on the three coefficient window family the definition of the three coefficient window family is extended to the form w t b 0 5 1 b 0 5 cos 2 pi t t 0 5b cos 4 pi t t mod t mod

an exact forward backward maximum likelihood autoregressive parameter estimation method a method for obtaining an exact maximum likelihood estimate mle of the autoregressive ar parameters is proposed the method is called the forward backward maximum likelihood algorithm based on a new form of the log likelihood function for a gaussian ar process an iterative maximization is used to obtain an mle of the inverse covariance matrix the ar parameters are then determined via the normal equations experimental results comparing the new method with other popular ar spectrum estimation methods indicate the new method achieves low bias and low variance ar parameter estimates comparable with the existing methods

on the exact maximum likelihood estimation of gaussian autoregressive processes it is shown that the true maximum likelihood estimates of a gaussian zero mean ar process can be calculated the steps toward their obtainment with standard subroutines are calculating extrema are given the likelihood of the data is maximized in contrast to current approximate methods however the computational cost is significantly higher also the order p of the process is presumed known

analysis of the short time unbiased spectrum estimation algorithm the short time unbiased spectrum estimation stuse algorithm is analyzed and expressions for the mean and variance of the spectrum estimates are derived the stuse algorithm deliberately adds biased spectrum estimates in order to yield unbiased estimates and at the same time have excellent spectral leakage suppression capabilities computer simulations are presented verifying the theoretical results and also comparing the stuse algorithm with the conventional weighted overlapped segment averaging wosa method

sigma delta modulation with leaky integration and constant input exact descriptions of the behavior of quantization noise for single loop multistage cascade and multiloop sigma delta modulators for a variety of input signals have been found during recent years under the assumption of ideal integration the techniques used to solve the ideal integrator case do not easily extend to the more realistic model of a leaky integrator sigma delta in this paper a dynamical system representation for the leaky integrator sigma delta with a constant input is developed several properties of the resulting piecewise monotone and piecewise linear transformation t on the interval

complete branching rules for specht modules abstract we give a combinatorial description for when the specht module of an arbitrary diagram admits a complete branching rule this description given in terms of the maximal rectangles of the diagram generalizes all previously known branching rules for specht modules such as those given by reiner and shimozono for northwest diagrams and by the present author for forest diagrams

recursive maximum likelihood estimation of autoregressive processes a new method of autoregressive parameter estimation is presented the technique is a closer approximation to the true maximum likelihood estimator than that obtained using linear prediction techniques the advantage of the new algorithm is mainly for short data records and or sharply peaked spectra simulation results indicate that the parameter bias as well as the variance is reduced over the yule walker and the forward backward approaches of linear prediction also spectral estimates exhibit more resolution and less spurious peaks a stable all pole filter estimate is guaranteed the algorithm operates in a recursive model order fashion which allows one to successively fit higher order models to the data

some windows with very good sidelobe behavior some of the windows presented by harris 1 are not correct in terms of their reported peak sidelobes and optimal behavior we present corrected plots of harris windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints the temporal weightings are characterized as a sum of weighted cosines over a finite duration the plots enable the reader to select a window to suit his requirements in terms of bias due to nearby sidelobes and bias due to distant sidelobes

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

fourier based reconstruction for fully 3 d pet optimization of interpolation parameters fourier based approaches for three dimensional 3 d reconstruction are based on the relationship between the 3 d fourier transform ft of the volume and the two dimensional 2 d ft of a parallel ray projection of the volume the critical step in the fourier based methods is the estimation of the samples of the 3 d transform of the image from the samples of the 2 d transforms of the projections on the planes through the origin of fourier space and vice versa for forward projection reprojection the fourier based approaches have the potential for very fast reconstruction but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions in our previous work we have investigated optimal interpolation parameters for the fourier based forward and back projectors for iterative image reconstruction the optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator this work presents an optimization of interpolation parameters of the 3 d direct fourier method with fourier reprojection 3d frp for fully 3 d positron emission tomography pet data with incomplete oblique projections the reprojection step is needed for the estimation from an initial image of the missing portions of the oblique data in the 3d frp implementation we use the gridding interpolation strategy combined with proper weighting approaches in the transform and image domains we have found that while the 3 d reprojection step requires similar optimal interpolation parameters as found in our previous studies on fourier based iterative approaches the optimal interpolation parameters for the main 3d frp reconstruction stage are quite different our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling which is a common practice to decrease errors caused by interpolation in fourier reconstruction

