curvature diameter homotopy groups and cohomology rings we establish two topological results a if m is a 1 connected compact n manifold and q 2 then the minimal number of generators for the qth homotopy group q m mng q m is bounded above by a number depending only on mng h m and q where h m is the homology group c let mathscr m n y be the collection of compact orientable n manifolds whose oriented bundles admit so n invariant fibrations over y with fiber compact nilpotent manifolds such that the induced so n actions on y are equivalent then q m finitely generated m mathscr m n y contains only finite isomorphism classes depending only on n y q together with the results of cg and gr1 from a we conclude that i if m is a complete n manifold of nonnegative curvature then mng q m is bounded above by a number depending only on n and q 2 together with the results of ch and cfg from c we conclude that ii if m is a compact n manifold whose sectional curvature and diameter satisfy secm and diamm d then q m has a finite number of possible isomorphism classes depending on n d q 2 provided q m is finitely generated we also show that b if m is a compact n manifold with secm and diam m d then the cohomology ring h m may have infinitely many isomorphism classes in particular b answers some questions raised by k grove gro

a controlled plus construction for crumpled laminations given a closed n manifold m n 4 and a finitely generated perfect subgroup p of it1 m we previously developed a controlled version of quillen s plus construction namely a cobordism w m n with the inclusion j n f w a homotopy equivalence and kernel of i i1 m f it1 w equalling the smallest normal subgroup of xl1 m containing p together with a closed map p w 0 1 such that p l t is a closed n manifold for every t e 0 1 and in particular m p 1 o and n p l l we accomplished this by constructing an acyclic map of manifolds f m f n having the right fundamental groups and w arose as the mapping cylinder of f with a collar attached along n the main result here presents a condition under which the desired controlled plus construction can still be accomplished in many cases even when it1 m contains no finitely generated perfect subgroups by products of these results include a new method for constructing wild embeddings of codimension one manifolds and a better understanding of perfect subgroups of finitely presented groups

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

stationary turbulent closure via the hopf functional equation exact closed form solutions are exhibited for the hopf equation for stationary incompressible 3d navier stokes flow for the cases of homogeneous forced flow including a solution with depleted nonlinearity and inhomogeneous flow with arbitrary boundary conditions this provides an exact method for computing two and higher point moments given the mean flow

simply connected 4 manifolds with a given boundary let m be a closed oriented connected 3 manifold for each bilinear symmetric pairing zn l our goal is to calculate the set vl m of all oriented homeomorphism types of compact 1 connected oriented 4manifolds with boundary m and intersection pairing isomorphic to zn l for each pair zn l which presents h m we construct a double coset space bl m and a function ct vl m bl m the set bt m is the quotient of the group of all link pairing preserving isomorphisms of the torsion subgroup of h1 m by two naturally occuring subgroups when zn l is an even pairing we construct another double coset space bl m a function 6l vl m b fl m and a projection p2 bl m bl m such that p2 c l ct our main result states that when zn l is even the function c l is injective as is the function c x a vl m bl m x z 2 when z l is odd here a is a kirby siebenmann obstruction to smoothing it follows that the sets vl m are finite and of an order bounded above by a constant depending only on h1 m we also show that when hi m q 0 and z l is even ct p2 c 6l is injective it seems likely that via the functions cl x a and 6l the sets bl m x z 2 and bl m calculate vl m when zn l is respectively odd and even we verify this in several cases most notably when h1 m is free abelian the results above are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between two 1connected 4 manifolds extending a given homeomorphism of their boundaries the theory developed is then applied to show that there is an m 0 depending only on h1 m such that for any self homeomorphism f of m fm extends to a self homeomorphism of any 1 connected compact 4 manifold with boundary m introduction in m freedman s fundamental paper fr he classified closed simply connected oriented 4 manifolds up to orientation preserving homeomorphism he showed that modulo the kirby siebenmann invariant these manifolds are in bijective correspondence through their intersection pairings with the set of unimodular bilinear symmetric pairings over z see theorem 1 5 of fr and corollary 2 2 3 of q in this paper we begin a classification of simply connected 4 manifolds with connected boundary our results with regard to this problem are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between 1 connected 4 manifolds extending a given homeomorphism of their boundaries received by the editors september 19 1985 1980 mathematics subject classification 1985 revision primary 57n15 research supported by an nserc canada post doctoral fellowship 1986 american mathematical society 0002 9947 86 1 00 25 per page

