array interpolation and doa mse reduction interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing this operation allows arrays of any geometry to be used with fast direction of arrival doa estimators designed for linear arrays in an earlier companion paper a first order condition for zero doa bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the doa estimate bias this bias minimizing theory is now extended to minimize not only bias but also to consider finite sample effects due to noise and reduce the doa mean square error mse an analytical first order expression for mapped doa mse is derived and a design algorithm for the transformation matrix that minimizes this mse is proposed generally doa mse is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the doa estimator criterion function the analytical mse expression and the design algorithm are supported by simulations that show not only conspicuous mse improvements in relevant scenarios but also a more robust preprocessing for low signal to noise ratios snrs as compared with the pure bias minimizing design developed in the previous paper

matrix representation of osp 2 2 in the u 1 1 basis vector coherent state theory is applied to matrix representations of osp 2 2 in the u 1 1 basis the branching rule of osp 2 2 1u 1 is derived finite dimensional irreducible matrix representations of osp 2 2 in the u 1 1 basis are discussed and matrix elements of osp 2 2 generators are obtained by using the k matrix technique

transformations of some induced osp 3 2 modules in an so 3 sp 2 basis the modules of the orthosymplectic lie superalgebra osp 3 2 induced from finite dimensional irreducible submodules of the stability subalgebra so 3 gl 1 are investigated the corresponding infinite dimensional irreducible or indecomposable modules the kac modules and the related typical and atypical modules are studied in detail every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so 3 sp 2 for each of these infinite dimensional or finite dimensional irreducible or indecomposable modules relations are written down giving the transformations of the basis under the action of the algebra generators

finite dimensional irreducible representations of the quantum superalgebra u q gl n 1 it is shown that every finite dimensional irreducible module over the general linear lie superalgebragl n 1 can be deformed to an irreducible module ofu q gl n 1 aq analogue of the universal enveloping algebra ofgl n 1 the results are extended also to all kac modules which in the atypical cases remain indecomposible within each module expressions for the transformations of the gel fand zetlin basis under the action of the algebra generators are written down an analogoue of the poincare birkhoff witt theorem is formulated

on the eigenvalue problem for arbitrary odd elements of the lie superalgebra and applications in a wigner quantum mechanical model with a solution in terms of the lie superalgebra one is faced with determining the eigenvalues and eigenvectors for an arbitrary self adjoint odd element of in any unitary irreducible representation w we show that the eigenvalue problem can be solved by the decomposition of w with respect to the branching the eigenvector problem is much harder since the gel fand zetlin basis of w is involved and the explicit actions of generators on this basis are fairly complicated using properties of the gel fand zetlin basis we manage to present a solution for this problem as well our solution is illustrated for two special classes of unitary representations the so called fock representations and the ladder representations

3d unstructured mesh ale hydrodynamics with the upwind discontinuous finite element method abstract we describe a numerical scheme to solve 3d arbitrary lagrangian eulerian ale hydrodynamics on an unstructured mesh using discontinuous finite element space and an explicit runge kutta time discretization this scheme combines the accuracy of a higher order godunov scheme with the unstructured mesh capabilities of finite elements that can be explicitly evolved in time the spatial discretization uses trilinear isoparametric elements tetrahedrons pyramids prisms and hexahedrons in which the primitive variables mass density velocity and pressure are piecewise trilinear upwinding is achieved by using roe s characteristic decomposition of the inter element boundary flux depending on the sign of characteristic wave speeds the characteristics are evaluated at the roe average of variables on both sides of the inter element boundary for a general equation of state an explicit second order runge kutta time stepping is used for the time discretization to capture shocks we have generalized van leer s 1d nonlinear minmod slope limiter to 3d using a quadratic programming scheme for very strong shocks we find it necessary to supplement this with a godunov stabilization where the trilinear representation of the variables is reduced to its constant average value the resulting numerical scheme has been tested on a variety of problems relevant to icf inertial confinement fusion target design and appears to be robust it accurately captures shocks and contact discontinuities without unstable oscillations and has second order accuracy in smooth regions object oriented programming with the c programming language was used to implement our numerical scheme the object oriented design allows us to remove the complexities of an unstructured mesh from the basic physics modules and thereby enables efficient code development

