analytic torsion and holomorphic determinant bundles in this paper we prove that in the case of holomorphic locally kahler fibrations the analytic and algebraic geometry constructions of determinant bundles for direct images coincide we calculate the curvature of the holomorphic hermitian connection for the quillen metric on the determinant bundle we study the behavior of the quillen metric under change of metrics in the fibers and also on the twisting vector bundles we thus generalize the conformal anomaly formula to kahler manifolds of arbitrary dimension we also study the quillen metrics on determinants associated with exact sequences of vector bundles we prove that the quillen metric is smooth on the grothendieck knudsen mumford determinant for arbitrary holomorphic fibrations

analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

inclusion principle for the rayleigh ritz based substructure synthesis according to this substructure synthesis the motion of every substructure is modeled in terms of quasicomparison functions which are linear combinations of admissible functions capable of satisfying all the boundary conditions

effects of the poisson ratio and negative thrust on the dynamic stability of a free plate subjected to a follower force abstract the macroscopic poisson ratio of a large plate like truss structure may vary due to the geometry of the truss studied are the effects of the poisson ratio and negative thrust on the dynamic stability of a flexible rectangular plate which has four free edges one of the four edges is subjected to a tangential follower thrust the model is simplified to a continuous isotropic plate and is investigated by means of modal analysis a change in poisson ratio sometimes reduces the flutter load drastically the drastic reduction comes from the existence of a weak flutter instability it is also shown that there may exist both flutter and divergence even for negative thrust and that the tensile divergence load is smaller than the compressive one

a new approach to the modelling of distributed non self adjoint systems abstract this paper is concerned with the modelling of distributed non self adjoint systems such as damped structures in using the method of weighted residuals to produce an approximate solution to the eigenvalue problem the displacement of a non self adjoint structure is ordinarily represented by a linear combination of comparison functions i e functions that satisfy all the boundary conditions for many problems comparison functions are difficult to generate so that the question arises as to an alternative approach clearly solutions in terms of comparison functions satisfy the boundary conditions exactly but experience errors in the differential equation the new approach consists of constructing an approximate solution to the eigenvalue problem from the field of quasi comparison functions defined as linear combinations of admissible functions capable of satisfying all the boundary conditions of the problem the newly developed quasi comparison functions have been used with considerable success for self adjoint structures this paper demonstrates that the same remarkable convergence properties characterize approximate solutions in terms of quasi comparison functions for non self adjoint systems

optimal control in laser induced population transfer for two and three level quantum systems we apply the techniques of control theory and of sub riemannian geometry to laser induced population transfer in two and three level quantum systems the aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences sub riemannian geometry and singular riemannian geometry provide a natural framework for this minimization where the optimal control is expressed in terms of geodesics we first show that in two level systems the well known technique of pulse transfer in the rotating wave approximation emerges naturally from this minimization in three level systems driven by two resonant fields we also find the counterpart of the pulse transfer this geometrical picture also allows one to analyze the population transfer by adiabatic passage

a method for solving exact controllability problems governed by closed quantum spin systems the liouville von neumann master equation models closed quantum spin systems that arise in nuclear magnetic resonance applications in this paper an efficient and robust computational framework to solve exact controllability problems governed by the liouville von neumann master equation is presented the proposed control framework is based on a new optimisation formulation of exact controllability quantum spin problems that allows the application of efficient computational techniques this formulation results in an optimality system with four differential equations and an optimality condition the differential equations are approximated with an appropriate modified crank nicholson scheme and the resulting discretised optimality system is solved with a matrix free krylov newton scheme combined with a cascadic nonlinear conjugate gradient initialisation results of numerical experiments demonstrate the ability of the proposed framework to solve quantum spin exact controllability control problems

friction induced vibration in periodic linear elastic media for a one dimensional finite elastic continuum with distributed contacts and periodic boundary conditions the presence of unstable waves is investigated the stability of the waves is evaluated and explanations for instabilities under a constant coefficient of friction are provided a negative slope in the coefficient of friction as a function of sliding speed is not a necessary condition for the occurrence of dynamic instability dynamic instability occurs in the form of self excited unstable travelling waves the stabilizing effects of external and internal damping were studied low and high frequency terms of the travelling waves are stabilized by adding external and internal damping respectively responses corresponding to unstable eigenvalues can dominate the system response it is presumed that this can lead to squeaking or squealing noise in applications

a cascadic multigrid algorithm for semilinear elliptic problems summary we propose a cascadic multigrid algorithm for a semilinear elliptic problem the nonlinear equations arising from linear finite element discretizations are solved by newton s method given an approximate solution on the coarsest grid on each finer grid we perform exactly one newton step taking the approximate solution from the previous grid as initial guess the newton systems are solved iteratively by an appropriate smoothing method we prove that the algorithm yields an approximate solution within the discretization error on the finest grid provided that the start approximation is sufficiently accurate and that the initial grid size is sufficiently small moreover we show that the method has multigrid complexity