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

heegaard floer homology of matsumoto s manifolds abstract we consider a homology sphere m n k 1 k 2 presented by two knots k 1 k 2 with linking number 1 and framing 0 n we call the manifold matsumoto s manifold we show that m n t 2 3 k 2 never bounds any contractible 4 manifold if n 2 k 2 holds we also give a formula of ozsvath szabo s invariant as the total sum of the euler numbers of the reduced filtration we compute the invariants of the twisted whitehead doubles of torus knots and correction terms of the branched covers of the whitehead doubles by using owens and strle s obstruction we show that the 12 twisted whitehead double of the 2 7 torus knot and the 20 twisted whitehead double of the 3 7 torus knot are not slice but the double branched covers bound rational homology 4 balls these are new examples having a gap between what a knot is slice and what a double branched cover bounds a rational homology 4 ball

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

instanton filtering for the stochastic burgers equation we address the question of whether one can identify instantons in direct numerical simulations of the stochastically driven burgers equation for this purpose we first solve the instanton equations using the chernykh stepanov method 2001 phys rev e 64 026306 these results are then compared to direct numerical simulations by introducing a filtering technique to extract prescribed rare events from massive data sets of realizations using this approach we can extract the entire time history of the instanton evolution which allows us to identify the different phases predicted by the direct method of chernykh and stepanov with remarkable agreement

on locally constructible spheres and balls durhuus and jonsson 1995 introduced the class of locally constructible lc 3 spheres and showed that there are only exponentially many combinatorial types of simplicial lc 3 spheres such upper bounds are crucial for the convergence of models for 3d quantum gravity

simple full field method for the elastic characterization of orthotropic composite plates a speckle shearing interferometer with a simple setup is designed and tested for full field characterization of the elastic properties of isotropic and orthotropic composite plates the technique is straightforward and provides comparable results obtained by standard methods the proposed method has the advantages of being noncontact and full field in nature beam specimens cut from the plate were loaded under the standard four point bending configuration gradients of bending deformation are measured by the speckle shearing interferometer directly curvature of each bended beam is calculated from the slope of the fitted line of the gradient data the elastic moduli and poisson s ratios of the plate material are determined from the curvature of the beam specimens comparing the present approach to other full field techniques reported in literature that are mostly based on deformation measurement of a specimen subjected to a complicated load field the present method is much easier to apply and the image analysis procedure is much simpler

markovian solutions of inviscid burgers equation for solutions of inviscid forceless one dimensional burgers equation with random initial condition it is heuristically shown that a stationary feller markov property with respect to the space variable at some time is conserved at later times and an evolution equation is derived for the infinitesimal generator previously known explicit solutions such as frachebourg martin s white noise initial velocity and carraro duchon s levy process intrinsic statistical solutions including brownian initial velocity are recovered as special cases

a path integral for turbulence in incompressible fluids in this paper a classical path integral is formulated for incompressible fluids that evolve according to the navier stokes equation the path integral propagates probability distributions deterministically on the space gvol of solenoidal velocity fields we construct a set of isp 2 charges associated with the geometry of gvol and its poisson structure and a pair of supersymmetry charges connected with the hamiltonian these charges generate exact symmetries of the classical path integral when the viscosity is set equal to zero when the effect of dissipation is included the charges associated with the poisson structure and the hamiltonian are no longer conserved charges that generate kolmogorov scaling and galilean transformations are also constructed the classical path integral is formulated in terms of vorticity as well

surgery in dimension four and noncompact 5 manifolds this paper describes a precise relationship between the problems of completing surgery in dimension four and finding boundaries for noncompact 5 manifolds two outstanding problems of low dimensional topology are completing 4 dimensional surgery and finding boundaries for noncompact 5 dimensional manifolds although no complete theory is known for either problem some interesting results have been found see 1 4 5 10 and addendum in this paper we describe a complete relationship between these two problems consequently knowledge of 4 dimensional surgery yields information about noncompact 5 manifolds and conversely all manifolds and maps in this paper are assumed to be smooth each manifold is provided with a basepoint and when appropriate basepaths will be chosen to given 2 spheres without explicit mention i wish to thank gerald a anderson and frank quinn for helpful discussions also i wish to thank patrick gilmer for his advice and encouragement during this project 1 statement of results let f b m am y x be a degree one normal map in the sense of wall 11 where m is a compact connected 4 manifold and y x is a poincare pair not necessarily simple if x 0 then we require that f jam am x induces an isomorphism of homology groups with a z vi y coefficients also we assume that f is 2 connected k2 m is a free a module and the surgery obstruction a f b e lh 7 c is zero if h c k2 m is a subkernel we will say that h is representable in m if we can find disjoint framed embedded 2 spheres si sr c int m such that the inclusion m ui si m induces an isomorphism of fundamental groups and the classes of sl sr in h2 m a 7t2 m form a basis over a for h the subkernel h is stably representable if for some integer k 0 h ed kei ek is representable in m k s2 x s2 here ei denotes the class of s2 x 1 c ith summand s2 x s2 and e1 ek is the submodule generated by el ek we regard h ed ke ek as received by the editors august 10 1982 1980 mathematics subject classification primary 57r65 secondary 57m99 1985 american mathematical society 0002 9947 85 1 00 25 per page

