high order finite difference simulations of marine csem surveys using a correspondence principle for wave and diffusion fields the computer time required to solve a typical 3d marine controlled source electromagnetic surveying csem simulation can be reduced by more than one order of magnitude by transforming low frequency maxwell equations in the quasi static or diffusive limit to a hyperbolic set of partial differential equations that give a representation of electromagnetic fields in a fictitious wave domain the dispersion and stability analysis can be made equivalent to that of other types of wave simulation problems such as seismic acoustic and elastic modeling second order to eighth order spatial derivative operators are implemented for flexibility fourth order and sixth order methods are the most numerically efficient implementations for this particular scheme an implementation with high order operators requires that both electric and magnetic fields are extrapolated simultaneously into the air layer the stability condition given for high order staggered derivative operators here should be equally valid for seismic wave simulation the bandwidth of recovered fields in the diffusive domain is independent of the bandwidth of the fields in the fictitious wave domain the fields in the fictitious wave domain do not represent observable fields propagation paths and interaction reflection amplitudes are not altered by the transform from the fictitious wave domain to the diffusive frequency domain however the transform contains an exponential decay factor that damps down late arrivals in the fictitious wave domain the propagation paths that contribute most to the diffusive domain fields are airwave shallow water plus typically postcritical events such as refracted and guided waves the transform from the diffusive frequency domain to the fictitious wave domain is an ill posed problem the transform is nonunique this gives a large degree of freedom in postulating temporal waveforms for boundary conditions in the fictitious wave domain that reproduce correct diffusive frequency domain fields

flat endofinite modules prime ideals and duality abstract bijective correspondences are established between endofinite injective left modules endofinite flat right modules finite collections of minimal noetherian prime ideals normalized rank functions on left ideals and characters endofinite flat modules are identified as flat covers of modules associated to a minimal noetherian prime ideal while endofinite flat injectives are characterized by localizations with a semiprimary qf 3 quotient ring

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

the solvability and explicit solutions of two integral equations via generalized convolutions abstract this paper presents the necessary and sufficient conditions for the solvability of two integral equations of convolution type the first equation generalizes from integral equations with the gaussian kernel and the second one contains the toeplitz plus hankel kernels furthermore the paper shows that the normed rings on l 1 r d are constructed by using the obtained convolutions and an arbitrary hermite function and appropriate linear combination of those functions are the weight function of four generalized convolutions associating f and f the open question about hermitian weight function of generalized convolution is posed at the end of the paper

endoproperties of modules and local duality abstract let r be any ring and n i i n i be a direct sum of finitely presented left r modules n i suppose that d n and d n i are the local duals of n and n i for each i i we prove that the lattice of endosubmodules of n is anti isomorphic to the lattices of matrix subgroups of d n and of m i i d n i as consequences n is endoartinian if and only if m or d n is endonoetherian and n is endonoetherian if and only if m or d n is pure injective we obtain in particular that if r is a krull schmidt ring and m is an indecomposable pure injective endonoetherian right r module which is the source of a left almost split morphism in mod r then m is endofinite as an application a ring r is of finite representation type if and only if every pure injective right r module is endonoetherian

the finite hartley new convolutions and solvability of the integral equations with toeplitz plus hankel kernels abstract the main aim of this work is to consider integral equations of convolution type with the toeplitz plus hankel kernels firstly posed by tsitsiklis and levy 1981 11 by constructing eight new generalized convolutions for the finite hartley transforms we obtain a necessary and sufficient condition for the solvability and unique explicit l 2 solution of those equations thanks to this convolution approach the solvability condition obtained here is remarkably different from those in tsitsiklis and levy 1981 11 and in other papers

elementary duality of modules let r be a ring a formula x in the language of left r modules is called a positive primitive formula ppf if it is of the form y ab x y 0 where a and b are matrices of appropriate size with entries in r we apply prest s notion of d x the ppf in the language of right r modules dual to to show that the model theory of left r modules as developed by ziegler z is in some sense dual to the model theory of right r modules we prove that the topologies on the left and right ziegler spectra are isomorphic proposition 4 4 when the lattice of ppfs is well behaved there is a homeomorphism d between the left and right ziegler spectra which assigns to a given pure injective indecomposable left r module u the dual pure injective indecomposable right r module du

