simple diagonal locally finite lie algebras the ground field f is an algebraically closed field of zero characteristic and bbb n is the set of natural numbers let l be a locally finite dimensional or em locally finite for brevity lie algebra assume for simplicity that l has countable dimension then one can choose finite dimensional subalgebras l i i in bbb n of l in such a way that l i subset l i 1 for all i and l bigcup i in bbb n l i the set l i mid i in bbb n is called a em local system of l assume that l is simple then all l i can be chosen to be perfect that is l i l i l i we shall call such local systems em perfect let s i s i 1 oplus ldots oplus s i n i be a levi subalgebra of l i where s i 1 ldots s i n i are simple components of s i and let v i k be the standard s i k module since l i is perfect for every k there exists a unique irreducible l i module cal v i k such that the restriction cal v i k downarrow s i k is isomorphic to v i k an embedding l i to l i 1 is called em diagonal if for each l any non trivial composition factor of the restriction cal v i 1 l downarrow l i is isomorphic to cal v i k or its dual cal v i k for some k we prove that a simple locally finite lie algebra l can be embedded into a locally finite associative algebra if and only if there exists a perfect local system l i i in bbb n of l such that all embeddings l i to l i 1 are diagonal note that this result can be considered as a version of ado s theorem for simple locally finite lie algebras let v be a vector space an element x in frak gl v is called em finitary if dim xv infty the finitary transformations of v form an ideal frak fgl v of frak gl v and any subalgebra of frak fgl v is called a em finitary lie algebra we classify all finitary simple lie algebras of countable dimension it turns out that there are only three frak sl infty f frak so infty f and frak sp infty f the author has classified all finitary simple lie algebras and will describe this in a subsequent paper the analogous problem in group theory has been recently solved by j i hall he classified simple locally finite groups of finitary linear transformations 1991 mathematics subject classification 17b35 17b65

weak convergence of some classes of martingales with jumps this paper deals with weak convergence of stochastic integrals with respect to multivariate point processes the results are given in terms of an entropy condition for partitioning of the index set of the integrands which is a sort of l 2 bracketing we also consider valued martingale difference arrays and present natural generalizations of jain marcus s and ossiander s central limit theorems as an application the asymptotic behavior of log likelihood ratio random fields in general statistical experiments with parameters is derived

algebras of quotients of graded lie algebras abstract in this paper we explore graded algebras of quotients of lie algebras with special emphasis on the 3 graded case and answer some natural questions concerning its relation to maximal jordan systems of quotients

classification of the direct limits of involution simple associative algebras and the corresponding dimension groups abstract a classification of the countable direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained this also classifies the corresponding dimension groups the set of invariants consists of two supernatural numbers and two real parameters

feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band limited reflection data abstractbecause seismic reflection data are band limited acoustic impedance profiles derived from them are nonunique the conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients by making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data drawing only on first principles the zoeppritz equation in this case the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band limited data the local layer cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness provided that the objective is to reconstruct a smooth version

quasiclassical lie algebras abstract in this paper we study finite dimensional non semisimple lie algebras that can be obtained as lie algebras of skew symmetric elements of associative algebras with involution we call such algebras quasiclassical and characterize them in terms of existence of so called plain representations we show that the theory of plain representations for quasiclassical lie algebras is almost equivalent to representation theory of associative algebras with involution

a bott borel weil theory for direct limits of algebraic groups we develop a bott borel weil theory for direct limits of algebraic groups some of our results apply to locally reductive ind groups g in general i e to arbitrary direct limits of connected reductive linear algebraic groups our most explicit results concern root reductive ind groups g the locally reductive ind groups whose lie algebras admit root decomposition given a parabolic subgroup p of g and a rational irreducible p module we consider the irreducible g sheaves inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i and their duals inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i these sheaves are locally free in general of infinite rank we prove a general analog of the bott borel weil theorem for inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i namely that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i is nonzero for at most one index q q 0 and that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i is isomorphic to the dual of a rational irreducible g module v for q 0 0 we show that in contrast to the finite dimensional case v need not admit an irreducible p submodule there however one has a larger parabolic subgroup w p p constructed from p and a weyl group element w of length q 0 such that v is generated by an irreducible w p submodule consequently certain g modules v can appear only for q 0 0 never for q 0 0 for inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i we show that there is no analog of bott s vanishing theorem more precisely that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i can have arbitrarily many nonzero cohomology groups finally we give an explicit criterion for the projectivity of the ind variety g p showing that g p is in general not projective

simultaneous multitrace impedance inversion with transform domain sparsity promotion abstractthe impedance inversion technique plays a crucial role in seismic reservoir properties prediction however most existing impedance inversion methods often suffer from spatial discontinuities and instability because each vertical profile is processed independently in the inversion we tested a transform domain sparsity promotion simultaneous multitrace impedance inversion method to address this issue the approach was implemented through minimizing a data misfit term and a transform domain sparsity constraint term that incorporates the 2d or 3d structural information into the inversion processing a 2d synthetic data example was applied to mainly explain the roles of the transform domain sparsity constraint we determined that the transform domain sparsity constraint can help in stabilizing the inversion reducing the influence of high wavenumber noise on the inverted result and exploring spatial continuities of structures furthermore a 3d field data example was used to examine the effectiven