inverse evaluation of material constants for composite plates by optical interferometry method electronic speckle pattern interferometry espi is a powerful tool for the full field noncontact and real time measurement method of surface displacements for deformed bodies as compared with the conventional film recording and optical reconstruction procedures used for holographic interferometry the interferometric fringes of espi are produced instantly by a video recording system in this study the amplitude fluctuation espi af espi optical system is used for measuring the resonant frequencies and mode shapes of vibrating composite plates by making use of the resonant frequencies for free plates obtained experimentally an inverse evaluation for the material constants is developed using the rayleigh ritz technique and the simplex method for function minimization finally finite element calculation is used to construct the mode shapes from the obtained material constants by inverse evaluation and the results are compared with the experimental observations the experimental method based on optical af espi setup and the inverse algorithms proposed might become a reliable and self consistent methodology for evaluating material constants of composite plates

the global structure of simple space times according to a standard definition of penrose a space time admitting well defined future and past null infinitiesi andi is asymptotically simple if it has no closed timelike curves and all its endless null geodesics originate fromi and terminate ati the global structure of such space times has previously been successfully investigated only in the presence of additional constraints the present paper deals with the general case it is shown thati is diffeomorphic to the complement of a point in some contractible open 3 manifold the strongly causal regioni0 ofi is diffeomorphic to mathbb s 2 times mathbb r and every compact connected spacelike 2 surface ini is contained ini0 and is a strong deformation retract of bothi0 andi moreover the space time must be globally hyperbolic with cauchy surfaces which subject to the truth of the poincare conjecture are diffeomorphic to 3

exact theory for the self similarity and decay of homogeneous turbulence it is shown that space time dilatation invariance x 1x t 2t with concomitant transformations for dependent variables and linearity of the equation engender an exact time explicit generic form for the solution applicable to freely decaying homogeneous incompressible fluid turbulence this solution features a summation over mutually independent dynamical modes labeled by the dilatation scaling index n 1 without the assumption of isotropy nor introduction of a closure approximation procedure the theory provides an explanation for the experimentally observed self similarity of the correlation tensors and the decay laws u x t 2 t n for the different types and decay stages of homogeneous turbulence

a family of freely slice good boundary links we show that every good boundary link with a pair of derivative links on a seifert surface satisfying a homotopically trivial plus assumption is freely slice this subsumes all previously known methods for freely slicing good boundary links with two or more components and provides new freely slice links

the inviscid burgers equation with brownian initial velocity the law of the hopf cole solution of the inviscid burgers equation with brownian initial velocity is made explicit as examples of applications we investigate the smoothness of the solution the statistical distribution of the shocks we determine the exact hausdorff function of the lagrangian regular points and investigate the existence of lagrangian regular points in a fixed borel set

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

source solutions and asymptotic behavior in conservation laws abstract we study the uniqueness of the solutions to the scalar conservation law u t u x 0 when the initial datum is a finite measure the case of a dirac mass is particularly emphasized it is shown how it provides a description of the asymptotic behavior of the solutions initiated by an arbitrary integrable function this behavior is proved to depend on one parameter in the case when is odd while it depends on two when is convex

on the direct determination of invariant parameters governing anisotropic plate bending problems abstract many papers deal with the determination of flexural rigidities of anisotropic plates from only one specimen subjected to one or several loading conditions in such a problem one of the main questions is the best identification of the unknown parameters according to the type of material the shape of the specimen and the loading conditions it seems that no general rule giving the best configuration leading to an accurate determination has been established one of the main reasons is the anisotropic nature of the tested plates which leads the mechanical configuration to be dependent on the material itself this problem would be avoided by the direct measurement of invariant parameters from which the rigidities are easily deduced these invariant parameters reveal the intrinsic elastic behavior of the tested plate contrary to the rigidities usually considered which are directional quantities this paper describes a procedure for the identification of invariant parameters governing the bending of anisotropic plates it is shown that the whole displacement field processing of the surface strain fields obtained in two particular loading cases directly provides those parameters a numerical simulation shows the stability of the present method