sh wave propagation in heterogeneous media velocity stress finite difference method a new finite difference fd method is presented for modeling sh wave propagation in a generally heterogeneous medium this method uses both velocity and stress in a discrete grid density and shear modulus are similarly discretized avoiding any spatial smoothing therefore boundaries will be correctly modeled under an implicit formulation standard problems quarter plane propagation sedimentary basin propagation are studied to compare this method with other methods finally a more complex example a salt dome inside a two layered medium shows the effect of lateral propagation on seismograms recorded at the surface a corner wave always in phase with the incident wave and a head wave will appear which will pose severe problems of interpretation with the usual vertical migration methods

differential operator related to the generalized superradiance integral equation abstract in this paper we consider a class of problems which are generalized versions of the three dimensional superradiance integral equation a commuting differential operator will be found for this generalized problem for the three dimensional superradiance problem an alternative set of complete eigenfunctions will also be provided the kernel for the superradiance problem when restricted to one dimension is the same as appeared in the works of slepian landau and pollak cf slepian and pollak 1961 1 landau and pollak 1961 1962 2 3 slepian 1964 1978 4 5 the uniqueness of the differential operator commuting with that kernel is indicated

two dimensional transient electromagnetic responses the time domain electromagnetic tem modeling method of oristaglio and hohmann is reformulated here in terms of the secondary field this finite difference method gives a direct explicit time domain solution for a two dimensional body in a conductive earth by advancing the field in time with dufort frankel time differencing as a result solving for the secondary field defined as the difference between the total field and field of a half space is not only more efficient but is also simpler and eliminates several problems inherent in the solution for the total field for example because the secondary field varies slowly both in space and time it can be modeled on a coarse grid with large time steps in addition for a simple body the field is local therefore because the field can be assumed to satisfy a simple boundary condition in the earth computation is greatly simplified our tests show that for the same accuracy the secondary field solution is roughly five times faster than the total field so

toeplitz and hankel kernels for estimating time varying spectra of discrete time random processes for a nonstationary random process the dual time correlation function and the dual frequency loeve spectrum are complete theoretical descriptions of second order behavior that is each may be used to synthesize the random process itself according to the cramer loeve spectral representation when suitably transformed on one of its two variables each of these descriptions produces a time varying spectrum this spectrum is in fact the expected value of the rihaczek distribution in this paper we derive two large families of estimators for this spectrum one based on a diagonal toeplitz diagonal dtd factorization of smoothing kernels and the other based on a diagonal hankel diagonal dhd factorization the dtd factorization produces noncoherent averages of the time varying spectrogram and the dhd factorization produces coherent averages some of the dtd estimators may be called time varying power spectrum estimators and some of the dhd estimators may be called time varying wigner ville wv estimators the former may always be implemented as multiwindow spectrum estimators and in some casts they are true time variations on the blackman tukey rosenblatt grenander btgr spectrogram the latter are variations on the stankovic class of wv estimators

indecomposable decompositions of pure injective objects and the pure semisimplicity abstract we give a criterion for the existence of an indecomposable decomposition of pure injective objects in a locally finitely presented grothendieck category a theorem 2 5 as a consequence we get theorem 3 2 asserting that an associative unitary ring r is right pure semisimple if and only if every right r module is a direct sum of modules that are pure injective or countably generated some open problems are formulated in the paper

a finite difference time domain solution for three dimensional electromagnetic modeling we have developed a finite difference solution for three dimensional 3 d transient electromagnetic problems the solution steps maxwell s equations in time using a staggered grid technique the time stepping uses a modified version of the du fort frankel method which is explicit and always stable both conductivity and magnetic permeability can be functions of space and the model geometry can be arbitrarily complicated the solution provides both electric and magnetic field responses throughout the earth because it solves the coupled first order maxwell s equations the solution avoids approximating spatial derivatives of physical properties and thus overcomes many related numerical difficulties moreover since the divergence free condition for the magnetic field is incorporated explicitly the solution provides accurate results for the magnetic field at late times an inhomogeneous dirichlet boundary condition is imposed at the surface of the earth while a homogeneous dirichlet condition is employed along the subsurface boundaries numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth order difference method at early times and a second order method at other times numerical checks against analytical integral equation and spectral differential difference solutions show that the solution provides accurate results execution time for a typical model is about 3 5 hours on an ibm 3090 600s computer for computing the field to 10 ms that model contains 100 x 100 x 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry with the smallest grid spacing at 10 m and the highest resistivity at 100 omega m the execution time indicates that the solution is computer intensive but it is valuable in providing much needed insight about tem responses in complicated 3 d situations

