symmetries and algebras of the integrable dispersive long wave equations in 2 1 dimensional spaces similarly to the kadomtsev petviashvili kp equation a set of generalized symmetries with arbitrary functions of t is given by a simple constructable formula for the integrable dispersive long wave equations in 2 1 space dimensions these symmetries constitute an infinite dimensional lie algebra which is a generalization to the known winfinity algebra

the n 2 super wess zumino novikov witten model valued in superdiffeomorphism sdiff m2 is self dual supergravity in four dimensions it is shown that the pure topological term of the n 2 super wess zumino novikov witten swznw model valued in the area preserving diffeomorphisms group of a two dimensional euclidean surface is self dual supergravity sdsg in 3 1 dimensions this is achieved by a suitable slicing and pasting procedure of the 2 0 0 2 n 2 swznw models determined by the embedding of the 2 0 0 2 superspace supercovariant derivatives into the 3 1 superspace ones preliminary steps are provided to show that the n 1 swznw model valued in the area preserving superdiffeomorphism group of a super riemann surface srs whose signature is 1 1 is self dual supergravity in 2 2 dimensions the so called atiyah ward space times

a rigid line in a confocal elliptic piezoelectric inhomogeneity embedded in an infinite piezoelectric medium an effective method is developed and used to investigate the elastic field and electric field of a rigid line in a confocal elliptic piezoelectric inhomogeneity embedded in an infinite piezoelectric medium the matrix is subjected to the remote antiplane shear and inplane electric field the analytical solution is obtained using the conformal mapping and the theorem of analytic continuation specific solutions which are compared with existing ones are provided the characteristics of the elastic field and electric field singularities at the rigid line tip are analyzed and the extension forces on the rigid line are derived

beyond ray tomography wavepaths and fresnel volumes two techniques that account for the band limited nature of seismic data are incorporated into tomographic traveltime inversion schemes the first technique the wavepath algorithm is based upon the wave equation the born approximation and an adjoint method for computing frechet derivatives computation of a single wavepath requires the forward propagation of the seismic wavefield as well as the reverse propagation of a residual wavefield the second technique the fresnel volume approach is based upon the paraxial ray approximation the fresnel volume algorithm requires little more computation than does conventional ray tracing and an order of magnitude less computer time than our calculation of wavepaths when the fresnel volume sensitivity functions are normalized by the area of the fresnel ellipse perpendicular to the ray the sensitivity estimates are very similar to the wavepaths in particular there is heightened sensitivity to velocity structure near the source and receiver locations the normalization by the fresnel ellipse area is necessary to ensure ray theoretical results in the limit of infinite frequency tomographic inversion based upon wavepaths or fresnel volumes is more appropriate when considering the arrival time of the peak of the initial pulse rather than the first arrival time furthermore using the traveltime of the peak instead of the first arrival time reduces the bias of tomograms to high velocity anomalies the raypath wavepath and fresnel volume techniques were applied to a set of cross borehole traveltime observations gathered at the grimsel rock laboratory all methods imaged a low velocity fracture zone in the granitic site in agreement with independent well information estimates of model parameter resolution are similar for the wavepath and fresnel volume schemes the source receiver regions are the most well resolved areas however the model parameter resolution computed using a conventional ray based formalism is more evenly distributed over the cross borehole area

self dual gravity via hitchin s equations in this work half flat metrics are obtained from hitchin s equations the su hitchin s equations are obtained and as a consequence of them the husain park equation is found certain solutions of hitchin s equations with gauge group su 2 associated with liouville sinh gordon and painleve iii equations are used to find solutions of the su hitchin s equations this is achieved via the moyal deformation of hitchin s equations from these solutions hamiltonian vector fields are determined which in turn are used to construct the half flat metrics following an approach of dunajski mason and woodhouse it is also possible to construct half flat metrics on m cp1 where m is r2 or s2

poisson lie group of pseudodifferential symbols we introduce a lie bialgebra structure on the central extension of the lie algebra of differential operators with scalar or matrix coefficients on the line and on the circle this defines a poisson lie structure on the dual group of pseudodifferential symbols of an arbitrary real or complex order we show that the usual second benney gl n kdv or gl n adler gelfand dickey and kp poisson structures are naturally realized as restrictions of this poisson structure to submanifolds of this universal poisson lie group moreover the reduced sl n versions of these manifolds orw n algebras in physical terminology can be viewed as certain subspaces of the quotient of this poisson lie group by the dressing action of the group of functions on the circle or as a result of a poisson reduction finally we define an infinite set of commuting functions on the poisson lie group that give the standard families of hamiltonians when restricted to the submanifolds mentioned above the poisson structure and hamiltonians on the whole group interpolate between the poisson structures and hamiltonians of benney kp and kdv flows we also discuss the geometrical meaning ofw as a limit of poisson algebraswe as e 0

