a generalization of the caginalp phase field system based on the cattaneo law abstract we consider in this article a generalization of the caginalp model for phase transitions based on the maxwell cattaneo law instead of the classical fourier law in particular we prove the existence and uniqueness of solutions we finally study the spatial behavior of the solutions in a semi infinite cylinder

testing nonlinear regression parameters under heteroscedastic normally distributed errors summary likelihood ratio tests for parameters estimated assuming normally distributed errors are examined under a variety of homoscedastic and heteroscedastic variance assumptions it is assumed that yij the jth observation from the ith population is distributed as n u xij wbi ai a xij oi 2 by varying a and oi this model contains the most obvious examples of homoscedastic and heteroscedastic variability under this model the null hypothesis of equal jbi s can easily be tested using the likelihood ratio criterion also considered is the two sample chi square statistic x u s u where u is the difference vector of nonlinear least squares parameter estimates and s is an estimate of the covariance matrix of u monte carlo simulation using the von bertalanffy growth curve as an example is used to evaluate several test statistics for type i error rates under different sampling assumptions

factoring polynomials over algebraic number fields we show that if f x is a polynomial in z alpha x where alpha satisfies a monic irreducible polynomial over z then f x can be factored over q alpha x in polynomial time we also show that the splitting field of f x can be determined in time polynomial in splitting field of f x q log x

a comparison of several exact and approximate tests for structural shift under heteroscedasticity abstract it is known that the chow test for equality of regression coefficients is not robust to heteroscedasticity much recent attention has been paid to this problem by way of new tests the bulk of the new procedures are justified only asymptotically and little has been done to examine finite sample properties even less attention has been focused on comparisons of tests under either the null or alternative hypotheses in this paper we redress these shortcomings and also contribute by suggesting additional tests the results indicate that there are tests available with good sampling characteristics some of which are computationally easy to carry out from both the standpoint of the researcher s time and computation time

a unified procedure for construction of theories of deformable media i classical continuum physics a new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper the procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal electrical and magnetic effects the basic energetic ingredients that are included in the balance of energy depend of course on the nature of the particular theory of material behaviour desired the advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws involving new kinetic quantities are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation indeed in the formulation of such new theories usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws and in this connection the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance in this paper first the basic features of the new procedure are illustrated in the context of classical thermomechanics generalizations of this thermomechanical theory are then discussed in two cases 1 in the presence of an additional kinematic variable and 2 in the presence of full electromagnetic effects both of these generalizations bring out some interesting novel features when new theories are being constructed

algorithms in algebraic number theory in this paper we discuss the basic problems of algorithmic algebraic number theory the emphasis is on aspects that are of interest from a purely mathematical point of view and practical issues are largely disregarded we describe what has been done and more importantly what remains to be done in the urea we hope to show that the study of algorithms not only increases our understanding of algebraic number fields but also stimulates our curiosity about them

growth and uniqueness in thermoelasticity a uniqueness theorem is proved for two theories of thermoelasticity capable of admitting finite speed thermal waves the theories having been proposed by green naghdi uniqueness is proved under

computing automorphisms of abelian number fields let l q be an abelian number field of degree n most algorithms for computing the lattice of subfields of l require the computation of all the conjugates of this is usually achieved by factoring the minimal polynomial m x of over l in practice the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size in this paper we describe a fast probabilistic algorithm for computing the conjugates of which is based on p adic techniques given m x and a rational prime p which does not divide the discriminant disc m x of m x the algorithm computes the frobenius automorphism of p in time polynomial in the size of p and in the size of m x by repeatedly applying the algorithm to randomly chosen primes it is possible to compute all the conjugates of

energy decay of type iii linear thermoelastic plates with memory abstract we analyze the decay properties of the solution semigroups generated by an abstract version of the linear systems u t t 2 u t 0 t t t u t 0 and u t t 2 u t 0 t t 0 s t t s d s u t 0 ruling the evolution of linear thermoelastic plates within the theory of heat conduction of type iii

welch s approximate solution for the behrens fisher problem the wald likelihood ratio and score statistics have been calculated for the behrens fisher problem these statistics provide asymptotically equivalent and weakly optimal tests the test based on the wald statistic was found to be very similar to the v test discussed by welch 1937 hence the v test was compared with the likelihood ratio and score tests in a power study since the powers were very similar and the v test was more convenient to use from several points of view we recommend this test sizes of the v test as well as a power comparison with the usual pooled t test were also obtained

on a phase field system based on the cattaneo law abstract our aim in this paper is to study a generalization of the caginalp phase field system based on the maxwell cattaneo law for heat conduction and endowed with neumann boundary conditions in particular we obtain well posedness results and study the dissipativity of the associated solution operators we also prove when the enthalpy is conserved the existence of the global attractor we finally study the spatial behavior of solutions in a semi infinite cylinder assuming that such solutions exist and have a proper spatial decay at infinity

convergence to equilibrium for a parabolic hyperbolic phase field model with cattaneo heat flux law abstract in this paper we consider the well posedness and the asymptotic behavior of solutions to the following parabolic hyperbolic phase field system 0 1 t 3 0 t t div q 0 q t q 0 in 0 subject to the homogeneous neumann boundary condition for 0 2 n 0 on 0 and no heat flux boundary condition for q 0 3 q n 0 on 0 and the initial conditions 0 4 0 0 0 0 q 0 q 0 in where r 3 is a bounded domain with a smooth boundary and n is the outward normal direction to the boundary in this paper we first establish the existence and uniqueness of a global strong solution to 0 1 0 2 0 3 0 4 then we prove its convergence to an equilibrium as time goes to infinity

