the structure and analysis of spherical time dependent processes the class of all spherical processes is investigated irrespective of moments properties of these processes are studied including their structure representations and linear and nonlinear spaces a basic representation is x t a 1 2 y t t in t where ais nonnegative and y t is gaussian time series analysesnot requiring moments are set forth in both the time and frequency domains including spectral analysis solutions of forecasting problems are found to be linear when the process is spherical with the property that errors of the optimal forecasts are stochasticalay most concentrated about zero these developments apply to the alpha sub gaussian processes and are advanced for use with certain heavy tailed processes arising in economics engineering and the physical sciences

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

the differentiation matrix for daubechies based wavelets on an interval the differentiation matrix for a daubechies based wavelet basis defined on an interval is constructed it is shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions

a high order discontinuous galerkin method for wave propagation through coupled elastic acoustic media we introduce a high order discontinuous galerkin dg scheme for the numerical solution of three dimensional 3d wave propagation problems in coupled elastic acoustic media a velocity strain formulation is used which allows for the solution of the acoustic and elastic wave equations within the same unified framework careful attention is directed at the derivation of a numerical flux that preserves high order accuracy in the presence of material discontinuities including elastic acoustic interfaces explicit expressions for the 3d upwind numerical flux derived as an exact solution for the relevant riemann problem are provided the method supports h non conforming meshes which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength as well as dynamic adaptivity to track solution features the use of high order elements controls numerical dispersion enabling propagation over many wave periods we prove consistency and stability of the proposed dg scheme to study the numerical accuracy and convergence of the proposed method we compare against analytical solutions for wave propagation problems with interfaces including rayleigh lamb scholte and stoneley waves as well as plane waves impinging on an elastic acoustic interface spectral rates of convergence are demonstrated for these problems which include a non conforming mesh case finally we present scalability results for a parallel implementation of the proposed high order dg scheme for large scale seismic wave propagation in a simplified earth model demonstrating high parallel efficiency for strong scaling to the full size of the jaguar cray xt5 supercomputer

structural induction in institutions abstract we develop a general logic independent structural induction proof method at the level of abstract institutions this provides a solid and uniform mathematical foundation to induction proof methodologies for a wide variety of actual logic based formal specification frameworks our development is based technically upon an axiomatic approach to substitutions within institution theory

ultraproducts and possible worlds semantics in institutions we develop possible worlds kripke semantics at the categorical abstract model theoretic level provided by the so called institutions our general abstract modal logic framework provides a method for systematic kripke semantics extensions of logical systems from computing science and logic we also extend the institution independent method of ultraproducts of r diaconescu institution independent ultraproducts fundamenta informaticae 55 3 4 2003 321 348 to possible worlds semantics and prove a fundamental preservation result for abstract modal satisfaction as a consequence we develop a generic compactness result for possible worlds semantics

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

non conforming curved finite element schemes for time dependent elastic acoustic coupled problems high order numerical methods for solving time dependent acoustic elastic coupled problems are introduced these methods based on finite element techniques allow for a flexible coupling between the fluid and the solid domain by using non conforming meshes and curved elements since characteristic waves travel at different speeds through different media specific levels of granularity for the mesh discretization are required on each domain making impractical a possible conforming coupling in between advantageously physical domains may be independently discretized in our framework due to the non conforming feature consequently an important increase in computational efficiency may be achieved compared to other implementations based on conforming techniques namely by reducing the total number of degrees of freedom differently from other non conforming approaches proposed so far our technique is relatively simpler and requires only a geometrical adjustment at the coupling interface at a preprocessing stage so that no extra computations are necessary during the time evolution of the simulation on the other hand as an advantage of using curvilinear elements the geometry of the coupling interface between the two media of interest is faithfully represented up to the order of the scheme used in other words higher order schemes are in consonance with higher order approximations of the geometry concerning the time discretization we analyze both explicit and implicit schemes these schemes are energy conserving and for the explicit case the stability is guaranteed by a cfl condition in order to illustrate the accuracy and convergence of these methods a set of representative numerical tests are presented