seismic sparse layer reflectivity inversion using basis pursuit decomposition a basis pursuit inversion of seismic reflection data for reflection coefficients is introduced as an alternative method of incorporating a priori information in the seismic inversion process the inversion is accomplished by building a dictionary of functions representing reflectivity patterns and constituting the seismic trace as a superposition of these patterns basis pursuit decomposition finds a sparse number of reflection responses that sum to form the seismic trace when the dictionary of functions is chosen to be a wedge model of reflection coefficient pairs convolved with the seismic wavelet the resulting reflectivity inversion is a sparse layer inversion rather than a sparse spike inversion synthetic tests suggest that a sparse layer inversion using basis pursuit can better resolve thin beds than a comparable sparse spike inversion application to field data indicates that sparse layer inversion results in the potentially improved detectability and resolution of some thin layers and reveals a

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

unitary highest weight modules of inductive limit lie algebras and groups abstract representations of inductive limits of finite dimensional lie groups and algebras am our main objects of study such representations can be constructed by taking inductive limits of the representations of the finite dimensional groups or algebras for finite dimensional lie groups and algebras of hermitian symmetric type enright howe wallach classified those highest weight representations which are unitarizable in this paper we consider the limits of the algebras u p n so 2n and sp n r the limits of the corresponding maximal compact subgroup and the limits of the corresponding generalized verma modules we give necessary and sufficient conditions for the inductive limit representation to be unitarizable in all three cases we show that a necessary condition for unitarizability is that the highest weight is eventually constant we also give sufficient conditions depending on the constant which will ensure that the limit is unitarizable

the central limit theorem for stochastic processes the main result is that the necessary and sufficient conditions for the central limit theorem for centered second order processes given by gine and zinn 6 can be obtained without any basic measurability condition furthermore we extend some of their results

concentration inequalities large and moderate deviations for self normalized empirical processes we consider the supremum w n of self normalized empirical processes indexed by unbounded classes of functions f such variables are of interest in various statistical applications for example the likelihood ratio tests of contamination using the herbst method we prove an exponential concentration inequality for w n under a second moment assumption on the envelope function of f this inequality is applied to obtain moderate deviations for w n we also provide large deviations results for some unbounded parametric classes f

probability inequalities for empirical processes and a law of the iterated logarithm given a class f of functions on x we can view vn as a stochastic process indexed by f and consider limit theorems for this process to prove such theorems it is often helpful to have bounds on the tail of the r v sup w i n f i see for example dudley 1978 kuelbs and dudley 1980 dudley and phillip 1983 or gine and zinn 1983 our main question of interest is for what classes f can best possible bounds be obtained so first we must ask what are these best possible bounds of course

branching laws for tensor modules over classical locally finite lie algebras abstract let g and g be isomorphic to any two of the lie algebras gl sl sp and so let m be a simple tensor g module we introduce the notion of an embedding g g of general tensor type and derive branching laws for triples g g m where g g is an embedding of general tensor type more precisely since m is in general not semisimple as a g module we determine the socle filtration of m over g due to the description of embeddings of classical locally finite lie algebras given by dimitrov and penkov in 2009 our results hold for all possible embeddings g g unless g gl

finitary lie algebras abstract an algebra is called finitary if it consists of finite rank transformations of a vector space we classify finitary simple and finitary irreducible lie algebras over an algebraically closed field of characteristic 2 3

a fast automatic multichannel blind seismic inversion for high resolution impedance recovery abstractthe inversion of seismic reflection data for acoustic impedance ai is a common and accepted method for the interpretation of poststack seismic data the original mathematical problem is nonlinear due to the nonlinearity of relation between the ai and the earth reflectivity series and also the insufficiency of information about the source wavelet furthermore the problem is ill posed due to the lack of low and high frequencies in the data we have developed a multichannel blind inversion and solved it for obtaining the ai model and the wavelet directly from seismic reflection data we found a solution to the overall problem by alternating between two subproblems corresponding to the ai and wavelet recovery having an estimation of the wavelet the algorithm directly inverts multichannel data for a high resolution ai model having blocky structures in the sense of total variation tv regularization while satisfying a priori low frequency information the advantages of the split bregman techniq

