adaptive lexicographic optimization in multi class m gi 1 queues we consider a multi class m gi 1 system in which an average response time objective is associated with each class the performance of each class is measured by the ratio of the average response time over the corresponding value of the objective to achieve fairness in service allocation it is required to find a policy that lexicographically minimizes the vector of performance ratios arranged in nonincreasing order we provide such a policy that is adaptive uses only knowledge of arrival and departure instants and is thus easy to implement we also consider a variant of this policy which adapts faster to changes in the statistical parameters of the model both policies are analyzed via associated stochastic recursions using techniques of stochastic approximation

homogenization limits and wigner transforms we present a theory for carrying out homogenization limits for quadratic functions called energy densities of solutions of initial value problems ivps with anti self adjoint spatial pseudo differential operators pdos the approach is based on the introduction of phase space wigner matrix measures that are calculated by solving kinetic equations involving the spectral properties of the pdo the weak limits of the energy densities are then obtained by taking moments of the wigner measure the very general theory is illustrated by typical examples like semi classical limits of schrodinger equations with or without a periodic potential the homogenization limit of the acoustic equation in a periodic medium and the classical limit of the dirac equation 1997 john wiley sons inc

dimension of fuzzy spaces abstract a generalization of fuzzy spaces is given two families of sets open and closed are defined as collections of maps from a nonempty set x into the closed unit interval 0 1 some properties of so defined gf space are investigated as closure interior and boundary a fuzzy dimension function f ind is defined and studied in particular it is shown that the function f ind is monotone and that zero f dimensional spaces are totally disconnected

on the homology of the hilbert scheme of points in the plane geir ellingsrud 1 and stein arild stromme 2 i matematisk institutt universitetet i oslo blindern n oslo 3 norway 2 matematisk institutt universitetet i bergen n 5014 bergen norway although several authors have been interested in the hilbert scheme hilba ip z parametrizing finite subschemes of length d in the projective plane i1 i2 f 1 f2 br among others not much is known about the topological properties of this space the picard group has been calculated i f2 and the homology groups of hilb3 ip 2 have been computed hi in this paper we give a precise description of the additive structure of the homology of hilba ip2 applying the results of birula bialynicki b1 b2 on the cellular decompositions de fined by a torus action to the natural action of a maximal torus of sl 3 on hilbe ipz a rather easy consequence of the fact that this action has finitely many fixpoints is that the cycle maps between the chow groups and the homology groups are isomorphisms in particular there is no odd homology and the homology groups are all free the main objective of this work is to compute their ranks the betti numbers of hilba ipz as a byproduct of our method we get similar results on the homology of the punctual hilbert scheme and of the hilbert scheme of points in the affine plane it seems natural to generalize our results to any toric smooth surface however we give the results only for the rational ruled surfaces if with an indication of the necessary changes in the proofs for simplicity we work over the field of complex numbers but with an appropriate interpretation of the word homology our results remain valid over any base field

iterative analysis of the steady state weight fluctuations in lms type adaptive filters an iterative method is proposed for the analysis of the steady state weight fluctuations in an lms type adaptive fir filter without the widely used independence assumption a power series of the weight error correlation matrix is derived in terms of the stepsize some new effects are observed e g a decrease of the weight fluctuations along the tapped delay line

discrete approximation of quantum stochastic models we develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation the wide applicability of the method is illustrated in a variety of examples our main theorem which is based on the trotter kato theorem is not restricted to a specific noise model and does not require boundedness of the limit coefficients

on the interplay of singular perturbations and wide band stochastic fluctuations a class of nonlinear singularly perturbed systems driven by wide band noise is considered the asymptotic behavior of the slow variables is studied when the fast variables are sufficiently fast represented by mu to 0 and the wide band noise is sufficiently wide represented by varepsilon to 0 a reduced order markov model which represents the behavior of the slow variables is derived it is shown that the slow variables converge weakly to the solution of this reduced order model as varepsilon and mu tend to zero the coefficients of this reduced order model depend in general on the speeds of varepsilon and mu as they approach zero the implication of such dependence on the engineering practice of neglecting parasitic elements is discussed special cases where the model is independent of the speeds of varepsilon and mu are explored