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

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

a new optimal window signal processing an optimal window that can provide the best tradeoff between the peak sidelobe level and the total sidelobe level is presented necessary and sufficient conditions are established for the optimal window a design algorithm is presented and examples are discussed the examples demonstrate that the window is capable of much better performance than previously available windows such as the hamming window relationships between the maximum error and the mean squared error are explored for the window optimization problem it is concluded that the minimax and least squares approximations are both fundamentally inefficient this conclusion is supported by experimental evidence and mathematical analyses

optimum binary windows for discrete fourier transforms a class of windows called binary windows for the frequency domain implementation of the discrete fourier transform is proposed while the conventional time domain windowing requires n 2 stored values of the data window and n multiplications the binary windows do not require multiplications or stored constants rather they are replaced by shift and add operations typical hardware structures are presented for efficient implementation of the binary windows

fir filters with sigma delta modulation encoding two methods are presented for building fir finite impulse response digital filters where either the impulse response or the input signal is encoded using sigma delta modulation for each method both single loop and two stage sigma delta modulation are used for encoding these systems are operated at a sampling rate higher than the nyquist rate of the signal and their performance depends on the oversampling ratio except in the decoding circuit these filters require no multiplication and hence can be built using simple hardware an analysis of the systems is provided and examples for filters realized using these approaches are given

approximate synthesis of nonseparable design responses for rectangular arrays a method is presented for the approximation of any real symmetrical nonseparable array design response polynomial of order m 1 by n 1 for rectangular arrays with m by n uniformly spaced elements m geq n previously a sampling method has been used to exactly synthesize response functions of a single variable by n element line arrays 1 and nonseparable functions of two variables by n times n square arrays the sampling method is extended herein to apply to rectangular arrays by deriving the element weights for an m by n rectangular array that exactly yield the values of any desired real symmetrical array response function on an m by n grid of the interelement phase shifts this would yield the designed array response exactly everywhere if the design equation were of order m 1 with respect to one dimension and of order n 1 with respect to the other dimension to approximate this condition the original design function of order n 1 in both dimensions is modified to make it of order m 1 in one dimension and of order n 1 along a single grid line in the other dimension a second function is derived with these roles reversed the resulting function has the form of the original design function exactly equaling it along the n grid lines of m points each and along the single perpendicular chosen grid line of n points and closely approximating it throughout the entire range of the variables this technique is illustrated for chebyshev response functions for which the two approximating functions are derived and evaluated for several combinations of m and n the responses are shown to have generally uniform sidelobe regions with all but a small percentage of the sidelobes within 1 db of the designed sidelobe value

two stage sigma delta modulation an exact analysis of the nonlinear difference equation describing a discrete time two stage sigma delta quantizer with dc and sinusoidal inputs is presented it is shown that for dc inputs the binary quantizer error of the second quantizer which appears at the output of the modulator as a second order difference is asymptotically white uniformly distributed and uncorrelated with the input for sinusoidal inputs this result holds with one exception the autocorrelation which is a sum of weighted bessel functions does not correspond to that of a white noise process at large oversampling ratios the autocorrelation is approximately white and hence the white additive noise model is a good approximation for evaluating the first and second order moments it is found that for both a sinc sup 3 decoder filter and an ideal low pass filter decoder the average quantization noise power is inversely proportional to the fifth power of the oversampling ratio r for both types of inputs this represents an improvement over the single loop sigma delta quantizer by a factor of r sup 2 simulation results that agree with the theoretical analysis are presented