observational logic constructor based logic and their duality observability and reachability are important concepts for formal software development while observability concepts are used to specify the required observable behavior of a program or system reachability concepts are used to describe the underlying data in terms of datatype constructors in this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability then we develop in a completely analogous way the constructor based logic institution which formalizes a novel treatment of reachability both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view we show that there is a methodological and even formal duality between both frameworks in particular we establish a correspondence between observer operations and datatype constructors observational and constructor based algebras fully abstract and reachable algebras and observational and inductive consequences of specifications the formal duality between the observability and reachability concepts is established in a category theoretic setting

absorbing boundary conditions for elastic media a class of new absorbing boundary conditions for numerical modelling of two dimensional linear time dependent elasticity is introduced many existing absorbing boundary conditions are included as special cases the mechanism used to formulate these new conditions is the complete absorption at a certain number of prescribed incidence angles successful applications to finite difference models of elastic wave scattering from defect like features in solids are presented

a perfectly matched layer for fluid solid problems application to ocean acoustics simulations with solid ocean bottoms a time domain legendre spectral element method is described for full wave simulation of ocean acoustics models i e coupled fluid solid problems in unbounded or semi infinite domains taking into account shear wave propagation in the ocean bottom the technique can accommodate range dependent and depth dependent wave speed and density as well as steep ocean floor topography for truncation of the infinite domain to efficiently absorb outgoing waves a fluid solid complex frequency shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique the complex stretching is rigorously taken into account in the derivation of the fluid solid matching condition inside the absorbing layer which has never been done before in the time domain two implementations are designed a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high order time schemes leading to reduced numerical dispersion and dissipation a topic of importance in particular in long range ocean acoustics simulations the method is validated for a two dimensional fluid solid pekeris waveguide and for a three dimensional seamount model which shows that the technique is accurate and numerically long time stable compared with widely used paraxial absorbing boundary conditions the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves

accurate and efficient seismic modeling in random media the optimum method for seismic modeling in random media must 1 be highly accurate to be sensitive to subtle effects of wave propagation 2 allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths this is necessary to obtain statistically meaningful overall attributes of wavefields high order staggered grid finite difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling investigations for random media reveal that both methods lead to nearly identical wavefields the small differences can be attributed mainly to differences in the numerical dispersion this result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous the differentiator can be longer than the medium scale leng

on minimality and interpolation of harmonizable stable processes it is shown that a harmonizable symmetric alpha stable process i e the fourier coefficients of a process with independent symmetric alpha stable increments with spectral density w is minimal if and only if w 0 a e and w 1 alpha 1 in l 1 algorithms for the linear interpolator and interpolation error of such processes are given when several values of the process are missing the algorithm for the linear interpolator is convergent if w satisfies muckenhoupt s a alpha condition

linearized acoustic perturbation equations for low mach number flow with variable density and temperature when the mach number tends to zero the compressible navier stokes equations converge to the incompressible navier stokes equations under the restrictions of constant density constant temperature and no compression from the boundary this is a singular limit in which the pressure of the compressible equations converges at leading order to a constant thermodynamic background pressure while a hydrodynamic pressure term appears in the incompressible equations as a lagrangian multiplier to establish the divergence free condition for the velocity in this paper we consider the more general case in which variable density variable temperature and heat transfer are present while the mach number is small we discuss first the limit equations for this case when the mach number tends to zero the introduction of a pressure splitting into a thermodynamic and a hydrodynamic part allows the extension of numerical methods to the zero mach number equations in these non standard situations the solution of these equations is then used as the state of expansion extending the expansion about incompressible flow proposed by hardin and pope j c hardin d s pope an acoustic viscous splitting technique for computational aeroacoustics theor comput fluid dyn 6 1995 323 340 the resulting linearized equations state a mathematical model for the generation and propagation of acoustic waves in this more general low mach number regime and may be used within a hybrid aeroacoustic approach

prediction of stable processes spectral and moving average representations for stable processes which are fourier transforms of processes with independent increments we obtain a wold decomposition we characterize their regularity and singularity and in the discrete parameter case we derive their linear predictors in sharp contrast with the gaussian case regular stable processes which are fourier transforms of processes with independent increments are not moving averages of stable motion

