on kawai theorem for orbifold riemann surfaces we prove a generalization of kawai theorem for the case of orbifold riemann surface the computation is based on a formula for the differential of a holomorphic map from the cotangent bundle of the teichmuller space to the mathrm psl 2 mathbb c character variety which allows to evaluate explicitly the pullback of goldman symplectic form in the spirit of riemann bilinear relations as a corollary we obtain a generalization of goldman s theorem that the pullback of goldman symplectic form on the mathrm psl 2 mathbb r character variety is a symplectic form of the weil petersson metric on the teichmuller space

complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

exact integration of constitutive equations in elasto plasticity a unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity assuming the total strain rate direction to be constant this unified approach includes all previous exact integration procedures as special cases and in addition some new closed form solutions are derived for combined kinematic and isotropic hardening special emphasis is laid on combined kinematic and isotropic hardening for von mises material and on isotropic hardening for mohr coulomb and tresca materials

the weil petersson hessian of length on teichmuller space we present a brief but nearly self contained proof of a formula for the weil petersson hessian of the geodesic length of a closed curve either simple or not simple on a hyperbolic surface the formula is the sum of the integrals of two naturally defined positive functions over the geodesic proving convexity of this functional over teichmuller space due to wolpert 1987 we then estimate this hessian from below in terms of local quantities and distance along the geodesic the formula extends to proper arcs on punctured hyperbolic surfaces and the estimate to laminations wolpert s result that the thurston metric is a multiple of the weil petersson metric directly follows on taking a limit of the formula over an appropriate sequence of curves we give further applications to upper bounds of the hessian especially near pinching loci recover through a geometric argument wolpert s result on the convexity of length to the half power and give a lower bound for growth of length in terms of twist

uniform bounds for weil petersson curvatures we find bounds for weil petersson holomorphic sectional curvature and the weil petersson curvature operator in several regimes that do not depend on the topology of the underlying surface among other results we show that the minimal weil petersson holomorphic sectional curvature of a sufficiently thick hyperbolic surface is comparable to 1 independently of the genus this provides a counterexample to some suggestions that the weil petersson metric becomes asymptotically flat as the genus g goes to infinity in some loci in teichmuller space adopting a different perspective on curvature we also show that the minimal most negative eigenvalue of the curvature operator at any point in the teichmuller space teich sg of a closed surface sg of genus g is uniformly bounded away from zero restricting to a thick part of teich sg we show that the minimal eigenvalue is uniformly bounded below by an explicit constant which does not depend on the topology of the surface but only on the given bound on injectivity radius

the inverses of toeplitz band matrices abstract the elements of the inverse of a toeplitz band matrix are given in terms ofthe solution of a difference equation the expression for these elements is a quotient of determinants whose orders depend the number of nonzero superdiagonals but not on the order of the matrix thus the formulae are particularly simple for lower triangular and lower hessenberg toeplitz matrices when the number of nonzero superdiagonals is small sufficient conditions on the solution of the abovementioned difference equation can be given to ensure that the inverse matrix is positive if the inverse is positive the row sums can be expressed in terms of the solution of the difference equation

length of a curve is quasi convex along a teichmuller geodesic we show that for every simple closed curve alpha the extremal length and the hyperbolic length of alpha are quasi convex functions along any teichmuller geodesic as a corollary we conclude that in teichmuller space equipped with the teichmuller metric balls are quasi convex

behavior of geodesic length functions on teichmuller space let t be the teichmuller space of marked genus g n punctured riemann surfaces with its bordification t the augmented teichmuller space of marked riemann surfaces with nodes abi77 ber74 pro vided with the wp metric t is a complete cat 0 metric space dw03 wol03 yam04 an invariant of a marked hyperbolic struc ture is the lengthof the geodesic in a free homotopy class a basic feature of teichmuller theory is the interplay of two dimensional hyperbolic geometry weil petersson wp geometry and the behavior of geodesic length functions our goal is to develop the understanding of the intrinsic local wp geometry through a study of the gradient and hessian of geodesic length functions considerations include ex pansions for the wp pairing of gradients expansions for the hessian and covariant derivative comparability models for the wp metric as well as the behavior of wp geodesics including a description of the alexandrov tangent cone at the augmentation approximations and applications for geodesics close to the augmentation are developed an application for fixed points of group actions is described bound ing configurations and functions on the hyperbolic plane is basic to our approach considerations include analyzing the orbit of a dis crete group of isometries and bounding sums of the inverse square exponential distance

