a generalization of bieberbach s theorem in 1912 bieberbach proved that every compact flat riemannian manifold m is finitely covered by a flat torus more precisely m has the form f g h where g is a group of translations of euclidean space f c g is a discrete subgroup and h is a finite group of isometries of the space of right cosets f g for a proof see e g wolf 18 the condition that m has a flat riemannian metric can be separated into two conditions first m has an affine structure a distinguished covering by coordinate charts whose coordinate changes are affine second m has a riemannian metric whose coefficients in the affine charts are constants in this paper we relax the second condition a polynomial riemannian metric on the affine manifold m is a riemannian metric whose local expression in affine coordinates has the form gi x dxidx where the gij are polynomial functions on euclidean space e by letting the gij be rational functions on e we arrive at the more general notion of a rational riemannian metric it is not assumed that these expressions define riemannian metrics on all of e the object of this paper is to determine which affine manifolds have polynomial riemannian metrics and to give examples of affine manifold having rational riemannian metrics

ergodic theory group representations and rigidity in these lectures we discuss some topics concerning the relationship of ergodic theory representation theory and the structure of lie groups and their discrete subgroups

removable lateral singularities of semilinear parabolic pdes and besov capacities suppose 1 2 lis a second order elliptic differential operator in rdanddis a bounded smooth domain in rd let q r dand let be a compact set on the lateral boundary of q we prove that is a removable lateral singularity for the equationu lu u in q if and only if cap1 2 0 where cap stands for the besov capacity on the boundary

a unified approach for the formulation of interaction problems by the boundary element method a unified formulation is presented based on boundary element method in a form suitable for performing the interaction analyses by substructure method for solid solid and soil structure problems the proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem such as unit displacement or load problem as required in conventional methods it eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions to explain the formulation it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input where both the inclusion and surrounding medium are treated as viscoelastic it is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation then the formulation is extended to other types of interaction problems a multi inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half space it is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis but also in the analysis involving diffraction of waves in a medium containing holes copyright 2005 john wiley sons ltd

flat affine or projective geometries on lie groups abstract this paper deals essentially with affine or projective transformations of lie groups endowed with a flat left invariant affine or projective structure these groups are called flat affine or flat projective lie groups we give necessary and sufficient conditions for the existence of flat left invariant projective structures on lie groups we also determine lie groups admitting flat bi invariant affine or projective structures these groups could play an essential role in the study of homogeneous spaces m g h having a flat affine or flat projective structures invariant under the natural action of g on m a medina asked several years ago if the group of affine transformations of a flat affine lie group is a flat projective lie group in this work we provide a partial positive answer to this question

the brownian snake and solutions of δu u2 in a domain we investigate the connections between the path valued process called the brownian snake and nonnegative solutions of the partial differential equation u u2 in a domain of d in particular we prove two conjectures recently formulated by dynkin the first one gives a complete characterization of the boundary polar sets which correspond to boundary removable singularities for the equation u u2 the second one establishes a one to one correspondence between nonnegative solutions that are bounded above by a harmonic function and finite measures on the boundary that do not charge polar sets this correspondence can be made explicit by a probabilistic formula involving a special class of additive functionals of the brownian snake our proofs combine probabilistic and analytic arguments an important role is played by a new version of the special markov property which is of independent interest

local limit theorems for transition densities of markov chains converging to diffusions we consider triangular arrays of markov chains that converge weakly to a diffusion process local limit theorems for transition densities are proved

polar boundary sets for superdiffusions and removable lateral singularities for nonlinear parabolic pdes suppose l is a second order elliptic differential operator in d and d is a bounded smooth domain in d let 1 2 and let be a closed subset of d it is known 13 that the following three properties are equivalent is polar that is is not hit by the range of the corresponding l superdiffusion in d the poisson capacity of is equal to 0 that is the integral is equal to 0 or for every measure where x is the distance to the boundary and k x y is the corresponding poisson kernel and is a removable boundary singularity for the equation lu u in d that is if u 0 and lu u in d and if u 0 on d then u 0 we investigate a similar problem for a parabolic operator in a smooth cylinder d let be a compact set on the lateral boundary of we show that the following three properties are equivalent a is polar that is is not hit by the graph of the corresponding l superdiffusion in b the poisson capacity of is equal to 0 that is the integral is equal to 0 or for every measure where k r x t y is the corresponding parabolic poisson kernel and c is a removable lateral singularity for the equation u lu u in that is if u 0 and u lu u in and if u 0 on and on d then u 0 1998 john wiley sons inc