error estimates for finite element methods for scalar conservation laws in this paper new a posteriors error estimates for the shock capturing streamline diffusion scsd method and the shock capturing discontinuous galerkin scdg method for scalar conservation laws are obtained these estimates are then used to prove that the scsd method and the scdg method converge to the entropy solution with a rate of at least h 1 8 and h 1 8 respectively in the l infty l 1 norm the triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k the result is independent of the dimension of the space

finite dimensional representations of the quantum superalgebra uq gl 3 2 in a reduced uq gl 3 2 contains implies uq gl 3 1 contains implies uq gl 3 basis for generic q we give expressions for the transformations of all essentially typical finite dimensional modules of the hopf superalgebra uq ql 3 2 the latter is a deformation of the universal enveloping algebra of the lie superalgebra gl 3 2 the basis within each module is similar to the gel fand zetlin basis for gl 5 we write down expressions for the transformations of the basis under the action of the chevalley generators

fock representations of the lie superalgebra q n 1 for the lie superalgebra q n 1 a description is given in terms of creation and annihilation operators in such a way that the defining relations of q n 1 are determined by quadratic and triple supercommutation relations of these operators fock space representations vp of q n 1 are defined by means of these creation and annihilation operators these new representations are introduced as quotient modules of some induced module of q n 1 the representations vp are not graded but they possess a number of properties that are of importance for physical applications for p a positive integer these representations vp are finite dimensional with a unique highest weight of multiplicity one the hermitian form that is consistent with the natural adjoint operation on q n 1 is shown to be positive definite on vp for q 2 these representations are dispin for the general case of q n 1 many structural properties of vp are derived

finite dimensional representations of the special linear lie superalgebra sl 1 n i typical representations in a series of two papers all finite dimensional irreducible representations of the special linear lie superalgebra sl 1 n are written down in a matrix form this paper develops a background for constructing the representations expressions for the transformation of the basis under the action of the generators are given for all induced and hence for all typical sl 1 n modules

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

a description of the quantum superalgebrauq sl n 1 m via creation and annihilation generators a description of the quantum superalgebra uq sl n 1 m and in particular of the special linear superalgebra sl n 1 m via creation and annihilation generators cags is given it provides an alternative to the canonical description of uq sl n 1 m in terms of chevalley generators a conjecture that the fock representations of the cags provide microscopic realizations of exclusion statistics is formulated

finite dimensional representations of the quantum superalgebra uq gl 2 2 ii nontypical representations at generic q the construction approach proposed in the previous paper n a ky j math phys 35 2583 1994 allows us there and in the present paper to construct at generic deformation parameter q all finite dimensional representations of the quantum lie superalgebra uq gl 2 2 the finite dimensional uq gl 2 2 modules wq constructed in the previous paper are either irreducible or indecomposable if a module wq is indecomposable i e when the condition 4 41 in the previous paper does not hold there exists an invariant maximal submodule of wq say iqk such that the factor representation in the factor module wq iqk is irreducible and called nontypical here in this paper indecomposable representations and nontypical finite dimensional representations of the quantum lie superalgebra uq gl 2 2 are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows ii efficient flux quadrature a new and efficient quadrature rule for the flux integrals arising in the space time discontinuous galerkin discretization of the euler equations in a moving and deforming space time domain is presented and analyzed the quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme the local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product gauss quadrature rules are used details of the approximation of the dissipation in the numerical flux are presented which render the scheme consistent and stable the method is successfully applied to the simulation of a three dimensional transonic flow over a deforming wing

aspects of conservation in finite element flow computations in this paper we consider different aspects of conservation in the finite element method in particular we address the problem of conservation using numerical integration related to mass lumping simplified projections quasilinear formulations and non conservative variables numerical results concerning simplified projection algorithms are given

implementation of the entropy viscosity method with the discontinuous galerkin method the notion of entropy viscosity method introduced in guermond and pasquetti 21 is extended to the discontinuous galerkin framework for scalar conservation laws and the compressible euler equations

representations of uq sl n at roots of unity the gelfand zetlin basis for representations of uq sl n is improved to better fit the case when q is a root of unity the usual q deformed representations as well as the nilpotent periodic cyclic semi periodic semi cyclic and also some atypical representations are now described with the same formalism