three results in connection with inverse matrices abstract first we show that the moore penrose solution of an arbitrary system of linear equations is a convex combination of the solutions of all uniquely solvable partial systems the other two results concern the elements of inverse toeplitz band matrices namely the asymptotic behavior of a determinant appearing in a formula of d s meek and a modification of a formula of w d hoskins and p j ponzo for matrices with binomial coefficients in the limit case

displacement rank and quasitriangular decomposition for r toeplitz matrices abstract an r toeplitz r t matrix can be regarded as a block toeplitz matrix of order mr from which an l shaped border of k r rows and columns is removed the concept of displacement rank is extended to r t matrices and it is shown that both an r t matrix and its inverse can be expressed as the sum of at most two products of r t matrices this result reduces to a standard lu decomposition in the case when an r t matrix becomes an arbitrary matrix an explicit expression for the inverse is given which contains three triangular matrices and one quasitriangular matrix furthermore the inverse of an r t matrix is completely determined by the elements in its first and last r rows and columns the results presented generalize known properties of toeplitz and block toeplitz matrices

fast algorithms for brownian matrices brownian motion is one of the most common models used to represent nonstationary signals the covariance matrix of a discrete time brownian motion has a very particular structure and is called a brownian matrix this note presents a number of results concerning linear problems appearing in digital signal processing with brownian matrices in particular it is shown that fast algorithms used for toeplitz matrices are simpler and faster for brownian matrices examples are given to illustrate the different results presented in the note

on the dimension of cat 0 spaces where mapping class groups act whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete cat 0 space of dimension less than g it fixes a point

toeplitz matrices with toeplitz inverses revisited abstract a necessary and sufficient condition derived by huang and cline for a nonsingular toeplitz matrix to have a toeplitz inverse is shown to hold under more general hypotheses than indicated by them

inversion of certain extensions of toeplitz matrices it is shown how an algorithm for inverting toeplitz matrices using o n2 operations can be modified to deal with a certain type of extension named conjugate toeplitz matrices the block partitioned case is also included

classification of weil petersson isometries this paper contains two main results the first is the existence of an equivariant weil petersson geodesic in teichmuller space for any choice of pseudo anosov mapping class as a consequence one obtains a classification of the elements of the mapping class group as weil petersson isometries which is parallel to the thurston classification the second result concerns the asymptotic behavior of these geodesics it is shown that geodesics that are equivariant with respect to independent pseudo anosov s diverge it follows that subgroups of the mapping class group which contain independent pseudo anosov s act in a reductive manner with respect to the weil petersson geometry this implies an existence theorem for equivariant harmonic maps to the metric completion

the i3 generalization of the galileo rankine tension criterion the paper presents a new tension failure criterion which generalizes the so called galileorankine formulation the criterion can be used as a component of the so called perfectly no tension model f

fast o n complexity algorithms for diagonal innovation matrices in general the direct solution of an n dimensional system of linear equations requires o n3 arithmetic operations frequently in high data rate signal processing fast algorithms of complexity lower than o n3 are required to solve a large system of linear equations in several interesting applications the specific structure of the coefficient matrix associated with the linear system may be used to reduce the required number of operations fast algorithms have been developed when the coefficient matrix is a toeplitz matrix a hankel matrix or when it can be represented as a sum of toeplitz and hankel matrices the arithmetic complexity associated with these fast algorithms is o n2 in this paper fast algorithms of o n are presented that can be used for a class of matrices called diagonal innovation matrices dim previous results for this class of matrices require an arithmetic complexity of o n2 a number of results are presented regarding linear systems having dim coefficient matrices and several special cases are examined the effect of recursively increasing the order of the coefficient matrix on the number of operations is studied and some observations are made

a note on diagonal innovation matrices by noting that a recently introduced class of so called diagonal innovation matrices has a form previously encountered in state space estimation problems new linear complexity algorithms are presented for their factorization and inversion

a c2 continuous approximation to the mohr coulomb yield surface abstract in spite of the development of more sophisticated constitutive models for soil the mohr coulomb yield criterion remains a popular choice for geotechnical analysis due to its simplicity and ease of use by practising engineers the implementation of the criterion in finite element programs however presents some numerical difficulties due to the gradient discontinuities which occur at both the edges and the tip of the hexagonal yield surface pyramid furthermore some implicit techniques utilising consistent tangent stiffness formulations are unable to achieve full quadratic convergence as the yield criteria is not c2 continuous this paper extends the previous work of abbo and sloan 1995 through the introduction of c2 continuous rounding of the mohr coulomb yield surface in the octahedral plane this approximation when combined with the hyperbolic approximation in the meridional plane abbo and sloan 1995 describes a yield surface that is c2 continuous at all stress states the new smooth yield surface can be made to approximate the mohr coulomb yield function as closely as required by adjusting only two parameters and is suitable for consistent tangent stiffness formulations

