fisher information for a complex gaussian random variable beamforming applications for wave propagation in a random medium we derive a general expression for the fisher information for a special class of complex gaussian random variables whose mean and covariance may be expressed in terms of a specific parameterized linear transformation the deterministic unknown parameter case is considered this class is descriptive of signals that propagate in a homogeneous or inhomogeneous medium and also occurs in numerous beamforming applications the fisher information derived here encompasses a wide range of previously derived well known results for complex gaussian signals propagating in a homogeneous medium and is also applicable to more recent models for signals propagating in an inhomogenous medium the conditions for the estimates of the azimuth and elevation to decouple from the estimates of the nuisance parameters are studied for monochromatic plane wave and spherical wave propagation in a random medium for propagation in an anisotropic medium it is found that in general the cramer rao lower bounds crlbs of the entire unknown parameter set will be coupled for special cases of propagation in an isotropic medium it is found that for plane waves the crlbs of the angles of arrival will be approximately decoupled from the crlbs of the other unknowns and for spherical waves the crlbs of the angles of arrival will be always be coupled to the crlbs of all other unknowns although the couplings may be minimized under certain conditions

combinatorial decompositions of a class of rings in this paper we introduce some combinatorial methods for the study of graded rings and use these methods to analyze a class of rings that are of importance in combinatorics our methods are based on a unique representation theorem which is shown section 2 to hold for any graded algebra and which in a sense is an extension of the direct sum decomposition for cohen macaulay algebras this unique representation is reminiscent of a similar result obtained by rees 20 both results yield a decomposition of the algebra however our result differs from that of rees in that it carries more information about the algebra our main results are concerned with a class of rings see section 3 for the definition associated to simplicial complexes there are several natural operations that can be performed on simplicial complexes to obtain new complexes which in turn have an interpretation for the corresponding rings we show sections 4 5 and 6 that our basic decompositions can be transferred during these operations from the original rings to the newly constructed ones the operations studied here are the chain transform or barycentric subdivision section 4 rank selection both for partially ordered sets and for simplicial complexes section s and localization section 6 as we develop these tools we give some applications in section 5 we give a new topological characterization of the cohen macaulay property for partially ordered sets an immediate consequence of which is the rankselection theorem baclawski 2 this characterization is closely related to those obtained by garsia in 14

distributed source modeling and direction of arrival estimation techniques in direction of arrival doa estimation the direction of a signal is usually assumed to be a point if the direction of a signal is distributed due to some environmental phenomenon however doa estimation methods based on the point source assumption may result in poor performance we consider doa estimation when the signal sources are distributed parametric and nonparametric models are proposed and estimation methods are considered under these models in addition the asymptotic distribution of estimation errors is obtained to show the models statistical properties

inherent limitations in the localization of a coherently scattered source this paper addresses the problem of localizing a single coherently scattered far field narrowband source emitting a gaussian signal and observed in additive gaussian noise an explicit expression for the cramer rao bound crb of the unknown spatial and spectral i e source and noise power level parameters of the source is presented for arbitrary array geometry the crb is used to study the inherent limitations in the estimation of the mean angle of a scattered source in comparison to the case of a point source at the same mean angle

alexander duality and stanley depth of multigraded modules abstract we apply miller s theory on multigraded modules over a polynomial ring to the study of the stanley depth of these modules several tools for stanley s conjecture are developed and a few partial answers are given for example we show that taking the alexander duality twice but with different centers is useful for this subject generalizing a result of apel we prove that stanley s conjecture holds for the quotient by a cogeneric monomial ideal

robustness of oversampled gabor transient detectors a comparison of energy and known location detectors this correspondence provides a context for previous studies on the use of linear time frequency transforms for transient signal detection in the case where signal component locations are assumed to be known the robustness of a known location detector kld based on the oversampled gabor transform is compared with that of the corresponding energy detector in the gabor domain as expected the kld was sensitive to location mismatch unexpectedly it was extremely sensitive to location mismatch