on the classification of clifford algebras and their relation to spinors in n dimensions a classification of all the clifford algebras is given in terms of kronecker products of the quaternion and dihedral groups the relationship to spinors in n dimensions is explicitly determined we show that the real clifford algebra in minkowski spacetime is distinct from both the algebra of dirac matrices and the algebra of majorana matrices and cannot be realized by the spinor framework the matrix representations of clifford algebras are discussed and are utilized to give a classification of the real forms of lie algebras we are thus able to relate clifford lie and spinor algebras in an intrinsic geometrical setting

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

comparison of methods for extracting adcigs from rtm abstractmethods for extracting angle domain common image gathers adcigs during 2d reverse time migration fall into three main categories direction vector based methods local plane wave decomposition methods and local shift imaging condition methods the direction vector based methods which use either amplitude gradients or phase gradients cannot handle overlapping events because of an assumption of one propagation direction per imaging point per imaging time however the adcigs from the direction vector based methods have the highest angle resolution a new direction vector based method using instantaneous phase gradients in space and time gives the same propagation directions and adcigs as those obtained by the poynting vector or polarization vector based methods where amplitudes are large angles calculated by the phase gradients have larger uncertainties at smaller amplitudes but they do not significantly degrade the adcigs because they contribute only small amplitudes the local plane wave d

the generalized moyal nahm and continuous moyal toda equations we present in detail a class of solutions to the 4d su moyal anti self dual yang mills asdym equations an effective 6d theory that are related to reductions of the generalized moyal nahm equations using the ivanova popov ansatz the former yields solutions to the asdym sdym equations for arbitrary gauge groups in four dimensions a further dimensional reduction of the above effective 6d equations yields solutions to the moyal anti self dual gravitational equations in four dimensions the self dual yang mills self dual gravity case requires a separate study the su 2 toda lattice and su continuous moyal toda lattice equations are derived from the moyal nahm equations an explicit map taking the moyal heavenly form after a rotational killing symmetry reduction of the moyal heavenly equations into the su 2 toda lattice field is found finally the generalized moyal nahm equations are conjectured that contain the continuous su moyal toda lattice equations after a suitable reduction process embeddings of the different types of moyal toda lattice equations into the moyal nahm equations are described

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

hyper kahler metrics and a generalization of the bogomolny equations we generalize the bogomolny equations to field equations on 3 n and describe a twistor correspondence we consider a general hyper kahler metric in dimension 4n with an action of the torustn compatible with the hyper kahler structure we prove that such a metric can be described in terms of thetn solution of the field equations coming from the twistor space of the metric

generalization of the algebra of the matrix pseudodifferential operators we introduce the new nonhomogeneous graded matrix algebra matn r over the ring r of the pseudodifferential operators of the arbitrary orders this algebra forms the generalization of the algebra of the standard matrix pseudodifferential operators we show that the matn r algebra admits the nontrivial central extension the case n 2 is considered in some detail as the example we consider the mat2 w1 mat2 virasoro and mat2 sl 2 c algebras

from dispersionless to soliton systems via weyl moyal like deformations the formalism of quantization deformation is reviewed and the weyl moyal like deformation is applied to systematic construction of the field and lattice integrable soliton systems from poisson algebras of dispersionless systems

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

gauge theories in noncommutative homogeneous kahler manifolds we construct a gauge theory on a noncommutative homogeneous kahler manifold where we employ the deformation quantization with separation of variables for kahler manifolds formulated by karabegov a key point in this construction is to obtaining vector fields which act as inner derivations for the deformation quantization we give an explicit construction of this gauge theory on noncommutative cpn and noncommutative chn

su super gauge theories and self dual super gravity it is shown that su self dual yang mills equations on a four dimensional flat euclidean background are equivalent to plebanski s second heavenly equation for the self dual gravitational background which is associated with the cotangent space of a suitable riemann surface the riemann surface in question is nothing but the internal two dimensional surface required in the formulation of su self dual yang mills theories such equivalence only occurs when a dimensional reduction has taken place after a discussion of euclidean supersymmetries the results are generalized to self dual super yang mills theories and self dual supergravity

