wave number based assessment of the doubly asymptotic approximation i frequency domain wet surface impedance the doubly asymptotic approximation daa is a canonical relationship for the interaction between surface normal velocity and pressure its validity for a slender hemicapped cylinder is examined by formulating a frequency domain version of daa using the global basis functions employed in the wave number based formulation of the surface variational principle k wu and j h ginsberg asme j vib acoust 120 392 400 1998 the wet surface impedance matrix which relates the spectral representation of normal velocity to a corresponding representation of pressure is obtained according to a second order version of daa and according to the surface variational principle comparison and interpretation of the results reveals that daa fails to account for highlights associated with transition from supersonic to subsonic surface waves as the surface wavelength decreases with frequency held constant

doubly asymptotic approximations for transient poroelastodynamics a doubly asymptotic approximation daa is an approximate temporal impedance relation at the boundary of a continuous medium here first and second order daas are formulated for an infinite external poroelastic medium described by biot s equations as with their acoustic elastodynamic and electromagnetic predecessors the poroelastodynamic daas approach exactness in both the early time high frequency and late time low frequency limits effecting a smooth transition between they also lend themselves to straightforward boundary element discretization producing matrix ordinary differential equations in time that are readily solved by numerical integration an initial examination of poroelastodynamic daa accuracy is presented for two problems with spherical symmetry

the characteristic maxpolynomial of a matrix abstract an analog of the characteristic polynomial is defined for a matrix over the algebraic structure r max and its properties are discussed

operators that preserve semiring matrix functions abstract characterizations are obtained of those linear operators over certain semirings that preserve 1 the rth coefficient of the rook polynomial those that preserve 2 the term rank of matrices with term rank r and those that preserve 3 the rth elementary symmetric permanental function our results apply to many algebraic systems of combinatorial interest including the nonnegative integer matrices boolean matrices and fuzzy matrices

the characterizations of h hemiregular hemirings and h intra hemiregular hemirings in this paper the concepts of fuzzy h bi ideals and fuzzy h quasi ideals of a hemiring are introduced and related properties are investigated the notion of h intra hemiregularity of a hemiring which is a generalization of the notion of intra regularity of a ring is provided some characterizations of h hemiregular hemirings h intra hemiregular hemirings and hemirings that are both h hemiregular and h intra hemiregular are derived in terms of fuzzy left fuzzy right h ideals fuzzy h bi ideals and fuzzy h quasi ideals

on the variety of a highest weight module 1 2 let u g be the enveloping algebra of g detailed information on the primitive spectrum prim u g of u g was summarized by conjecture 7 4 of 181 here a main question was to relate prim u g with the springer correspondence parts i ii of this conjecture were established in i ii and a partial solution to iii was given in 21 sufficient e g to treat g of type a meanwhile borho and brylinski 5 have established iii for induced ideals while barbasch and vogan 1 2 have established a version of iii in which gr i i e prim u g is replaced by a certain wavefront set known to be contained in y gr 1 this last work involves some case by case analysis and gives little indication as to why the springer correspondence should arise in the study of prim u g

doubly asymptotic approximations for vibration analysis of submerged structures doubly asymptotic approximations daa s are differential equations for boundary element analysis of the dynamic interaction between a complex structure and a surrounding infinite medium t l geers j acoust soc am 64 1500 1508 1978 p g underwood and t l geers int j solids struct 17 687 697 1981 in this paper the use of first and second order daa s for vibration analysis of submerged structures is examined first the governing discrete element equations for the general problem are set down and discussed then the accuracy of three daa forms is studied through the generation of numerical results for a submerged spherical shell although the first order daa is found to be inadequate the two second order forms show considerable promise work supported by the david w taylor naval ship r d center

matrices over semirings introducing the concept of semi invertibility of square matrices over semirings some sufficient conditions for semi invertibility of square matrices over various kinds of semirings are obtained also a necessary and sufficient condition for semi invertibility of square matrices over semirings is obtained

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

transient spheroidal elements for unbounded wave problems a wave envelope element numerical scheme is applied to the solution of unbounded wave problems the scheme is based on a fourier transformation of a discrete model formulated in the frequency domain this yields a discrete system of ordinary differential equations in time which are local in space oblate and prolate spheroidal element geometries are used the accuracy of the scheme is demonstrated by a comparison of computed and analytic solutions for axisymmetric test cases time harmonic and transient solution are presented an indirect solution procedure is also presented which permits the sparsity of the transient equations to be utilised more effectively

inversion of matrices over a commutative semiring it is a well known consequence of the elementary theory of vector spaces that if a and b are n by n matrices over a field or even a skew field such that ab 1 then ba 1 this result remains true for matrices over a commutative ring however it is not in general true for matrices over noncommutatives rings in this paper we show that if a and b are n by n matrices over a commutative semiring then the equation ab 1 implies ba 1 we give two proofs one algebraic in nature the other more combinatorial both proofs use a generalization of the familiar product law for determinants over a commutative semiring

