covariance and geometrical invariance in quantization several notions of invariance and covariance for products with respect to lie algebras and lie groups are investigated some examples including the poincare group are given the passage from the lie algebra invariance to the lie group covariance is performed the compact and nilpotent cases are treated

game theory approach to state estimation of linear discrete time processes and its relation to h optimal estimation a game theory approach to the state estimation of linear discrete time systems is presented the resulting state estimation suggests an alternative to the kalman filter in cases where the exact statistics of the input and the measurement noise processes is not known it turns out that the game theoretic filter provides an h optimal estimation moreover it is shown that the covariance matrix of the estimation error is bounded from above by the solution of a modified riccati equation

moment maps at the quantum level we introduce the notion of moment maps for quantum groups acting on their module algebras when the module algebras are quantizations of poisson manifolds we prove that the construction at the quantum level is a quantization of that at the semi classical level we also prove that the corresponding smashed product algebras are quantizations of the semi direct product poisson structures

a reorganized innovation approach to linear estimation this note will address a linear minimum variance estimation of discrete time systems with instantaneous and delayed measurements although the problem may be approached via system augmentation and standard kalman filtering the computation of filter may be expensive when the dimension of the system is high and the measurement lag is significant in this note a new tool termed as reorganized innovation sequence is presented for deriving the optimal filter the optimal filter is given by two riccati difference equations rdes with the same dimension as that of the original system the approach is shown to induce saving of computational cost as compared to the system augmentation approach especially when the delay is large further it can be extended to solving the more complicated h sub spl infin fixed lag smoothing in krein space

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

on geometric and analytic constraints in the h infty fixed lag smoothing limiting factors on achievable performance in the continuous and discrete time fixed lag smoothing problems are shown to include geometric constraints inherited from the fixed interval linfin problem and analytic constraints affected by the preview interval thus the fixed lag problem is viewed as a constrained version of its fixed interval counterpart the analysis sheds light on the dependence of achievable performance on the preview length and in particular on the generic presence of performance saturation at a finite preview interval

a formal model of berezin toeplitz quantization we give a new construction of symbols of the differential operators on the sections of a quantum line bundle l over a kahler manifold m using the natural contravariant connection on l these symbols are the functions on the tangent bundle tm polynomial on fibres for high tensor powers of l the asymptotics of the composition of these symbols leads to the star product of a deformation quantization with separation of variables on tm corresponding to some pseudo kahler structure on tm surprisingly this star product is intimately related to the formal symplectic groupoid with separation of variables over m we extend the star product on tm to generalized functions supported on the zero section of tm the resulting algebra of generalized functions contains an idempotent element which can be thought of as a natural counterpart of the bergman projection operator using this idempotent we define an algebra of toeplitz elements and show that it is naturally isomorphic to the algebra of berezin toeplitz deformation quantization on m

brief h performance of preview control systems performance of the preview control is investigated in terms of h criterion in the infinite horizon time setting the limitation of h performance in preview control action is characterized with the hamiltonian matrix by employing the property of hamiltonian matrix the solvability and analytic solution for the preview full information control problem are clarified based on an auxiliary introduced matrix riccati equation the property of resulting control law is illustrated with a numerical example

optimum performance levels for minimax filters predictors and smoothers abstract for both discrete and continuous time linear time varying systems we obtain the achievable performance levels for minimax filters predictors and smoothers in terms of the finite escape times of some related discrete and continuous time riccati equations our game theoretic approach also yields an alternative derivation for the corresponding minimax estimators which were first obtained in 1 they are all bayes estimators with respect to particular gaussian distributions and admit recursive structures