relating casl with other specification languages the institution level in this work we investigate various specification languages and their relation to casl the recently developed common algebraic specification language in particular we consider the languages larch obj3 and functional cafeobj act one asf and hep theories as well as various sublanguages of casl all these languages are translated to an appropriate sublanguage of casl the translation mainly concerns the level of specification in the small the logics underlying the languages are formalized as institutions and representations among the institutions are developed however it is also considered how these translations interact with specification in the large thus we obtain on the one hand translations of any of the above mentioned specification languages to an appropriate sublanguage of casl this allows us to take libraries and case studies that have been developed for other languages and re use them in casl on the other hand we set up institution representations going from the casl institution and some of its subinstitutions to simpler subinstitutions given a theorem proving tool for such a simpler subinstitution with the help of a representation it can also be used for a more complex institution thus first order theorem provers and conditional term rewriting tools become usable for casl

computation of flow noise using source terms in linearized euler s equations an acoustic analogy using linearized euler s equations lee forced with aerodynamic source terms is investigated to computetheacousticfare eld thishybridmethod isappliedto threemodelproblemssimulatedby solving navier stokes equations in this way its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the navier stokes equations the noise radiated by two corotating vortices is studied e rst in a medium at rest and second in a mean sheared e ow with no convection velocity then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated in this case a simplie ed formulation of lee is proposed to prevent the exponential growth of instability waves the acoustic e elds obtained by solving lee are in good agreement with the reference solution this study shows that the source terms introduced into the lee are appropriate for free sheared e ows and that acoustic mean e ow interactions are properly taken into account in the wave operator nomenclature b half width of the monopolar source c sound velocity e f h vectors in linearized euler s equations lee f frequency f0 fundamental frequency of the mixing layer k complex wave number kr ciki m mach number p pressure re reynolds number rc vortex core radius r0 initial half distance between the two vortices s sound source vector in lee si source terms in the momentum equations t period tij lighthill s tensor t time u unknown vector in lee u1 slow stream velocity of the mixing layer u2 rapid stream velocity of the mixing layer u velocity vector u1 u2 v initial tangential velocity of vortices

an optimal nearly analytic discrete weighted runge kutta discontinuous galerkin hybrid method for acoustic wavefield modeling abstractthe newly developed optimal nearly analytic discrete onad and the weighted runge kutta discontinuous galerkin wrkdg methods can effectively suppress the numerical dispersion caused by discretizing wave equations but it is difficult for onad to implement on flexible meshes whereas the wrkdg has high computational cost for wavefield simulations we have developed a new hybrid algorithm by combining the onad method with the wrkdg method in this hybrid algorithm the computational domain was split into several subdomains in which the subdomain for the onad method used regular cartesian grids whereas the subdomain for the wrkdg method used triangular grids the hybrid method was at least third order spatially accurate we have applied the proposed method to simulate the scalar wavefields for different models including a homogeneous model a rough topography model a fracture model and a cave model the numerical results found that the hybrid method can deal with complicated geometrical struc

some fundamental algebraic tools for the semantics of computation part 3 indexed categories abstract this paper presents indexed categories which model uniformly defined families of categories and suggests that they are a useful tool for the working computer scientist an indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms similarly an indexed functor which is a uniform family of functors between the components categories induces a flattened functor between the corresponding flattened categories under certain assumptions flattened categories are co complete if all their components are and flattened functors have left adjoints if all their components do several examples are given although this paper is part 3 of the series some fundamental algebraic tools for the semantics of computation it is entirely independent of parts 1 and 2

linear problems in linear problems in pth order and stable processes this work extends to processes with finite moments of order p 1 p 2 and to symmetric alpha stable processes 1 alpha 2 some of the basic linear theory known for processes with finite second moments p 2 and for gaussian processes alpha 2 here the covariation plays a role analogous to the covariance specifically stochastic integrals of two types are introduced and studied for pth order processes and in particular for symmetric stable processes regression estimates and linear estimates on certain symmetric stable processes are evaluated including regression and linear filtering of signal in noise also for certain symmetric stable inputs the identification of a linear system from the input covariation and the input output cross covariation is considered and the way the distribution of the output depends on the linear system is studied

harmonizable stable processes this paper examines properties of a class of complex valued stable processes which have spectral representation by means of independent increments processes a representation is derived by an application of schilder s stochastic integral also another construction of harmonizable stable processes by means of generalized stochastic processes is given and its relation to the stochastic integral is shown some limit theorems of the fourier transform of a sample from harmonizable stable processes are provided moreover a linear prediction theory which pertains to those processes is suggested as an extension of that of second order stationary processes