autour de la conjecture de l markus sur les varietes affines for any subgroupg of n we introduce some integer discg n called thediscompacity ofg this number measures to what extent the closure ofg is not compact the markus conjecture says that a compact affinely flat unimodular manifold is complete our main result called the discompact theorem is that this conjecture is true under the assumption that the linear holonomy i e the parallel transport has discompacity 1 because discso n 1 1 1 this ensures that a compact flat lorentz manifoldm is geodesically complete hence by a previous result of w goldman and y kamishima gk such am is up to finite covering a solvmanifold this achieves the proof of a bieberbach s theorem for compact lorentz flat manifolds

nonstandard lorentz space forms in their recent paper 8 kulharni and raymond show that a closed 3 manifold which admits a complete lorentz metric of constant curvature 1 henceforth called a complete lorentz structure must be seifert fibered over a hyperbolic base furthermore on every such seifert fibered 3 manifold with nonzero euler class they construct such a lorentz metric moreover the lorentz structure they construct has a rather strong additional property which they call standard a lorentz structure is standard if its causal double cover possesses a timelike killing vector field equivalently it possesses a riemannian metric locally isometric to a left invariant metric on sl 2 r kulkarni and raymond asked if every closed 3 dimensional lorentz structure is standard this paper provides a negative answer to this question theorem 1 and a positive answer to the implicit question raised in 8 7 1 1 theorem 3 theorem 1 let m3 be a closed 3 manifold which admits a homogeneous lorentz structure and satisfies h m r 0 then there exists a nonstandard complete lorentz structure on m in 8 it is shown that the unit tangent bundle of a closed surface admits a homogeneous lorentz structure therefore we obtain corollary 2 there exists a complete lorentz structure on the unit tangent bundle of any closed surface f of genus greater than one which is not standard the homogeneous lorentz structures are all classified in 8 a circle bundle of euler number j over a closed surface f f 0 has a homogeneous structure if and only if j f an analogous statement holds when m has singular fibers i e when f is an orbifold we also show theorem 3 let m3 be a 3 manifold which admits a complete lorentz structure then m3 is not covered by a product f x s fa closed surface theorem 3 implies that the euler class of the seifert fiber structure of m3 is nonzero

double extension symplectique d un groupe de lie symplectique resume lie groups carrying a left invariant symplectic form symplectic groups are described in terms of semi direct product of lie groups or symplectic reduction and principal fiber bundles with affine fiber we give a generalization of medina and revoy s symplectic double extension which realizes a symplectic group as the reduction of another symplectic group we show that every group obtained by this process carries an invariant lagrangian foliation such that the affine structure defined by the simplectic form over each leaf is complete

a state space coupling method for fluid structure interaction analysis of plates a state space coupling method is presented for the direct solution of fluid loaded natural frequencies and mode shapes of plates this method expands the frequency dependent term in the rayleigh integral in a power series on circular frequency after factoring out the frequency term from the integrands integration involved in setting up the acoustic impedance coefficient matrices is confined to a frequency independent part the acoustic impedance coefficient matrices are therefore frequency independent and can be coupled directly with the structural matrix into a canonical state space form to yield the fluid loaded modes via the direct eigenvalue analysis a fluid loaded stiffened plate is involved to demonstrate the method numerical results of the fluid loaded natural frequencies mode shapes and modal damping ratios are given to show the efficacy of the state space coupling method

a hybrid approach for simulating fluid loading effects on structures using experimental modal analysis and the boundary element method many structural acoustics problems involve a vibrating structure in a heavy fluid however obtaining fluid loaded natural frequencies and damping experimentally can be difficult and expensive this paper presents a hybrid experimental numerical approach to determine the heavy fluid loaded resonance frequencies and damping of a structure from in air measurements the approach combines in air experimentally obtained mode shapes with simulated in water acoustic resistance and reactance matrices computed using boundary element be analysis the procedure relies on accurate estimates of the mass normalized in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting which are then used as basis modes for the in water be analysis the method is validated on a 4 445 cm 1 75 in thick nickel aluminum bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in water measurements good agreement is shown for the fluid loaded natural frequencies and one third octave loss factors finally the limitations of the hybrid approach are examined