incorporating geologic information into reflection tomography in areas of complex geology prestack depth migration is often necessary if we are to produce an accurate image of the subsurface prestack depth migration requires an accurate interval velocity model with few exceptions the subsurface velocities are not known beforehand and should be estimated when the velocity structure is complex with significant lateral variations reflection tomography methods are often an effective tool for improving the velocity estimate unfortunately reflection tomography often converges slowly to a model that is geologically unreasonable or it does not converge at all the large null space of reflection tomography problems often forces us to add a sparse parameterization of the model and or regularization criteria to the estimation standard tomography schemes tend to create isotropic features in velocity models that are inconsistent with geology these isotropic features result in large part from using symmetric regularization operators or from choosing a poor model parameterization if we replace the symmetric operators with nonstationary operators that tend to spread information along structural dips the tomography will produce velocity models that are geologically more reasonable in addition by forming the operators in helical 1d space and performing polynomial division we apply the inverse of these space varying anisotropic operators the inverse operators can be used as a preconditioner to a standard tomography problem thereby significantly improving the speed of convergence compared with the typical regularized inversion problem results from 2d synthetic and 2d field data are shown in each case the velocity obtained improves the focusing of the migrated image

kaplan meier estimators of distance distributions for spatial point processes when a spatial point process is observed through a bounded window edge effects hamper the estimation of characteristics such as the empty space function f the nearest neighbor distance distribution g and the reduced second order moment function k here we propose and study product limit type estimators of f g and k based on the analogy with censored survival data the distance from a fixed point to the nearest point of the process is right censored by its distance to the boundary of the window the resulting estimators have a ratio unbiasedness property that is standard in spatial statistics we show that the empty space function f of any stationary point process is absolutely continuous and so is the product limit estimator of f the estimators are strongly consistent when there are independent replications or when the sampling window becomes large we sketch a clt for independent replications within a fixed observation window and asymptotic theory for independent replications of sparse poisson processes in simulations the new estimators are generally more efficient than the border method estimator but for estimators of k somewhat less efficient than sophisticated edge corrections

multichannel spatially correlated reflectivity inversion using block sparse bayesian learning abstractthe reflectivity inversion approach based on a variety of regularization terms was extensively developed and applied to image subsurface structure in recent years in addition multichannel reflectivity inversion or deconvolution considering the lateral continuity of reflection interfaces or reflectivity in adjacent channels has been developed however these processing operations seldom adaptively judge the stratal continuity or automatically alter the parameters of the corresponding algorithm to use the special correlation of the reflection information contained in the seismic data a multichannel spatially correlated reflectivity inversion using block sparse bayesian learning bsbl is introduced the method adopts a covariance matrix that describes the spatial relationship of reflectivity and simultaneously controls the temporal sparsity with an expectation maximization algorithm we can obtain the parameters of the multichannel reflectivity model including the mean i e the estimated mul

multichannel matching pursuit for seismic trace decomposition the technique of matching pursuit can adaptively decompose a seismic trace into a series of wavelets however the solution is not unique and is also strongly affected by data noise multichannel matching pursuit mcmp exploiting lateral coherence as a constraint might improve the uniqueness of the solution it extracts a constituent wavelet that has an optimal correlation coefficient to neighboring traces instead of to a single trace only according to linearity theory a wavelet shared by neighboring traces is the best match to the average of multiple traces and therefore it might effectively suppress the data noise and stabilize the performance it is found that the mcmp scheme greatly improves spatial continuity in decomposition and can generate a plausible time frequency spectrum with high resolution for reservoir detection

hellinger consistency of certain nonparametric maximum likelihood estimators consider a class mathscr p p theta theta in theta of probability measures on a measurable space mathscr x mathscr a dominated by a sigma finite measure mu let f theta dp theta d mu theta in theta and let theta n be a maximum likelihood estimator based on n independent observations from p theta 0 theta 0 in theta we use results from empirical process theory to obtain convergence for the hellinger distance h f hat theta n f theta 0 under certain entropy conditions on the class of densities f theta theta in theta the examples we present are a model with interval censored observations smooth densities monotone densities and convolution models in most examples the convexity of the class of densities is of special importance

a central limit theorem under metric entropy with l_2 bracketing let mathbf s rho be a metric space mathbf v mathscr v mu be a probability space and f mathbf s times mathbf v rightarrow mathbb r be a real valued function on mathbf s times mathbf v which has mean zero and is lipschitz in l 2 mu with respect to rho let v be a random variable defined on mathbf v mathscr v mu and let v i i geq 1 be a sequence of independent copies of v the limiting behavior of the process s n s n 1 2 sum n i 1 f s v i is studied under an integrability condition on the metric entropy with bracketing in l 2 mu this metric entropy condition is analogous to one which implies the continuity of the limiting gaussian process a tightness result is derived which in conjunction with the results of andersen and dobric 1987 shows that a central limit theorem holds for the s n process this result generalizes those of dudley 1978 dudley 1981 and jain and marcus 1975

simple locally finite dimensional lie algebras in positive characteristic abstract we prove two structure theorems for simple locally finite dimensional lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form r r z r r r or k r k r for a simple locally finite dimensional associative algebra r with involution the first proves that a condition we introduce known as locally nondegenerate along with the existence of an ad nilpotent element suffice the second proves that an ad integrable lie algebra is of this type if the characteristic of the ground field is sufficiently large lastly we construct a simple locally finite dimensional associative algebra r with involution such that k r k r k r to demonstrate the necessity of considering the commutator in the first two theorems