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

triangular dynamical r matrices and quantization abstract we study some general aspects of triangular dynamical r matrices using poisson geometry we show that a triangular dynamical r matrix r h 2 g always gives rise to a regular poisson manifold using the fedosov method we prove that non degenerate triangular dynamical r matrices i e those such that the corresponding poisson manifolds are symplectic are quantizable and that the quantization is classified by the relative lie algebra cohomology h2 g h

h sup spl infin control and estimation with preview part i matrix are solutions in continuous time preview control and fixed lag smoothing allow a noncausal component in the controller estimator time domain variational analysis is used in a reduction to an open loop differential game leading to a complete necessary and sufficient characterization of suboptimal values and an explicit state space design in terms of a parameterized nonstandard algebraic matrix riccati equation in a general continuous time linear system setting the solution offers insight into the appropriate structure of the associated hamiltonian where the state and co state are not the usual state of the original dynamic system and that of its adjoint rather the state and co state are selected to capture the respective lumped effects of initial data and future input selection in the allied game

an efficient symplectic reverse time migration method using a local nearly analytic discrete operator in acoustic transversely isotropic media with a vertical symmetry axis abstractreverse time migration rtm has become an extremely important imaging method due to its ability of handling complicated velocity models in recent years there has been an increasing need to perform rtm with anisotropic velocity models such as transversely isotropic media with a vertical symmetry axis vti finite difference fd is one of the most widely used numerical methods in rtm however it often suffers from serious numerical dispersion resulting in significant loss of imaging resolution over the years a nearly analytic discrete operator has been developed to approximate the high order spatial partial differential operators which is effective in suppressing numerical dispersion using this operator we developed a nearly analytic symplectic nas method to numerically solve acoustic vti wave equations which preserves the symplectic structure we have investigated its properties including the stability condition numerical dispersion relation and computational efficiency also we a

game theory approach to h sub spl infin optimal discrete time fixed point and fixed lag smoothing optimal h sub spl infin fixed point and fixed lag discrete time smoothing estimators are developed by applying a game theory approach a deterministic discrete time game is defined where the estimator plays against nature nature determines the system initial condition the driving input and the measurement noise whereas the estimator tries to find an estimate that brings a prescribed cost function that is based on the error of the estimation at a fixed time instant to a saddle point equilibrium the latter estimate yields the h sub spl infin optimal fixed point smoothing differently from the usual case in h sub spl infin optimal estimation and control the critical value of the scalar design parameter of the smoothing game is obtained in closed form explicitly in the terms of the corresponding h sub 2 solution unlike the h sub 2 case the recursive application of the h sub spl infin fixed point smoothing algorithm does not lead to fixed lag smoothing in the h sub spl infin norm sense the h sub spl infin fixed lag smoothing filter is derived by augmenting the state vector of the system with additional delayed states

quantization of formal classical dynamical r matrices the reductive case abstract in this paper we prove the existence of a formal dynamical twist quantization for any triangular and non modified formal classical dynamical r matrix in the reductive case the dynamical twist is constructed as the image of the dynamical r matrix by a l quasi isomorphism this quasi isomorphism also allows us to classify formal dynamical twist quantizations up to gauge equivalence

weyl manifolds and deformation quantization this paper deals with non commutative objects based on the weyl algebra from the differential geometric point of view we propose to extend familiar notions from manifolds to non commutative objects in this algebraic approach the basic object is not a point of a space but certain sections of bundles

deformations of momentum maps and g systems in this note we give an explicit formula for a family of deformation quantizations for the momentum map associated with the cotangent lift of a lie group action on rd this family of deformations is parametrized by the formal g systems introduced in b dherin and i mencattini g systems and deformations of g actions on rd j math phys 55 011702 2014 see also b dherin and i mencattini quantization of volume preserving actions on rd e print arxiv 1202 0886 and allows us to obtain classical invariant hamiltonians that quantize without anomalies with respect to the quantizations of the action prescribed by the formal g systems

h fixed lag smoothing for discrete linear time varying systems this paper is concerned with the finite horizon h fixed lag smoothing problem for discrete linear time varying systems the existence of an h smoother is first related to certain inertia condition of an innovation matrix the innovation matrix is traditionally computed via a riccati difference equation rde associated with the h filtering of an augmented system which is computationally expensive to avoid solving the rde of high dimension we introduce a re organized innovation and apply innovation analysis and projection theory in krein space to give a simple method of computing the innovation matrix the h smoother is computed as a projection in krein space by performing two rdes of the same dimension as that of the original system