kernel design for reduced interference distributions the authors present a class of time frequency signal representations tfrs called the reduced interference distribution rid an overview of commonly used tfrs is given and desirable distribution properties are introduced particular attention is paid to the interpretation of cohen s class of time frequency distributions of tfrs in the ambiguity temporal correlation spectral correlation and time frequency domains based on the desirable kernel requirements the rid is discussed and further defined a systematic procedure to create rid kernels or equivalently compute rids is proposed some aspects and properties of the rid are discussed the authors estimate design considerations for rids and compare various selections of the primitive window some experimental results demonstrating the performance of the rid are presented

orthogonal sets of data windows constructed from trigonometric polynomials suboptimal easily computable substitutes for the discrete prolate spheroidal windows used by d j thomson proc ieee vol 70 p 1055 1096 1982 for spectral estimation are given trigonometric coefficients and energy leakages of the window polynomials are tabulated

a recursive maximum likelihood algorithm for arma spectral estimation a spectral estimation technique is presented for autoregressive moving average arma processes the technique is based on a parameter estimation technique known as the rec ursive maximum likelihood rml method the recursive spectral estimation algorithm is presented and its asymptotic properties are discussed simulation results are presented to illustrate the performance of the estimator for various types of data

coincidences among skew schur functions new sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew schur function the sufficient conditions come from a variety of new operations related to ribbons also known as border strips or rim hooks the necessary conditions relate to the extent of overlap among the rows or among the columns of the skew diagram

a straightening algorithm for row convex tableaux abstract we produce a new basis for the schur and weyl modules associated to a row convex shape d the basis is indexed by a new class of straight tableaux which we introduce by weakening the usual requirements for standard tableaux spanning is proved via a new straightening algorithm for expanding elements of the representation into this basis for skew shapes this algorithm specializes to the classical straightening law the new straight basis is used to produce bases for flagged schur and weyl modules to provide groebner and sagbi bases for the homogeneous coordinate rings of some configuration varieties and to produce a flagged branching rule for row convex representations systematic use of supersymmetric letterplace techniques enables the representation theoretic results to be applied to representations of the general linear lie superalgebra as well as to the general linear group

addendum specht modules for column convex diagrams characteristic free results for weyl modules abstract it is shown that the results in reiner and shimozono 12 have characteristic free analogues for weyl modules

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

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

on the ranges of nonlinear set valued accretive operators in banach spaces abstract let e be a real banach space and a d a e 2 e b d b e 2 e be two set valued accretive operators we study the range problems of a i and a b i for 0 the results obtained in this paper generalize some other results

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

spectrum adapted tight graph wavelet and vertex frequency frames we consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs while the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum the filters proposed in this paper are adapted to the distribution of graph laplacian eigenvalues and therefore lead to atoms with better discriminatory power our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph we then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph laplacian eigenvalues we use this approach to construct computationally efficient spectrum adapted tight vertex frequency and graph wavelet frames we give numerous examples of the resulting spectrum adapted graph filters and also present an illustrative example of vertex frequency analysis using the proposed construction

a two parameter class of bessel weightings for spectral analysis or array processing the ideal weighting window pairs a unified theory for array processing in 1 2 or 3 dimensions is pointed out and illustrated by a two parameter class of bessel weightings this class subsumes the i 0 sinh weighting window pair as well as the ideal space factor of van der maas in one dimension the weightings that realize the ideal space factor in 2 and 3 dimensions are generalized functions more singular than the delta function required in 1 dimension

the gorenstein locus of minuscule schubert varieties in this article we explicitly describe the gorenstein locus of all minuscule schubert varieties this proves a special case of the conjecture of a woo and a yong alexander woo alexander yong governing singularities of schubert varieties j algebra 320 2 2008 495 520 regarding the gorenstein locus of schubert varieties

b spline design of maximally flat and prolate spheroidal type fir filters a digital fir filter is described that offers excellent passband and stopband characteristics for general applications design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of hermann 1971 and kaiser 1975 1979 to one having characteristics like the minimum sidelobe energy approximations of kaiser and saramaki 1989 the impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances unlike fir filters designed by window or frequency sampling methods the filter coefficients are determined from the inverse fourier transform in closed form once b splines have been used to replace sharp transition edges of the magnitude response although the filters are developed in the frequency domain a convergence window is identified in the convolution series and compared with windows of popular fir filters by means of example adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs the design technique is extended to create additional transitional filters from prototype window functions such as the transitional hann window filter the filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors

on 1 set contraction perturbations of accretive operators in cones of banach spaces abstract letpbe a cone in a banach spacee in this paper we show the existence of solutions of the operator equationy ax txfory p wheretis a 1 set contraction operator inpandais an accretive operator inpsatisfyingr i a pfor all 0 further a sufficient condition forr i a pis also given

delayed block transfer function in the frequency domain when the impulse response of a transfer system is long it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast fourier transform fft with a finite length window the bias error in the estimate is large especially around the resonant frequency of the transfer system in the paper therefore the authors propose an alternative new method to obtain an accurate estimate of the transfer function the delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window based on these transfer functions the total characteristics of the transfer system are estimated accurately in the latter half of the paper the authors derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods by thoroughly comparing the resultant expressions the superiority and the usefulness of the proposed method are theoretically confirmed finally the simulation experiments show the advantages of the proposed method

the gridding method for image reconstruction by fourier transformation the authors explore a computational method for reconstructing an n dimensional signal f from a sampled version of its fourier transform f spl circ the method involves a window function w spl circ and proceeds in three steps first the convolution g spl circ w spl circ f spl circ is computed numerically on a cartesian grid using the available samples of f spl circ then g wf is computed via the inverse discrete fourier transform and finally f is obtained as g w due to the smoothing effect of the convolution evaluating w spl circ f spl circ is much less error prone than merely interpolating f spl circ the method was originally devised for image reconstruction in radio astronomy but is actually applicable to a broad range of reconstructive imaging methods including magnetic resonance imaging and computed tomography in particular it provides a fast and accurate alternative to the filtered backprojection the basic method has several variants with other applications such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the radon hough transform

windows with rapidly decaying sidelobes and steerable sidelobe dips a window in the form of a sum of cosine terms is considered and the temporal weights are evaluated analytically so that it can have rapidly decaying sidelobes as well as steerable sidelobe dips an analytic expression is derived so that the window designer can exploit the trade off between a high sidelobe falloff rate slfor and many steerable sidelobe dips ssld the treatment is based on using the l degrees of freedom inherent in the l temporal weights of the l 1 term window in partially achieving the goals of a high slfor and many ssld in the extreme case where all degrees of freedom are used in achieving the maximum slfor a simple closed form expression is derived for the temporal weights thus formalizing and generalizing the results of nuttall 1981 the other extreme case where all degrees of freedom are used in creating many ssld has been recently treated by zhong et al see ibid vol 40 no 6 p 1452 1459 1992 combining both desired features in one unified mathematical framework is the main objective of this paper simulation results demonstrate the superior performance of a window having both features to that of a window having only one feature in extracting a weak sinusoidal signal dominated by a leakage from another stronger signal

design of windows with steerable sidelobe dips based on the frequency sampling method a novel and simple window design technique was established upon three theorems the technique produces a set of windows which have simple expressions and the steerable sidelobe dip ssld property by steering the dips in the sidelobes it is easy to reduce the edge of the mainlobe or to minimize the height of sidelobes or to create a hole in the sidelobes if its desired to reduce spectral leakage at a particular frequency it is found that windows constructed as a weighted sum of cosines over a finite support and with a 6 db oct sidelobe falloff rate can all be simulated by appropriate ssld distributions in this sense many good windows such as hamming blackman blackman harris and minimum sidelobe behaviors can be created with a minor constraint this renders design flexibility for various applications finally the new technique can be easily incorporated with other techniques to produce windows with hybrid merits

least squared error fir filter design with transition bands the authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least squared error fir digital filters with an explicit control of the transition band edges design formulas are derived for approximations to ideal frequency responses which use pth order spline transition functions a mixed analytical and numerical method for zero error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived a variable order spline transition function is developed and a method for choosing the optimal order to minimize the integral squared approximation error is given

