of the source signature secondly it is not generally recognized that statistical methods of wavelet estimation are unreliable thirdly many explorationists are unaware that it is practical in many cases to make meaningful measurements of the source signature the convolutional model of the reflection seismogram applies only for a point source and is the convolution of the source signature with the impulse response of the earth of green s function which contains all possible arrivals including reflections refractions multiples and diffractions stabilized deconvolution of the data with a known band limited signature is straightforward the signature can be obtained by independent measurements as described in the literature the recovery of the elastic layer parameters

an algorithm for the plane wave decomposition of point source seismograms the correct formulation of the plane wave decomposition of point source seismograms involves a sequence of fourier and hankel transforms which can be evaluated in several ways the procedure which is proposed here exploits the fact that the plane wave response is bandlimited along the horizontal slowness axis this property permits to expand the hankel transform into a fourier bessel series in practice this algorithm requires an interpolation in distance of the recorded dataset but allows a considerable reduction of bessel functions calculations numerical applications performed with synthetic and real data show that the fourier bessel summation technique yields results which are equivalent to a discrete integration of the hankel transform

a slant stack procedure for point source data the proper implementation of the p method for surface data excited by a point source requires a cylindrical slant stack usually the common cartesian slant stack is computed instead as an approximation to the geometrically correct procedure here we describe a formulation of the cylindrical slant stack as a weighted sum of cartesian slant stacks our cylindrical slant stack is computationally efficient to perform we show how although the usefulness of the slant stack is most easily seen with cartesian coordinates it can also be used with fourier bessel transforms an example of the method shows results computed from data recorded on the west florida shelf severe edge effect noise which overwhelms the cartesian slant stack is attenuated by the cylindrical slant stacking applications of the cylindrical slant stack to other seismological calculations such as lamb s problem are also discussed in particular we prove that the plane wave reflection coefficients apply exactly in the p domain hence

dual algorithms for fast calculation of the fourier bessel transform this paper presents a new procedure for the fast calculation of the fourier bessel transform the computation is performed in a dual mode and involves two matched algorithms the first of which provides the lower order components while the second yields intermediate and higher order samples of the transform the first algorithm is based on the fourier selection summation fss method derived in a previous study while the second relies on the bessel function large argument asymptotic expansion it is shown that the dual procedure constructed along these lines requires a computation time which is about four times that needed by a single n point fast fourier transform

conley type index applied to hamiltonian inclusions in the paper we develop the theory of a cohomological index of the conley type detecting invariant sets of a multivalued dynamical system generated by semilinear differential inclusion in an infinite dimensional hilbert space an application to the existence of periodic orbits to asymptotically linear hamiltonian inclusions is presented

functional calculus for semigroup generators via transference abstract in this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators in particular it is proved that if a generates a c 0 semigroup on a hilbert space then for each 0 the operator a has a bounded calculus for the closed ideal of bounded holomorphic functions on a sufficiently large right half plane that satisfy f z o e re z as z the bound of this calculus grows at most logarithmically as 0 as a consequence f a is a bounded operator for each holomorphic function f on a right half plane with polynomial decay at then we show that each semigroup generator has a so called strong m bounded calculus for all m n and that this property characterizes semigroup generators similar results are obtained if the underlying banach space is a umd space upon restriction to so called bounded semigroups the hilbert space results actually hold in general banach spaces

periodic solutions for second order differential equations with discontinuous restoring forces we deal with the existence of periodic solutions for problems with a jump discontinuity we use an approximation procedure and the method of the lower and upper solutions

an algorithm for computing general integer order hankel transforms a tomographic image reconstruction algorithm that we have been studying requires the nth order hankel transform for the nth function in a series where n varies over a set of integers unfortunately most previously proposed algorithms have either dealt with only zeroth order transforms or cannot be applied conveniently to our problem we propose an algorithm for computing general integer order hankel transforms the algorithm takes samples of equally spaced input functions and gives equally spaced samples of the transforms

source wavelet and its angular spectrum from plane wave seismograms in a typical seismic experiment land or marine the generated source wavelet is either unknown or known only approximately in order to solve many geophysical problems an accurate wavelet estimation is crucial this paper demonstrates a fast numerical algorithm which allows not only estimating the source wavelet but also its angular spectrum radiation pattern from plane wave decomposed seismograms surprisingly literature on this subject is virtually missing although a nonuniform angular spectrum of the generated wavelet can substantially affect the recorded data the technique presented here is based on the downward continuation dc and reverse time extrapolation rte of the recorded data both pressure and its vertical derivative the proposed method is iterative the rate of convergence does not depend on phase characteristics of the generated wavelet we demonstrate that both the wavelet signature and its angular spectrum can be estimated accurately from plane wave seismograms we also illu