on discrete time h sub spl infin fixed lag smoothing the h sub spl infin fixed lag smoothing problem for discrete time linear systems is considered it is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system however in order to check the solvability of the smoothing problem and compute the relevant gains one must solve a riccati equation involving the augmented system matrices which is an approach that may be inefficient especially for long lags in this paper efficient algorithms are worked out that permit checking of solvability and implementation of the smoother relying only on the solution of the h sub spl infin filtering riccati equation in particular this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level

stable p wave modeling for reverse time migration in tilted ti media we present an approach for p wave modeling in inhomogeneous transversely isotropic media with tilted symmetry axis tti media suitable for anisotropic reverse time migration the proposed approach is based on wave equations derived from first principles the equations of motion and hooke s law under the acoustic ti approximation consequently no assumptions are made about the spatial variation of medium parameters a rotation of the stress and strain tensors to a local coordinate system aligned with the ti symmetry axis makes it possible to benefit from the simple and sparse form of the ti elastic tensor in that system the resulting wave equations can be formulated either as a set of five first order or as a set of two second order partial differential equations for the constant density case the second order tti wave equations involve mixed and nonmixed second order spatial derivatives with respect to global nonrotated coordinates we propose a numerical implementation of these equations using high order centered finite differences to minimize modeling artifacts related to the use of centered first derivative operators we use discrete second derivative operators for the nonmixed second order spatial derivatives and repeated discrete first derivative operators for the mixed derivatives such a combination of finite difference operators leads to a stable wave propagator provided that the operators are designed properly in practice stability is achieved by slightly weighting down terms that contain mixed derivatives this has a minor practically negligible effect on the kinematics of wave propagation the stability of the presented scheme in inhomogeneous tti models with rapidly varying anisotropic symmetry axis direction is demonstrated with numerical examples

modeling the scalar wave equation with nystrom methods high accuracy numerical schemes for modeling of the scalar wave equation based on nystrom methods are developed in this paper space is discretized by using the pseudospectral algorithm for the time discretization nystrom methods are used a fourth order symplectic nystrom method with pseudospectral spatial discretization is presented this scheme is compared with a commonly used second order scheme and a fourth order nonsymplectic nystrom method for a typical time step size the second order scheme exhibits spatial dispersion errors for long time simulations while both fourth order schemes do not suffer from these errors numerical comparisons show that the fourth order symplectic algorithm is more accurate than the fourth order nonsymplectic one the capability of the symplectic nystrom method in approximately preserving the discrete energy for long time simulations is also demonstrated

quantized symplectic actions and w algebras with a nilpotent element in a semisimple lie algebra g one associates a finitely generated associative algebra w called a w algebra of finite type this algebra is obtained from the universal enveloping algebra u g by a certain hamiltonian reduction we observe that w is the invariant algebra for an action of a reductive group g with lie algebra g on a quantized symplectic affine variety and use this observation to study w our results include an alternative definition of w a relation between the sets of prime ideals of w and of the corresponding universal enveloping algebra the existence of a one dimensional representation of w in the case of classical g and the separation of elements of w by finite dimensional representations

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

an acoustic wave equation for anisotropic media a wave equation derived using the acoustic medium assumption for p waves in transversely isotropic ti media with a vertical symmetry axis vti media yields a good kinematic approximation to the familiar elastic wave equation for vti media the wavefield solutions obtained using this vti acoustic wave equation are free of shear waves which significantly reduces the computation time compared to the elastic wavefield solutions for exploding reflector type applications from this vti acoustic wave equation the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a ti medium are derived these equations based on the acoustic assumption shear wave velocity 0 are much simpler than their elastic counterparts yet they yield an accurate description of traveltimes and geometrical amplitudes numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex ti models

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

brief on the h fixed lag smoothing how to exploit the information preview the problem of the continuous time h fixed lag smoothing over the infinite horizon is studied the first solution to the problem is derived in terms of one algebraic riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the h filtering occur is clarified it is shown that the h smoother exploits the information preview in an h 2 manner

