contact models leading to variational hemivariational inequalities abstract a frictional contact model under the small deformations hypothesis for static processes is considered we model the behavior of the material by a constitutive law using the subdifferential of a proper convex and lower semicontinuous function the contact is described with a boundary condition involving clarke s generalized gradient our study focuses on the weak solvability of the model based on a fixed point theorem for set valued mappings we prove the existence of at least one weak solution the uniqueness the boundedness and the stability of the weak solution are also discussed the investigation is based on arguments in the theory of variational hemivariational inequalities finally we present several examples of constitutive laws and friction laws for which our theoretical results are valid

sums of squares in real analytic rings let a be an analytic ring we show 1 a has finite pythagoras number if and only if its real dimension is 2 and 2 if every positive semidefinite element of a is a sum of squares then a is real and has real dimension 2

boundary optimal control of a nonsmooth frictionless contact problem abstract we consider a mathematical model which describes the equilibrium of an elastic body in contact with a foundation the contact is frictionless and is modeled with a nonsmooth interface law which involves unilateral constraints and subdifferential conditions the weak formulation of the model is in the form of an elliptic hemivariational inequality governed by a number of parameters we prove the unique weak solvability of the problem then we state and prove a continuous dependence result of the solution with respect to the data and parameters next we formulate a boundary optimal control problem for which we prove the existence of optimal pairs we also study the dependence of the optimal pairs with respect to the data and parameters and prove a convergence result the proofs are based on arguments of monotonicity lower semicontinuity and clarke subdifferential calculus

some remarks on the computation of pythagoras numbers of real irreducible algebroid curves through gram matrices we clarify a difficulty that appears in r quarez j algebra 238 2001 139 to bound the pythagoras number of a real irreducible algebroid curve by its multiplicity

sums of two squares in analytic rings we study analytic singularities for which every positive semidefinite analytic function is a sum of two squares of analytic functions this is a basic useful property of the plane but difficult to check in other cases in particular what about z 2 xy z 2 yx 2 y 3 z 2 x 3 y 4 or z 2 x 3 xy 3 in fact the unique positive examples we can find are the brieskorn singularity the union of two planes in 3 space and the whitney umbrella conversely we prove that a complete intersection with that property other than the seven embedded surfaces already mentioned must be a very simple deformation of the two latter namely in particular except for the stems z 2 x 2 and z 2 yx 2 all singularities are real rational double points

noncoercive hyperbolic variational inequalities with applications to contact mechanics abstract in this paper we study a class of hyperbolic variational inequalities without a term depending on the first order derivative results on existence uniqueness and regularity of a solution to the variational inequality are provided through the rothe method a frictional dynamic contact problem for viscoelastic material with noncoercive viscosity and subdifferential boundary conditions is studied as an illustrative application

on testing departure from the binomial and multinomial assumptions this paper is concerned with testing the multinomial binomial assumption against the dirichlet multinomial beta binomial alternatives in particular we discuss the distribution of the asymptotic likelihood ratio lr test and obtain the c alpha goodness of fit test statistic the inadequacy of the regular chi square approximation to the lr test is supported by some monte carlo experiments the c alpha test is recommended based on empirical significance level and power and also computational simplicity two examples are given

fibers of flat morphisms and weierstrass preparation theorem abstract we characterize flat extensions of commutative rings satisfying the weierstrass preparation theorem using this characterization we prove a variant of the weierstrass preparation theorem for rings of functions on a normal curve over a complete local domain of dimension one this generalizes recent works of harbater hartmann and krashen with a different method of proof

the length and other invariants of a real field the length of a field is the smallest integer m such that any totally positive quadratic form of dimension m represents all sums of squares we investigate this field invariant and compare it to others such as the u invariant the pythagoras number the hasse number and the mordell function related to sums of squares of linear forms

a convex optimization model for finding non negative polynomials this paper presents a convex optimization model for the problem of finding some polynomials for which certain linear combinations are non negative polynomials this model is then applied to solve several filter design problems we first reformulate some low pass filter design problems with finite or infinite impulse response as optimization problems over non negative real or complex polynomials whose feasibility problems can be solved by applying our model the whole optimization problems are then solved by using a combination of a bisection search procedure on an appropriate parameter and our convex optimization model to solve the feasibility problems some numerical examples illustrate the method

pythagoras numbers of real irreducible algebroid curves and gram matrices abstract using elementary techniques of linear algebra in relation with gram matrices we bound the pythagoras number of a real irreducible algebroid curve by its multiplicity

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

a class of evolution variational inequalities with memory and its application to viscoelastic frictional contact problems abstract in this paper we consider the first order evolution variational inequality involving two history dependent operators a result on existence and uniqueness of solution is proved we illustrate the applicability of this result by considering a dynamic frictional contact problem for viscoelastic material with the normal compliance contact condition with memory and coulomb s law of dry friction

a locally most powerful test for homogeneity with many strata summary a locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting the test is based on the difference between the square of the score and the observed information about the nuisance parameters all evaluated at the null hypothesis several examples including constant normal mean with possibly different variances and matched case control studies are presented in detail the relative efficiencies of the unstratified estimator of parameter of interest versus the stratified one are calculated two data sets on matched case control studies are used for illustration

sums of squares in real rings let a be an excellent ring we show that if the real dimension of a is at least three then a has in finite pythagoras number and there exists a positive semidefinite element in a which is not a sum of squares in a