exponential inequalities for martingales with application to maximum likelihood estimation for counting processes we obtain an exponential probability inequality for martingales and a uniform probability inequality for the process gdn where n is a counting process and where g varies within a class of predictable functions g for the latter we use techniques from empirical process theory the uniform inequality is shown to hold under certain entropy conditions on g as an application we consider rates of convergence for nonparametric maximum likelihood estimators for counting processes a similar result for discrete time observations is also presented

the bott borel weil theorem for direct limit groups we show how highest weight representations of certain infinite dimensional lie groups can be realized on cohomology spaces of holomorphic vector bundles this extends the classical bott borel weil theorem for finite dimensional compact and complex lie groups our approach is geometric in nature in the spirit of bott s original generalization of the borel weil theorem the groups for which we prove this theorem are strict direct limits of compact lie groups or their complexifications we previously proved that such groups have an analytic structure our result applies to most of the familiar examples of direct limits of classical groups we also introduce new examples involving iterated embeddings of the classical groups and see exactly how our results hold in those cases one of the technical problems here is that in general the limit lie algebras will have root systems but need not have root spaces so we need to develop machinery to handle this somewhat delicate situation

interpolation and extrapolation using a high resolution discrete fourier transform we present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra this approach minimizes a cost function derived from bayes theorem the method is suitable for line spectra since a long tailed distribution is used to model the prior distribution of spectral amplitudes since the data themselves are used as constraints phase information can also be recovered and used to extend the data outside the original window the objective function is formulated in terms of hyperparameters that control the degree of fit and spectral resolution noise rejection can also be achieved by truncating the number of iterations spectral resolution and extrapolation length are controlled by a single parameter when this parameter is large compared with the spectral powers the algorithm leads to zero extrapolation of the data and the estimated fourier transform yields the periodogram when the data are sampled at a constant rate the algorithm uses one levinson recursion per iteration for irregular sampling the algorithm uses one cholesky decomposition per iteration the performance of the algorithm is illustrated with three different problems that arise in geophysical data 1 harmonic retrieval from a time series contaminated with noise 2 linear event detection from a finite aperture array of receivers 3 interpolation extrapolation of gapped data the performance of the algorithm as a spectral estimator is tested with the kay and marple 1981 data set

finitary simple lie algebras abstract an algebra is called finitary if it consists of finite rank transformations of a vector space we classify finitary simple lie algebras over a field of characteristic 0 we also describe finitary irreducible lie algebras

simple lie subalgebras of locally finite associative algebras abstract we prove that any simple lie subalgebra of a locally finite associative algebra is either finite dimensional or isomorphic to the commutator algebra of the lie algebra of skew symmetric elements of some involution simple locally finite associative algebra the ground field is assumed to be algebraically closed of characteristic 0 this result can be viewed as a classification theorem for simple lie algebras that can be embedded in locally finite associative algebras we also establish a link between this class of lie algebras and that of lie algebras graded by finite root systems

the central limit theorem for empirical processes under local conditions the case of radon infinitely divisible limits without gaussian component on obtient des resultats de convergence faible pour des processus empiriques indices par des classes f de fonctions dans le cas de limites de radon purement de poisson infiniment divisibles

simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis we present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records we based our technique on multichannel singular spectrum analysis mssa the technique entails organizing spatial data at a given temporal frequency into a block hankel matrix that in ideal conditions is a matrix of rank k where k is the number of plane waves in the window of analysis additive noise and missing samples will increase the rank of the block hankel matrix of the data consequently rank reduction is proposed as a means to attenuate noise and recover missing traces we present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets in addition we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm we apply mssa reconstruction to synthetic examples and a field data set synthetic examples were used to assess the performance of the method in two

universal central extensions of direct limits of lie superalgebras abstract we show that the universal central extension of a direct limit of perfect lie superalgebras l i is isomorphic to the direct limit of the universal central extensions of l i as an application we describe the universal central extensions of some infinite rank lie superalgebras

regularity of gaussian processes on donne la validite de la conjecture de fernique 1974 sur l existence de mesures de majoration pouvant caracteriser la limitation des processus gaussiens

recovery of the acoustic impedance from reflection seismograms this paper examines the problem of recovering the acoustic impedance from a band limited normal incidence reflection seismogram the convolutional model for the seismogram is adopted at the outset and it is therefore required that initial processing has removed multiples and recovered true amplitudes as well as possible in the first portion of the paper we investigate the effect of substituting the deconvolved seismic trace that is the band limited version of the reflectivity function into the standard recursion formula for the acoustic impedance the formalism of linear inverse theory is used to show that the logarithm of the normalized acoustic impedance estimated from the deconvolved seismogram is approximately an average of the true logarithm of the impedance moreover the averaging function is identical to that used in deconvolving the initial seismogram the advantage of these averages is that they are unique their disadvantage is that low frequency information which is crucial to making a g