a kalman filtering approach to stochastic global and region of interest tomography we define two forms of stochastic tomography in global tomography the goal is to reconstruct an object from noisy observations of all of its projections in region of interest roi tomography the goal is to reconstruct a small portion of an object an roi from noisy observations of its projections densely sampled in and near the roi and sparsely sampled away from the roi we solve both problems by expanding the object and its projections in a circular harmonic fourier series in the angular variable so that the radon transform becomes abel transforms of integer orders applied to the harmonics the algorithm has three major components first we fit state space models to each order of abel transform and thus represent the radon transform operation as a parallel bank of systems each of which computes the appropriate abel transform of a circular harmonic a variable transformation here allows either the global or roi problem to be solved second the object harmonics are modeled as a brownian branch this is a two point boundary value system which is markovianized into a form suitable for the kalman filter finally a parallel bank of kalman smoothing filters independently estimates each circular harmonic from the noisy projection data numerical examples illustrate the proposed procedure

algorithms to numerically evaluate the hankel transform abstract the efficient and accurate evaluation of the hankel transform is required in a number of applications this paper reviews a number of algorithms that have only recently been exposed in the literature results of a comparative study of some useful algorithms are presented it is found that the performance of all algorithms depends on the type of function to be transformed the projection based methods provide acceptable accuracy with better efficiency than numerical quadrature

fast hankel transform algorithm the hankel or fourier bessel transform is an important computational tool for optics acoustics and geophysics it may be computed by a combination of an abel transform which maps an axisymmetric two dimensional function into a line integral projection and a one dimensional fourier transform this paper presents a hankel transform algorithm using a fast linear time abel transform followed by an fft

nonlinear seismic trace interpolation the nonlinear correlation technique has been used to guide a seismic trace interpolant to fill gaps in seismic surveys replace noisy traces and produce evenly spaced arrays given an initial alignment nm0 correction for prestack data and manually inserted correlation lines for post stack data the correlation aligns corresponding features between adjacent seismic traces and quantifies the traveltime difference between the traces on a point for point basis this information is used to construct synthetic interpolated traces at any arbitrary distance between the correlated traces which preserve dip and amplitude changes of the individual reflectors assuming that such dip and amplitude changes occur linearly or some other specified functional form between the correlated traces the technique is applied to a 48 channel nm0 corrected cdp gather and to a stacked seismic section to demonstrate its use sensitivities and limitations in processing and geologic interpretation studies traces synthesized in the cdp gather filling an artificial gap 0 85 km wide reproduce the true traces from the gap with good fidelity correlation coefficients between the synthetic and real traces average 0 85 in another example 85 percent of the variance of the original 48 channel cdp gather is recovered through interpolation by using only 16 channels a stacked section with true trace spacing of 25 m was decimated to 100 m trace spacing then interpolated to restore the original 25 m spacing the interpolated traces reproduce the real traces with correlations of 0 95 thus recovering 90 percent of the variance of the original section

a differential semblance algorithm for the inverse problem of reflection seismology abstract this paper presents an analysis of stability and convergence for a special case of differential semblance optimization dso this approach to model estimation for reflection seismology is a variant of the output least squares inversion of seismograms enjoying analytical and numerical properties superior to those of more straightforward versions we study a specialization of dso appropriate to the inversion of convolutional approximation planewave seismograms over layered constant density acoustic media we prove that the differential semblance variational principle is locally convex in suitable model classes for a range of data noise moreover the structure of the convexity estimates suggest a family of quasi newton algorithms we describe an implementation of one of these algorithms and present some numerical results

one dimensional quaternion homogeneous polynomial differential equations in this paper we study the dynamics of real four dimensional polynomial differential equations of the forms q aqkq m or q qkaqm where q a are quaternions q is the conjugate of q and k and m are non negative integers in many parts of the work the quaternion structure is used along the proofs

a dual algorithm for the calculation of the h 1 0 transform abstract an integral transform which involves the zeroth order hankel function of the first kind h 0 1 is commonly encountered in wave analysis and with particular reference to studies of underwater sound seismology and electromagnetic phenomena this paper presents new methods for the numerical estimation of this transform based on the dual procedure concept the computation involves two matched algorithms the first of which provides the lower order components while the second yields intermediate and higher order estimates of the transform it is shown that a procedure constructed along these lines generates accurate transform samples and requires a computation time of the order of that of a few fast fourier transform operations