gel fand zetlin basis and clebsch gordan coefficients for covariant representations of the lie superalgebra gl m n a gel fand zetlin basis is introduced for the irreducible covariant tensor representations of the lie superalgebra gl m n explicit expressions for the generators of the lie superalgebra acting on this basis are determined furthermore clebsch gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl m n with the natural representation v 1 0 0 of gl m n with highest weight 1 0 0 are computed both results are steps for the explicit construction of the parastatistics fock space

highest weight irreducible representations of the lie superalgebra gl 1 two classes of irreducible highest weight modules of the general linear lie superalgebra gl 1 are constructed within each module a basis is introduced and the transformation relations of the basis under the action of the algebra generators are written down

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

enhanced puma for direction of arrival estimation and its performance analysis direction of arrival doa estimation is a problem of significance in many applications in practice due to the occurrence of coherent signals and or when the number of available snapshots is small it is a challenge to find doas accurately this problem is revisited here through a new enhanced principal singular vector utilization for modal analysis epuma doa estimation approach which improves the threshold performance by first generating p k doa candidates for k sources where p geq k and then judiciously selecting k of them the asymptotic variance of epuma is theoretically derived and numerical results are provided to validate the asymptotic analysis and illustrate the practical merits of epuma

eigenstructure variability of the multiple source multiple sensor covariance matrix with contaminated gaussian data several methods of current interest for counting and locating signal sources using data from a passive array depend on the accuracy of estimating the eigenstructure of the covariance matrix of the array s data vectors when errors in the measured data vectors are gaussian conventional covariance estimation is optimal but robust procedure are required for data with nongaussian additive contamination two different robust covariance estimators are compared by simulation with the conventional one for different degrees of contamination even in relatively good signal to noise ratios however closeness of signal sources in the temporal and spatial frequency domains can cause inaccurate signal related eigenvalue and eigenvector estimates the degree of adversity for these problems is also shown by simulation

irreducible finite dimensional representations of the lie superalgebra gl n 1 in a gel fand zetlin basis all finite dimensional irreducible representations of the general linear lie superalgebra gl n 1 are studied for each representation a concept of a gel fand zetlin basis is defined expressions for the transformation of the basis under the action of the generators are written down

finite dimensional representations of the lie superalgebra gl 2 2 in a gl 2 gl 2 basis ii nontypical representations all finite dimensional irreducible representations of the general linear lie superalgebra gl 2 2 are written down in matrix form the basis within each representation space is chosen in such a way that it makes evident the decomposition of gl 2 2 into irreducible representations of its even subalgebra gl 2 gl 2 special attention is devoted to the analysis of all nontypical representations and some indecomposible representations

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

finite dimensional representations of the quantum superalgebra u q gl n m and related q identities explicit expressions for the generators of the quantum superalgebrau q gl n m acting on a class of irreducible representations are given the class under consideration consists of all essentially typical representations for these a gel fand zetlin basis is known the verification of the quantum superalgebra relations to be satisfied is shown to reduce to a set ofq number identities

representations of the lie superalgebra gl 1 n in a gel fand zetlin basis and wigner quantum oscillators an explicit construction of all finite dimensional irreducible representations of the lie superalgebra in a gel fand zetlin basis is given particular attention is paid to the so called star type i representations unitary representations and to a simple class of representations v p with p any positive integer then the notion of wigner quantum oscillators wqos is recalled in these quantum oscillator models the unitary representations of are physical state spaces of the n particle d dimensional oscillator so far physical properties of wqos were described only in the so called fock spaces w p leading to interesting concepts such as non commutative coordinates and a discrete spatial structure here we describe physical properties of wqos for other unitary representations including certain representations v p of gl 1 dn these new solutions again have remarkable properties following from the spectrum of the hamiltonian and of the position momentum and angular momentum operators formulae are obtained that give the angular momentum content of all the representations v p of associated with the n particle three dimensional wqo for these representations v p we also consider in more detail the spectrum of the position operators and their squares leading to interesting consequences in particular a classical limit of these solutions is obtained that is in agreement with the correspondence principle

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method