a generalization of the caginalp phase field system with neumann boundary conditions abstract we study a generalized caginalp phase field system based on the theory of type iii heat conduction proposed by green and naghdi and supplemented with neumann boundary conditions in contrast to the dirichlet case the system exhibits a lack of dissipation on the thermal displacement variable however minus its spatial average is dissipative and we are able to prove the existence of the global attractor with optimal regularity for the associated semigroup

energy bounds for some non standard problems in thermoelasticity a e green f r s and p m naghdi developed two theories of thermoelasticity called type ii and type iii which are likely to be more natural candidates for the identification of a thermoelastic body than the usual theory we here derive energy bounds for a class of problem in which the initial data are given as a combination of data at time t 0 and at a later time t t such problems are in vogue in the mathematical literature and may be used for example to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time

box type approximations in nonparametric factorial designs abstract linear rank statistics in nonparametric factorial designs are asymptotically normal and in general heteroscedastic in a comprehensive simulation study the asymptotic chi squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite sample distribution motivated by this problem we propose simple finite sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure these approximations are based on an f distribution with estimated degrees of freedom that generalizes ideas of patnaik and box simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin wald test data driven guidelines are given to select the most appropriate test procedure these ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector

hypothesis testing in linear models when the error covariance matrix is nonscalar a well developed exact statistical theory exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic in the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n in this paper higher order asymptotic expansions are developed for comparing the size and power of some common procedures for testing linear hypotheses on the regression coefficients in a class of generalized normal linear models the class investigated is essentially the same as in breusch 4 and magnus 6 and includes many of the examples of heteroscedasticity and autocorrelation discussed in the literature we assume simply that the regressors are nonrandom and that the error covariance matrix is a smooth function of a few parameters that can be efficiently estimated by maximum likelihood tests based on the wald likelihood ratio and lagrange multiplier principles are considered these principles lead to three tests which though distinct in finite samples are locally asymptotically equivalent and share certain asymptotic optimality properties of course there are infinitely many other tests that are asymptotically equivalent to the ones examined here although the techniques of this paper can be applied to any of them our results concern only the tests arising from the three traditional principles we show that to a second order of approximation under local alternatives the likelihood ratio test statistic is a simple average of the wald statistic and the lagrange multiplier statistic when the null hypothesis is one dimensional the three tests are to second order equally powerful that is after the critical regions are adjusted so that the tests have to order n i the same size the local power functions differ by terms of smaller order than n when the null hypothesis contains more than one

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

a unified procedure for construction of theories of deformable media ii generalized continua in contrast to classical theories discussed in the accompanying paper part i the present paper deals exclusively with generalized continua a term that refers to a body embedded in a euclidean three dimensional space with each of its material points endowed with additional kinematic structure such generalized continua are conveniently identified here by cosserat or directed continua in which the additional structure is represented by independent director fields and the material domain of the body manifold is classified according to the four categories a a three dimensional volume b a two dimensional surface c a one dimensional space curve and d a point in the derivation of a thermomechanical theory for each of these categories we use the same unified procedure as in part i but now the various energies that enter the balance of energy must be modified to include additional kinetic ingredients new theories of this kind have increasingly provided over the last three decades effective means of formulating and studying new behaviour of materials in both fluid and solid mechanics that were not previously possible by the classical theories our attention is first focused in the development of the theory for the first category and this is discussed in two stages first for a cosserat continuum with a single director and then for n directors our derived results include for the first time a derivation from the balance of energy of balances of director momenta and balances of entropies in the presence of more than one independent temperature field the treatments of categories b to d are somewhat shorter since their developments are formally similar to that of category a

on the impossibility of localization in linear thermoelasticity in the middle of the 1990s green naghdi proposed three theories of thermoelasticity that they labelled as types i ii and ii the type ii theory which is also called thermoelasticity without energy dissipation is conservative and the solutions cannot decay with respect to time it is well known that in general in the linear theories of thermoelasticity of types i and iii the solutions decay with respect to time in many situations this decay is at least exponential in this paper we study whether this decay can be fast enough to guarantee the solutions to be zero in a finite time we investigate the impossibility of the localization in time of the solutions of linear thermoelasticity for the theories of green naghdi this means that the only solution that vanishes after a finite time is the null solution the main idea is to show the uniqueness of solutions for the backward in time problem to be precise for type iii thermoelasticity we will prove the impossibility of localization of solutions in the case of bounded domains and for the type i thermoelasticity in the case of exterior domains even when the solutions can be unbounded whether the spatial variable goes to infinity

tests for equality between sets of coefficients in two linear regressions under heteroscedasticity abstract structural shift is a common problem in a relationship dealing with time series data chow 1960 developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance structural shifts however often accompany changes in variance as well and the chow test is not robust to such changes two relatively robust tests are proposed and are found to be highly powerful

an approximate test for comparing heteroscedastic regression models abstract this article addresses the problem of testing whether the vectors of regression coefficients are equal for two independent regression models when the error variances are unequal the usual chow statistic appropriate when equality of variances can be assumed is modified by replacing the pooled residual variance in the denominator with a weighted average of the residual variances from each data set the weights are functions of the mean of the eigenvalues of w x 1 x 1 x 1 x 1 x 2 x 2 1 both numerator and denominator are then approximated by scalar multiples of chi squared distributions the parameters of these approximated distributions are chosen to equate their first two moments to those of the exact distribution the resulting approximation for the modified chow statistic c is an f distribution with degrees of freedom that depend on the two sample sizes the number of regressor variables the average eigenvalue of w and the true ratio of error variances since the latter is unknow