solving elastodynamics in a fluid solid heterogeneous sphere a parallel spectral element approximation on non conforming grids we present a spectral element approach for modeling elastic wave propagation in a solid fluid sphere where the local effects of gravity are taken into account the equations are discretized in terms of the displacement in the solid and the velocity potential in a neutrally stratified fluid the spatial approximation is based upon a spherical mesh of hexahedra in which local refinement allows for adapting the discretization to the variation of elastic parameters in both the solid and the fluid regions continuity constraints across the non conforming interfaces are introduced through lagrange multipliers which are further discretized by the mortar element method due to the spherical nature of the non conforming interfaces the mortar method turns out to be functionally conforming and allows for an equal order interpolation of the primal variables and the lagrange multipliers the method is shown to provide an accurate solution when compared to analytical calculations obtained for radial models of elastic parameters its parallel implementation is based upon a simple domain decomposition strategy which makes it efficient to solve large problems as those imposed by planetary scales

on some extremal problems in h p and the prediction ofl p harmonizable stochastic processes we providesimple andsuccinct solutions to two dual extremal problems in the hardy spacesh p and to an aspect of the linear prediction problem for a certain class of discrete and continuous parameter l p harmonizable stochastic processes for all 1 p two of the results presented appear new the methods of proof of the rest of the results provide alternatesimpler andshorter proofs for some earlier known theorems

a numerical homogenization method for heterogeneous anisotropic elastic media based on multiscale theory the development of reliable methods for upscaling finescale models of elastic media has long been an important topic for rock physics and applied seismology several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures in such cases the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation however such theories cannot be applied directly to homogenize elastic media with more complex arbitrary spatial heterogeneity therefore we have proposed a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous anisotropic elastic media specifically our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions homogenized effective medium parameters were then computed using these basis functions and the approach applied a numerical discretization that was similar to the rotated staggered grid finite difference scheme comparisons of the results from our method and from conventional analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry additional tests examined anisotropic models with arbitrary spatial heterogeneity in which the average size of the heterogeneities ranged from several centimeters to several meters and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100 comparisons to finite difference simulations proved that the numerical homogenization was equally accurate for these complex cases

alpha stable signals and adaptive filtering let d sub k x sub k be jointly stationary symmetric spl alpha stable processes with index 1 spl alpha 2 we first consider the problem of optimal fir linear and regression filters we then consider the signed error and sign sign adaptive filtering algorithms for the estimation of the desired signal d sub j on the basis of the input vector x sub j various convergence results are established for the signal and tap weights estimation errors

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

wave extrapolation in the spatial wavelet domain with application to poststack reverse time migration a wavelet transformation is performed over each of the spatial coordinates of the scalar wave equation this transformed equation is solved directly with a finite difference scheme for both homogeneous and smooth inhomogeneous media wavefield extrapolation is performed completely in the spatial wavelet domain without transforming back into the space domain at each time step the wavelet coefficients are extrapolated rather than the wavefield itself the numerical solution of the scalar wave equation in the spatial wavelet domain is closely related to the finite difference method because of the compact support of the wavelet bases poststack reverse time migration is implemented as an application the resolution spaces of the wavelet transform provide a natural framework for multigrid analysis migrated images are constructed from various resolution spaces

elastic modeling in discontinuous media results from elastic wave simulations in a simple model show that for models characterized by a set of layers with sharp boundaries discontinuous stiffness tensor traditional finite difference methods fail to correctly describe the dynamics of the propagation process the failure comes from the lack of distinction between model and field variables the same differential operator is applied to discontinuous model and continuous wavefield components this problem is solved with a modified high order finite difference modeling scheme dual operator method that uses two distinct operators for evaluating the model and field derivatives a modified version of virieux staggered grid and shoenberg muir averaging relations the dual operator method generates a dynamic response that is more accurate than traditional finite difference schemes and comparable to haskell thomson propagator matrix schemes with the advantage that it can be applied to structurally complex models the method produces stable accurate results for both solid and liquid layers