a feedback approach to the steady state performance of fractionally spaced blind adaptive equalizers this paper proposes a new approach to the analysis of the steady state performance of constant modulus algorithms cma which are among the most popular adaptive schemes for blind equalization a major feature of the proposed feedback approach is that it bypasses the need for working directly with the weight error covariance matrix in so doing approximate expressions for the steady state mean square error of several cm algorithms are derived including cma2 2 cma1 2 normalized cma and a new normalized cma variant with less bias a comparison among the various algorithms is also performed along with several simulation results the conclusions confirm the superior performance of cma2 2

retrieving the green s function in an open system by cross correlation a comparison of approaches l we compare two approaches for deriving the fact that the green s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions one approach is based on physical arguments exploiting the principle of time reversal invariance of the acoustic wave equation the other approach is based on rayleigh s reciprocity theorem using a unified notation we show that the result of the time reversal approach can be obtained as an approximation of the result of the reciprocity approach

convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients we propose a multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients the main purpose is to design a numerical method which is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution this is accomplished by incorporating the local microstructures of the differential operator into the finite element base functions as a consequence the base functions are adapted to the local properties of the differential operator in this paper we provide a detailed convergence analysis of our method under the assumption that the oscillating coefficient is of two scales and is periodic in the fast scale while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain a useful asymptotic solution structure the issue of boundary conditions for the base functions will be discussed our numerical experiments demonstrate convincingly that our multiscale method indeed converges to the correct solution independently of the small scale in the homogenization limit application of our method to problems with continuous scales is also considered

tracking analysis of an arma parameter estimation algorithm the problem of adaptively estimating parameters of a time varying autoregressive moving average arma process using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that an ordinary differential equation can be used to describe the mean behavior of the adaptive filter coefficients computer simulations are provided to substantiate the analysis

white noise and geometrical opticslimits of wigner moyal equation for beam waves in turbulent media ii two frequency formulation we introduce two frequency wigner distribution in the setting of parabolic approximation to study the scaling limits of the wave propagation in a turbulent medium at two different frequencies we show that the two frequency wigner distribution satisfies a closed form equation the two frequency wigner moyal equation in the white noise limit we show the convergence of weak solutions of the two frequency wigner moyal equation to a markovian model and thus prove rigorously the markovian approximation with power spectral densities widely used in the physics literature we also prove the convergence of the simultaneous geometrical optics limit whose mean field equation has a simple universal form and is exactly solvable

a smooth space of tetrahedra abstract we construct a smooth symmetric compactification of the space of all labeled tetrahedra in p 3

frobenius splitting and cohomology vanishing for schubert varieties let k be an algebraically closed field of characteristic p 0 and x be a projective variety over k we then have the absolute frobenius f x x and an injection ox f 6x given by f fp f e o9x if this makes ox a direct summand in f ox as an x module we call x a frobenius split variety for such a variety the vanishing theorem for ample line bundles follows trivially from serre s vanishing theorem for tensoring ox f ox by an ample line bundle l and noting that l f x f f l f lp projection formula we get that the map in cohomology h x l h x f lp h x lp is an injection iterating this we see that h x l injects into h x lp for every p but for large v the latter is zero thus frobenius split varieties have quite pleasant properties it also turns out that using duality for the frobenius morphism or equivalently the cartier operator one can give a manageable criterion for frobenius splitting the point here is the local nature of duality the relevance of the compatibility of local and global duality was suggested to us by grothendieck s proof of h x y 0 for a noncomplete variety x of dimension n 4 theorem 6 9 and by kempf s paper 10 by this criterion and the bott samelson demazure desingularisation of schubert varieties it follows very easily that schubert varieties in characteristic p are frobenius split the following vanishing theorem is then an immediate consequence let g be a reductive group over the field k of arbitrary characteristic zero or positive let q be a parabolic subgroup and x c g q a schubert variety let l be an ample line bundle on g q then hi x l 0 for i 0 and the restriction map h0 g q l h0 x l is surjective if char k 0 this is a consequence of the compatible frobenius splitting of x in g q and the char k 0 case is handled by semicontinuity the above result for special schubert varieties has been proved by seshadrimusili lakshmibai 12 13 and by kempf 9 by using characteristic free methods for x g q andersen 1 and haboush 5 have given simple proofs using characteristic p methods

on the boundary of fuzzy sets abstract we introduce and study a new concept of boundary of a fuzzy set in a fuzzy topological space this notion preserves the good properties of the warren s boundary and furthermore it allows to characterize the clopen fuzzy sets as those whose boundary is 0 x