positive semidefinite germs in real analytic surfaces we find all real analytic surface germs in mathbb r 3 on which every positive semidefinite function germ is a sum of squares in fact of two squares of analytic function germs

analyzing multiple emotions over time by autoregressive negative multinomial regression models abstract this article presents an autoregressive random coefficient model with overdispersed negative multinomial marginal distributions for the analysis of heterogeneity and serial dependencies in multivariate longitudinal count data the model structure consists of four components that take into account a individual difference effects b random time effects c multiple event categories and d autodependencies the last component is based on a stochastic integer valued autoregressive process proposed by mckenzie the model is applied to analyze count data from a panel diary study about the relationship between personality factors and emotion experiences it is shown that there are large and stable individual personality differences in the incidence and duration of self reported emotional experiences theoretical and clinical implications of this result are discussed

on the pythagoras numbers of real analytic curves we show that the pythagoras number of a real analytic curve is the supremum of the pythagoras numbers of its singularities or that supremum plus 1 this includes cases when the pythagoras number is infinite

monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations we use a generalized mortar method based on dual lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies in the case of unilateral contact problems pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers here we generalize these techniques to nonmatching triangulations where the constraints are realized in terms of weak integral conditions the basic new idea is the construction of a nested sequence of nonconforming constrained spaces we use suitable basis transformations and a multiplicative correction in contrast to other approaches no outer iteration scheme is required the resulting monotone method is of optimal complexity and can be implemented as a multigrid method numerical results illustrate the performance of our approach in two and three dimensions

on the positive extension property and hilbert s 17th problem for real analytic sets in this work we study the positive extension pe property and hilbert s 17th problem for real analytic germs and sets a real analytic germ x 0 of r 0 n has the pe property if every positive semidefinite analytic function germ on x 0 has a positive semidefinite analytic extension to r 0 n analogously one states the pe property for a global real analytic set x in an open set q of r 0 n these pe properties are natural variations of hilbert s 17th problem here we prove that 1 a real analytic germ x 0 subset of r 0 3 has the pe property if and only if every positive semidefinite analytic function germ on x 0 is a sum of squares of analytic function germs on x 0 and 2 a global real analytic set x of dimension 2 and local embedding dimension 3 has the pe property if and only if it is coherent and all its germs have the pe property if that is the case every positive semidefinite analytic function on x is a sum of squares of analytic functions on x moreover we classify the singularities with the pe property

sum of squares length of real forms for n d ge 1 let p n 2d denote the smallest number p such that every sum of squares of degree d forms in mathbb r x 1 ldots x n is a sum of p squares we establish lower bounds for p n 2d that are considerably stronger than the bounds known so far combined with known upper bounds they give p 3 2d in d 1 d 2 in the ternary case assuming a conjecture of iarrobino kanev on dimensions of tangent spaces to catalecticant varieties we show that p n 2d sim const cdot d n 1 2 for d rightarrow infty and all n ge 3 for ternary sextics and quaternary quartics we determine the exact value of the invariant showing p 3 6 4 and p 4 4 5

bayesian tests of extra binomial variability a simple model for extra binomial variability is the beta binomial a complication in testing the binomial against the beta binomial alternative is that the binomial lies on the boundary of the beta binomial which forces modifications to the usual asymptotic arguments in this paper we propose a bayesian test using a pair of approximate bayes factors one for the case in which the maximum likelihood estimator mle of the extra binomial variability is zero and one for the case in which it is positive these approximate bayes factors are easy to compute we evaluate the operating characteristics of the bayes factors and find them to be more powerful than the likelihood ratio test we then apply the method to three data sets including one in which the issue is whether a logistic regression intercept should be considered a random effect in each case our approximate bayes factors are close to the exact bayes factors which may also be computed with additional effort copyright 2004 john wiley sons ltd

testing goodness of fit of a multinomial model against overdispersed alternatives the problem of testing the goodness of fit of the multinomial sampling model against an overdispersed dirichlet multinomial alternative is studied and an improved approximate sampling distribution is presented for the corresponding c ca test statistic the elements of this improvement include better control of test size and increased power against overdispersion the pearson chi square test is also considered for the detection of this form of overdispersion and its asymptotic efficiency relative to the c a test is obtained and shown to be always less than or equal to 1 monte carlo investigations suggest that the gain in power of the c a test relative to the pearson chi square test is small unless there is substantial inequality among the dirichlet multinomial sample sizes

sums of squares in function fields over henselian local fields we give upper bounds for the level and the pythagoras number of function fields over fraction fields of integral henselian excellent local rings in particular we show that the pythagoras number of mathbb r x 1 dots x n is le 2 n 1 which answers positively a question of choi dai lam and reznick

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

eigenvalues of symmetric matrices over integral domains abstract given an integral domain a we consider the set of all integral elements over a that can occur as an eigenvalue of a symmetric matrix over a we give a sufficient criterion for being such an element in the case where a is the ring of integers of an algebraic number field this sufficient criterion is also necessary and we show that the size of matrices grows linearly in the degree of the element the latter result settles a questions raised by bass estes and guralnick

weighted sums of squares in local rings and their completions i let a be an excellent regular local ring of dimension two let t be a finitely generated preordering in a and let widehat t be the preordering generated by t in the completion widehat a of a we study the question when the property of being saturated descends from widehat t to t and establish conditions of geometric nature which allow to decide this question as an application we classify all principal preorderings in a of degree 3 which are saturated in the case where a has a real closed residue field these results have direct implications for nonnegativity certificates for real polynomials on two dimensional semi algebraic sets