numerical simulation of interface waves by high order spectral modeling techniques few problems in elastodynamics have a closed form analytical solution the others can be investigated with semianalytical methods but in general one is not sure whether these methods give reliable solutions the same happens with numerical techniques for instance finite difference methods solve in principle any complex problem including those with arbitrary inhomogeneities and boundary conditions however there is no way to verify the quantitative correctness of the solutions the major problems are stability with respect to material properties numerical dispersion and the treatment of boundary conditions in practice these problems may produce inaccurate solutions in this paper the study of complex problems with two different numerical grid techniques in order to cross check the solutions is proposed interface waves in particular are emphasized since they pose the major difficulties due to the need to implement boundary conditions the first method is based on global differential operators where the solution is expanded in terms of the fourier basis and chebyshev polynomials while the second is the spectral element method an extension of the finite element method that uses chebyshev polynomials as interpolating functions both methods have spectral accuracy up to approximately the nyquist wave number of the grid moreover both methods implement the boundary conditions in a natural way particularly the spectral element algorithm we first solve lamb s problem and compare numerical and analytical solutions then the problem of dispersed rayleigh waves and finally the two quarter space problem we show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist the combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics

harmonizable stable processes on groups spectral ergodic and interpolation properties this work extends to symmetric stable s s processes 1 2 which are fourier transforms of independently scattered random measures on locally compact abelian groups some of the basic results known for processes with finite second moments and for gaussian processes analytic conditions for subordination of left right stationarily related processes and a weak law of large numbers are obtained the main results deal with the interpolation problem characterization of minimal and interpolable processes on discrete groups are derived also formulas for the interpolator and the corresponding interpolation error are given this yields a solution of the interpolation problem for the considered class of stable processes in this general setting

a discontinuous galerkin method for poroelastic wave propagation the two dimensional case abstract in this paper we consider a high order discontinuous galerkin dg method for modelling wave propagation in coupled poroelastic elastic media the upwind numerical flux is derived as an exact solution for the riemann problem including the poroelastic elastic interface attenuation mechanisms in both biot s low and high frequency regimes are considered the current implementation supports non uniform basis orders which can be used to control the numerical accuracy element by element in the numerical examples we study the convergence properties of the proposed dg scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions

towards a method for solving partial differential equations by using wavelet packet bases abstract in this paper we present a new methodology based on the wavelet packet concept in order to define an adaptive method for the approximation of partial differential equations the wavelet packet framework allows us to define the notion of a minimal basis that has proven to be an efficient procedure for data compression the purpose here is to take benefit of this compression to represent accurately and economically the solution of a time dependent pde the time discretization is a standard multistep scheme the spacial discretization is defined by inferring a reduced basis for the solution at the new time step from the knowledge of the previous ones

interpolation in grothendieck institutions it is well known that interpolation properties of logics underlying specification formalisms play an important rule in the study of structured specifications they have also many other useful logical consequences in this paper we solve the interpolation problem for grothendieck institutions which have recently emerged as an important mathematical structure underlying heterogenous multilogic specification our main result can be used in the applications in several different ways it can be used to establish interpolation properties for multi logic grothendieck institutions but also to lift interpolation properties from unsorted logics to their many sorted variants the importance of the latter resides in the fact that unlike other structural properties of logics many sorted interpolation is a non trivial generalisation of unsorted interpolation the concepts results and the applications discussed in this paper are illustrated with several examples from conventional logic and algebraic specification theory

finite element computation of three dimensional elastoacoustic vibrations abstract in this paper the interior elastoacoustic problem in a 3d domain is solved displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation a non standard discretization is used consisting of classical linear tetrahedral finite element for the solid and raviart thomas elements of lowest order for the fluid a new unknown is introduced on the interface between solid and fluid to impose the transmission conditions

characterizing specification languages which admit initial semantics abstract the paper proposes an axiomatic approach to specification languages and introduces notions of reducibility and equivalence as tools for their study and comparison algebraic specification languages are characterized up to equivalence they are shown to be limited in expressive power by implicational languages

institutional semantics for many valued logics we develop many valued logic including a generic abstract model theory over a fully abstract syntax we show that important many valued logic model theories such as traditional first order many valued logic and fuzzy multi algebras may be conservatively embedded into our abstract framework our development is technically based upon the so called theory of institutions of goguen and burstall and may serve as a template for defining at hand many valued logic model theories over various concrete syntaxes or from another perspective to combine many valued logic with other logical systems we also show that our generic many valued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods

numerical modelling of wave propagation in elastic rectangular block media novel formulations for numerical modelling of elastic waves in block media are developed in this paper a single differential difference equation which can be discretized to give explicit finite difference models of wave propagation in elastic block media is obtained after incorporating continuity conditions of stresses into the equation of motion further decompositions of the differential difference equation also lead to a parallel algorithm for computing the wave field

