likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

on the formulation of wald tests of nonlinear restrictions this paper utilizes asymptotic expansions of the edgeworth type to investigate alternative forms of the wald test of nonlinear restrictions some formulae for the asymptotic expansion of the distribution of the wald statistic are provided for a general case that should include most econometric applications when specialized to the simple cases that have been studied recently in the literature these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors it is further shown how the corrections delivered by edgeworth expansions may be used to find transformations of the restrictions which accelerate convergence to the asymptotic distribution

a computational multilevel approach for solving 2d navier stokes equations over non matching grids a multilevel approach with parallel implementation is developed for obtaining fast solutions of the navier stokes equations solved on domains with non matching grids the method relies on computing solutions over different subdomains with different multigrid levels by using multiple processors a local vanka type relaxation operator for the multigrid solution of the navier stokes system allows solutions to be computed at the element level the natural implementation on a multiprocessor architecture results in a straightforward and flexible algorithm numerical computations are presented using benchmark applications in order to support the method parallelization is discussed to achieve proper accuracy load balancing and computational efficiency between different processors 2005 elsevier b v all rights reserved

riemannian geometry of the motion of an ideal incompressible magnetohydrodynamical fluid abstract this paper presents a riemannian geometrical formalism of the hydrodynamics of an ideal incompressible fluid originally proposed by arnold and then extends it to include the magnetohydrodynamics mhd of such a fluid for the motion of an ideal incompressible fluid a right invariant metric the induced riemannian levi civita connection and then the geodesics are firstly defined on the lie group d m of all diffeomorphisms of an n manifold m being the ambient space of the lie group d m of volume preserving diffeomorphisms of m next the associated covariant derivatives on the tangent space t d m to d m at d m d m are orthogonally projected onto t d m and finally the geodesic equation on d m is obtained in the same way the equation of motion for an ideal incompressible mhd fluid is obtained too in this case the appropriate configuration space is the semidirect product of d m with the space 1 m of 1 forms on m denoted s m d m 1 m and as its ambient space the semidirect product group s m d m 1 m is considered in addition as on a finite dimensional manifold classical tensor calculus is performed on the considered infinite dimensional lie groups when m is an n three dimensional flat torus the curvature tensors responsible for the instability of these systems are also obtained

a second order accurate projection method for the incompressible navier stokes equations on non graded adaptive grids we present an unconditionally stable second order accurate projection method for the incompressible navier stokes equations on non graded adaptive cartesian grids we employ quadtree and octree data structures as an efficient means to represent the grid we use the supra convergent poisson solver of c h min f gibou h ceniceros a supra convergent finite difference scheme for the variable coefficient poisson equation on fully adaptive grids cam report 05 29 j comput phys in press a second order accurate semi lagrangian method to update the momentum equation an unconditionally stable backward difference scheme to treat the diffusion term and a new method that guarantees the stability of the projection step on highly non graded grids we sample all the variables at the grid nodes producing a scheme that is straightforward to implement we propose two and three dimensional examples to demonstrate second order accuracy for the velocity field and the divergence free condition in the l1 and l norms

pre testing for linear restrictions in a regression model with spherically symmetric disturbances abstract in this paper we derive the exact risk under quadratic loss of pre test estimators of the prediction vector and of the error variance of a linear regression model with spherically symmetric disturbances the pre test in question is one of the validity of a set of exact linear restrictions on the model s coefficient vector we demonstrate how the known results for the model with normal disturbances can be extended to this broader case we also show that the critical value of unity results in a minimum of the risk of the pre test estimator of the error variance to illustrate the results we assume multivariate student t regression disturbances and numerically evaluate the derived expressions

estimation of the error variance after a preliminary test of homogeneity in a regression model with spherically symmetric disturbances abstract in this paper we consider the risk under quadratic loss of an estimator of the error variance after a pre test for homogeneity of the variances in the two sample linear regression model we investigate the effects on risk of assuming normal disturbances when in fact the error distribution is spherically symmetric we also broaden the standard assumption that the never pool variance estimators are based on the least squares principle to illustrate the results numerically we consider two families of variance mixing distributions one of which results in multivariate student t disturbances our results show that in some situations we should always pre test even if the error variances are equal and we provide the optimal test critical value the evaluations also show that using the least squares technique to form the never pool estimators may not always be the preferred strategy

testing for autoregressive against moving average errors in the linear regression model abstract this paper presents a new approach to hypotheses testing problems which are non nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model in particular the application of the approach to testing for ar 1 disturbances against ma 1 disturbances is explored in some detail practical difficulties are discussed and selected upper bounds for the test s five percent significance points are tabulated the small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test

joint tests for zero restrictions on nonnegative regression coefficients summary three tests for zero restrictions on regression coefficients that are known to be nonnegative are considered the classical f test the likelihood ratio test and a one sided t test in a particular direction critical values for the likelihood ratio test are given for the cases of two and three restrictions and the power function is calculated for the case of two restrictions the analysis is conducted in terms of a characterization of the clas all similar tests for the problem of which each of the above tests is a member the likelihood ratio test emerges as the preferred test