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

convergence estimates for multigrid algorithms without regularity assumptions a new technique for proving rate of convergence estimates of multi grid algorithms for symmetric positive definite problems will be given in this paper the standard multigrid theory requires a regularity and approxima tion assumption in contrast the new theory requires only an easily verified approximation assumption this leads to convergence results for multigrid re finement applications problems with irregular coefficients and problems whose coefficients have large jumps in addition the new theory shows why it suffices to smooth only in the regions where new nodes are being added in multigrid refinement applications

accurate computing of higher vibration modes of thin flexible structures motivated by the need for high fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications a novel scheme is proposed to accurately compute higher modes of vibration for one dimensional structures by coupling the classic ritz method as a predictor and the linear two point boundary value problem solver supore as a corrector the ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes these estimates are then used as initial guesses by supore which employs superposition and reorthonormalization to accurately solve the governing boundary value problem compared to a high fidelity ritz approximation or a highly refined finite element modeling procedure this is a simple computationally less expensive and yet highly accurate method to compute mode shapes for applications that require higher modes this scheme is used to compute mode shapes within an absolute and relative

chladni figures for completely free parallelogram plates an analytical study abstract this paper communicates the first comprehensive analytical study of the title problem the ritz method with admissible functions in the form of legendre polynomials is used and is shown to provide rapid convergence and highly economic eigensolutions for a given problem the robustness of the method is demonstrated and proof is given of its validity at extreme skew angles chladni figures are presented for the first six modes of plates with three different aspect ratios and six different skew angles making a total of 108 cases additional results can be inferred for two more plate aspect ratios thus raising the total number of chladni figures to 180 outstanding agreement is obtained between all the analytically derived nodal patterns from this work and the experimental work of other investigators the dependence of frequency on the skew angle the aspect ratio and the poisson ratio is also investigated and extensive results are presented in diagrammatic and graphical format

natural frequencies of rectangular plates using a set of static beam functions in rayleigh ritz method abstract a fast converging series consisting of a set of static beam functions which is a combination of sine series and polynomials is developed and these functions are used as the basis functions in the rayleigh ritz method to study the vibrational characteristics of thin isotropic rectangular plates in applications a relatively small number of functions are required and consequently a modest amount of computation is necessary the approach is very simple and straightforward some numerical results are given for rectangular plates with various aspects ratios and boundary conditions good accuracy and fast convergence of the method are demonstrated by comparison with available results complicating factors orthotropic properties in plane forces etc can also be taken into account without formal difficulties

non linear structural vibrations under combined parametric and external excitations abstract a set of second order equations with weak quadratic and cubic non linearities is considered simultaneous parametric and external forcing excitations are included the frequency of the parametric excitation is near a natural frequency of the system and three cases are analyzed i the external excitation is absent ii the external excitation is present but is not involved in a resonance and iii the external frequency is the same as the parametric frequency results are obtained by the method of multiple scales frequency response curves are presented for various combinations of excitation amplitudes damping coefficients and phase shift between the excitations it is found that stable multi modal responses may exist in the first order asymptotic solution even though only one mode is involved in the resonance and no internal resonance condition is present

on the discretization of an elastic rod with distributed sliding friction a one dimensional elastic system with distributed contact under fixed boundary conditions is investigated in order to study dynamic behavior under sliding friction a partial differential equation of motion is established and its exact solution is presented due to the friction the eigenvalue problem is non self adjoint mathematical methods for handling the non self adjoint system such as the non self adjoint eigenvalue problem and the eigenvalue problem with a proper inner product are reviewed and applied the exact solution showed that the undamped elastic system under fixed boundary conditions is neutrally stable when the coefficient of friction is a constant the assumed mode approximation and the lumped parameter discretization method are evaluated and their solutions are compared with the exact solution as a cautionary example the assumed modes approximation leads to false conclusions about stability the lumped parameter discretization algorithm generates reliable results