inner ideals of simple locally finite lie algebras abstract inner ideals of simple locally finite dimensional lie algebras over an algebraically closed field of characteristic 0 are described in particular it is shown that a simple locally finite dimensional lie algebra has a non zero proper inner ideal if and only if it is of diagonal type regular inner ideals of diagonal type lie algebras are characterized in terms of left and right ideals of the enveloping algebra regular inner ideals of finitary simple lie algebras are described

the classification of locally finite split simple lie algebras one of the great early achievements in lie theory is the classification of the finite dimensional simple complex lie algebras by w killing and e cartan more than 50 years later new aspects were added to this classification by the theory of coxeter groups and the visualization of the classification in terms of dynkin diagrams furthermore serre s description of the simple lie algebras by generators and relations provided a direct way to construct the lie algebras from the cartan matrix corresponding to the choice of a root base i e a system of simple roots

the central limit theorem for empirical processes on vapnik cervonenkis classes sufficient conditions which under weak additional assumptions are also necessary are found for the central limit theorem for empirical processes indexed by classes of functions which have the vapnik cervonenkis property this improves an earlier theorem of pollard 1982a and leads to necessary and sufficient conditions for the clt for weighted empirical processes indexed by vapnik cervonenkis classes of sets

representations of finitary lie algebras abstract let f be an algebraically closed field of characteristic 2 3 w a f vector space and l gl w with nilwl 0 dimfl suppose l fgl w is a finitary subalgebra the faithful irreducible l modules are determined it is shown that l has minimal ideals if a minimal ideal s is infinite dimensional then sw is a completely reducible l module suppose l fgl w 0 w is l irreducible and char f 3 then l is classified in terms of l fgl w

a clt for empirical processes involving time dependent data for stochastic processes xt t e we establish sufficient conditions for the empirical process based on ixt y pr xt y t e y r to satisfy the clt uniformly in t e y r corollaries of our main result include examples of classical processes where the clt holds and we also show that it fails for brownian motion tied down at zero and e 0 1

an artinian theory for lie algebras abstract complemented lie algebras are introduced in this paper a notion similar to that studied by o loos and e neher in jordan pairs we prove that a lie algebra is complemented if and only if it is a direct sum of simple nondegenerate artinian lie algebras moreover we classify simple nondegenerate artinian lie algebras over a field of characteristic 0 or greater than 7 and describe the lie inner ideal structure of simple lie algebras arising from simple associative algebras with nonzero socle

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

shot domain deblending using least squares inversion abstractsimultaneous source acquisition which allows a temporal overlap between shot records has significant advantages to improve data quality e g denser shooting and reduce acquisition cost e g efficient wide azimuth shooting we have developed a novel shot domain deblending approach for a wide azimuth simultaneous shooting survey based on an inversion scheme the inverse problem is formulated by introducing two convolution operators that can respectively destruct the signal and interference and is solved by a conjugate gradient algorithm in the least squares sense our approach breaks down the limit that source separation can only be implemented in some domains other than the shot domain based on the incoherency principle our shot domain approach does not require the random dithering time thus it is very flexible to use in a wide azimuth simultaneous shooting survey three numerically blended synthetic examples were developed to demonstrate the excellent performance of our method the feas

some results on the lil in banach space with applications to weighted empirical processes we examine the cluster set of s n a n for banach space valued random variables and investigate the relationship between the central limit theorem and the law of the iterated logarithm in this setting in the case of hilbert space valued random variables necessary and sufficient conditions are given for the law of the iterated logarithm some interesting examples are also included we then apply our results to weighted empiricals both in the supremum norm and the l 2 lbrack 0 1 rbrack norm

characterizations of almost surely continuous p stable random fourier series and strongly stationary processes on etend le probleme de dudley fernique aux processus p stables fortement stationnaires 1 p 2

the jordan algebras of a lie algebra abstract we attach a jordan algebra l x to any ad nilpotent element x of index of nilpotence at most 3 in a lie algebra l this jordan algebra has a behavior similar to that of the local algebra of a jordan system at an element thus l x inherits nice properties from l and keeps relevant information about the element x

cartan subalgebras of root reductive lie algebras abstract root reductive lie algebras are direct limits of finite dimensional reductive lie algebras under injections which preserve the root spaces it is known that a root reductive lie algebra is a split extension of an abelian lie algebra by a direct sum of copies of finite dimensional simple lie algebras as well as copies of the three simple infinite dimensional root reductive lie algebras sl so and sp as part of a structure theory program for root reductive lie algebras cartan subalgebras of the lie algebra gl were introduced and studied in k h neeb i penkov cartan subalgebras of gl canad math bull 46 2003 597 616 in the present paper we refine and extend the results of k h neeb i penkov cartan subalgebras of gl canad math bull 46 2003 597 616 to the case of a general root reductive lie algebra g we prove that the cartan subalgebras of g are the centralizers of maximal toral subalgebras and that they are nilpotent and self normalizing we also give an explicit description of all cartan subalgebras of the simple lie algebras sl so and sp we conclude the paper with a characterization of the set of conjugacy classes of cartan subalgebras of the lie algebras gl sl so and sp with respect to the group of automorphisms of the natural representation which preserve the lie algebra