brst cohomology and phase space reduction in deformation quantization in this article we consider quantum phase space reduction when zero is a regular value of the momentum map by analogy with the classical case we define the brst cohomology in the framework of deformation quantization we compute the quantum brst cohomology in terms of a quantum chevalley eilenberg cohomology of the lie algebra on the constraint surface to prove this result we construct an explicit chain homotopy both in the classical and quantum case which is constructed out of a prolongation of functions on the constraint surface we have observed the phenomenon that the quantum brst cohomology cannot always be used for quantum reduction because generally its zero part is no longer a deformation of the space of all smooth functions on the reduced phase space but in case the group action is sufficiently nice e g proper which is the case for all compact lie group actions it is shown for a strongly invariant star product that the brst procedure always induces a star product on the reduced phase space in a rather explicit and natural way simple examples and counterexamples are discussed

formal symplectic groupoid of a deformation quantization we give a self contained algebraic description of a formal symplectic groupoid over a poisson manifold m to each natural star product on m we then associate a canonical formal symplectic groupoid over m finally we construct a unique formal symplectic groupoid with separation of variables over an arbitrary kahler poisson manifold

fedosov quantization on symplectic ringed spaces we expose the basics of the fedosov quantization procedure placed in the general framework of symplectic ringed spaces this framework also includes some poisson manifolds with nonregular poisson structures presymplectic manifolds complex analytic symplectic manifolds etc

fedosov products and quantum momentum maps the purpose of this paper is to study various aspects of star products on a symplectic manifold related to the fedosov method by introducing the notion of quantum exponential maps we give a characterization of fedosov connections as an application a geometric realization is obtained for the equivalence between an arbitrary product and a fedosov one every fedosov product is shown to be a vey product consequently we find that every product is equivalent to a vey product a classical result of lichnerowicz quantization of a hamiltonian g space and in particular quantum momentum maps are studied lagrangian submanifolds are also studied under a deformation quantization

a survey on symplectic and multi symplectic algorithms we simply review symplectic and multi symplectic algorithms in the paper these algorithms have many superiorities to general non symplectic algorithms such as they have long time behavior they can preserve the symplectic geometry structure of the hamiltonian system exactly and they can simulate original physical phenomena well some commonly used methods to construct symplectic and multi symplectic schemes are simply surveyed numerical examples are also enumerated to illustrate their performances

g systems and deformation of g actions on rd given a smooth action of a lie group g on rd we construct a differential graded algebra whose maurer cartan elements are in one to one correspondence with some class of deformations of the induced g action on c rd in the final part of this note we discuss the cohomological obstructions to the existence and to the uniqueness in a sense to be clarified of such deformations

h sub infinity fixed lag smoothing filter for scalar systems the solution of the h sub infinity optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete system the smoother is obtained from the solution of a linear equation and a spectral factorization calculation the pole zero properties of the optimal smoother are obvious in the polynomial representation and insights into the measurement noise rejection properties of the smoother are obtained allowance is made for both dynamic cost weighting and colored measurement noise the polynomial form of the smoothing filter may be incorporated into a self tuning algorithm and a simple adaptive smoother is discussed

coupled equations for reverse time migration in transversely isotropic media reverse time migration rtm images reflectors by using time extrapolation modeling codes to synthesize source and receiver wavefields in the subsurface asymptotic analysis of wave propagation in transversely isotropic ti media yields a dispersion relation describing coupled p and sv wave modes this dispersion relation can be converted into a fourth order scalar partial differential equation pde increased computational efficiency can be achieved using equivalent coupled second order pdes analysis of the corresponding dispersion relations as matrix eigenvalue systems allows one to characterize all possible coupled linear second order systems equivalent to a given linear fourth order pde and to determine which ones yield optimally efficient finite difference implementations setting the shear velocity along the axis of symmetry to zero yields a simpler approximate ti wave equation that is more efficient to implement this simpler approximation however can become unstable for some plausible combinations of anisotropic parameters the same eigensystem analysis can be applied using finite vertical shear velocity to obtain solutions that avoid these instability problems

when does the h sup spl infin fixed lag smoothing performance saturate for a finite smoothing lag a notable difference between the h sup 2 and h sup spl infin smoothing is that the achievable performance in the latter problem might saturate as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag in this note necessary and sufficient conditions under which such a saturation occurs are derived in particular it is shown that the h sup spl infin performance saturates only if the h sup spl infin norm of the optimal error system is achieved at the infinite frequency i e if the worst case disturbance for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable

simulation of acoustic wavefields in heterogeneous media a robust method for automatic suppression of numerical dispersion numerical dispersion limits the application of numerical simulation methods for solving the acoustic wave equation in largescalecomputation thenearlyanalyticdiscretemethodnadm and its improved version for suppressing numerical dispersion weredevelopedrecently thisnewmethodisarefinementoftwo previousmethodsandfurtherincreasestheabilityofsuppressing numerical dispersion for modeling acoustic wave propagation in 2d heterogeneous media which uses acoustic wave displacement particle velocity and their gradients to restructure the acoustic wavefield via the truncated taylor expansion and the high order interpolation approximate method for the method proposed weinvestigateitsimplementationandcompareitwith the higher order lax wendroff correction lwc scheme the original nearly analytic discrete method nadm and its improved version with regard to numerical dispersion computational costs and computer storage requirements the numerical dispersionrelationsprovidedbytherefinedalgorithmfor1dand 2d cases are analyzed as well as the numerical results obtained bythismethodagainsttheexactsolutionforthe2dacousticcase numerical results show that the refined method gives no visible numericaldispersionforverylargespatialgridincrements itcan simulatehigh frequencywavepropagationforagivengridinterval and automatically suppress the numerical dispersion when the acoustic wave equation is discretized when too few samples per wavelength are used or when models have large velocity contrasts unlike the high order lwc methods our present methodcansavesubstantialcomputationalcostsandmemoryrequirements because very large grid increments can be used the refined method can be used for the simulation of large scale wavefields

toeplitz operators and hamiltonian torus actions this paper is devoted to semi classical aspects of symplectic reduction consider a compact prequantizable kahler manifold m with a hamiltonian torus action in the seminal paper v guillemin s sternberg geometric quantization and multiplicities of group representations invent math 67 3 1982 515 538 guillemin and sternberg introduced an isomorphism between the invariant part of the quantum space associated to m and the quantum space associated to the symplectic quotient of m provided this quotient is non singular we prove that this isomorphism is a fourier integral operator and that the toeplitz operators of m descend to toeplitz operators of the reduced phase space we also extend these results to the case where the symplectic quotient is an orbifold and estimate the spectral density of a reduced toeplitz operator a result related to the riemann roch kawasaki theorem

an effective imaging condition for reverse time migration using wavefield decomposition reverse time migration rtm exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models however low frequency high amplitude noises commonly seen in a typical rtm image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly we propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image the method works by first decomposing the source and receiver wavefields to their one way propagation components followed by applying a correlation based imaging condition to the appropriate combinations of the decomposed wavefields we first give the physical explanation of the principle of such noises in the conventional rtm image then we provide the detailed mathematical theory for the new imaging condition finally we propose an efficient scheme for its numerical implementation it replaces the computationally intensiv

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

identification of berezin toeplitz deformation quantization we give a complete identification of the deformation quantization which was obtained from the berezin toeplitz quantization on an arbitrary compact kahler manifold the deformation quantization with the opposite star product proves to be a differential deformation quantization with separation of variables whose dassifying form is explicitly calculated its characteristic dass which dassifies star products up to equivalence is obtained the proof is based on the microlocal description of the szego kernel of a strictly pseudoconvex domain given by boutet de monvel and sjostrand

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

brst reduction of quantum algebras with involutions in this paper we investigate the compatibility of the brst reduction procedure with the hermiticity of star products first we introduce the generalized notion of abstract brst algebras with corresponding involutions in this setting we define adjoint brst differentials and as a consequence one gets new brst quotients passing to the quantum brst setting we show that for compact lie groups the new quantum brst quotient and the quantum brst cohomology are isomorphic in zero degree implying that reduction is compatible with hermiticity

h sub spl infin filtering for multiple time delay measurements the aim of this paper is to study the h sub spl infin filtering problem for linear continuous time systems with both current and multiple time delay measurements the key technique applied for deriving the filter is the reorganized innovation analysis approach in krein space a necessary and sufficient condition for the existence of an h sub spl infin filter is derived and the solution to the h sub spl infin filter is given in terms of solutions of riccati and matrix differential equations an example is finally presented to show the effectiveness of the proposed approach