a unified approach to nonparametric spectrum estimation algorithms different approaches to spectrum estimation can be broadly classified as parametric and nonparametric methods in the parametric techniques an underlying model is assumed in the formulation of the spectrum estimation problem and one estimates the parameters of the model for nonparametric methods no such model is assumed in this paper several nonparametric spectrum estimation algorithms are brought under a unified framework by the introduction of a generalized nonparametric spectrum estimation algorithm a four stage approach is employed it contains as special cases the blackman tukey algorithm the weighted overlapped segment averaging wosa method the lag reshape approach rader s algorithm and the short time unbiased spectrum estimation stuse algorithm the framework proposed in the paper is more general than the one recently proposed by nuttall and carter theoretical expressions for the spectrum estimation variance of the generalized algorithm are derived and then verified via simulation example also several nonparametric approaches for obtaining unbiased spectrum estimates are discussed and compared finally we conclude the paper with a brief discussion of the applicability and usefulness of several methods in specific situations

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

an efficient multiscale method for time domain waveform tomography this efficient multiscale method for time domain waveform tomography incorporates filters that are more efficient than hamming window filters a strategy for choosing optimal frequency bands is proposed to achieve computational efficiency in the time domain a staggered grid explicit finite difference method with fourth order accuracy in space and second order accuracy in time is used for forward modeling and the adjoint calculation the adjoint method is utilized in inverting for an efficient computation of the gradient directions in the multiscale approach multifrequency data and multiple grid sizes are used to overcome somewhat the severe local minima problem of waveform tomography the method is applied successfully to 1d and 2d heterogeneous models it can accurately recover low and high wavenumber components of the velocity models the inversion result for the 2d model demonstrates that the multiscale method is computationally efficient and converges faster than a conventional single scale method

the synchronized short time fourier transform properties and definitions for multichannel source separation this paper proposes the use of a synchronized linear transform the synchronized short time fourier transform sstft for time frequency analysis of anechoic mixtures we address the short comings of the commonly used time frequency linear transform in multichannel settings namely the classical short time fourier transform cstft we propose a series of desirable properties for the linear transform used in a multichannel source separation scenario stationary invertibility relative delay relative attenuation and finally delay invariant relative windowed disjoint orthogonality dirwdo multisensor source separation techniques which operate in the time frequency domain have an inherent error unless consideration is given to the multichannel properties proposed in this paper the sstft preserves these relationships for multichannel data the crucial innovation of the sstft is to locally synchronize the analysis to the observations as opposed to a global clock improvement in separation performance can be achieved because assumed properties of the time frequency transform are satisfied when it is appropriately synchronized numerical experiments show the sstft improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis

asymptotic statistical analysis of the high order ambiguity function for parameter estimation of polynomial phase signals the high order ambiguity function haf is a nonlinear operator designed to detect estimate and classify complex signals whose phase is a polynomial function of time the haf algorithm introduced by peleg and porat 1991 estimates the phase parameters of polynomial phase signals measured in noise the purpose of this correspondence is to analyze the asymptotic accuracy of the haf algorithm in the case of additive white gaussian noise it is shown that the asymptotic variances of the estimates are close to the cramer rao bound crb for high snr however the ratio of the asymptotic variance and the crb has a polynomial growth in the noise variance

geometry of graph varieties first published in transactions of the american mathematical society in volume 355 2003 4151 4169 published by the american mathematical society

a fast estimation method for arma processes an improvement of a batch algorithm for parameter estimation of an arma process is presented a fast and iterative algorithm is presented and provides estimates with the same asymptotic distribution as the maximum likelihood estimates this algorithm is a modified version of the method suggested by mayne and firoozan 1982 linear identification of arma processes automatica 18 461 466 and requires one less regression than the previous method if only one pass is executed

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

a new window and comparison to standard windows a new window w t 0 62 0 48 mod t mod 0 38 cos 2 pi t mod t mod or 1 2 is introduced it is shown that the window is of a group with similar but different tradeoff properties with the bartlett the hanning and the hamming windows the proposed window is more effective than the bartlett and the hanning in the near sidelobes and more effective than the bartlett and the hamming in the far sidelobes