periodic solutions of abel equations with jumps abstract we study for given t 0 the abel like equation f 0 j 1 m f j j k 1 n a k j k where each f j 0 t r j 0 m is a t periodic function of bounded variation and each term a k j k k 1 n is a jump in of state dependent amplitude a k at state dependent instant k 0 t under appropriate conditions the equation is shown to admit an absolutely continuous t periodic solution with derivative of bounded variation having preassigned jumps a k j k by the contraction principle a bound is obtained for the rate of point wise convergence to the solution of a sequence of picard iterates an algorithm to calculate iterated convolutions is developed and applied to a riccati equation and to an abel equation from cosmology

symmetry properties and solutions of nonlinear dispersive thin film equations in three dimensions the lie point symmetries are obtained for each one of two nonlinear dispersive thin film equations in 2 1 variables by means of the invariants of the one and two dimensional subgroups all reductions to ordinary differential equations and to partial differential equations in two variables are obtained solutions are provided for a number of the reduced equations it is also ascertained that neither one of the two considered thin film equations is integrable in some cases solitary and periodic wave solutions having curved wavecrests are obtained

bounded and almost periodic solutions of convex lagrangian systems abstract we study some properties of bounded and almost periodic solutions of convex lagrangian systems in the presence of almost periodic forcing d dt x l t x t x t x l t x t x t then we establish a result of existence and uniqueness of the almost periodic solution

dynamics in coupled oscillators with recurrent random forcing a pde approach the current paper is devoted to the study of coupled oscillators with recurrent random forcing special attention is given to the solutions having the same recurrence randomness as that of the forcing recurrent random solutions for short by embedding coupled oscillators into coupled parabolic equations it establishes a general theorem on the existence of recurrent random solutions it also finds conditions under which such solutions are unique when the recurrent forcing is actually quasi periodic or almost periodic recurrent solutions are refereed to as quasi periodic or almost periodic solutions in a weak sense and they are quasi periodic or almost periodic in the classical sense under the uniqueness conditions in addition applications of the general theory to coupled duffing type oscillators and josephson junctions are considered and the results obtained extend several existing ones for quasi periodic duffing oscillators

on the periodic dynamics of memristor based neural networks with time varying delays abstract in this paper we study the existence uniqueness and stability of periodic solution for a wide class of memristor based neural networks with time varying delays by employing the topological degree theory in set valued analysis differential inclusions theory and a new lyapunov function method we prove that the neural network has a unique periodic solution which is globally exponentially stable moreover we prove the existence uniqueness and global exponential stability of equilibrium point for time varying delayed memristor based neural networks with constant coefficients the obtained results improve and extend previous works on memristor based or usual neural network dynamical systems with continuous or discontinuous right hand side finally two numerical examples are provided to show the applicability and effectiveness of our main results

comparison of plane wave decomposition and slant stacking of point source seismic data the plane wave decomposition and slant stacking of point source seismic data are not identical processes they are however related we have found that the algorithm for slant stacking can be used for plane wave decomposition if we apply a weighting function depending on frequency and offset and including a pi 4 phase shift before slant stacking and a p dependent correction after the slant stacking this procedure requires only a small extra effort to incorporate the geometrical spreading and phase shift not accounted for by the slant stacking in this process we use the asymptotic approximation for the zeroth order bessel function this approximation reduces the number of computations significantly but it is valid only for omega px greater than 2 or 3 using this approximation we have been able to obtain the correct plane wave decomposition of expanding spread profile data for ray parameters as low as 0 03 s km for smaller p the exact bessel function should be used we have performed model studies to compare plane wave decomposition and slant stacking using a possible velocity model for the north atlantic transect nat expanding spread profile esp 5 we computed synthetic seismograms at a 50 m spacing using the reflectivity method and then computed the plane wave decomposition and slant stacks of these seismograms on comparing these with the exact tau p seismograms for this model we found that the waveforms the frequency content and the amplitudes were exactly reproduced in the plane wave decomposition but were significantly different in the slant stacks we also computed the plane wave decomposition and slant stacks of real data nat esp 5 the results in this case show that the amplitudes of deep crustal arrivals in plane wave decomposition are higher than in slant stacks and therefore these arrivals can be identified much better in the plane wave decomposition

locally lipschitzian guiding function method for odes by generalizing the well known guiding function method such an approach can be found in several works however under some heavier assumptions for example in m f is assumed to be locally lipschitzian and the guiding function to be c in gp f needs to be of the caratheodory type only while the corresponding guiding function must be still c in fact in gp the more general multivalued problem x t t x t x 0 x t 1