affine manifolds and orbits of algebraic groups this paper is the sequel to the radiance obstruction and parallel forms on a ffne manifolds lyans amer math soc 286 1984 629 649 which introduced a new family of secondary characteristic classes for affine structures on manifolds the present paper utilizes the representation of these classes in lie algebra cohomology and algebraic group cohomology to deduce new results relating the geometric properties of a compact affine manifold mn to the action on rn of the algebraic hull a r of the affine holonomy group r c aff rn a main technical result of the paper is that if m has a nonzero cohomology class represented by a parallel k form then every orbit of a r has dimension k when m is compact then a r acts transitively provided that m is complete or has parallel volume the converse holds when r is nilpotent a 4 dimensional subgroup of aff r3 is exhibited which does not contain the holonomy group of any compact affine 3 manifold when m has solvable holonomy and is complete then m must have parallel volume conversely if m has parallel volume and is of the homotopy type of a solvmanifold then m is complete if m is a compact homogeneous affine manifold or if m possesses a rational riemannian metric then it is shown that the conditions of parallel volume and completeness are equivalent this paper is the sequel to our previous paper 22 in that paper we exploited certain characteristic classes exterior powers of the radiance obstruction to obtain relationships between various properties of affine manifolds our results supported the conjecture first made by l markus 36 that a compact affine manifold is complete if and only if it has parallel volume we shall refer to this as the main conjecture let m be a compact affine manifold with developing map dev m e and affine holonomy representation h 7r h 7r r c aff e here 1r is the group of deck transformations of the universal cover m e is the vector space rn and aff e is the group of affine automorphisms of e the map dev is a locally affine immersion which is equivariant respecting h the linear holonomy homb morphism is the composition a 1r gl e of h with the natural homomorphism l aff e gl e the obstruction to r fixing a point in e is a 1 dimensional cohomology class cm e h1 m ex with coefficients in e twisted by a it comes from a universal class in the group cohomology h1 aff e el which contains the crossed homomorphism u aff e e g g 0 received by the editors december 12 1984 and in revised form may 29 1985 1980 mathematics subject classification 1985 revision primary 57r99 53c05 secondary 53c10 55r25 1 research partially supported by fellowships and grants from the national science foundation a 1986 american mathematical society 0002 9947 86 1 00 25 per page

etale representations for reductive algebraic groups with one dimensional center abstract a complex vector space v is a prehomogeneous g module if g acts rationally on v with a zariski open orbit the module is called etale if dim v dim g we study etale modules for reductive algebraic groups g with one dimensional center for such g even though every etale module is a regular prehomogeneous module its irreducible submodules have to be non regular for these non regular prehomogeneous modules we determine some strong constraints on the ranks of their simple factors this allows us to show that there do not exist etale modules for g gl 1 s s with s simple

radiation impedance matrices for rectangular interfaces within rigid baffles calculation methodology and applications the coupling of sound fields through a finite sized aperture in a plane rigid baffle where the region half space on one side is unbounded can be described by an integral equation which constitutes a boundary condition for the field on the other side of the aperture such a boundary condition when the pressure and the normal velocity are expanded in basis functions defined over the aperture can be recast into a matrix form relating the coefficients of the basis functions in the expansions the principal feature being a matrix of fourfold double area integrals analogous to those encountered in studies of radiation from flexible pistons in rigid baffles a substantial analytical reduction to sums of single nonsingular integrals is derived for the elements of this radiation impedance matrix when the aperture is rectangular and the basis functions are expressible as a sum of products of exponential functions of the cartesian coordinates of the aperture plane with the exponential coefficients being arbitrary complex numbers the validity of the result is substantiated by its reduction to previously published results for less general cases its utility is demonstrated with the example of diffraction by a square hole in a screen

three dimensional affine crystallographic groups those groups r which act properly discontinuously and aillnely on ii with compact fundamental domain are classified first it is shown that such a group f contains a solvable subgroup of finite index thus establishing a conjecture of auslander in dimension three then unimodular simply transitive altine actions on ir are classified this leads to a classification of attine crystallographic groups acting on ir3 a characterization of which abstract groups admit such an action is given moreover it is proved that every isomorphism between virtually solvable atline crystallographic groups respectively simply transitive afline groups is induced by conjugation by a polynomial automorphism of the affrne space a characterization is given of which closed 3 manifolds can be represented as quotients of ir by groups of afftne transformations a closed 3 manifold m admits a complete atline structure if and only if m has a finite covering homeomorphic or homotopy equivaient to a 2 torus bundle over the circle