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

on the existence of a unique class of yield and failure criteria comprising tresca von mises drucker prager mohr coulomb galileo rankine matsuoka nakai and lade duncan in this paper it is mathematically demonstrated that classical yield and failure criteria such as tresca von mises drucker prager mohr coulomb matsuoka nakai and lade duncan are all defined by the same equation this can be seen as one of the three solutions of a cubic equation of the principal stresses and suggests that all such criteria belong to a more general class of non convex formulations which also comprises a recent generalization of the galileo rankine criterion the derived equation is always convex and can also provide a smooth approximation of continuity of at least class c 2 of the original tresca and mohr coulomb criteria it is therefore free from all the limitations which restrain the use of some of them in numerical analyses the mathematical structure of the presented equation is based on a separate definition of the meridional and deviatoric sections of the graphical representation of the criteria this enables the use of an efficient implicit integration algorithm which results in a very short machine runtime even when demanding boundary value problems are analysed

efficient solution of a toeplitz plus hankel coefficient matrix system of equations there are well known fast algorithms such as the levinson recursion for solving linear equations with a toeplitz or hankel coefficient matrix this paper extends the saving obtained by the levinson recursion for inversion of a toeplitz matrix to problems involving the inversion of matrices which are the sum of toeplitz and hankel matrices

the mixed complementarity problem arising from non associative plasticity with non smooth yield surfaces abstract an elastic domain with multiple yield surfaces brings about huge troubles to numerical computations due to singularities while non associative plasticity leads further to the open issue of whether constitutive integration is well posed this study reduces the constitutive integration of non associative plasticity with multiple yield surfaces to a mixed complementarity problem represented by micp a special case of finite dimensional variational inequalities by means of the projection contraction algorithm for finite dimensional variational inequalities and the idea of the gauss seidel method a new projection contraction algorithm for micp is designed and denoted by gspc applying the monotonicity of the mapping of the micp gspc is proved convergent theoretically for associative plasticity for non associative plasticity the sufficient condition for gspc to be convergent is also established if the tension part of the mohr coulomb elastic domain is cut off typical examples are designed to illustrate gspc is highly efficient accurate and stable some of which cannot be solved by the conventional return mapping method in all the cases the computational efficiency of gspc is apparently above the mapping return method

geodesics distance and the cat 0 property for the manifold of riemannian metrics given a fixed closed manifold m we exhibit an explicit formula for the distance function of the canonical l 2 riemannian metric on the manifold of all smooth riemannian metrics on m additionally we examine the metric completion of the manifold of metrics with respect to the l 2 metric and show that there exists a unique minimal path between any two points this path is also given explicitly as an application of these formulas we show that the metric completion of the manifold of metrics is a cat 0 space

matrices with block toeplitz inverses abstract conditions for a nonsingular matrix to have a block toeplitz inverse are obtained a simpler criterion for a block toeplitz matrix to have a block toeplitz inverse is also given the results generalize those of huang and cline for toeplitz matrices with scalar entries for which alternative statements and proofs are also indicated

the weil petersson metric and volumes of 3 dimensional hyperbolic convex cores we present a coarse interpretation of the weil petersson distance dwp x y between two finite area hyperbolic riemann surfaces x and y using a graph of pants decompositions introduced by hatcher and thurston the combinatorics of the pants graph reveal a connection between riemann surfaces and hyperbolic 3 manifolds conjectured by thurston the volume of the convex core of the quasi fuchsian manifold q x y with x and y in its conformal boundary is comparable to the weil petersson distance dwp x y in applications we relate the weil petersson distance to the hausdorff dimen sion of the limit set and the lowest eigenvalue of the laplacian for q x y and give a new finiteness criterion for geometric limits mathematics department university of chicago 5734 s university ave chicago il 60637 e mail address brock math uchicago edu

efficient return algorithms for associated plasticity with multiple yield planes a new return method for implicit integration of linear isotropic yield criteria is presented the basic idea is to perform all the manipulations in the principal stress space and thereby achieve very simple formulae for calculating the plastic corrector stresses based on the constant gradient of such criteria the return formulae are in closed form and no iteration is required the method accounts for three types of stress return return to a single yield plane to a discontinuity line at the intersection of two yield planes and to a discontinuity point at the intersection between three or more yield planes the infinitesimal and the consistent elastoplastic constitutive matrix are calculated for each type of stress return as are the conditions to ascertain which type of return is required the method is exemplified with the mohr coulomb yield criterion