study of the hopf functional equation for turbulence duhamel principle and dynamical scaling we consider a formulation for the hopf functional differential equation which governs statistical solutions of the navier stokes equations by introducing an exponential operator with a functional derivative we recast the hopf equation as an integro differential functional equation by the duhamel principle on this basis we introduce a successive approximation to the hopf equation as an illustration we take the burgers equation and carry out the approximations to the leading order scale invariance of the statistical navier stokes equations in d dimensions is formulated and contrasted with that of the deterministic navier stokes equations for the statistical navier stokes equations critical scale invariance is achieved for the characteristic functional of the d th derivative of the vector potential in d dimensions the deterministic equations corresponding to this choice of the dependent variable acquire the linear fokker planck operator under dynamic scaling in three dimensions it is the vorticity gradient that behaves like a fundamental solution more precisely source type solution of deterministic navier stokes equations in the long time limit physical applications of these ideas include study of a self similar decaying profile of fluid flows moreover we reveal typical physical properties in the late stage evolution by combining statistical scale invariance and the source type solution this yields an asymptotic form of the hopf functional in the long time limit improving the well known hopf titt solution in particular we present analyses for the burgers equations to illustrate the main ideas and indicate a similar analysis for the navier stokes equations

near invariance under dynamic scaling for navier stokes equations in critical spaces a probabilistic approach to regularity problems we make a detailed comparison between the navier stokes equations and their dynamically scaled counterpart the so called leray equations the navier stokes equations are invariant under static scaling transforms but are not generally invariant under dynamic scaling transforms we will study how close they can be brought together using the critical dependent variables and discuss the implications on the regularity problems assuming that the navier stokes equations written in the vector potential have a solution that blows up at t 1 we derive the leray equations by dynamic scaling we observe 1 the leray equations have only one term extra on top of those of the navier stokes equations 2 we can recast the navier stokes equations as a wiener path integral and the leray equations as another ornstein uhlenbeck path integral by the maruyama girsanov theorem both equations take the identical form modulo the maruyama girsanov density which is valid up to t 2 2 by the novikov condition 3 the global solution of the leray equations is given by a finite dimensional projection r of a functional of an ornstein uhlenbeck process and a probability measure if r remains smooth beyond t 1 under an absolute continuous change of the probability measure we can rule out finite time blowup by contradiction there are two cases a r given by a finite number of wiener integrals and b otherwise ruling out blowup in a is straightforward for b a condition based on a limit passage in the picard iterations is identified for such a contradiction to come out the whole argument equally holds in r d for any d 2

stable mapping class groups of 4 manifolds with boundary we give a complete algebraic description of the mapping class groups of compact simply connected 4 manifolds with boundary up to connected sum with copies of s 2 s 2

discrete morse theory for manifolds with boundary we introduce a version of discrete morse theory specific for manifolds with boundary the idea is to consider morse functions for which all boundary cells are critical we obtain relative morse inequalities relating the homology of the manifold to the number of interior critical cells we also derive a ball theorem in analogy to forman s sphere theorem the main corollaries of our work are 1 for each d 3 and for each k 0 there is a pl d sphere on which any discrete morse function has more than k critical d 1 cells this solves a problem by chari 2 for fixed d and k there are exponentially many combinatorial types of simplicial d manifolds counted with respect to the number of facets that admit discrete morse functions with at most k critical interior d 1 cells this connects discrete morse theory to enumerative combinatorics discrete quantum gravity 3 the barycentric subdivision of any simplicial constructible d ball is collapsible this almost solves a problem by hachimori 4 every constructible ball collapses onto its boundary minus a facet this improves a result by the author and ziegler 5 any 3 ball with a knotted spanning edge cannot collapse onto its boundary minus a facet this strengthens a classical result by bing and a recent result by the author and ziegler

an exact representation of the space time characteristic functional of turbulent navier stokes flows with prescribed random initial states and driving forces by adopting a formal operator viewpoint the space time characteristic functional associated with navier stokes turbulence is expressed in terms of a linear operator acting on the space of functionals obtained by a simple similarity transformation of the local translation operator generated by the nonlinear terms in the navier stokes equation this operator is unitary with respect to the formal scalar product of functionals the equivalence of this operator representation to the functional integral representation of rosen is shown and for gaussian initial velocity and external force fields some consequences of this representation are presented