some comments on the non self dual nahm equations some empirical results on the cubic algebra 2a i sum limits j a j a j a i are presented the algebra is satisfied at the residue of any pole in a solution to nahm s non self dual equations

w gravity n 2 strings and 2 2 su yang mills instantons it is conjectured that w gravity can be interpreted as the gauge theory of diffeomorphisms in the space of dimensionally reduced d 2 2 su yang mills instantons these diffeomorphisms preserve a volume three form and are those that furnish the correspondence between the dimensionally reduced plebanski equation and the kp equation in 1 2 dimensions a supersymmetric extension furnishes super w gravity the super plebanski equation generates self dual complexified super gravitational backgrounds sdsg in terms of the super plebanski second heavenly form since the latter equation yields n 1 d 4 sdsg complexified backgrounds associated with the complexified cotangent space of the riemannian surface t c required in the formulation of su complexified self dual yang mills theory sdym it naturally follows that the recently constructed d 2 2 n 4 sdsym theory as the consistent background of the open n 2 superstring can be embedded into the n 1 su complexified self dual super yang mill

formal series of generalized functions and their application to deformation quantization foundations of the formal series calculus in deformation quantization are discussed several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced the notion of non negativity in formal series calculus is proposed problems with defining quantum states over the set of formal series are analyzed foundations of the formal series calculus in deformation quantization are discussed several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced the notion of non negativity in formal series calculus is proposed problems with defining quantum states over the set of formal series are analyzed

on higher order relations in fedosov supermanifolds higher order relations existing in normal coordinates between affine extensions of the symplectic curvature tensor and basic objects for any fedosov supermanifolds are derived representation of these relations in general coordinates is discussed

the logarithm of the derivative operator and higher spin algebras of w type we use the notion of the logarithm of the derivative operator to describew type algebras as central extensions of the algebra of differential operators we also provide closed formulae for the truncations ofw1 to higher spin algebras withs m for allm 2 the results are extended to matrix valued differential operators introducing a logarithmic generalization of the maurer cartan cocycle

symmetry reduction for the kadomtsev petviashvili equation using a loop algebra the kadomtsev petviashvili kp equation ut 3uux 2 1 4 uxxx x 3 uyy 4 0 allows an infinite dimensional lie group of symmetries i e a group transforming solutions amongst each other the lie algebra of this symmetry group depends on three arbitrary functions of time t and is shown to be related to a subalgebra of the loop algebra a 1 4 low dimensional subalgebras of the symmetry algebra are identified specifically all those of dimension n 3 and also a physically important six dimensional lie algebra containing translations dilations galilei transformations and quasirotations new solutions of the kp equation are obtained by symmetry reduction using the one dimensional subalgebras of the symmetry algebra these solutions contain up to three arbitrary functions of t

the classification of monopoles for the classical groups by studying a construction of nahm we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forsu n so n andsp n these are found to be equivalent to spaces of holomorphic maps from 1 into flag manifolds

deformations and renormalisations ofw deformations of the infiniten limit of the zamolodchikovwn algebra are discussed a recent one due to pope romans and shen with non zero central extensions for every conformal spin is shown to be formally renormalisable to one representable in moyal bracket form another deformation is discovered which like the algebra of pope et al possesses automatic closure but has non zero central extension only in the virasoro subalgebra

piezoelectric solid with an elliptic inclusion or hole the two dimensional problem of an elliptic hole in a solid of anisotropic piezoelectric material is studied the stroh formalism is adopted here real form solutions are obtained along the hole boundary in the case of an arbitrarily prescribed vector field on the hole surface for an elliptic rigid inclusion of electric conductor subjected to a line force a torque and a line charge a real form solution at the interface is obtained finally general solutions for an elliptic piezoelectric inclusion with uniform loading at infinity are investigated

on the moyal deformation of nahm equations in seven dimensions we show how the reduced anti self dual yang mills equations to seven dimensions described by the nahm equations can be carried over to the weyl wigner moyal formalism in the process some new solutions for the cases of gauge groups su 2 and sl 2 r are explicitly obtained

some comments on the adhm construction in 4k dimensions a class of completely solvable gauge field equations is investigated these equations are shown to be closely analogous to the four dimensional self duality equations a similar geometrical interpretation is exhibited and a generalisation of the adhm construction is shown to provide solutions