anisotropic wave propagation through finite difference grids an algorithm is presented to solve the elastic wave equation by replacing the partial differentials with finite differences it enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models the space derivatives are calculated using discrete convolution sums while the time derivatives are replaced by a truncated taylor expansion a centered finite difference scheme in cartesian coordinates is used for the space derivatives leading to staggered grids the use of finite difference approximations to the partial derivatives results in a frequency dependent error in the group and phase velocities of waves for anisotropic media the use of staggered grids implies that some of the elements of the stress and strain tensors must be interpolated to calculate the hook sum this interpolation induces an additional error in the wave properties the overall error depends on the precision of the derivative and interpolation operators the anisotropic symmetry system its orientation and the degree of anisotropy the dispersion relation for the homogeneous case was derived for the proposed scheme since we use a general description of convolution sums to describe the finite difference operators the numerical wave properties can be calculated for any space operator and an arbitrary homogeneous elastic model in particular phase and group velocities of the three wave types can be determined in any direction we demonstrate that waves can be modeled accurately even through models with strong anisotropy when the operators are properly designed

robust h filtering for discrete time varying uncertain systems with a known deterministic input in this paper a new discrete time dynamic game where two players seek to reinforce and suppress the output of a system under the influence of a known deterministic input is considered a necessary and sufficient condition for the existence of a saddle point solution to this game is derived in terms of a discrete time riccati difference equation the result of the game is used to solve the robust h x filtering problem for discrete time varying systems subject to a known deterministic input and norm bounded parameter uncertainties occurring in both the state and the output matrices of the state space model there is no restriction on the form of the filter this allows the effect of the known input on the estimation error due to system uncertainties to be optimally reduced without any prior assumption on the filter structure

h sup spl infin control and estimation with preview part ii fixed size are solutions in discrete time h sup spl infin preview control and fixed lag smoothing problems are solved in general discrete time linear systems via a reduction to equivalent open loop differential games to prevent high order riccati equations found in some solutions the state of the hamilton jacobi system resides in a quotient space of an auxiliary extended state space system the dimension of that auxiliary space is equal to the state space dimension of the original system ignoring the delay

the formal path integral and quantum mechanics given an arbitrary lagrangian function on rd and a choice of classical path one can try to define feynman s path integral supported near the classical path as a formal power series parameterized by feynman diagrams although these diagrams may diverge we compute this expansion and show that it is formally if there are ultraviolet divergences invariant under volume preserving changes of coordinates we prove that if the ultraviolet divergences cancel at each order then our formal path integral satisfies a fubini theorem expressing the standard composition law for the time evolution operator in quantum mechanics moreover we show that when the lagrangian is inhomogeneous quadratic in velocity such that its homogeneous quadratic part is given by a matrix with constant determinant then the divergences cancel at each order thus by cutting and pasting and choosing volume compatible local coordinates our construction defines a feynman diagrammatic formal path integral for the nonrelativistic q

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

reverse time migration in acoustic vti media using a high order stereo operator abstractwith the capability of handling complicated velocity models reverse time migration rtm has become a powerful imaging method improving imaging accuracy and computational efficiency are two significant but challenging tasks in the applications of rtm despite being the most popular numerical technique applied in rtm finite difference fd methods often suffer from undesirable numerical dispersion leading to a noticeable loss of imaging resolution a new and effective fd operator called the high order stereo operator has been developed to approximate the partial differential operators in the wave equation from which a numerical scheme called the three step stereo method tsm has been developed and has shown effectiveness in suppressing numerical dispersion numerical results show that compared with the conventional numerical methods such as the lax wendroff correction lwc scheme and the staggered grid sg fd method this new method significantly reduces numerical dispersion and computati

morita equivalence of poisson manifolds poisson manifolds are the classical analogue of associative algebras for poisson manifolds symplectic realizations play a similar role as representations do for associative algebras in this paper the notion of morita equivalence of poisson manifolds a classical analogue of morita equivalence of algebras is introduced and studied it is proved that morita equivalent poisson manifolds have equivalent categories of complete symplectic realizations for certain types of poisson manifolds the geometric invariants of morita equivalence are also investigated