construction of group actions on four manifolds it is shown that any cyclic group of odd prime order acts on any closed simply connected topological 4 manifold inducing the identity on integral homology the action is locally linear except perhaps at one isolated fixed point in the case of primes greater than three a more careful argument is used to show that the action can be constructed to be locally linear introduction in this paper we shall show that every closed simply connected topological 4 manifold m4 admits an action of any cyclic group zp of odd prime order p the action will be homologically trivial that is induce the identity on integral homology be pseudofree that is have only isolated fixed points except in certain cases when p 3 and be locally linear except perhaps at one isolated fixed point when p 2 and the intersection form of m4 has even type then the same conclusion holds this is also due to s kwasik and p vogel 1985 by a somewhat different proof if p 2 and the intersection form of m has odd type however then an action of z2 which is homologically trivial must have a fixed point set containing two dimensional components see 7 further it is harder to control the kirby siebenmann triangulation obstruction which is then not determined by the intersection form it is interesting to ask whether these actions can be locally linear or smooth when m4 is smooth the existence of a locally linear z2 action implies the vanishing of the kirby siebenmann obstruction see kwasik and vogel 1984 we shall show however that for p 3 in general these actions can be constructed to be locally linear in a recent preprint kwasik has shown that this is the case for the fake cp2 when p is odd by a rather different proof these actions are homologically trivial and have only isolated fixed points except sometimes when p 3 the g signature theorem shows that not every simply connected 4 manifold admits pseudofree locally linear actions when p 3 we shall see for example that neither the e8 manifold the kummer surface nor a nontrivial connected sum of copies of cp2 admits such an action for p 3 in broad outline our construction goes as follows let a closed oriented simply connected 4 manifold m be given by studying equivariant framed links we construct a compact smooth 4 manifold with boundary having the intersection form of m and admitting a smooth zp action which is pseudofree and homologically trivial the action is free on the boundary homology sphere e in a paper primarily focused on equivariant plumbing diagrams for high dimensional highly connected manifolds with even intersection forms weintraub 1975 carried out most of this we give an independent development because we need to be able to better control received by the editors october 16 1985 and in revised form january 7 1986 1980 mathematics subject classification 1985 revision primary 57s17 57s25 57n15 research supported in part by a grant from the national science foundation 1987 american mathematical society 0002 9947 87 1 00 25 per page

decompositions of simplicial balls and spheres with knots consisting of few edges constructibility is a condition on pure simplicial complexes that is weaker than shellability in this paper we show that non constructible triangulations of the d dimensional sphere exist for every d geq 3 this answers a question of danaraj and klee 10 it also strengthens a result of lickorish 16 about non shellable spheres furthermore we provide a hierarchy of combinatorial decomposition properties that follow from the existence of a non trivial knot with few edges in a 3 sphere or 3 ball and a similar hierarchy for 3 balls with a knotted spanning arc that consists of few edges

a surgery sequence in dimension four the relations with knot concordance we present a systematic treatment of the classification problem for compact smooth 4 manifolds m it is modeled on the surgery exact sequence the central theorem in the classification of n manifolds n 5 the price for the extension to dimension 4 is a hole in m where a homotopy 1 skeleton should be there is no homotopy theoretic or surgical obstruction to complet ing m with a wedge of circles so that the completion has the topology of a compact smooth manifold this point set problem is all that stands between 4 manifolds and the tranquility that prevails in higher dimensions when m is simply connected only a point is missing from the model the applications of this are discussed in f and fq 1 the general theory has application to knot and link theory in particular knots with alexander polynomial 1 are characterized geometrically as knots admitting a certain

linking and causality in globally hyperbolic space times the classical linking number lk is defined when link components are zero homologous in 15 we constructed the affine linking invariant alk generalizing lk to the case of linked submanifolds with arbitrary homology classes here we apply alk to the study of causality in lorentzian manifolds

a diffeomorphism classification of manifolds which are like projective planes we give a complete diffeomorphism classification of 1 connected closed manifolds m with integral homology h m z z z provided that dim m 6 4

morse theory from an algebraic viewpoint forman s discrete morse theory is studied from an algebraic viewpoint and we show how this theory can be extended to chain complexes of modules over arbitrary rings as applications we compute the homologies of a certain family of nilpotent lie algebras and show how the algebraic morse theory can be used to derive the classical anick resolution as well as a new two sided anick resolution

direct identification of elastic constants of anisotropic plates by modal analysis experimental results abstract the determination of the six elastic stiffnesses of thin anisotropic plates from vibration tests is usually performed with numerical procedures based on the finite element or the rayleigh ritz method which both require assumptions concerning the studied mode shapes the present paper describes a method based on the measurement and the processing of natural frequencies as well as mode shapes of the vibrating tested plate as a result the unknown stiffnesses are determined directly without any iterative calculations the experimental aspects of the method are presently described and several results illustrate the relevance of the approach