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

a highly accurate discontinuous galerkin method for complex interfaces between solids and moving fluids we have extended a new highly accurate numerical scheme for unstructured 2d and 3d meshes based on the discontinuous galerkin approach to simulate seismic wave propagation in heterogeneous media containing fluid solid interfaces because of the formulation of the wave equations as a unified first order hyperbolic system in velocity stress the fluid can be in movement along the interface the governing equations within the moving fluid are derived from well known first principles in fluid mechanics the discontinuous galerkin approach allows for jumps of the material parameters and the solution across element interfaces which are handled by riemann solvers or numerical fluxes the use of riemann solvers at the element interfaces makesthe treatment of the fluid particularly simple bysetting the shearmodulus in the fluid region to zero no additional compatibility relations such as vanishing shear stress or continuity of normal stresses are necessary to couple the solid and fluid along an interface the

foundations of logic programming in hybrid logics with user defined sharing abstract the present contribution advances an abstract notion of hybrid logic by supplementing the definition of institution with an additional structure to extract frames the foundation of logic programming is set in the general framework proposed by defining the basic concepts such as horn clause query and solution and proving fundamental results such as the existence of initial model of horn clauses and herbrand s theorem the abstract results are then applied to hybrid logics with user defined sharing where the possible worlds share a common domain and the variables used for quantification are interpreted uniformly across the worlds

on the existence of free models in abstract algebraic institutions abstract to provide a formal framework for discussing specifications of abstract data types we restrict the notion of institution due to goguen and burstall 1984 which formalises the concept of a logical system for writing specifications and deal with abstract algebraic institutions these are institutions equipped with a notion of submodel which satisfy a number of technical conditions our main results concern the problem of the existence of free constructions in abstract algebraic institutions we generalise a characterization of algebraic specification languages that guarantee the existence of reachable initial models for any consistent set of axioms given by mahr and makowsky 1984 then the more general problem of the existence of free functors left adjoints to forgetful functors for any theory morphism is analysed we give a construction of a free model of a theory over a model of a subtheory with respect to an arbitrary theory morphism which requires only the existence of initial models this yields a characterization of strongly liberal abstract algebraic institutions we also show how to specialise there characterisation results for the partial algebras

finite difference modeling of wave propagation in a fluid solid configuration finite difference fd techniques are widely used to model wave propagation through complex structures two main sources of error can be identified 1 from numerical dispersion and numerical anisotropy and 2 by modeling the response of internal grid boundaries conventional discretization criteria to reduce the effects of numerical dispersion and numerical anisotropy have long been established 5 8 gridpoints per wavelength for a fourth order accurate fd scheme we analyze the second source of errors comparing different staggered grid fd solutions to the cagniard de hoop solution in models with fluid solid contacts our results confirm that it is sufficient to rely on conventional discretization criteria if the fluid solid interface is aligned with the grid if accurate modeling of the scholte wave is required then a new imaging method we propose should be used to allow for conventional sampling of the wavefield to minimize numerical dispersion however for an interface not aligned with the grid irregular interfaces a spatial sampling of at least 15 gridpoints per minimum wavelength is required to obtain acceptable results particularly in seismic seabed applications where scholte waves may need to be modeled more accurately

an axiomatic approach to structuring specifications in this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions which means two levels of institution independence this abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators and moreover it unifies the theory and the model oriented approaches within this framework we develop concepts and results about abstract structured specifications such as co limits model amalgamation compactness interpolation sound and complete proof theory and pushout style parameterization with sharing all of them in a top down manner dictated by the upper level of institution independence

stable processes moving averages versus fourier transforms we study the relationship between fourier transforms and moving averages of stable processes the two classes have a large intersection however as soon as the noise is required to be bounded they become disjoint

the spectral representation of stable processes harmonizability and regularity we show that symmetric stable moving average processes are not harmonizable however we show that a concept of generalized spectrum holds for alll p bounded processes o p 2 in capep 2 generalized spectrum is a measure and the classical representation follows for strongly harmonizable symmetric stable processes we derive necessary and sufficient conditions for the regularity and the singularity for 0 2 using known results on the invariant subspaces we also get cramer wold decomposition for the case 0 2