joint 2 d doa estimation and phase calibration for uniform rectangular arrays a precise model of the array response is required to maintain the performance of direction of arrival doa estimation when modeling errors are present or the sensor environment is time varying autocalibration becomes necessary in this paper the problem of phase autocalibration for uniform rectangular array ura geometries is considered for the case with a single source a simple and robust least squares algorithm for joint 2 d doa estimation and phase calibration is presented when performing phase autocalibration with a ura the phase and doa parameters cannot be identified together without ambiguity this problem is discussed and a suitable remedy is suggested an approximate cramer rao bound and analytical expressions for the mean squared error performance of the proposed estimator are presented the proposed algorithm for phase autocalibration is extended for the case with multiple sources the results are evaluated using a representative body of simulations

robust adaptive beamforming based on steering vector estimation with as little as possible prior information a general notion of robustness for robust adaptive beamforming rab problem and a unified principle for minimum variance distortionless response mvdr rab techniques design are formulated this principle is to use standard mvdr beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information differences between various mvdr rab techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques a new mvdr rab technique which uses as little as possible and easy to obtain imprecise prior information is developed the objective for estimating the steering vector is the maximization of the beamformer output power while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations the prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies mathematically the proposed mvdr rab is expressed as the well known non convex quadratically constrained quadratic programming problem with two constraints which can be efficiently and exactly solved some new results for the corresponding optimization problem such as a new algebraic way of finding the rank one solution from the general rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank one are derived our simulation results demonstrate the superiority of the proposed method over other previously developed rab techniques

stanley depth of multigraded modules abstract the stanley s conjecture on cohen macaulay multigraded modules is studied especially in dimension 2 in codimension 2 similar results were obtained by herzog soleyman jahan and yassemi as a consequence of our results stanley s conjecture holds in 5 variables

depth and stanley depth of symbolic powers of cover ideals of graphs abstract let g be a graph with n vertices and let s k x 1 x n be the polynomial ring in n variables over a field k assume that j g is the cover ideal of g and j g k is its k th symbolic power we prove that the sequences sdepth s j g k k 1 and sdepth j g k k 1 are non increasing and hence convergent suppose that o g denotes the ordered matching number of g we show that for every integer k 2 o g 1 the modules j g k and s j g k satisfy the stanley s inequality we also provide an alternative proof for 9 theorem 3 4 which states that depth s j g k n o g 1 for every integer k 2 o g 1

a field theoretic approach to non equilibrium work identities we study non equilibrium work relations for a space dependent field with stochastic dynamics model a jarzynski s equality is obtained through symmetries of the dynamical action in the path integral representation we derive a set of exact identities that generalize the fluctuation dissipation relations to non stationary and far from equilibrium situations these identities are prone to experimental verification furthermore we show that a well studied invariance of the langevin equation under supersymmetry which is known to be broken when the external potential is time dependent can be partially restored by adding to the action a term which is precisely jarzynski s work the work identities can then be retrieved as consequences of the associated ward takahashi identities

stanley depth of squarefree monomial ideals in this paper we answer a question posed by y h shen we prove that if i is an m generated squarefree monomial ideal in the polynomial ring s k x1 xn with k a field then sdepthi n m 2 the proof is inductive and uses the correspondence between a stanley decomposition of a monomial ideal and a partition of a particular poset into intervals established by herzog vladoiu and zheng

local cohomology of modules of covariants abstract let g be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let w u be two finite dimensional representations of g in this paper we compute the local cohomology of u sw g provided a certain relatively weak technical condition is true

prime filtrations of monomial ideals and polarizations abstract we show that an arbitrary monomial ideal i is pretty clean if and only if its polarization i p is clean this yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree and it also implies that a multicomplex is shellable if and only the simplicial complex corresponding to its polarization is non pure shellable we also discuss stanley decompositions in relation to prime filtrations