a globalized newton method for the accurate solution of a dipole quantum control problem a theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nanoelectronic devices and quantum computing this method is based on a reduced hessian krylov newton scheme applied to a norm preserving discrete model of a dipole quantum control problem the use of second order numerical methods for solving the control problem is justified proving the existence of optimal solutions and analyzing first and second order optimality conditions criteria for the discretization of the nonconvex optimization problem and for the formulation of the hessian are given to ensure accurate gradients and a symmetric hessian robustness of the newton approach is obtained using a globalization strategy with a robust linesearch procedure results of numerical experiments demonstrate that the newton approach presented in this paper is able to provide fast and accurate controls for high energy state transitions

dynamic stability of a rectangular plate with four free edges subjected to a follower force one of the four free edges of the plate is subjected to a tangential follower force the flutter load and divergence load are obtained for various slenderness ratios of the rectangular plate by means of modal analysis in the calculation many weak instabilities were found

formulation and numerical solution of finite level quantum optimal control problems optimal control of finite level quantum systems is investigated and iterative solution schemes for the optimization of a control representing laser pulses are developed the purpose of this external field is to channel the system s wavefunction between given states in its most efficient way physically motivated constraints such as limited laser resources or population suppression of certain states are accounted for through an appropriately chosen cost functional first order necessary optimality conditions and second order sufficient optimality conditions are investigated for solving the optimal control problems a cascadic non linear conjugate gradient scheme and a monotonic scheme are discussed results of numerical experiments with a representative finite level quantum system demonstrate the effectiveness of the optimal control formulation and efficiency and robustness of the proposed approaches

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

cyclic schemes for pde based image analysis we investigate a class of efficient numerical algorithms for many partial differential equations pdes in image analysis they are applicable to parabolic or elliptic pdes that have bounded coefficients and lead to space discretisations with symmetric matrices our schemes are easy to implement and well suited for parallel implementations on gpus since they are based on the explicit diffusion scheme in the parabolic case and the jacobi method in the elliptic case by supplementing these methods with cyclically varying time step sizes or relaxation parameters we achieve efficiency gains of several orders of magnitude we call the resulting algorithms fast explicit diffusion fed and fast jacobi fj methods to achieve a good compromise between efficiency and accuracy we show that one should use parameter cycles that result from factorisations of box filters for these cycles we establish stability results in the euclidean norm our schemes perform favourably in a number of applications including isotropic nonlinear diffusion filters with widely varying diffusivities as well as anisotropic diffusion methods for image filtering inpainting and regularisation in computer vision moreover they are equally suited for higher dimensional problems as well as higher order pdes and they can also be interpreted as efficient first order methods for smooth optimisation problems

sensitivity analysis for problems of dynamic stability abstract in mechanics as well as in physics the most general and important thing is to study the dependence of the characteristics of a physical process on problem parameters problems of dynamic stability for non conservative systems involve determination of eigenvalues and eigenvectors for these problems it is shown in general how the different sensitivity analyses can be performed without any new eigenvalue analyses the main question relates to the change in flutter load as a function of change in stiffness mass boundary conditions or load distribution discretized as well as non discretized examples are presented in details

a basic norm equivalence for the theory of multilevel methods subspace decompositions of finite element spaces based onl 2 like orthogonal projections play an important role for the construction and analysis of multigrid like iterative methods recently several authors have proved the equivalence of the associated discrete norms with theh 1 norm the present paper gives an elementary self contained derivation of this result which is based on the use ofk functionals known from the theory of interpolation spaces

free vibration of a cantilevered beam with multiple steps comparison of several theoretical methods with experiment abstract the flexural free vibration of a cantilevered beam with multiple cross section steps is investigated theoretically and experimentally experimental results are compared against euler bernoulli beam theory solutions from rayleigh ritz and component modal analyses as well as finite element results using the commercial package ansys finite elements are also used to investigate a timoshenko beam a two dimensional shell and a three dimensional solid element model a detectable difference in the first in plane bending natural frequency is noted between the beam theory results and those of the higher dimensional finite element models and experimental observation the convergence of the several theoretical approaches and their effectiveness as analysis and design methods for multiple stepped beams are also discussed

vibration analysis of rectangular plates with general elastic boundary supports abstract in this investigation the rayleigh ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so called residual displacement function at the edges as a result a drastic improvement of the convergence can be expected of the solution expressed as a series expansion in terms of the admissible functions perhaps more importantly this study has developed a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions several numerical examples are given to demonstrate the accuracy and convergence of the current solution

nature of stationarity of the natural frequencies at the natural modes in the rayleigh ritz method abstract a variational formulation of the rayleigh ritz method to obtain approximate natural frequencies and natural modes is presented the stationarity of the natural frequencies with respect to the arbitrary coefficients in the linear combination of the assumed deflection shapes and also at the natural modes is investigated it is concluded that the natural frequencies are stationary and need not always be minimum with respect to the arbitrary coefficients however they are minimum with respect to the natural modes this may provide a means of checking the accuracy of the computed natural frequencies obtained by using energy techniques such as the rayleigh ritz galerkin and finite element methods