a diffusion process for the asymptotic limit of a noncentred stochastic system the diffusion effects of solution processes for a large class of stochastic equations have been characterized by khasminskii s limit theory compared to either the ito or the stratonovich interpretation of stochastic differential equations this theory has been effective from a modelling point of view in that the drift coefficient of the resultant kolmogorov backward equation may include a term from the centred random field a noncentred stochastic system on an asymptotically infinite interval is studied in this article on the basis of the limit theory and it is motivated by a singular behaviour of classical waves in a random multilayer the extended kolmogorov fokker planck equation for the transition probability density is derived and the solution of this equation is represented by an explicit approximate form based upon the pseudodifferential operator theory and wiener s path integral representation

stochastic averaging in continuous time and its applications to extremum seeking we investigate stochastic averaging theory in continuous time for locally lipschitz systems and the applications of this theory to stability analysis of stochastic extremum seeking algorithms first we establish a general stochastic averaging principle and some related stability theorems for a class of continuous time nonlinear systems with stochastic perturbations and remove or weaken several significant restrictions present in existing results global lipschitzness of the nonlinear vector field equilibrium preservation under the stochastic perturbation global exponential stability of the average system and compactness of the state space of the perturbation process then we propose a continuous time extremum seeking algorithm with stochastic excitation signals instead of deterministic periodic signals we analyze the stability of stochastic extremum seeking for static maps and for general nonlinear dynamic systems

geometry of the tetrahedron space abstract let x be the space of all labeled tetrahedra in p 3 in e babson p e gunnells r scott a smooth space of tetrahedra adv math 165 2 2002 285 312 we constructed a smooth symmetric compactification x of x in this article we show that the complement x x is a divisor with normal crossings and we compute the cohomology ring h x q

connectedness and dimension of gf spaces abstract connectedness of gf spaces defined by means of open closed sets is studied this leads to the notion of a i monotone function using connectedness the notion of a f component is introduced the relationship between connectedness and zero dimensionality is considered

speech enhancement in discontinuous transmission systems using the constrained stability least mean squares algorithm in this paper a novel constrained stability least mean squares lms algorithm for filtering speech sounds is proposed in the adaptive noise cancellation anc problem it is based on the minimization of the squared euclidean norm of the weight vector change under a stability constraint over the a posteriori estimation errors to this purpose the lagrangian methodology has been used in order to propose a nonlinear adaptation in terms of the product of differential input and error convergence analysis is also studied in terms of the evolution of the natural modes to the optimal wiener hopf solution so that the stability performance depends exclusively on the adaptation parameter and the eigenvalues of the difference matrix r1 the algorithm shows superior performance over the referenced algorithms in the anc problem of speech discontinuous transmission systems which are characterized by rapid transitions of the desired signal the experimental analysis carried out on the aurora 3 speech databases provides an extensive performance evaluation together with an exhaustive comparison to the standard lms algorithms i e the normalized lms nlms and other recently reported lms algorithms such as the modified nlms the error nonlinearity lms or the normalized data nonlinearity lms adaptation

the limiting behavior of lms a realization oriented analysis is given of the gradient noise misadjustment and lag misadjustment performance of the lms least mean square algorithm new formulas are given for both of these components of excess mean square error it is shown that the traditional formula for lag misadjustment needs to be modified by adding further terms due to gradient noise and noise variance to perform the analysis it is necessary to study the convergence with probability one of the noise free fixed parameter lms algorithm convergence is found under simple conditions that improve on those previously obtained

nelder mead simplex modifications for simulation optimization when the nelder mead method is used to optimize the expected response of a stochastic system e g an output of a discrete event simulation model the simplex resizing steps of the method introduce risks of inappropriate termination we give analytical and empirical results describing the performance of nelder mead when it is applied to a response function that incorporates an additive white noise error and we use these results to develop new modifications of nelder mead that yield improved estimates of the optimal expected response compared to nelder mead the best performance was obtained by a modified method rs s9 in which a the best point in the simplex is reevaluated at each shrink step and b the simplex is reduced by 10 rather than 50 at each shrink step in a suite of 18 test problems that were adapted from the minpack collection of netlib the expected response at the estimated optimal point obtained by rs s9 had errors that averaged 15 less than at the original method s estimated optimal point at an average cost of three times as many function evaluations two well known existing modifications for stochastic responses the n 3 rule and the next to worst rule were found to be inferior to the new modification rs s9