proper affine actions and geodesic flows of hyperbolic surfaces let to c 0 2 1 be a schottky group and let h2 to be the corresponding hyperbolic surface let s denote the space of unit length geodesic currents on s the cohomology group if1 to v parametrizes equivalence classes of affine deformations tu of to acting on an irreducible representation v of 0 2 1 we define a continuous biaffine map i s x hl to v u which is linear on the vector space h1 fo v an affine deformation tu acts properly if and only if x u 7 0 for all jl e s consequently the set of proper affine actions whose linear part is a schottky group identifies with a bundle of open convex cones in hl to v over the fricke teichmiiller space of e

an improved state space method for coupled fluid structure interaction analysis this paper presents an improved state space method for incorporating fluid structure interaction into structural acoustic analyses giordano and koopmann j a giordano and g h koopmann state space boundary element finite element coupling for fluid structure interaction analysis j acoust soc am 98 363 372 1995 introduced a state space approach for the coupled analysis of fluid loaded structures giordano s method employed a third order interpolation of the fluid impedance coupled with state space formalism permitting the direct eigenvalue analysis of the coupled system and thereby yielding the fluid loaded modes and natural frequencies this is in contrast to the common technique of sweeping through a range of frequencies so as to identify the natural frequencies and mode shapes the original state space approach yielded system matrices of order 4n where n is the number of degrees of freedom in the underlying model where giordano s method employed an interpolation based on surface velo

the structure of assosymmetric algebras in this paper we study the structure of an assosymmetric algebra a by investigating various radicals and show that the wedderburn principal theorem holds when a r a has no 1 dimensional factor where r a is the radical of a and also discuss a pierce decomposition of a

left symmetric structures on simple modular lie algebras abstract this paper investigates left symmetric structures on finite dimensional simple lie algebras g over a field k if k is of characteristic 0 then g does not admit any left symmetric structure this is known in the theory of affine manifolds in the modular case however such structures may exist the main purpose of this paper is to show that classical simple lie algebras of characteristic p 3 admit left symmetric structures only in case p divides dim g the proof involves the computation of the first cohomology groups of classical lie algebras for certain g modules of small dimension here g is regarded as the lie algebra of a connected semisimple algebraic group over an algebraically closed field of characteristic p 0 most of these computations are due to jantzen for nonrestricted simple lie algebras of cartan type it is shown that many more left symmetric structures can be found one studies so called adjoint structures induced by nonsingular derivations of g the simple algebra l g of block of dimension pn 1 for example admits adjoint structures for every p 0 if p 2 the results are more complicated

modal decomposition of exterior acoustic structure interaction a modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented the fluid loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem the eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented the modal sound power contributions using both fluid loaded structural modes and acoustic radiation modes are presented the results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem

convex affine domains and markus conjecture in this paper we show that any properly convex quasi homogeneous affine domain with irreducible projective automorphism group is projectively equivalent to a homogeneous affine domain then as an application we answer positively the markus conjecture when the manifold m is in a certain class of convex affine manifolds

superdiffusions and parabolic nonlinear differential equations we establish connections between superdiffusion processes and one class of nonlinear parabolic differential equations analytic results due to brezis and friedman baras and pierre and others are used to investigate the graphs of superdiffusions a survey of the literature and general comments are presented in section 4

the law of the euler scheme for stochastic differential equations i convergence rate of the distribution function we study the approximation problem ofef x t byef x t n where x t is the solution of a stochastic differential equation x t n is defined by the euler discretization scheme with stept n andf is a given function for smoothf s talay and tubaro have shown that the erroref x t f x t n can be expanded in powers of 1 n which permits to construct romberg extrapolation precedures to accelerate the convergence rate here we prove that the expansion exists also whenf is only supposed measurable and bounded under an additional nondegeneracy condition of hormander type for the infinitesimal generator of x t to obtain this result we use the stochastic variations calculus in the second part of this work we will consider the density of the law ofx t n and compare it to the density of the law ofx t