modules with indecomposable decompositions that complement maximal direct summands generalizing a fundamental property of semisimple modules anderson w x and fuller 1 introduced the following important concept for direct decompositions of modules a decomposition m s m is said to ig i i complement direct summands in case for each direct summand a of m w there is a subset h i such that m s a m cf also 2 p ig h i x 141 such a decomposition is necessarily an indecomposable decomposition and it is an interesting problem to study under which conditions an indecomposable decomposition complements direct summands there is w x an extensive literature concerning this problem by 1 theorem 6 right perfect rings can be characterized by the property that all projective right modules have decompositions that complement direct summands fuller w x 7 showed that over a generalized uniserial ring every module has a decomposition that complements direct summands thus providing a first class of non semisimple rings satisfying this property more generally w x tachikawa 14 proved that every left and right module over a ring of finite representation type has a decomposition that complements direct summands and that the converse is also true was established by fuller and w x w x reiten 9 restricting just to one side fuller 8 showed that rings over which every right module has a decomposition that complements direct summands are precisely the rings over which every right module is a direct sum of finitely generated modules they are also called right pure semisim

3d time domain simulation of electromagnetic diffusion phenomena a finite element electric field approach we present a finite element time domain fetd approach for the simulation of 3d electromagnetic em diffusion phenomena the finite element algorithm efficiently simulates transient electric fields and the time derivatives of magneticfields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms to compute transient electromagnetic fields theelectricfielddiffusionequationistransformedinto asystemofdifferentialequationsviagalerkin smethodwith homogeneous dirichlet boundary conditions to ensure numerical stability and an efficient time step the system of the differential equations is discretized in time using an implicit backward euler scheme the resultant fetd matrix vector equation is solved using a sparse direct solver along with a fill inreducedorderingtechnique whenadvancingthesolution in time the fetd algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution to simulate a step off source waveform the 3d fetd algorithm also incorporates a 3d finite element direct current fedcalgorithmthatsolvespoisson sequationusingasecondarypotentialmethodforageneralanisotropicearthmodel examples of controlled source fetd simulations are compared with analytic and or 3d finite difference time domain solutions and are used to confirm the accuracy and efficiencyofthe3dfetdalgorithm

finite difference calculations of the transient field of an axially symmetric earth for vertical magnetic dipole excitation a finite difference formulation of the coaxial loop or wire loop transient electromagnetic em prospecting systems is used to model the fields from a buried cylindrical conductor whose axis is coincident with that of the field system solutions are obtained directly in the time domain the formulation is implicit and two dimensional 2 d in space the variable directions method reduces each advance of one step in time from one 2 d problem to a large number of one dimensional 1 d problems the result is a reduction in computational effort in order to avoid including the air in the finite difference grid an integral equation approach is used to formulate the surface boundary condition thus two sets of 1 d finite difference solutions and one fredholm integral equation solution are required for each step forward in time comparison with analytical solutions shows excellent agreement in the case of a four layer earth all computations were carried out for a perfectly conducting basement but the method

a hybrid finite difference and integral equation method for modeling and inversion of marine controlled source electromagnetic data abstractone of the major problems in the modeling and inversion of marine controlled source electromagnetic csem data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment at the same time the corresponding forward modeling algorithms should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter receiver positions to this end we have developed a novel 3d modeling and inversion approach which combines the advantages of the finite difference fd and integral equation ie methods in the framework of this approach we have solved maxwell s equations for anomalous electric fields using the fd approximation on a staggered grid once the unknown electric fields in the computation domain of the fd method are computed the electric and magnetic fields at the receivers are calculated using the ie method with the corresponding green s tensor for the background conduc