self averaging scaling limits for random parabolic waves we consider several types of scaling limits for the wigner moyal equation of the parabolic waves in random media the limiting cases of which include the standard radiative transfer limit the geometrical optics limit and the white noise limit we show under fairly general assumptions on the random refractive index field that sufficient amount of medium diversity thus excluding the white noise limit leads to statistical stability or self averaging in the sense that the limiting law is deterministic and is governed by one of the 6 different types of transport boltzmann or fokker planck equations depending on the specific scaling involved we discuss the connection to the statistical stability of time reversal procedure and the decoherence effect in quantum mechanics

a two way parabolic equation for acoustic backscattering in the ocean the parabolic equation pe method is generalized to handle backscattered acoustic energy in the ocean the two way pe is based on the single scattering approximation and the approach of two way coupled modes in which range dependent environments are approximated by a sequence of range independent regions at the vertical boundaries between regions the solution of the two way pe is required to satisfy two continuity conditions the range derivative in one of the conditions is replaced by a higher order pe depth operator the reflected and transmitted fields that satisfy these conditions are computed with an efficient iteration scheme the outgoing and incoming fields are propagated by two way range marching the two way pe which is presently implemented for two dimensional problems is a practical method for solving large scale reverberation problems the accuracy of the two way pe is demonstrated by comparisons with reference solutions the two way pe is applied to simulate the localization of a source of backscattering using the method of back propagation

on inductive dimensions for fuzzy topological spaces an approach to the dimension theory for fuzzy topological spaces is being developed the appropriate context for this theory is not the category cft of chang fuzzy topological spaces or some of its modifications but the category hut introduced in the paper this category is a slight extension of the category h of hutton fuzzy topological spaces hutton 1980 the frames of this category allow us to make exposition simple and uniform and on the other hand to make it applicable in quite a general setting

estimating a green s function from field field correlations in a random medium traditional imaging methods use coherent signals as data here we discuss recent developments in imaging that aim at exploiting as data incoherent noisy signals that are not associated with well defined arrival times indeed signal constituents that in a classical setting may be regarded as noise may contain important information about the medium to be imaged we show how it is possible to use the statistics of such noisy signals specifically the second order statistics for imaging we consider two particular situations first the estimation of an empirical green s function from noisy signals which can subsequently be used in imaging second the localization of a cluster of random sources from noisy signals passive imaging the analysis presented here is based on assuming a remote sensing scaling and the paraxial approximation and it uses in part the results set forth in papanicolaou ryzhik and solna siam j appl math 64 2004 pp 1133 1155 that relate to time reversal statistical

a uniform diffusion limit for random wave propagation with turning point a random wave propagation problem with turning point is considered for a refractive layered random medium the variations of the medium structure are assumed to have two spatial scales microscopic random fluctuations are superposed upon slowly varying macroscopic variations an extension of a limit theorem for stochastic differential equations with multiple spatial scales is derived and proved to obtain a uniformly valid diffusion limit for random multiple scattering up to the turning point region the scale dependence of the infinitesimal generator of the backward kolmogorov equation provides an insight into the interplay of internal refraction and random scattering as one approaches the turning point

on zero dimensionality in fuzzy topological spaces abstract different concepts of zero dimensionality in fuzzy topological spaces are studied it is shown that the c zero dimensionality and the strongly c zero dimensionality are not good extensions in the lowen sense of the zero dimension for the inductive topological dimensions ind and ind respectively some properties of these spaces and their relationship with the adnadjevic fuzzy topological dimension are also stated

unbiased and stable leakage based adaptive filters the paper develops a leakage based adaptive algorithm referred to as circular leaky which in addition to solving the drift problem of the classical least mean squares lms adaptive algorithm it also avoids the bias problem that is created by the standard leaky lms solution these two desirable properties of unbiased and bounded estimates are guaranteed by circular leaky at essentially the same computational cost as lms the derivation in the paper relies on results from averaging theory and from lyapunov stability theory and the analysis shows that the above properties hold not only in infinite precision but also in finite precision arithmetic the paper further extends the results to a so called switching spl sigma algorithm which is a leakage based solution used in adaptive control