characterizations of hemirings by νq k fuzzy ideals in this paper we define q k fuzzy h sub hemirings q k fuzzy h bi ideals q k fuzzy h quasi ideals we characterize h hemiregular and h intra hemiregular hemirings by the properties of their q k fuzzy h ideals q k fuzzy h bi idealsand q k fuzzy h quasi ideals some of these characterizations are generalizations of the characterizations given in 36 x ma j zhan generalized fuzzyh bi ideals and h quasi ideals of hemirings inform sci 179 2009 1249 1268

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

partitioned formulation of internal fluid structure interaction problems by localized lagrange multipliers abstract a partitioned formulation of compressible internal fluid structure interaction problems is presented by employing a displacement model for both the fluid and structure partitioning is effected by a localized version of the method of lagrange multipliers which assigns two independent sets of lagrange multipliers to the structural and fluid interfaces two major features of the present formulation include an interface compliance normalization that helps capture the predominant physics of interaction phenomena when the interfaces are characterized by two radically different rigidities and a novel transformation of the displacement model into a fluid pressure model that is suitable for both transient and vibration analyses the present formulation first solves for the interface lagrange multipliers which are subsequently used to solve for the structural displacements and the fluid displacement or pressure by employing two independent analysis modules

a new boundary finite element method for fluid structure interaction problems in order to study problems on fluid structure interaction we have used a mixed formulation which couples the classical functional of the structure with a new variational formulation by integral equations for the fluid this formulation has the advantage over the finite element methods of avoiding the discretization of the fluid domain furthermore unlike collocation methods the explicit calculation of the hadamard finite part of the singular integrals is avoided this leads after discretization by boundary finite elements to a small and symmetrical algebraic system typical examples are presented that demonstrate the efficiency of this variational formulation by studying the sound transmission through a baffled plane structure and through a flexible panel backed by a rigid cavity these include the calculation of the transmission loss factor and the determination of which modes dominate the noise transmission good agreement is obtained between numerical results and analytical results found in the literature

on fuzzy h ideals in hemirings the fuzzy setting of a left h ideal in a hemiring is constructed and basic properties are investigated using a collection of left h ideals of a hemiring s fuzzy left h ideals of s are established the notion of a finite valued fuzzy left h ideal is introduced and its characterization is given fuzzy relations on a hemiring s are discussed

three dimensional wave envelope elements of variable order for acoustic radiation and scattering part i formulation in the frequency domain a variable order infinite wave envelope element scheme is formulated for transient unbounded acoustical problems the transient formulation which is local in space and time is obtained by applying an inverse fourier transformation to a time harmonic wave envelope model whose formulation is described in a companion article this procedure yields a coupled system of second order differential equations which can be integrated in time to yield transient pressure histories at discrete nodal points far field transient pressures can also be obtained at adjusted times the method can be applied quite generally to two dimensional and three dimensional problems and is compatible with a conventional finite element model in the near field the utility of the method is confirmed by the presentation of transient solutions for axisymmetric and fully three dimensional test problems an implicit time integration scheme is used and computed results are compared to analytic solutions and to solutions obtained from alternative numerical schemes close correspondence is demonstrated and the scheme is shown to be stable for the problems which are presented cpu times for a large three dimensional problem are shown to compare favorably with those required for an equivalent transient boundary element computation

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

invertible matrices and semilinear spaces over commutative semirings this paper deals with invertible matrices and semilinear spaces over commutative semirings some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained the condition under which the cardinality of each basis of semilinear space of n dimensional vectors is n is given in the end the factor rank of matrices over semirings is investigated

on invertible matrices over antirings abstract an antiring is a semiring which is zerosumfree i e a b 0 implies a b 0 for any a b in this semiring in this paper the complete description of the invertible matrices over a commutative antiring is given and some necessary and sufficient conditions for a matrix over a commutative antiring to be invertible are obtained also cramer s rule over commutative antirings is presented the main results in this paper generalize and develop the corresponding results for the boolean matrices the fuzzy matrices the lattice matrices and the incline matrices

lie superalgebras clifford algebras induced modules and nilpotent orbits let g be a classical simple lie superalgebra to every nilpotent orbit o in g0 we associate a clifford algebra over the field of rational functions on o we find the rank k o of the bilinear form defining this clifford algebra and deduce a lower bound on the multiplicity of a u g module with o or an orbital subvariety of o as associated variety in some cases we obtain modules where the lower bound on multiplicity is attained using parabolic induction the invariant k o is in many cases equal to the odd dimension of the orbit g o where g is a lie supergroup with lie superalgebra g