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

a formality theorem for hochschild chains abstract we prove tsygan s formality conjecture for hochschild chains of the algebra of functions on an arbitrary smooth manifold m using the fedosov resolutions proposed in math qa 0307212 and the formality quasi isomorphism for hochschild chains of r y 1 y d proposed in paper math qa 0010321 by shoikhet this result allows us to describe traces on the quantum algebra of functions on an arbitrary poisson manifold

classical a n w geometry by analyzing theextrinsic geometry of two dimensional surfaces chirally embedded incp n thecp n w surface 1 we give exact treatments in various aspects of the classical w geometry in the conformal gauge first the basis of tangent and normal vectors are defined at regular points of the surface such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the conformal a n toda lax pair since the latter is known to be intrinsically related with the w symmetries this gives the geometrical meaning of thea n w algebra second w surfaces are put in one to one correspondence with solutions of the conformally reduced wznw model which is such that the toda fields give the cartan part in the gauss decomposition of its solutions third the additional variables of the toda hierarchy are used as coordinates ofcp n this allows us to show that w transformations may be extended as particular diffeomorphisms of this target space higher dimensional generalizations of the wznw equations are derived and related with the zakharov shabat equations of the toda hierarchy fourth singular points are studied from a global viewpoint using our earlier observation 1 that w surfaces may be regarded as instantons the global indices of the w geometry which are written in terms of the toda fields are shown to be the instanton numbers for associated mappings of w surfaces into the grassmannians the relation with the singularities of w surface is derived by combining the toda equations with the gauss bonnet theorem

symmetry algebras of the potential nizhnik novikov veselov model two sets of generalized symmetries of the potential nizhnik novikov veselov equation are given in a simple formula by developing a generalized formal series method for searching symmetries of one type of generalized partial differential equations these two sets of symmetries constitute an infinite dimensional lie algebra which contains three types of virasoro algebras and three w type algebras as its special cases

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

validation of first order diffraction theory for the traveltimes and amplitudes of propagating waves ultrasonic measurements of acoustic wavefields scattered by single spheres placed in a homogenous background medium water are presented the dimensions of the spheres are comparable to the wavelength and the wavelength and represent both positive rubber and negative teflon velocity anomalies with respect to the background medium the sensitivity of the recorded wavefield to scattering in terms of traveltime delay and amplitude variation is investigated the results validate a linear first order diffraction theory for wavefields propagating in heterogeneous media with anomaly contrasts on the order of 15 the diffraction theory is compared further with the exact results known from literature for scattering from an elastic sphere formulated in terms of legendre polynomials to investigate the 2d case the first order scattering theory is tested against 2d elastic finite difference calculations as the presented theory involves a volume integral it is applicable to any geometric shape and the scattering object does not need to be spherical or any other specific symmetrical shape furthermore it can be implemented easily in seismic data inversion schemes which is illustrated with examples from seismic crosswell tomography and a reflection experiment

extensions and contractions of the lie algebra ofq pseudodifferential symbols on the circle abstract we construct cocycles on the lie algebra of pseudo and q pseudodifferential symbols of one variable and on their close relatives the sine algebra and the poisson algebra on two torus a quantum godbillon vey cocycle on pseudo differential operators appears in this construction as a natural generalization of the gelfand fuchs 3 cocycle on periodic vector fields a nontrivial embedding of the virasoro algebra into a completion of q pseudodifferential symbols is proposed we describe q analogs of the kp and kdv hierarchies admitting an infinite number of conserved charges as well as q deformed gelfand dickey structures

the algebra of q pseudodifferential symbols and the q wkp n algebra in this paper we continue with the program to explore the topography of the space of w type algebras in the present case the starting point is the work of khesin lyubashenko and roger on the algebra of q deformed pseudodifferential symbols and their associated integrable hierarchies the analysis goes on by studying the associated hamiltonian structures for which compact expressions are found the fundamental poisson brackets yield q deformations of wkp and related w type algebras which in specific cases coincide with the ones constructed by frenkel and reshetikhin the construction underlies a continuous correspondence between the hamiltonian structures of the toda lattice and the kp hierarchies

some geometric structures associated with a k symplectic manifold a canonical connection is attached to any k symplectic manifold we study the properties of this connection and its geometric applications to k symplectic manifolds in particular we prove that under some natural assumptions any k symplectic manifold admits an ehresmann connection discuss some corollaries of this result and find vanishing theorems for characteristic classes on a k symplectic manifold