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

adaptive multivlevel methods in three space dimensions we consider the approximate solution of self adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non uniform tetrahedral mesh which is generated adaptively the arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner here the accuracy of the iterative solution is coupled with the discretization error as the performance of hierarchical bases preconditioners deteriorates in three space dimensions the bpx preconditioner is used taking special care of an efficient implementation reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements to illustrate the theoretical results we consider a familiar model problem involving reentrant corners and a real life problem arising from hyperthermia a recent clinical method for cancer therapy

newton methods for the optimal control of closed quantum spin systems an efficient and robust computational framework for solving closed quantum spin optimal control and exact controllability problems with control constraints is presented closed spin systems are of

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

a posteriori error estimates for elliptic problems in two and three space dimensions let u in h be the exact solution of a given selfadjoint elliptic boundary value problem which is approximated by some tilde u in mathcal s mathcal s being a suitable finite element space efficient and reliable a posteriors estimates of the error u tilde u measuring the local quality of tilde u play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh a well known class of error estimates can be derived systematically by localizing the discretized defect problem by using domain decomposition techniques in this paper we provide a guideline for the theoretical analysis of such error estimates we further clarify the relation to other concepts our analysis leads to new error estimates which are specially suited to three space dimensions the theoretical results are illustrated by numerical computations

free vibrations of beams with general boundary conditions a simple and unified approach is presented for the vibration analysis of a generally supported beam the flexural displacement of the beam is sought as the linear combination of a fourier series and an auxiliary polynomial function the polynomial function is introduced to take all the relevant discontinuities with the original displacement and its derivatives at the boundaries and the fourier series now simply represents a residual or conditioned displacement that has at least three continuous derivatives as a result not only is it always possible to expand the displacement in a fourier series for beams with any boundary conditions but also the solution converges at a much faster speed the reliability and robustness of the proposed technique are demonstrated through numerical examples

heights and arakelov s intersection theory introduction this paper relates the neron tate height on jacobian varieties to an intersection theory on arithmetic surfaces constructed by s arakelov a1 here i extend and prove a statement of arakelov to the effect that his intersection pairing is a neron pairing a2i i use this to prove an analogue of the hodge index theorem for arithmetic surfaces a result due independently to g faltings the results of this paper have been extracted from my thesis written under the direction of michael artin it differs from the thesis in three ways firstly it employs the language of local height functions as defined by a neron and j tate and expounded by s lang li in the thesis i used neron s language of local intersection pairings n1 the second major difference is in the proof of theorem 1 3 in my thesis i proved this result by using work of raynaud and picard functors r 1 this method was suggested by m artin in this paper i provide a simpler proof observed by s lang and independently by b gross finally the development of arakalov s theory in the context of neron functions in section 2 is due to s lang who has kindly given me leave to publish it this exposition of my results is due in considerable part to s lang it is essentially an edited transcript of a series of conversations between us which he provided it is my great pleasure to thank both him and michael artin for their help and encouragement 1 the neron pairing neron ne has given a pairing between divisors and points on abelian varieties and also on arbitrary varieties under suitable conditions we shall give a complement to the neron theory on curves let c be a curve by which we mean a complete regular curve geometrically irreducible over a field k with an absolute value v let

stopping criteria for iterations in finite element methods this work extends the results of arioli 1 2 on stopping criteria for iterative solution methods for linear finite element problems to the case of nonsymmetric positive definite problems we show that the residual measured in the norm induced by the symmetric part of the inverse of the system matrix is relevant to convergence in a finite element context we then use krylov solvers to provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria

a multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations standard multigrid algorithms have proven ineffective for the solution of discretizations of helmholtz equations in this work we modify the standard algorithm by adding gmres iterations at coarse levels and as an outer iteration we demonstrate the algorithm s effectiveness through theoretical analysis of a model problem and experimental results in particular we show that the combined use of gmres as a smoother and outer iteration produces an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as 200 for fixed wave numbers it displays grid independent convergence rates and has costs proportional to the number of unknowns