large scale three dimensional seismic models and their interpretive significance finite difference seismic models are commonly set up in 2 d space such models must be excited by a line source which leads to different amplitudes than those in the real data commonly generated from a point source moreover there is no provision for any out of plane events these problems can be eliminated by using 3 d finite difference models the fundamental strategy in designing efficient 3 d models is to minimize computational work without sacrificing accuracy this was accomplished by using a 4 2 differencing operator which ensures the accuracy of much larger operators but requires many fewer numerical operations as well as significantly reduced manipulation of data in the computer memory such a choice also simplifies the problem of evaluating the wave field near the subsurface boundaries of the model where large operators cannot be used we also exploited the fact that unlike the real data the synthetic data are free from ambient noise consequently one can retain sufficient resolution in th

transient electromagnetic inversion based on an approximate solution to the forward problem a rapid algorithm for forward one dimensional modeling is based on the graphical construction of a multi layered apparent resistivity curve using an appropriate combination of two layered curves a collection of two layered curves is calculated only once for fixed geoelectrical parameters and saved for future use an arbitrary two layered curve within the wide range of the geoelectrical parameters is then obtained by simple interpolation this method reduces computation time over other fast algorithms by at least one order of magnitude in addition it does not produce any significant computation errors in the late stage as do most other methods a maximum relative error of about 10 to 15 percent may occur at a few points usually two to three in the vicinity of the intersection of the two layered curves in most cases however this error does not affect the inversion since the relative contributions of these points to an objective function are small the application of such a rapid forward algorithm al

numerical modeling of the electromagnetic response of three dimensional conductors in a layered earth this paper describes a numerical modeling program which was developed for computing the electromagnetic response of a three dimensional conductor in a layered earth the algorithm is a hybrid one in the sense that a finite element method is combined with an integral equation approach for the complete solution of the problem in this approach two relatively small matrices are inverted to obtain the secondary magnetic fields at the interior nodes of the subdivided volume the finite element method requires special attention at low frequencies i e when the body dimensions are small compared with the skin depth the method was tested with various models involving spheres and rectangular dikes and comparisons have been made with analytical numerical and scale modeling data these comparisons generally show good agreement between our numerical model and the other models tested examples are given which show the flexibility and usefulness of this modeling algorithm when applied to a ground or airborne prospecting system with a coil separation of 10 m

transient electromagnetic response of a three dimensional body in a layered earth the three dimensional 3 d electromagnetic scattering problem is first formulated in the frequency domain in terms of an electric field volume integral equation three dimensional responses are then fourier transformed with sine and cosine digital filters or with the decay spectrum the digital filter technique is applied to a sparsely sampled frequency sounding which is replaced by a cubic spline interpolating function prior to convolution with the digital filters typically 20 to 40 frequencies at five to eight points per decade are required for an accurate solution a calculated transient is usually in error after it has decayed more than six orders in magnitude from early to late time the decay spectrum usually requires ten frequencies for a satisfactory solution however the solution using the decay spectrum appears to be less accurate than the solution using the digital filters particularly after early times checks on the 3 d solution include reciprocity and convergence checks in the frequenc

on the sparsity of representations of rings of pure global dimension zero it is shown that the rings r all of whose left modules are direct sums of finitely generated modules satisfy the following finiteness condition for each positive integer n there are only finitely many isomorphism types of a indecomposable left r modules of length n b finitely presented indecomposable right r modules of length n c indecomposable right r modules having minimal projective resolutions with n relations moreover our techniques yield a very elementary proof for the fact that the presence of the above decomposability hypothesis for both left and right r modules entails finite representation type

baer and mittag leffler modules over tame hereditary algebras we develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras the baer modules and the mittag leffler ones a right r module m is called baer if rm ext 1 r m t 0 for all torsion modules t and m is mittag leffler in case the canonical map m otimes r prod i in i q i to prod i in i m otimes rq i is injective where q i i in i are arbitrary left r modules we show that a module m is baer iff m is p filtered where p is the preprojective component of the tame hereditary algebra r we apply this to prove that the universal localization of a baer module is projective in case we localize with respect to a complete tube using infinite dimensional tilting theory we then obtain a structure result showing that baer modules are more complex then the infinite dimensional preprojective modules in the final section we give a complete classification of the mittag leffler modules

endofinite modules and pure semisimple rings let r be a right pure semisimple ring i e a ring r such that every right r module is a direct sum of finitely generated modules it is proved that r is of finite representation type if and only if every finitely presented indecomposable right r module is endofinite if and only if every finitely presented right r module has a left artinian endomorphism ring as applications we obtain an alternative proof of the pure semisimplicity conjecture for pi rings and new criteria for a right pure semisimple ring to be of finite representation type