nonlinear schrodinger equation with a white noise potential phase space approach to spread and singularity we propose a phase space formulation for the nonlinear schr odinger equation with a white noise potential in order to shed light on two issues the rate of spread and the singularity formation in the average sense our main tools are the energy law and the variance identity the method is completely elementary for the problem of wave spread we show that the ensemble averaged dispersion in the critical or defocusing case follows the cubic in time law while in the supercritical and subcritical focusing cases the cubic law becomes an upper and lower bound respectively we have also found that in the critical and supercritical focusing cases the presence of a white noise random potential results in different conditions for singularity with positive probability from the homogeneous case but does not prevent singularity formation we show that in the supercritical focusing case the ensemble averaged self interaction energy and the momentum variance can exceed any fixed level in a finite time with positive probability c 2005 elsevier b v all rights reserved

high frequency wave propagation in random media a unified approach high frequency wave propagation in a random medium over long propagation distances where the fluctuations in the wave field are not small and caustic formation is likely is studied techniques based on the geometrical optics approximation or ray theory as well as those based on the parabolic wave equation are examined it is shown that for small fluctuations in the refractive index of order sigma sigma ll 1 and long propagation distances of order sigma 2 3 that both these methods are equivalent at high frequencies at least away from caustics since previous theories have identified this sigma sigma 2 3 distance scale as that on which random caustics first appear we also derive a regularization of the ray approximation which is called the beam method and which is uniformly valid in the vicinity of caustics on the sigma 2 3 scale the random ray process converges to a diffusion markov process and equations can be derived for the joint distribution of an a

bott s formula and enumerative geometry we outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of bott as an example gromov witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed the results are consistent with predictions made from mirror symmetry compu tations we also compute degrees of some loci in the linear system of plane curves of degrees less than 10 like those corresponding to sums of powers of linear forms and curves carrying inscribed polygons mathematical institute university of oslo p 0 box 1053 n 0316 oslo norway e mail address ellingsr0math uio no mathematical institute university of bergen alleg 55 n 5007 bergen norway e mail address strommeti i uib no this content downloaded from 157 55 39 29 on tue 12 apr 2016 10 23 14 utc all use subject to http about jstor org terms

constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels in this paper we introduce a parameterized generalization of the well known superimposed codes we give algorithms for their construction and provide non existential results we apply our new combinatorial structures to the efficient solution of new group testing problems and access coordination issues in multiple access channels

continuous time stochastic averaging on the infinite interval for locally lipschitz systems we investigate stochastic averaging on the infinite time interval for a class of continuous time nonlinear systems with stochastic perturbation and remove or weaken several restrictions present in existing results global lipschitzness of the nonlinear vector field equilibrium preservation under the stochastic perturbation global exponential stability of the average system and compactness of the state space of the perturbation process if an equilibrium of the average system is exponentially stable we show that the original system is exponentially practically stable in probability if in addition the original system has the same equilibrium as the average system then the equilibrium of the original system is locally asymptotically stable in probability these results extend the deterministic general averaging for aperiodic functions to the stochastic case

borel weil theorem for configuration varieties and schur modules we present a generalization of the classical schur modules ofgl n exhibiting the same interplay among algebra geometry and combinatorics a generalized young diagramdis an arbitrary finite subset ofn n for eachd we define the schur modulesdofgl n we introduce a projective variety fdand a line bundle ld and describe the schur module in terms of sections of ld for diagrams with the northeast property i1 j1 i2 j2 d min i1 i2 max j1 j2 d which includes the skew diagrams we resolve the singularities of fdand show analogues of bott s and kempf s vanishing theorems finally we apply the atiyah bott fixed point theorem to establish a weyl type character formula of the form charsd x txwt t i j 1 xix 1j dij t wheretruns over certain standard tableaux ofd our results are valid over fields of arbitrary characteristic

sound source localization in a randomly inhomogeneous medium using matched statistical moment method this paper investigates the problem of sound source localization from acoustical measurements obtained by an array of microphones the sound propagation medium is assumed to be randomly inhomogeneous being modelled by a random function of space in this case classical source localization methods e g beamforming near field acoustical holography and time reversal cannot be used anymore therefore an approach based on the statistical moments of acoustical measurement is proposed to solve the aforementioned problem in this work a karhunen loeve expansion is used so that the random medium can be represented by a small number of uncorrelated and identically distributed random variables the statistical characteristics of the measurements in terms of probability density function and statistical moments are also studied then the sound source is localized by minimizing the error of statistical moments between the real measurements obtained from the microphone array and the measurements simulated from an assumed source finally a numerical example is introduced to justify the proposed method this experiment shows that the random field can be replicated by a very small number of random variables the statistical moments of measurements guarantee the convergence and the source location can be accurately estimated using the proposed source localization method