a probabilistic approach to one class of nonlinear differential equations we establish connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes as an application we improve results on superprocesses by using the recent progress in the theory of removable singularities for differential equations

mirror symmetry via logarithmic degeneration data i this paper lays the foundations of a program to study mirror symmetry by studying the log structures of illusie fontaine and kato on degenerations of calabi yau manifolds the basic idea is that one can associate to certain sorts of degenerations of calabi yau manifolds a log calabi yau space which is a log structure on the degenerate fibre the log cy space captures essentially all the information of the degeneration and hence all mirror statements for the large complex structure limit given by the degeneration can already be derived from the log cy space in this paper we begin by discussing affine manifolds with singularities given such an affine manifold along with a polyhedral decomposition we show how to construct a scheme consisting of a union of toric varieties in certain non degenerate cases we can also construct log structures on these schemes conversely given certain sorts of degenerations one can build an affine manifold with singularities structure on the dual intersection complex of the degeneration mirror symmetry is then obtained as a discrete legendre transform on these affine manifolds thus providing an algebro geometrization of the strominger yau zaslow conjecture the deepest result of this paper shows an isomorphism between log complex moduli of a log cy space and log kahler moduli of its mirror

compact affine manifolds with precompact holonomy are geodesically complete abstract this note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact

state space boundary element finite element coupling for fluid structure interaction analysis state space coupling is a new approach for handling computational fluid structure interaction problems in the low to medium frequency range the method is based on standard boundary element bem and finite element fem discretizations of the acoustic and structural domains respectively the implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion once expanded the acoustic energy of the fluid is directly coupled to that of the structure via hamilton s principle the coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid loaded structure biorthogonality properties of the state space eigensystem allow for an uncoupled modal solution of the forced problem results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach

the radiance obstruction and parallel forms on affine manifolds a manifold m is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine when they are locally linear m is called radiant the obstruction to radiance is a one dimensional class cm with coefficients in the flat tangent bundle of m exterior powers of cm give information on the existence of parallel forms on m especially parallel volume forms as applications various kinds of restrictions are found on the holonomy and topology of compact affine manifolds introduction an affine manifold m is a manifold with a distinguished maximal atlas of charts all of whose coordinate changes are locally affine on such a manifold there is an intrinsic notion of a parallel tensor one whose components in any affine chart are constants more generally there is the notion of a polynomial tensor field of given degree in 1962 l markus conjectured in mk that a compact orientable affine n dimensional manifold has parallel volume form if and only if it is complete meaning that its universal covering is affinely isomorphic to euclidean n space rn the problem of constructing a parallel volume form determines an n dimensional twisted real cohomology class originally studied by j smillie sm2 in this paper we express this class as the nth exterior power of a twisted one dimensional real class which we call the radiance obstruction cm by computing cm in various cohomology theories cech singular de rham and others we are able to exploit cm in several ways to yield more information on the structure of affine manifolds some of these results will appear in a subsequent paper gh3 the basic tool used is a formula proved in 2 6 which expresses the cohomology class of a parallel exterior k form in terms of the k th exterior power of the radiance obstruction akcvf min 2 7 the special case of a parallel volume form on a compact n dimensional manifold m is examined the existence of such a form implies that ancm 0 in 2 8 we show that the affine holonomy group f of such an m cannot preserve a proper affine subspace in gh3 this result will be improved by showing that r preserves no proper semialgebraic subset of rn in 2 10 we show that there tend to be plenty of parallel forms on a compact affine manifold with nilpotent affine holonomy received by the editors may 26 1983 1980 mathematics subject classification primary 57r99 53c05 secondary 53c10 55r25 4c1984 amencan mathematical society 0002 9947 84 1 00 25 per page

left invariant affine structures on reductive lie groups we describe left invariant affine structures that is left invariant flat torsion free affine connections on reductive linear lie groupsg they correspond bijectively to lsa structures on the lie algebra g ofg here lsa stands for left symmetric algebra if g has trivial or one dimensional center z then the affine representation 1 of g induced by any lsa structure g on g isradiant i e the radiance obstructionc h1 g g vanishes if dim z 1 we prove that g s z where s is split simple admits lsa structures if and only if s is of typeal that is g gln here we have the associative lsa structure given by ordinary matrix multiplication corresponding to the bi invariant affine structure on gl n which was believed to be essentially the only possible lsa structure on gln we exhibit interesting lsa structures different from the associative one they arise as certain deformations of the matrix algebra then we classify all lsa structures on glnusing a result of baues forn 2 we compute all structures explicitly over the complex numbers