indecomposable modules over pure semisimple hereditary rings abstract if r is a hereditary left artinian ring then r is left pure semisimple if and only if the family r ind of all finitely generated indecomposable left r modules has a unique ext injective partition r ind u this partition is used to give a complete description of the distribution of all indecomposable modules over a left pure semisimple hereditary indecomposable ring r of infinite representation type more precisely r ind is the disjoint union of the countable set of all preinjective modules and the finite set of all preprojective modules and countable sets of auslander reiten components of the form k u k for all limit ordinals constructed from the ext injective partition of r ind in particular we show that an indecomposable left r module m is not the source of a left almost split morphism in r mod if and only if m belongs to u where is an infinite limit ordinal and the direct sum of modules in u is not endofinite for each infinite limit ordinal moreover the endomorphism ring of each indecomposable left r module is a division ring

3d vector finite element electromagnetic forward modeling for large loop sources using a total field algorithm and unstructured tetrahedral grids abstractunstructured tetrahedral grids with local refinement facilitate the use of total field solution approaches to geophysical electromagnetic em forward problems these approaches when combined with the vector finite element fe method and with refinement near transmitters and receivers can give accurate solutions and can easily handle realistic models with complex geometry and topography we have applied this approach to 3d forward modeling for fixed and moving loop configurations mumps a direct solver was used to solve the linear system of equations generated by fe analysis a direct solver is particularly suited to the moving loop configuration for which the right side is different for every transmitter loop but for which the coefficient matrix is unchanged therefore the coefficient matrix need only be factorized once and then the system can be solved efficiently for all different right sides we compared our results with several typical scenarios from the literature a conductive bric

a parallel finite difference approach for 3d transient electromagnetic modeling with galvanic sources a parallel finite difference algorithm for the solution of diffusive three dimensional 3d transient electromagnetic field simulations is presented the purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources grounded wires over arbitrarily complicated distributions of conductivity and magnetic permeability using a staggered grid and a modified dufort frankel method the scheme steps maxwell s equations in time electric field initialization is done by a conjugate gradient solution of a 3d poisson problem as is common in 3d resistivity modeling instead of calculating the initial magnetic field directly its time derivative and curl are employed in order to advance the electric field in time a divergence free condition is enforced for both the magnetic field time derivative and the total conduction current density providing accurate results at late times in order to simulate large realistic earth models the algorithm has been designed to run on parallel computer platforms the upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two dimensional parallel fast fourier transform example simulations are compared with analytical integral equation and spectral lanczos decomposition solutions and demonstrate the accuracy of the scheme

integral equation solution for the transient electromagnetic response of a three dimensional body in a conductive half space the time domain integral equation for the three dimensional vector electric field is formulated as a convolution of the scattering current with the tensor green s function the convolution integral is divided into a sum of integrals over successive time steps so that a numerical scheme can be formulated with a time stepping approximation of the convolution of past values of the solution with the system impulse response this together with spatial discretization leads to a matrix equation in which previous solution vectors are multiplied by a series of matrices and fed back into the system by adding to the primary field source vector the spatial discretization based on a modification of the usual pulse basis formulation in the frequency domain includes an additional subset of divergence free basis functions generated by integrating the green s function around concentric closed rectangular paths the inductive response of the body is more accurately modeled with these additional basis functions and a

a key module over pure semisimple hereditary rings abstract let r be a hereditary indecomposable left pure semisimple ring inspired by i reiten c m ringel infinite dimensional representations of canonical algebras canad j math 58 2006 180 224 we investigate the perfect cotorsion pair c d in r mod generated by the preinjective component q we show that there is a finitely generated product complete tilting and cotilting left r module w such that c cogen w and d gen w the finite subcategory w of r mod given by the indecomposable summands of w stores important information on r for example if we assume r of infinite representation type then by b zimmermann huisgen strong preinjective partitions and representation type of artinian rings proc amer math soc 109 1990 309 322 there are non preinjective indecomposable modules occurring as direct summands of products of preinjective modules and it turns out that w is precisely the class of such modules moreover we prove that r has finite representation type if and only if every module in w is source of a left almost split map in r mod finally we address the question when w is endofinite