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

on algebras of toeplitz matrices abstract necessary and sufficient conditions for toeplitz and block toeplitz matrices to have toeplitz inverse are given maximal algebras of scalar toeplitz matrices are fully described

completions branched covers artin groups and singularity theory we study the curvature of metric spaces and branched covers of riemannian manifolds with applications in topology and algebraic geometry here curvature bounds are expressed in terms of the cat inequality we prove a general cat extension theorem giving sufficient conditions on and near the boundary of a locally cat metric space for the completion to be cat we use this to prove that a branched cover of a complete riemannian manifold is locally cat if and only if all tangent spaces are cat 0 and the base has sectional curvature bounded above by we also show that the branched cover is a geodesic space using our curvature bound and a local asphericity assumption we give a sufficient condition for the branched cover to be globally cat and the complement of the branch locus to be contractible we conjecture that the universal branched cover of cn over the mirrors of a finite coxeter group is cat 0 conditionally on this conjecture we use our machinery to prove the arnoldpham thom conjecture on k 1 spaces for artin groups also conditionally we prove the asphericity of moduli spaces of amply lattice polarized k3 surfaces and of the discriminant complements of all the unimodal hypersurface singularities in arnold s hierar

the determination of companion matrices characterizing toeplitz and r toeplitz matrices abstract it is shown that the unknown elements in the companion matrix used to characterize a nonsingular toeplitz matrix are easily found from the elements of the inverse of the toeplitz matrix similar formulae are obtained for the two companion like matrices characterizing an r toeplitz matrix this case includes the result for a block toeplitz matrix

a note on solving nearly triangular toeplitz systems abstract an algorithm is presented which reduces the problem of solving a toeplitz system 1 tx y to simple recursive computations and solving a related toeplitz system which is of lower order if t is nearly triangular the method does not require that t or any of its principal submatrices be nonsingular but only that 1 have a solution x for the given y in the case where t 1 exists a formula is given for it in terms of the inverse of an associated matrix discovered by widom

efficient markov chain monte carlo for combined subset simulation and nonlinear finite element analysis abstract typical probabilistic problems in an engineering context include rare event probability estimation for physical models where spatial autocorrelation of material property parameters is significant subset simulation a markov chain monte carlo technique can be used to estimate rare event probabilities in physical models more efficiently than monte carlo simulation this efficiency gain is important when the sampling operation is computationally demanding as is the case in the solution of stochastic partial differential equations in high dimensional spaces where polynomial chaos or other direct integration techniques become intractable sampling methods may be the only way to compute integral functions in probabilistic analysis in this paper subset simulation is applied to probability of failure estimation in nonlinear elasto plastic finite element problems further a derivation of confidence intervals for subset simulation relative errors is presented this new technique allows for vastly improved efficiency in the computation of error estimates for subset simulation significantly the numerical studies presented indicate that for the tested finite element problems metropolis hastings sampling can outperform componentwise metropolis hastings and gibbs sampling this result is relevant to the design of efficient subset simulation methodologies

shearing coordinates and convexity of length functions on teichmuller space we prove that there are fenchel nielsen coordinates for the teichmuller space of a finite area hyperbolic surface with respect to which the length functions are convex

a ring of brownian matrices abstract conditions are given for the product of two brownian matrices to be brownian a special class of brownian matrices is then introduced which forms a ring and it is shown that the determinant the eigenvalues and the eigenvectors for matrices in this class can all be determined in o n flops the inverse of a nonsingular matrix in this class is also found in o n flops compared with o n 2 for general brownian matrices generalized inverses when the matrix is singular are shown to belong to the class and are also found in o n flops a connection with magic square matrices is also discussed

the eigenproblem of a tridiagonal 2 toeplitz matrix abstract the characteristic polynomial of a tridiagonal 2 toeplitz matrix is shown to be closely connected to polynomials which satisfy the three point chebyshev recurrence relationship this is an extension of the well known result for a tridiagonal toeplitz matrix when the order of the matrix is odd the eigenvalues are found explicitly in terms of the chebyshev zeros the eigenvectors are found in terms of the polynomials satisfying the three point recurrence relationship