mirror manifolds in higher dimension we describe mirror manifolds in dimensions different from the familiar case of complex threefolds we isolate certain simplifying features present only in dimension three and supply alternative methods that do not rely on these special characteristics and hence can be generalized to other dimensions although the moduli spaces for calabi yaud folds are not special kahler manifolds whend 3 they still have a restricted geometry and we indicate the new geometrical structures which arise we formulate and apply procedures which allow for the construction of mirror maps and the calculation of order by order instanton corrections to yukawa couplings mathematically these corrections are expected to correspond to calculating chern classes of various parameter spaces hilbert schemes for rational curves on calabi yau manifolds our mirror aided calculations agree with those chern class calculations in the limited number of cases for which the latter can be carried out with current mathematical tools finally we make explicit some striking relations between instanton corrections for various yukawa couplings derived from the associativity of the operator product algebra

specht series for column convex diagrams abstract we give a specht series for the specht module s d associated to a diagram d in two cases 1 when d is column convex 2 when d is the complement of a column convex diagram within a rectangular box

parabolic wave equation approximations in heterogenous media the properties of different variants of parabolic approximations of scalar wave equations are analyzed these equations are of general form which includes those used in seismology underwater acoustics and other applications a new version of the parabolic approximation is derived for heterogeneous media it has optimal properties with respect to wave reflection at material interfaces the amplitudes of the reflected and transmitted waves depend continuously on the interface existence uniqueness and energy estimates are proved

white noise and geometrical optics limits of wigner moyal equation for wave beams in turbulent media starting with the wigner distribution formulation for beam wave propagation in holder continuous non gaussian random refractive index fields we show that the wave beam regime naturally leads to the white noise scaling limit and converges to a gaussian white noise model which is characterized by the martingale problem associated to a stochastic differential integral equation of the ito type in the simultaneous geometrical optics the convergence to the gaussian white noise model for the liouville equation is also established if the ultraviolet cutoff or the fresnel number vanishes sufficiently slowly the advantage of the gaussian white noise model is that its n point correlation functions are governed by closed form equations

on time splitting spectral approximations for the schrodinger equation in the semiclassical regime in this paper we study time splitting spectral approximations for the linear schrodinger equation in the semiclassical regime where the planck constant e is small in this regime the equation propagates oscillations with a wavelength of o e and finite difference approximations require the spatial mesh size h o e and the time step k o e in order to obtain physically correct observables much sharper mesh size constraints are necessary for a uniform l2 approximation of the wave function the spectral time splitting approximation under study will be proved to be unconditionally stable time reversible and gauge invariant it conserves the position density and gives uniform l2 approximation of the wave function for k o e and h o e extensive numerical examples in both one and two space dimensions and analytical considerations based on the wigner transform even show that weaker constraints e g k independent of e and h o e are admissible for obtaining correct observables finally we address the application to nonlinear schrodinger equations and conduct some numerical experiments to predict the corresponding admissible meshing strategies

wave field reciprocity and optimization in remote sensing a unified approach to local optimization techniques and wave field reciprocity as applied to constructing solutions to remote sensing imaging and inversion problems in acoustic elastic and electromagnetic wave theory is presented the starting point is a system of linear first order partial differential equations in space time of the class to which the indicated wave phenomena gives rise for this system three types of remote sensing problems the inverse source the inverse scattering and the inverse transducted wave field problems are formulated and the construction of their solutions via local optimization techniques is discussed emphasis is placed on iterative algorithms that are based on a guaranteed decrease in the mismatch between modelled and observed data at each update of the medium subsequently the wave field reciprocity theorems of the time convolution and the time correlation types are derived and their occurrence in the optimization procedures is discussed also attention is paid to approximate methods in particular to the rayleigh gans born approximation approximations of this sort provide the means to invoke the method of preconditioning in the process of inverting the operator equations exotic media for example chiral media in electromagnetics are included in the analysis

fourth moment analysis for wave propagation in the white noise paraxial regime in this paper we consider the ito schrodinger model for wave propagation in random media in the paraxial regime we solve the equation for the fourth order moment of the field in the regime where the correlation length of the medium is smaller than the initial beam width in terms of applications we prove that the centered fourth order moments of the field satisfy the gaussian summation rule we derive the covariance function of the intensity of the transmitted beam and the variance of the smoothed wigner transform of the transmitted field the second application is used to explicitly quantify the scintillation of the transmitted beam and the third application to quantify the statistical stability of the wigner transform