natural linear additive functionals of superprocesses we investigate natural linear additive nla functionals of a general critical xi k psi superprocess x we prove that all of them have only fixed discontinuities all homogeneous nla functionals of time homogeneous superprocesses are continuous this was known before only in the case of quadratic branching we introduce an operator mathscr e u defined in terms of xi k psi and we prove that the potential h and the log potential u of a nla functional a are connected by the equation u mathscr e u h the potential is always an exit rule for xi and the condition h mathscr e h infty a e is sufficient for an exit rule h to be a potential in an accompanying paper these results are applied to boundary value problems for partial differential equations involving nonlinear operator lu u alpha where l is a second order elliptic differential operator and 1 alpha leq 2

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

small time edgeworth type expansions for weakly convergent nonhomogeneous markov chains we consider triangular arrays of markov chains that converge weakly to a diffusion process second order edgeworth type expansions for transition densities are proved the paper differs from recent results in two respects we allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero small time asymptotics are motivated by statistical applications and by resulting approximations for the joint density of diffusion values at an increasing grid of points

density estimates for a random noise propagating through a chain of differential equations we here provide two sided bounds for the density of the solution of a system of n differential equations of dimension d the first one being forced by a non degenerate random noise and the n 1 other ones being degenerate the system formed by the n equations satisfies a suitable hormander condition the second equation feels the noise plugged into the first equation the third equation feels the noise transmitted from the first to the second equation and so on so that the noise propagates one way through the system when the coefficients of the system are lipschitz continuous we show that the density of the solution satisfies gaussian bounds with non diffusive time scales the proof relies on the interpretation of the density of the solution as the value function of some optimal stochastic control problem

modal parameter estimation for fluid loaded structures from reduced order models a model reduction method is developed to estimate modal parameters of fluid loaded structures the method uses a matrix free formulation of rational krylov projection to construct reduced order models of the fluid loaded structures from forced responses at selected interpolation frequencies due to small sizes of the reduced order models eigenpairs of the associated eigenvalue problems are available at a very low computational cost resonance frequencies modal damping ratios and mode shapes of the original systems are recovered from the forced responses and the eigenpairs of the reduced order models nonphysical modes introduced by the model reduction process are filtered out by a modal damping ratio test and double checked by the condition number of the dynamic stiffness matrix efficiency and accuracy of the present method are demonstrated on a benchmark model of a water loaded plate clamped in a baffle

left symmetric algebras for mathfrak gl n we study the classification problem for left symmetric algebras with commutation lie algebra gr n in characteristic 0 the problem is equivalent to the classification of etale affine representations of g n algebraic invariant theory is used to characterize those modules for the algebraic group sl n which belong to affine etale representations of gr n from the classification of these modules we obtain the solution of the classification problem for gl n as another application of our approach we exhibit left symmetric algebra structures on certain reductive lie algebras with a one dimensional center and a non simple semisimple ideal

the surface variational principle applied to an acoustic cavity this paper presents the development and application of the surface variational principle svp for the evaluation of axisymmetric interior acoustic domains the interior form of the svp is first developed in the same manner as the existing exterior form then the surface pressure and normal velocity are represented with a ritz expansion using basis functions that span the entire wetted surface of the object of interest the resultant formulation is used to analyze the interior acoustic response of a harmonically forced right circular elastic cylinder this validation model was chosen as both the structural and acoustic responses can be solved analytically results are presented for two models one with a length to radius ratio of 2 4 and another with a ratio of 12 3 the svp is shown to well reproduce the analytical solution for this geometry and displays the asymptotic convergence expected of its variational formulation the svp formulation developed here is not restricted to right circular cylindrical geometries and may indeed be readily applied to any axisymmetric body

algebres de lie kahleriennes et double extension resume a kahler lie algebra is a real lie algebra carrying a symplectic 2 cocycle and an integrable complex structure j such that x j y is a scalar product we give a process called kahler double extension which realizes a kahler lie algebra as the kahler reduction of another one we show that every kahler algebra is obtained by a sequence of such a process from 0 or a flat kahler algebra it is obtained from 0 iff it contained a lagrangian sub algebra these methods allow us to prove that any completely solvable and unimodular kahler algebra is commutative