on the eigenvalue problem for toeplitz band matrices abstract a formula is given for the characteristic polynomial of an n th order toeplitz band matrix with bandwidth k n in terms of the zeros of a k th degree polynomial with coefficients independent of n the complexity of the formula depends on the bandwidth k and not on the order n also given is a formula for eigenvectors in terms of the same zeros and k coefficients which can be obtained by solving a k k homogeneous system

rigidity of teichmuller space we prove the holomorphic rigidity conjecture of teichmuller space which loosely speaking states that the action of the mapping class group uniquely determines the teichmuller space as a complex manifold the method of proof is through harmonic maps we prove that the singular set of a harmonic map from a smooth n dimensional riemannian domain to the weil petersson completion overline mathcal t of teichmuller space has hausdorff dimension at most n 2 and moreover u has certain decay near the singular set combining this with the earlier work of schumacher siu and jost yau we provide a proof of the holomorphic rigidity of teichmuller space in addition our results provide as a byproduct a harmonic maps proof of both the high rank and the rank one superrigidity of the mapping class group proved via other methods by farb masur and yeung

characterisation and properties of r toeplitz matrices abstract an r toeplitz rt matrix can be regarded as a block toeplitz matrix with order some multiple of r from which a bottom border and a right hand border have been removed it is shown that some known properties of toeplitz matrices extend to this new class in particular a necessary and sufficient condition is given in terms of a linear matrix equation for a nonsingular matrix to have rt form from which it follows that the elements of the inverse are completely determined by those in its first and last r rows and columns in addition some results are presented for cases when the inverse of an rt matrix has certain banded forms

from dynamics on surfaces to rational points on curves has no integer solutions with x y z 1 inspiring generations of work in number theory its proof was finally achieved by wiles a qualitative result finite fermat was obtained earlier by faltings it says the fermat equation has only a finite number of solutions for each given n up to rescaling this paper is an appreciation of some of the topological intuitions behind number theory it aims to trace a logical path from the classification of surface diffeomorphisms to the proof of finite fermat the route we take is the following

linear toeplitz covariance structure models with optimal estimators of variance components this paper deals with the problem of optimal quadratic unbiased estimation for statistical models with linear toeplitz covariance structure the main result is a necessary and sufficient condition for these models to have an optimal unbiased estimator for any linear combination of variance components this result is obtained by means of special jordan algebras which are a powerful tool to characterize optimality in quadratic unbiased estimation

a complementary energy formulation of no tension masonry like solids in the present work a complementary energy formulation for the solution of the static equilibrium problem of no tension solids is presented the main feature of the work is systematic use of the augmented lagrangian approach for the regularisation of the nonsmooth and nondifferentiable anelastic deformation potential the proposed formulation is applied to derive a finite element formulation using the subspace of the self equilibrated stresses as primal variables the code implements the augmented lagrangian algorithm for the determination of the inelastic deformations some numerical examples are included to illustrate the performance of the proposed approach

iterative methods for restoring noisy images an iterative image restoration algorithm is presented that is based on the best linear mean square estimate of the wiener filter technique and the iterative approach of the first order stationary linear jacobi method the iterative algorithm incorporates a priori knowledge concerning the image and noise statistics directly into the iterative procedure it also assumes the image covariance to be described by a separable first order markov field and exploits the resulting toeplitz structure the usefulness and validity of this algorithm are demonstrated by implementation and testing on real images the advantages offered by the algorithm are that it is computationally efficient since only a small number of computations per pixel per iteration is required it requires a small amount of memory it has a fast rate of convergence and it exhibits neither high noise sensitivity nor significant loss of resolution

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material

on some properties of positive definite toeplitz matrices and their possible applications abstract various properties of a real symmetric toeplitz matrix m with elements jk a j k 1 j k m are reviewed here matrices of this kind often arise in applications in statistics econometrics psychometrics structural engineering multichannel filtering reflection seismology etc and it is desirable to have techniques which exploit their special structure possible applications of the results related to their inverse determinant and eigenvalue problem are suggested

explicit and asymptotic formulas for ldmt factorization of banded toeplitz matrices abstract we study the ldmt factorization of banded toeplitz matrices we show that under fairly general conditions the l m and d factors exhibit exponential convergence along diagonals we also give explicit formulas for the limiting values our method of proof involves a generalization to matrices of the theory of continued fractions of quadratic irrationals