efficient numerical simulation for long range wave propagation we develop an efficient algorithm for simulating wave propagation over long distances with both weak and strong scatterers in domains with weak heterogeneities the wave field is decomposed into forward propagating and back scattered modes using two coupled parabolic equations in the region near strong scatterers the helmholtz equation is used to capture the strong scattering events the key idea in our method is to combine these two regimes using a combined domain decomposition and wave decomposition method a transparent interface condition is derived to couple these two regions together numerical examples show that the simulated field is close to the field obtained using the full helmholtz equation in the whole domain

tracking and identification of regime switching systems using binary sensors this work is concerned with tracking and system identification for time varying parameters the parameters are markov chains and the observations are binary valued with noise corruption to overcome the difficulties due to the limited measurement information wonham type filters are developed first then based on the filters two popular estimators namely mean squares estimator msq and maximum posterior map estimator are constructed for the mean squares estimator we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation the asymptotic normality is then used to derive error bounds when the markov chain is infrequently switching we derive error bounds for map estimators when the markovian parameters are fast varying we show that the averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and that can be estimated using empirical measures upper and lower error bounds on estimation errors are also established

stability of markov modulated discrete time dynamic systems motivated by various control applications this paper develops stability analysis of discrete time systems with regime switching in which the dynamics are modulated by markov chains with two time scales using the high contrast of the different transition rates among the markovian states singularly perturbed markov chains are used in the formulations taking into consideration of the regime changes and time scale separation makes the stability analysis a difficult task in this work asymptotic stability analysis is carried out using perturbed liapunov function techniques it is demonstrated that if the limit system is stable then the original system is also stable in addition we examine path excursion derive bounds on mean recurrence time and obtain the associated probability bounds

observations preprocessing and quantization for nonlinear filters methods of preprocessing the observations for nonlinear filters are investigated the aim being to reduce the computational labor involved in their implementation an example of preprocessing is quantization which involves the replacement of real valued observation samples by discrete values because the resulting likelihood functions have finite support they can be held in look up tables kept in some type of rapid access memory which renders their real time evaluation trivial preprocessed observations of this sort carry less information than raw observations this loss of information is characterized here for filters with substantially noisy observation samples by means of a functional central limit theorem among other things this supplies an asymptotic effective signal to noise ratio for preprocessed filters methods of optimizing preprocessing operations with respect to this quantified information loss are developed in particular optimal quantization thresholds are found for observations that are contaminated by gaussian noise and it is shown that the loss of information for quite coarse quantization schemes is small for example the asymptotic effective signal to noise ratio for a filter with one bit quantized observations is 2 pi times that for the same filter with raw observations simulations on two examples demonstrate the validity of the asymptotic characterization even when the observation samples are only modestly contaminated by noise

on a grauert riemenschneider vanishing theorem for frobenius split varieties in characteristic p it is known that the grauert riemenschneider vanishing theorem is not valid in characteristic p 1 here we show that it may be restored in the presence of a suitable frobenius splitting the proof uses interchanging two projective limits one involving iterated frobenius maps cf 2 and 4 the other coming from grothendieck s theorem on formal functions that leads to the following general vanishing theorem which we then apply in the situation of the grauert riemenschneider theorem

strong points of weak convergence a study using rpa gradient estimation for automatic learning this paper analyzes the behavior of adaptive control schemes for automatic learning estimates of the sensitivities are used in a gradient based stochastic approximation procedure in order to drive the process along the steepest descent trajectory in search for the optimum the learning rates are kept constant for adaptability for such procedures convergence can be established in a weak sense a model problem of a flexible machine is presented for which the control parameter is a probability vector we propose a new sensitivity estimator generalizing the phantom rare perturbation analysis rpa estimator to multi valued decisions from the basic properties of the estimators we build several updating rules based on the weak convergence theory to ensure asymptotic optimality we illustrate the predicted theoretical behavior with computer simulations finally we present the comparison between the behavior of our proposed scheme with a regenerative one for which we can establish strong convergence our results show that weak convergence yields a dramatic improvement in the rate of convergence in addition to the capability of adaptation or tracking