a discrete approach for a generalized beck s column in parametric resonance abstract a galerkin projection based on non standard bases is conceived to derive an equivalent discrete model of a continuous system under non conservative forces the problem of deriving a discrete model capable of describing critical and post critical scenarios for non selfadjoint systems is discussed and an heuristic rule for a proper choice of trial functions is given the procedure is utilized to analyze the effect of non conservative autonomous and non autonomous pulsating forces acting on a linearly damped beck s column involving geometrical nonlinearities the linear and nonlinear behaviours arising from the analysis of the proposed discrete model are in good agreement with those observed through the unavoidably more involved direct continuous approach critical scenarios for the autonomous and non autonomous cases are investigated and the multiple scales method is applied in order to obtain the bifurcation equations in the neighborhood of a hopf bifurcation point in primary parametric resonance a comparison between critical and post critical continuous and discrete model is performed adopting two control parameters namely the amplitudes of the static and dynamic components of the forces playing the role of detuning and bifurcation parameters respectively

monotonic time discretized schemes in quantum control most of the numerical simulations in quantum bilinear control have used monotonically convergent algorithms of krotov introduced by tannor et al 15 of zhu rabitz 16 or their unified formulation in 17 however the properties of the discrete version of these procedures have not been yet tackled with we present in this paper a stable time and space discretization which preserves the monotonic properties of the monotonic algorithms numerical results show that the newly derived algorithms are stable and enable various experimentations

optimal bilinear control of an abstract schro dinger equation well posedness of abstract quantum mechanical systems is considered and the existence of optimal control of such systems is proved first order optimality systems are derived convergence of the monotone scheme for the solution of the optimality system is proved

convergence of the classical rayleigh ritz method and the finite element method it is demonstrated in this paper that convergence of the classical rayleigh ritz method can be vastly improved by introducing a new class of admissible functions called quasi comparison functions

optimal quantum control by an adapted coordinate ascent algorithm this paper explores an adaption of the coordinate ascent approach to quantum control problems it was motivated by the observation that several of the existing monotone converging schemes for quantum control may be viewed as approximations of the well known coordinate ascent method our implementation employs line searches in coordinate directions in control space using only evaluations of the performance functional without invoking its derivatives it is based on recasting the performance functional as a local tracking function which gives the future quality of a control at each moment in time back propagation of a basis of the target space enables these performance functional i e tracking function evaluations to be done efficiently the performance functional may include or not include regularization terms as needed convergence of the resulting algorithm and its relation to previous schemes are discussed and numerical examples are provided in our tests the coordinate ascent algorithm exhib

some estimates of the rate of convergence for the cascadic conjugate gradient method abstract the paper deals with a cascadic conjugate gradient method shortly called the ccg algorithm which was proposed by p deuflhard and can be considered as a simpler version of a multigrid multilevel method we define it recurrently for discrete self adjoint positive definite problems on a sequence of grids on the coarsest grid the linear discrete algebraic system is solved directly on the finer grids the system is iteratively solved by the conjugate gradient method where the starting guess is an interpolation of the approximated solution on the previous grid any preconditioning or restriction to coarser grids is not implemented nevertheless the ccg algorithm has the same optimal property compared to multigrid methods namely the algorithm converges with a rate which is independent of the number of unknowns and the number of grids as an example this property is proved for elliptic second order dirichlet problems in two dimensional convex polygonal bounded domains for ensuring convergence the number of iterations on each grid level has to increase from finer to coarser grids the optimal dependence of these numbers is established with respect to the mesh size and the number of unknowns the theory has been presented in an abstract setting which allows the application to both finite element and finite difference methods

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

the cascadic multigrid method for elliptic problems the paper deals with certain adaptive multilevel methods at the confluence of nested multigrid methods and iterative methods based on the cascade principle of 10 from the multigrid point of view no correction cycles are needed from the cascade principle view a basic iteration method without any preconditioner is used at successive refinement levels for a prescribed error tolerance on the final level more iterations must be spent on coarser grids in order to allow for less iterations on finer grids a first candidate of such a cascadic multigrid method was the recently suggested cascadic conjugate gradient method of 9 in short ccg method whichused the cg method as basic iteration method on each level in 18 it has been proven that the ccg method is accurate with optimal complexity for elliptic problems in 2d and quasi uniform triangulations the present paper simplifies that theory and extends it to more general basic iteration methods like the traditional multigrid smoothers moreover an adaptive control strategy for the number of iterations on successive refinement levels for possibly highly non uniform grids is worked out on the basis of a posteriori estimates numerical tests confirm the efficiency and robustness of the cascadic multigrid method

vibration of orthotropic plates discussion on the completeness of the solutions used in direct methods fil rosales marta beatriz consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet bahia blanca argentina universidad nacional del sur departamento de ingenieria argentina