handbook of differential equations chapter headings definitions and concepts transformations exact analytical methods exact methods for odes exact methods for pdes approximate analytical methods numerical methods concepts numerical methods for odes numerical methods for pdes list of tables list of programs list of figures subject index

multiple solutions for nonlocal system of p x q x kirchhoff type abstract in this paper we study the existence of solutions for a neumann elliptic system with variable exponents under some suitable conditions and by applying an equivalent variational approach to a recent ricceri s three critical points theorem we established the existence of at least three weak solutions

a hybrid fast hankel transform algorithm for electromagnetic modeling a hybrid fast hankel transform algorithm has been developed that uses several complementary features of two existing algorithms anderson s digital filtering or fast hankel transform fht algorithm and chave s quadrature and continued fraction algorithm a hybrid fht subprogram called hybfht written in standard fortran 77 provides a simple user interface to call either subalgorithm the hybrid approach is an attempt to combine the best features of the two subalgorithms in order to minimize the user s coding requirements and to provide fast execution and good accuracy for a large class of electromagnetic problems involving various related hankel transform sets with multiple arguments special cases of hankel transforms of double order and double argument are discussed where use of hybfht is shown to be advantageous for oscillatory kernel functions

stable plane wave decomposition and spherical wave reconstruction applications to converted s mode separation and trace interpolation plane wave decomposition of the vertical displacement component of a spherical wave field corresponding to a compressional point source is solved as a set of inverse problems the solution method utilizes the power and stability of backus and gilbert smallest and flattest model construction techniques and achieves computational efficiency through the use of analytical solutions to the involved integrals the theory and algorithms developed in this work allow stable and efficient reconstruction of spherical wave fields from a relatively sparse set of their plane wave components comparison of the algorithms with discrete integration of the hankel transform shows very little or no advantage for the transformation from the time distance t x domain to the intercept time angle of emergence tau gamma domain if the seismograms are equisampled spatially however when the observed seismograms are not equally spaced or the transformation tau gamma to t x is performed the proposed schemes are superior to the discrete integration of the hankel transform applicability of the algorithms to reflection seismology is demonstrated by means of the solution of the problem of trace interpolation and also that of the separation of converted s modes from other modes presented in common source gathers in both cases the application of the algorithms to a set of synthetic reflection seismograms yields satisfactory results

a boundary element numerical scheme for the two dimensional convection diffusion equation in this study the theoretical and numerical fundamentals of biem techniques for the two dimensional convection diffusion problem are presented after an extended presentation of the basic integral formulation the discretizing and iterative processes for its resolution are introduced interesting remarks on general expressions versus previously published particularized results are worth mentioning a numerical solution scheme is provided which has been completely developed and designed to the physical problem posed a novel scheme based in the simultaneous solving of the potential and the gradient of the potential boundary integral equations is included a diversity of problems is tested to prove the possibilities of the method copyright 2008 john wiley sons ltd

on an instability exhibited by the ballistic diffusive heat conduction model of xu and hu we show that the constitutive relation for the thermal flux proposed by xu hu 2011 admits an unconditional instability we also highlight the difference between mathematical models containing delay and those that include relaxation effects

periodic solutions to hamiltonian inclusions abstract we prove the existence of periodic trajectories of hamiltonian inclusions which reduce to the usual hamiltonian equations in the presence of smoothness this is accomplished via a direct variational principle involving a new action integral in an extended sense

an efficient maximum entropy technique for 2 d isotropic random fields a linear mem maximum entropy spectral estimation method algorithm for 2 d isotropic random fields is introduced unlike general 2 d covariances isotropic covariance functions that are positive definite on a disk are known to be extendible a computationally efficient procedure is developed for computing the mem isotropic covariance function that is given over a finite disk of radius 2r it is shown that the isotropic mem problem has a linear solution and that it is equivalent to the problem of constructing the optimal linear filter for estimating the underlying isotropic field at a point on the boundary of a disk radius r given noisy measurements of the field inside the disk the procedure is guaranteed to yield a valid isotropic spectral estimate and is computationally efficient since it requires only o brl sup 2 operations where l is the number of points used to discretize the interval 0 r and b is the bandwidth in the wave number plane of the spectrum that to be estimated examples are presented to illustrate the behaviour of the algorithm and its high resolution property

fast nth order hankel transform algorithm an nth order hankel transform also called fourier bessel transform algorithm designed for many analytically defined functions is presented this algorithm is not restricted to order zero as such it provides greater generality than many others the traditional difficulty in the evaluation of hankel transforms the presence of bessel functions in the kernel of the integral transform is eliminated in this new hankel transform algorithm the algorithm presented is composed of a fast linear time nth order chebyshev transform followed by a fast fourier transform