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

a broadband maximum likelihood imager for a class of extended space time separable sources an algorithm is presented that reconstructs the shape of an extended incoherent source using only the broadband signals radiated from the source to a sparse array the source is modeled with a small set of parameters for the specific class of space time separable sources which have similar spatial structure at multiple frequencies the information radiated at each frequency is recombined into a broadband likelihood function in order to improve the estimation of the source parameters expressions for the cramer rao bounds crbs are provided and the performance of the algorithm is demonstrated for a gaussian lump shaped source

simplicity of rings of differential operators in prime characteristic let w be a finite dimensional representation of a linearly reductive group g over a field k motivated by their work on classical rings of invariants levasseur and stafford asked whether the ring of invariants under g of the symmetric algebra of w has a simple ring of differential operators in this paper we show that this is true in prime characteristic indeed if r is a graded subring of a polynomial ring over a perfect field of characteristic p 0 and if the inclusion r hookrightarrow s splits then d k r is a simple ring in the last section of the paper we discuss how one might try to deduce the characteristic zero case from this result as yet however this is a subtle problem and the answer to the question of levasseur and stafford remains open in characteristic zero http www luc ac be research algebra 1991 mathematics subject classification 16s32 16g60 13a35

parametric localization of distributed sources most array processing algorithms are based on the assumption that the signals are generated by point sources this is a mathematical constraint that is not satisfied in many applications in this paper we consider situations where the sources are distributed in space with a parametric angular cross correlation kernel we propose an algorithm that estimates the parameters of this model using a generalization of the music algorithm the method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors we study two particular cases coherent and incoherent spatial source distributions the spatial correlation function for a uniformly distributed signal is derived from this we find the array gain and show that in contrast to point sources it does not increase linearly with the number of sources we compare our method to the conventional point source music algorithm the simulation studies show that the new method outperforms the music algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources it is also shown that the threshold signal to noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method

dualizing complexes of affine semigroup rings for an affine semigroup ring we construct the dualizing complex in terms of the semigroup and the homology of the face lattice of the polyhedral cone spanned by the semigroup as a consequence there are characterizations of locally cohen macaulay rings buchsbaum rings and cohen macaulay rings as well as serre s condition 9 introduction let s denote a finitely generated submonoid of the additive monoid n n being a positive integer by the affine semigroup ring i s of s over a field x let us denote the subring of x xl xn generated by all monomials xs s e s so one has up to isomorphisms a one to one correspondence between affine semigroup rings and affine varieties given parametrically by monomials now it is of some interest to characterize ring theoretic properties as cohenmacaulay gorenstein etc in terms of the semigroup s a first breakthrough in this direction was done by kempf et al kkms and hochster hol who showed that x s is a cohen macaulay ring provided it is normal moreover the normality of x s is described in terms of s see hol another particular case if s is a simplicial semigroup is treated by goto suzuki and watanabe gsw resp stanley st2 who showed that x s is a cohen macaulay ring if it satisfies the 22 condition of serre note that normality is equivalent to 5y2 and r1 moreover there is a description of the 5 condition in terms of s see theorem 6 3 in general the 52 condition is not sufficient for i s to be a cohen macaulay ring as follows by examples in hol resp th 1 2 on the other side grobner g posed the problem to classify cohen macaulay affine semigroup rings the solution of this problem was done by hoa and trung th related to structural properties of graded rings is a technical tool of the duality theory this is the dualizing complex introduced by grothendieck see ha in recent years it became a helpful tool in commutative algebra in particular its knowledge allows characterizations of cohen macaulay rings locally cohenmacaulay rings buchsbaum rings gorenstein rings and the 5 conditions of received by the editors december 18 1988 1980 mathematics subject classification 1985 revision primary 13h10 secondary 14m05 06a99 1990 american mathematical society 0002 9947 90 1 q0 25 per page