some central limit theorems for l valued semimartingales and their applications this paper is devoted to the generalization of central limit theorems for empirical processes to several types of l valued continuous time stochastic processes t x t n x t n where is a non empty set we deal with three kinds of situations as follows each coordinate process t x t n is i a general semimartingale ii a stochastic integral of a predictable function with respect to an integer valued random measure iii a continuous local martingale some applications to statistical inference problems are also presented we prove the functional asymptotic normality of generalized nelson aalen s estimator in the multiplicative intensity model for marked point processes its asymptotic efficiency in the sense of convolution theorem is also shown the asymptotic behavior of log likelihood ratio random fields of certain continuous semimartingales is derived

infinite kostant cascades and centrally generated primitive ideals of u n in types a c abstract we study the center of u n where n is the locally nilpotent radical of a splitting borel subalgebra of a simple complex lie algebra g sl c so c sp c there are infinitely many isomorphism classes of lie algebras n and we provide explicit generators of the center of u n in all cases we then fix n with largest possible center of u n and characterize the centrally generated primitive ideals of u n for g sl c sp c in terms of the above generators as a preliminary result we provide a characterization of the centrally generated primitive ideals in the enveloping algebra of the nilradical of a borel subalgebra of sl n c sp 2 n c

locally simple subalgebras of diagonal lie algebras abstract we describe up to isomorphism all locally simple subalgebras of any diagonal locally simple lie algebra

multichannel blind deconvolution of seismic signals a new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given to remove the inherent ambiguity in this blind deconvolution problem we introduce relevant a priori information our major assumption is sparseness of the reflectivity which corresponds to a layered earth model this allows nonminimum phase wavelets to be recovered reliably and closely spaced reflectors to be resolved to combine a priori knowledge and data we use a bayesian framework and derive a maximum a posteriori estimate computing this estimate is a difficult optimization problem solved by a suboptimal iterative procedure the procedure alternates steps of wavelet estimation and reflectivity estimation the first step only requires a simple least squares fit while the second step is solved by the iterated window maximization algorithm proposed by kaaresen this enables better efficiency and optimality than established alternatives the resulting optimization method can easily handle multichannel models with only a moderate increase of the computational load lateral continuity of the reflectors is achieved by modeling local dependencies between neighboring traces major improvements in both wavelet and reflectivity estimates are obtained by taking the wavelet to be invariant across several traces the practicality of the algorithm is demonstrated on synthetic and real seismic data an application to multivariate well log segmentation is also given

stochastic sparse spike deconvolution sparse spike deconvolution can be viewed as an inverse problem where the locations and amplitudes of a number of spikes reflectivity are estimated from noisy data seismic traces the main objective is to find the least number of spikes that when convolved with the available band limited seismicwaveletestimate fitthedatawithinagiventolerance errormisfit thedetectionofthespikes timelagsisahighly nonlinearoptimizationproblemthatcanbesolvedusingvery fastsimulatedannealingsa amplitudesareeasilyestimated using linear least squares at each sa iteration at this stage quadratic regularization is used to stabilize the solution to reduce its nonuniqueness and to provide meaningful reflectivitysequences thusavoidingtheneedtoconstrainthe spikes time lags and or amplitudes to force valid solutions impedanceconstraintsalsocanbeincludedatthisstage providing the low frequencies required to recover the acoustic impedance oneadvantageoftheproposedmethodoverother sparse spike deconvolution techniques is that the uncertaintyoftheobtainedsolutionscanbeestimatedstochastically further errorsinthephaseofthewaveletestimatearetolerated foranoptimumconstant phaseshiftisobtainedtocalibratetheeffectivewaveletthatispresentinthedata results using synthetic data including simulated data for the marmousi2 modelandfield 3d data show that physically meaningful high resolution sparse spike sections can be derived fromband limitednoisydata evenwhentheavailablewaveletestimateisinaccurate

the socle of a nondegenerate lie algebra we define the socle of a nondegenerate lie algebra as the sum of all its minimal inner ideals the socle turns out to be an ideal which is a direct sum of simple ideals and satisfies the descending chain condition on principal inner ideals every classical finite dimensional lie algebra coincides with its socle while relevant examples of infinite dimensional lie algebras with nonzero socle are the simple finitary lie algebras and the classical banach lie algebras of compact operators on an infinite dimensional hilbert space this notion of socle for lie algebras is compatible with the previous ones for associative algebras and jordan systems we conclude with a structure theorem for simple nondegenerate lie algebras containing abelian minimal inner ideals and as a consequence we obtain that a simple lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank one element