new approximations of external acoustic structural interactions derivation and evaluation new approximate models for external acoustics interacting with flexible structures are developed the basic form of the present models is obtained by a combination of the laplace transformed retarded and advanced potentials with the weighting parameter as part of the model equation it is shown that the maximum attainable time derivative of convergent approximate models is two hence any attempt to include higher orders will lead to non convergent models the present external acoustic model is implemented and interfaced with a finite element structural analyzer for the transient response analysis of submerged spherical and cylindrical shells subjected to a series of incident waves comparisons of the present results with the classical analytical solutions and the doubly asymptotic approximations daas show that proposed model offers improved accuracy especially for early time responses exhibits computational robustness and maintains the impulse response consistency that are desirable for inverse problems the present model is applied for a shock response correlation of an experimental complex ring cylinder which demonstrates the applicability of the proposed approximate model to practical engineering problems

on generalized fuzzy matrices with periods in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some properties and characterizations for generalized fuzzy matrices with periods are established and an expression for the transitive closure of a generalized fuzzy matrix with a period as a sum of its powers is shown reduction of generalized fuzzy matrices is defined and some properties for reduction of generalized fuzzy matrices with periods are obtained also the structure of all standard eigenvectors for a generalized fuzzy matrix with a period is determined

sheets and topology of primitive spectra for semisimple lie algebras abstract let g be a semisimple lie algebra consider the set x of primitive ideals of the enveloping algebra u g given the jacobson topology a basic open problem is to describe x as a countable union of algebraic varieties v with strata v as large as possible towards this aim the notion of a sheet in x is introduced here in analogy with the notion of sheet in the adjoint orbit space g g the sheets in x are classified and given a purely topological description moreover goldie rank is constant and maximal on a dense open subset of a sheet for every positive integer n it is shown that there are only finitely many sheets in x with maximal goldie rank n for n 1 which corresponds to completely prime ideals an extension of the dixmier map from some adjoint orbits to primitive ideals is introduced with the aim of showing that the sheets with n 1 are homeomorphic to sheets in g g and hence explicitly described as algebraic varieties this goal is partly though not fully achieved the proofs of the above results require a detailed knowledge of goldie rank polynomials and even a new difficult result concerning the support of their restrictions to the walls an extension of a theorem of soergel on the topology of x is also required and for this a new approach is given which is both simpler and more general

a simple impedance infinite element for the finite element solution of the three dimensional wave equation in unbounded domains this paper is concerned with the development of an efficient and accurate impedance infinite element that can be used either in the frequency or directly in the time domain for the modeling and solution of problems described by the scalar three dimensional wave equation in infinite or semi infinite domains the infinite domain is truncated and the effect of the truncated infinite region is simulated by the introduction of an absorbing boundary condition prescribed on the truncation boundary a systematic procedure for the construction of a family of such conditions of increasing accuracy and complexity is developed with explicit formulas given for approximations up to second order a central feature of this high order approximation is that it can be expressed within the context of a finite element formulation as a set of local infinite elements located at the boundary of the computational domain with each element defined by a pair of symmetric time invariant stiffness and damping matrices this makes it possible to incorporate readily the new local boundary element into finite element software developed for purely interior regions for applications involving steady state harmonic or transient excitations whereas the theory has been developed formally for arbitrary smooth boundary surfaces here details are provided for ellipsoidal and spherical boundaries thus far only the latter has been implemented and tested in problems involving cavities and rigid scatterers of spherical and cubic shape numerical experiments in both the frequency and time domain attest to the efficacy and accuracy of the proposed new element

the minimal nilpotent orbit the joseph ideal and differential operators abstract fix a simple complex lie algebra g not of type g 2 f 4 or e 8 let min denote the zariski closure of the minimal non zero nilpotent orbit in g and let g n h n be a triangular decomposition we prove theorem 1 if g is not of type a n then there exists an irreducible component x of min n such that u g j o d x where j o is the joseph ideal and d x denotes the ring of differential operators on x 2 if g is of type a n then for n 2 of the n irreducible components x i of min n there exist distinct maximal ideals j i of u g such that u g j i d x i

mapped spheroidal wave envelope elements for unbounded wave problems this paper describes a family of axisymmetric spheroidal wave envelope elements for modelling exterior wave problems they are of variable radial order and can be used to represent steady and transient wave fields the formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries these offer the prospect of reduced dimensionality in comparison to conventional spherically formulated elements when used to represent wave fields in the vicinity of slender or flat objects conjugated weighting functions are used to give frequency independent acoustic mass stiffness and damping matrices this facilitates a simple extension of the method to transient problems the effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation by a rigid sphere excited from rest and by a circular plate vibrating in a plane baffle