parabolic and gaussian white noise approximation for wave propagation in random media the parabolic or forward scattering approximation has been used extensively in the study of wave propagation this approximation is combined with a gaussian white noise approximation for waves propagating in a random medium the validity of this approximation is proved for stratified weakly fluctuating random media in the high frequencies regime the limiting distribution of the wave field is characterized as the unique solution of a random schrodinger equation studied by dawson and papanicolaou appl math optim 12 1984 pp 97 114 the proofs are based on various generalizations of the perturbed test function method developed by kushner approximation and weak convergence methods for random processes mit press 1984

the space of triangles vanishing theorems and combinatorics abstract we consider compactifications of pn 3 ij the space of triples of distinct points in projective space one such space is a singular variety of configurations of points and lines another is the smooth compactification of fulton and macpherson and a third is the triangle space of schubert and semple we compute the sections of line bundles on these spaces and show that they are equal as gl n representations to the generalized schur modules associated to bad generalized young diagrams with three rows borel weil theorem on the one hand this yields weyl type character and dimension formulas for the schur modules on the other a combinatorial picture of the space of sections cohomology vanishing theorems play a key role in our analysis

a two way paraxial system for simulation of wave backscattering by a random medium this paper presents a probabilistic analysis of an iterative two way paraxial scheme for the simulation of wave propagation in anisotropic random media this scheme has the computational cost of the standard one way paraxial wave equation but has the accuracy of the full wave equation in a regime beyond the classical paraxial regime more precisely it accurately predicts the statistics of the reflected wave field the accuracy depends on two parameters the order of the iterative scheme and the ratio of the random backscattering intensity over the random forward scattering intensity

a note on stochastic schrodinger equations with fractional multiplicative noise abstract this work is devoted to non linear stochastic schrodinger equations with multiplicative fractional noise where the stochastic integral is defined following the riemann stieljes approach of zahle under the assumptions that the initial condition is in the sobolev space h q r n for a dimension n less than three and q an integer greater than or equal to zero that the noise is a q fractional brownian motion with hurst index h 1 2 1 and spatial regularity h q 4 r n as well as appropriate hypotheses on the non linearity we obtain the local existence of a unique pathwise solution in c 0 0 t h q r n c 0 0 t h q 2 r n for any 0 h contrary to the parabolic case standard fixed point techniques based on the mild formulation of the spde cannot be directly used because of the weak smoothing in time properties of the schrodinger semigroup we follow here a different route and our proof relies on a change of phase that removes the noise and leads to a schrodinger equation with a magnetic potential that is not differentiable in time

tracking analysis of a generalized adaptive notch filter the paper presents results of local performance analysis of a generalized adaptive notch filter ganf ganfs are used for identification tracking of quasi periodically varying dynamic systems and can be considered an extension to the system case of classical adaptive notch filters the tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique even though restricted to a single frequency case the presented analysis provides valuable insights into the tracking mechanisms of ganf including the associated speed accuracy tradeoffs the achievable performance bounds and tracking limitations in addition it allows one to formulate some useful rules of thumb for choosing design parameters

schur functors and schur complexes the study of schur functors has a relatively long history its main impetus derived from representation theory originally in characteristic zero over the years however with the development of modular representations and algebraic geometry over fields of positive characteristic the need for a theory of universal polynomial functors increased and since the mid 1960s approaches to a characteristic free treatment of schur functors have been developing see for instance the recent book of green 1 l in which the treatments by carter and lusztig 6 higman 12 and towber 20 among others are discussed our own interest in such a treatment was awakened by the work of lascoux 141 on resolutions of determinantal ideals although his thesis treated only the characteristic zero case it suggested that a general and elementary theory of schur functors could be developed using only the rudiments of multilinear algebra involving the hopf algebra structures of the symmetric exterior and divided power algebras moreover this elementary development admitted of a natural generalization to the idea of schur complexes whose usefulness was demonstrated for instance in our construction of a universal minimal

large deviations for markov processes with discontinuous statistics ii random walks let 1 and 2 be borel probability measures on d with finite moment generating functions the main theorem in this paper proves the large deviation principle for a random walk whose transition mechanism is governed by 1 when the walk is in the left halfspace 1 x d x 1 0 and whose transition mechanism is governed by 2 when the walk is in the right halfspace 2 x d x 1 0 when the measures 1 and 2 are equal the main theorem reduces to cramer s theorem