a class of simple matrix algebras abstract fix an infinite set i and consider the associative matrix algebra m i f where f is a base field with char f 2 for any couple of bijective maps i i such that and 2 2 we introduce a linear subspace of m i f we endow it with a structure of non associative algebra for a certain bilinear product and obtain a wide class of non associative algebras containing in particular the lie algebras lie m i f t we show that each algebra is simple

donsker classes and random geometry on donne des conditions geometriques aleatoires pour que le processus empirique indice par la classe des fonctions de carre integrable satisfasse le theoreme central limite

the central limit theorem and the law of iterated logarithm for empirical processes under local conditions a clt and a lil are proved under weak l2 gaussian bracketing conditions weaker than the usual ones these results have wide applicability and in particular provide an improvement of the jain marcus central limit theorem for c s valued random variables

irreducible finitary lie algebras over fields of characteristic zero abstract a lie subalgebralof g l k v is said to befinitaryif it consists of elements of finite rank we show that if char k 0 if dim k vis infinite and iflacts irreducibly onv then the derived algebra oflis simple

infinite dimensional irreducible lie algebras containing transformations of finite rank let mathbb f be a field of characteristic zero and let v be an infinite dimensional vector space over mathbb f a linear transformation x of v is called finitary if dim xv infty the aim of this paper is to describe irreducible lie subalgebras of mathfrak g mathfrak l v containing nonzero finitary transformations it turns out that any such algebra is a semidirect product of a finite dimensional lie algebra and a dense lie subalgebra of mathfrak g mathfrak l w for some vector space w

f xy eigenimage noise suppression f xy eigenimage filtering works by replacing constant frequency slices with the sum of their first few weighted eigenimages and can be used to remove random noise from stacked 3d seismic volumes it performs equally well on flat or dipping events and has no effect on noiseless data when the number of dips is no more than the number of summed eigenimages it is also independent of many x and y consistent effects such as reordering statics and filtering one consequence is that it tends to do a good job along the boundaries of the 3d grid execution time is comparable to f xy prediction filtering but can be greatly reduced using approximations based on lanczos bidiagonalization

seismic trace interpolation in the fourier transform domain a data adaptive interpolation method is designed and applied in the fourier transform domain f k or f kx ky for spatially aliased data the method makes use of fast fourier transforms and their cyclic properties thereby offering a significant cost advantage over other techniques that interpolate aliased data the algorithm designs and applies interpolation operators in the f k or f kx ky domain to fill zero traces inserted in the data in the t x or t x y domain at locations where interpolated traces are needed the interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data this operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies and corresponds to the f k or f kx ky domain version of the well known f x or f x y domain trace interpolators the method is applicable to 2d and 3d data recorded sparsely in a horizontal plane the most comm

consistent specification tests for semiparametric nonparametric models based on series estimation methods abstract this paper considers the problem of consistent model specification tests using series estimation methods the null models we consider in this paper all contain some nonparametric components a leading case we consider is to test for an additive partially linear model the null distribution of the test statistic is derived using a central limit theorem for hilbert valued random arrays the test statistic is shown to be able to detect local alternatives that approach the null models at the order of op n 1 2 we show that the wild bootstrap method can be used to approximate the null distribution of the test statistic a small monte carlo simulation is reported to examine the finite sample performance of the proposed test we also show that the proposed test can be easily modified to obtain series based consistent tests for other semiparametric nonparametric models

the jordan socle and finitary lie algebras in this paper we introduce the notion of jordan socle for nondegenerate lie algebras which extends the definition of socle given in a fernandez lopez et al 3 graded lie algebras with jordan finiteness conditions comm algebra in press for 3 graded lie algebras any nondegenerate lie algebra with essential jordan socle is an essential subdirect product of strongly prime ones having nonzero jordan socle these last algebras are described up to exceptional cases in terms of simple lie algebras of finite rank operators and their algebras of derivations when working with lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0 the exceptions disappear and the algebras of derivations are computed

locally semisimple and maximal subalgebras of the finitary lie algebras gl sl so and sp abstract we describe all locally semisimple subalgebras and all maximal subalgebras of the finitary lie algebras gl sl so and sp for simple finite dimensional lie algebras these classes of subalgebras have been described in the classical works of a malcev and e dynkin

autoregressive recovery of the acoustic impedance this paper presents a method of recovering the acoustic impedance from reflection seismograms using autoregressive ar modeling an approach originally applied to deconvolution by lines and clayton 1977 the algorithm which we describe is novel both in the manner in which the missing low and high frequency information is predicted and in the fact that the prediction may be constrained if acoustic impedance information is available the prediction of the low frequencies treats the missing data as a gap which extends from the low frequency cut off in the negative frequency band to the corresponding frequency in the positive frequency band the conjugate symmetry which governs the behavior of the spectrum in the band is taken into account in the prediction the missing high frequencies are predicted using a modified minimum entropy norm in the frequency domain both synthetic and field examples are presented and illustrate the robustness of the new ar algorithm under a variety of conditions the field e