the generalized chern conjecture for manifolds that are locally a product of surfaces abstract we consider closed manifolds that admit a metric locally isometric to a product of symmetric planes for such manifolds we prove that the euler characteristic is an obstruction to the existence of flat structures confirming an old conjecture proved by milnor in dimension 2 in particular the chern conjecture follows in these cases the proof goes via a new sharp milnor wood inequality for riemannian manifolds that are locally a product of hyperbolic planes furthermore we analyze the possible flat vector bundles over such manifolds over closed hilbert blumenthal modular varieties we show that there are finitely many flat structures with nonzero euler number and none of them corresponds to the tangent bundle some of the main results were announced in m bucher t gelander milnor wood inequalities for manifolds locally isometric to a product of hyperbolic planes c r acad sci paris ser i 346 2008 661 666

removable singularities for lu ψ u and orlicz capacities suppose l is a second order elliptic differential operator in rd and let 1 baras and pierre have proved in 1984 that is removable for lu u if and only if its bessel capacity cap2 0 we extend this result to a general equation lu u where u is an increasing convex function subject to 2 and 2 conditions namely we prove that is removable for lu u if and only if its orlicz capacity is zero that is the integral b dx x y 2 d dy is equal to 0 or for every measure concentrated on where b stands for any ball containing

nonlinear parabolic p d e and additive functionals of superdiffusions suppose that e is an arbitrary domain in r d l is a second order elliptic differential operator in s r x e and s e is the extremal part of the martin boundary for the corresponding diffusion let 1 2 we investigate a boundary value problem u r lu u in s u v on s e u 0 on x e involving two measures and for the existence of a solution we give sufficient conditions in terms of a martin capacity and necessary conditions in terms of hitting probabilities for an l superdiffusion x if a solution exists then it can be expressed by an explicit formula through an additive functional a of x an l superdiffusion is a branching measure valued process a natural linear additive nla functional a of x is determined uniquely by its potential h defined by the formula p a 0 h r x dr dx for all m the determining set of a every potential h is an exit rule for and it has a unique decomposition into extremal exit rules if and are measures which appear in this decomposition then can be replaced by an integral equation u r x p r x t dy u t y ds h r x where p r x t dy is the transition function of we prove that h is the potential of a nla functional if and only if has a solution u moreover u r x log p r x e a 0 by applying these results to homogeneous functionals of time homogeneous superdiffusions we get a stronger version of theorems proved in an earlier publication the foundation for our present investigation is laid by a general theory developed in the accompanying paper

the sensitivity of structural acoustic response to attachment feature scale representation this paper presents a technique to assess the impact on model fidelity introduced through discretization of attachments on harmonically forced fluid loaded structural acoustic models while fluid loading is included it is not a requirement or restriction to the methods presented the perspective taken is one of knowledge of a reference state with a desire to determine the impact on the total radiated acoustic power due to perturbations in the reference state such perturbations change the predicted resonance frequencies of a structure under consideration and hence change the predicted response amplitudes the method uses a single degree of freedom response model in the local region of each fluid loaded resonance coupled with eigenvalue sensitivities to estimate the perturbation impact the sensitivity of the eigenvalues to changes in model detail is derived based on variations in the spatial representation of attached features e g point versus distributed attachments elements of the analysis me

computing fluid coupled resonance frequencies mode shapes and damping loss factors using the singular value decomposition in many acoustic design problems it would be useful to be able to compute fluid coupled resonance frequencies mode shapes and their associated damping levels unfortunately conventional eigenvalue solution procedures are either computationally inefficient unreliable or have limited applicability sophisticated methods for identifying modal parameters using the singular value decomposition have recently emerged in the area of experimental modal analysis where the available data typically consists of velocity to force transfer functions for several drive point locations in this paper we show that these techniques can be applied to numerically generated frequency domain data and are even more effective because full matrices of transfer function data are available this typically allows the modes to be completely separated from each other such that the modal parameters can be identified using analytical formulas several benchmark example problems are solved numerically including a rectangular cantilever plate a baffled circular plate and a baffled circular plate covered by an open ended rigid walled pipe