some solutions of the yang mills equations in dimension greater than four the yang mills equations for gauge fields of an arbitrary semisimple lie group g in euclidean spaces rn with dimension n 4 is considered for gauge fields aa we introduce the ansatze which reduce the yang mills equations in rn to a set of nonlinear differential matrix equations rouhani ward equations this permits us to write out the explicit form of cosmological plane wave and other types of solutions

wave equation tomography the relation between ray trace and diffraction tomography is usually obscured by formulation of the two methods in different domains the former in space the latter in wavenumber here diffraction tomography is reformulated in the space domain under the title of wave equation tomography with this transformation wave equation tomography projects monochromatic scattered wavefields back over source receiver wavepaths just as ray trace tomography projects traveltime delays back over source receiver raypaths derived under the born approximation these wavepaths are wave theoretic back projection patterns for reflected energy derived under the rytov approximation they are wave theoretic back projection patterns for transmitted energy differences between ray trace and wave equation tomography are examined through comparison of wavepaths and raypaths followed by their application to a transmission geometry synthetic data set rytov wave equation tomography proves superior to ray trace tomography in de

linearized wave equation migration velocity analysis by image warping seismic imaging produces images of contrasts in physical parameters in the subsurface e g velocity or impedance to build such images a background model describing the wave kinematics in the earth is necessary in practice the structural image and background velocity model are unknown and have to be estimated from the acquired data migration velocity analysis deals with estimation of the background model in the framework of seismic migration and relies on two main elements data redundancy and invariance of the structures with respect to different seismic experiments because all the experiments probe the same model the reflectors must be invariant in suitable domains e g shots or reflection angle the semblance principle is the tool used to measure the invariance of a set of multiple images we measure the similarity of the structural features between pairs of single shot migrated images obtained from adjacent experiments by using the estimated warping vector field between two migrated images we construct an image perturbation which describes the difference in reflectivity observed by two shots we derive an expression for the image perturbation that drives a migration velocity analysis procedure based on a linearization of the wave equation with respect to the model parameters synthetic 2d examples show promising results in retrieving errors in the velocity model this methodology can be directly applied to 3d

self duality in super yang mills theories the self dual condition in superspace is analysed forn 1 2 4 super yang mills theories a complete solution of all the constraints in terms of a light cone superfieldj is presented where the only equation thatj satisfies is a susy generalization of the yang equation by reduction of that equation we obtain various two dimensional susy models we introduce the associated linear problem in terms ofj whose integrability condition gives us back the super yang equation and allows us to obtain the kac moody algebra structure of the theory

killing vectors in self dual euclidean einstein spaces using the formalism of complex h spaces we show that all real euclidean self dual spaces that admit at least one killing vector may be gauged so that only two distinct types of killing vectors appear in kahler coordinates these are the generators of a translational or a rotational symmetry we give explicit forms both for the killing vectors and for the constraint on the kahler potential function which allows for such a killing vector in the translational case we show how all such spaces are determined by the general solution of the three dimensional flat laplace s equation and how these are related to the multi taub nut metrics of gibbons and hawking in the rotational case we simplify the equation determining but this is not sufficient to obtain the general solution

acoustic inverse scattering via helmholtz operator factorization and optimization we present a joint acoustic seismic inverse scattering and finite frequency reflection tomography program formulated as a coupled set of optimization problems in terms of inhomogeneous helmholtz equations we use a higher order finite difference scheme for these helmholtz equations to guarantee sufficient accuracy we adapt a structured approximate direct solver for the relevant systems of algebraic equations which addresses storage requirements through compression to yield a complexity for computing the gradients or images in the optimization problems that consists of two parts viz the cost for all the matrix factorizations which is roughly o rn for example o rnlogn when d 2 times the number of frequencies and the cost for all solutions by substitution which is roughly o n for example o nlog rlogn when d 2 times the number of frequencies times the number of sources events where n n d if n is the number of grid samples in any direction and r is a parameter depending on the preset accuracy and the problem at hand with this complexity the multi frequency approach to inverse scattering and finite frequency tomography becomes computationally feasible with large data sets in dimensions d 2 and 3