lie algebras graded by finite root systems and the intersection matrix algebras of slodowy this paper is about toroidal lie algebras certain intersection matrix lie algebras defined by slodowy and their relationship to one another and to certain lie algebra analogues of steinberg groups the main result of the paper is the identification of the intersection matrix algebras arising from multiply affinized cartan matrices of types a d and e with certain steinberg lie algebras and toroidal lie algebras propositions 5 9 and 5 10 a major part of the paper studies and classifies lie algebras graded by finite root systems these become the princi pal tool in our analysis of intersection matrix algebras each lie algebra graded by a simply laced finite root system of rank 2 has attached to it an algebra which according to the type and rank is either commutative and associative only associative or alternative all these possibilities occur in our description of inter section matrix algebras let r be any associative algebra with identity not necessarily finite dimen sional over a field k of characteristic 0 for each positive integer n the associative algebra m r of n n matrices with coefficients in r forms a lie algebra over k under the commutator product we denote this lie algebra by ol r let eis be the i j matrix unit of m r and assume that n 2 the subalgebra e r of oi r generated by the elements reis r r i 4 j is an ideal of 91 r and is perfect i e it is its own derived algebra now any perfect lie algebra o has a universal central extension also perfect called a universal covering algebra u c a of o ga so in particular e r has a u c a that we will denote by t r we define 112 r by the exact sequence 0 1 0 f2 r t r e r 0 dedicated to our teacher maria j wonenburger both authors gratefully acknowledge the support of the natural sciences and engineering research council of canada

pseudo analytical finite difference elastic wave extrapolation based on the k space method abstractcost effective elastic wave modeling is the key to practical elastic reverse time migration and full waveform inversion implementations we have developed an efficient elastic pseudo analytical finite difference pafd scheme for elastic wave extrapolation the elastic pafd scheme is based on a modified pseudo spectral method k space method in which a pseudo analytical operator is used to ensure the high accuracy of elastic wave extrapolation however the k space method is motivated for a pure wave mode and thus its application in coupled first order elastic wave equations may cause the elastic pseudo analytical operators to suffer from crosstalk between the p and s wavefields the approaches presented attempt to overcome these shortcomings by introducing two improvements to achieve the goal this is done first by performing a predictor corrector strategy in first order elastic wave equations to eliminate those errors during wave extrapolation considering the massive computational cost in

unitary highest weight representations in hilbert spaces of holomorphic functions on infinite dimensional domains abstract automorphism groups of symmetric domains in hilbert spaces form a natural class of infinite dimensional lie algebras and corresponding banach lie groups we give a classification of the algebraic category of unitary highest weight modules for such lie algebras and show that infinite dimensional versions of the lie algebras s o 2 n have no unitary highest weight representations and thus do not meet the physical requirement of having positive energy highest weight modules correspond to unitary representations of global banach lie groups realized in hilbert spaces of vector valued holomorphic functions on the relevant domains in hilbert spaces the construction of such holomorphic representations of certain banach lie groups followed by the application of the general framework of harish chandra type groups in an appropriate banach setting leads to the integration of the lie algebra representation to a group representation the extension of this theory to infinite dimensional settings is explored

2 d bayesian deconvolution inverse problems can be solved in different ways one way is to define natural criteria of good recovery and build an objective function to be minimized if instead we prefer a bayesian approach inversion can be formulated as an estimation problem where a priori information is introduced and the a posteriori distribution of the unobserved variables is maximized when this distribution is a gibbs distribution these two methods are equivalent furthermore global optimization of the objective function can be performed with a monte carlo technique in spite of the presence of numerous local minima application to multitrace deconvolution is proposed in traditional 1 d deconvolution a set of unidimensional processes models the seismic data while a markov random field is used for 2 d deconvolution in fact the introduction of a neighborhood system permits one to model the layer structure that exists in the earth and to obtain solutions that present lateral coherency moreover optimization of an appropriated objective function by simulated annealing allows one to control the fit with the input data as well as the spatial distribution of the reflectors extension to 3 d deconvolution is straightforward

invariance principles for sums of banach space valued random elements and empirical processes almost sure and probability invariance principles are established for sums of independent not necessarily measurable random elements with values in a not necessarily separable banach space it is then shown that empirical processes readily fit into this general framework thus we bypass the problems of measurability and topology characteristic for the previous theory of weak convergence of empirical processes

local singular value decomposition for signal enhancement of seismic data singular value decompositionsvd is a coherency based technique that provides both signal enhancement and noise suppression it has been implemented in a variety of seismic applications mostly on a global scale in this paper we use svd to improve the signal to noise ratio of unstacked and stacked seismic sections but apply it locally to cope with coherent events that vary with both time and offset the local svd technique is compared with f x deconvolution and median filtering on a set of synthetic and real data sections local svd is better than f x deconvolution and median filtering in removing background noise but it performs less well in enhancing weak events or events with conflicting dips combining f x deconvolution or median filtering with local svd overcomes the main weaknesses associated with each individual method and leads to the best results