the finite frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis we have derived a broadband sensitivity kernel that relates the residual moveout rmo in prestack depth migration psdm to velocity perturbations in the migration velocity model we have compared the kernel with the rmo directly measured from the migration image the consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation based on this broadband sensitivity kernel we propose a new tomography method for migration velocity analysis and updating specifically for the shot record psdm and shot index common image gather as a result time consuming angle domain analysis is not required we use a fast one way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel using synthetic data sets we can successfully invert velocity perturbations from the migration rmo this wave equation based method naturally incorporates the wave phenomena and is best teamed with the wave

subalgebras of w 1 infinity and their quasifinite representations we propose a series of new subalgebras of the w1 infinity algebra parametrized by polynomials p omega and study their quasifinite representations we also investigate the relation between such subalgebras and the gl infinity algebra as an example we investigate the winfinity algebra which corresponds to the case p omega w presenting its free field realizations and kac determinants at lower levels

three dimensional eigenfunction analysis of a crack in a piezoelectric material abstract a three dimensional analysis of a semi infinite crack embedded in a transversely isotropic piezoelectric material was performed by means of the eigenfunction expansions method the results show the characteristic 1 r singular behavior of the stress tensor in the vicinity of the crack a similar behavior is also revealed for the electric field in addition the study demonstrates that coupling or decoupling of the mechanical and electrical variables is a function of the distance to the crack tip as well as of the crack orientation

twisted deformation quantization of algebraic varieties abstract let x be a smooth algebraic variety over a field k containing the real numbers we introduce the notion of twisted associative resp poisson deformation of the structure sheaf o x these are stack like versions of usual deformations we prove that there is a twisted quantization operation from twisted poisson deformations to twisted associative deformations which is canonical and bijective on gauge equivalence classes this result extends work of kontsevich and our own earlier work on deformation quantization of algebraic varieties

the fresnel volume and transmitted waves in seismic imaging experiments it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high frequency limit consequently it is assumed that waves propagate along infinitely narrow lines through space called rays that join the source and receiver in reality recorded waves have a finite frequency content the band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path this volume is called the fresnel volume in this tutorial we introduce the physics of the fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves the finite frequency wave theory specifies sensitivity kernels that linearly relate the traveltime and amplitude of band limited transmitted and reflected waves to slowness variations in the earth the fresnel zone and the finite frequency sensitivity kernels are closely connected through the concept of constructive interference of waves the finite frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the wavefield also it turns out that fermat s theorem in the context of geometric ray theory is a special case of the finite frequency wave theory in the limit of infinite frequency last we address the misconception that the width of the fresnel volume limits the resolution in imaging experiments

integrable discretizations of chiral models via deformation of the differential calculus a construction of conservation laws for chiral models generalized models on a two dimensional spacetime continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions this is achieved via a deformation of the ordinary differential calculus in particular the nonlinear toda lattice results in this way from the linear continuum wave equation the method is applied to several further examples we also construct lax pairs and backlund transformations for the class of models considered in this work

new developments concerning piezoelectric materials with defects abstract the problem of a piezoelectric body with an elliptic cavity is revisited within the frame work of two dimensional electro elasticity in contrast to our previous formulation the present analysis is based on the use of exact electric boundary conditions at the rim of the hole thus avoiding the common assumption of electric impermeability expressions for the elastic and electric variables induced inside and outside the cavity are derived in closed form in terms of complex potentials comparisons between present exact and previous approximate models are effected to establish the limitations associated with the assumption of the impermeable hole in particular when it becomes a slit crack

schwinger terms and cohomology of pseudodifferential operators we study the cohomology of the schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra we prove that for all pseudodifferential operators in 3 1 dimensions of this type the schwinger term is equivalent to the twisted radul cocycle a modified version of the radul cocycle arising in non commutative differential geometry in the process we also show how the ordinary radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component

cotangent bundle quantization entangling of metric and magnetic field for manifolds of noncompact type endowed with an affine connection for example the levi civita connection and a closed 2 form magnetic field we define a hilbert algebra structure in the space and construct an irreducible representation of this algebra in this algebra is automatically extended to polynomial in momenta functions and distributions under some natural conditions this algebra is unique the non commutative product over is given by an explicit integral formula this product is exact not formal and is expressed in invariant geometrical terms our analysis reveals that this product has a front which is described in terms of geodesic triangles in the quantization of functions induces a family of symplectic reflections in and generates a magneto geodesic connection on this symplectic connection entangles on the phase space level the original affine structure on and the magnetic field in the classical approximation the 2 part of the quantum product contains the ricci curvature of and a magneto geodesic coupling tensor