restricted least squares pre test ols and stein rule estimators risk comparisons under model misspecification abstract the predictive squared error risk behavior of a restricted least squares estimator rls pre test estimator pt and stein rule sr estimator are each compared to the behavior of the ols estimator when relevant variables are omitted risk superiority conditions dependent on prior constraint error and this model specification error in a two dimensional parameter space are exhibited among the consequences of this model misspecification it is found that i perfectly correct prior constraints do not ensure risk superiority of any of the alternatives to ols ii the risk difference between ols and pt is no longer bounded and iii the sr no longer dominates ols the usefulness of risk superiority hypothesis tests based on the doubly non centralf distribution is examined

a note on pooling variances abstract the estimation of variance in the normal distribution is studied under statistical inference based on conditional specification when there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population the experimenter usually uses a test to resolve the uncertainty when the test is not significant the samples are pooled to obtain a pooled estimator otherwise the individual sample variance is used the bias and mean squared error of such a preliminary test estimator are studied it is shown that the preliminary test estimator has a smaller mean squared error than the usual unbiased estimator when the level of significance for the preliminary test is appropriately chosen

hypothesis testing with a restricted parameter space abstract this paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis multivariate one sided tests are a leading example optimal tests called directed tests are derived using a weighted average power criterion exact results are established first for gaussian linear regression models with known variance asymptotic analogues are then established for dynamic nonlinear models simulation is used to compare the tests discussed in the paper the d w directed test is found to perform best in an overall sense for multivariate one sided alternatives with the likelihood ratio test being a close second the d w and likelihood ratio tests are found to perform best for mixed one and two sided alternatives

reduction of sufficient conditions for optimal control problems with subgroup symmetry in this paper we apply symmetry reduction techniques from geometric mechanics to sufficient conditions for local optimality in optimal control problems after reinterpreting some previous results for left invariant problems on lie groups we focus on optimal control problems with subgroup symmetry for these problems the necessary conditions for optimality can be simplified by exploiting symmetries so as to reduce the number of variables needed to describe trajectories of the system we show that sufficient conditions for optimality based on the non existence of conjugate points can be simplified in an analogous way to the necessary conditions we demonstrate these simplifications by analyzing an optimal control problem that models a spinning top in a gravitational field and we give particular attention to the example of an axisymmetric sleeping top the results we derive in this paper allow us to determine which trajectories of a sleeping top are locally optimal solutions of the optimal control problem which is a new result that has not appeared in previous literature

coadjoint orbits vortices and clebsch variables for incompressible fluids this paper is a study of incompressible fluids especially their clebsch variables and vortices using symplectic geometry and the lie poisson structure on the dual of a lie algebra following ideas of arnold and others it is shown that euler s equations are lie poisson equations associated to the group of volume preserving diffeomorphisms the dual of the lie algebra is seen to be the space of vortices and kelvin s circulation theorem is interpreted as preservation of coadjoint orbits in this context clebsch variables can be understood as momentum maps the motion of n point vortices is shown to be identifiable with the dynamics on a special coadjoint orbit and the standard canonical variables for them are a special kind of clebsch variables point vortices with cores vortex patches and vortex filaments can be understood in a similar way this leads to an explanation of the geometry behind the hald beale majda convergence theorems for vorticity algorithms symplectic structures on the coadjoint orbits of a vortex patch and filament are computed and shown to be closely related to those commonly used for the kdv and the schrodinger equations respectively

a riemannian geometrical description for lie poisson systems and its application to idealized magnetohydrodynamics this paper presents a general theorem which enables description of lie poisson systems for semi direct product groups in terms of riemannian geometry the method employed is unique in that it changes the non quadratic right or left invariant hamiltonian to the quadratic form in a right or left invariant i form on the corresponding group by removing the respective invariance which obtains the riemannian metric and its induced riemannian levi civita connection the resultant geodesic equation proves to be equivalent to the equation of motion while the corresponding jacobi equation determines its instability in addition this method is applied to idealized magnetohydrodynamics having isentropic flow with a simple example being provided that considers the motion of an isentropic gas with no magnetic field present

symmetric function products and plethysms and the boson fermion correspondence we use the boson fermion correspondence for s and q functions to establish some interesting properties concerning outer products and plethysms of s functions or q functions by power sum symmetric functions the techniques which are developed are also applied to computing the inverse kostka foulkes matrix which is the transition matrix between hall littlewood symmetric functions and s functions in some simple cases

exact tests and confidence sets in linear regressions with autocorrelated errors this article proposes a general method to build exact tests and confidence sets in linear regressions with first order autoregressive gaussian disturbances because of a nuisance parameter problem we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context given an exact confidence set for the autocorrelation coefficient we describe how to obtain a similar simultaneous confidence set for the autocorrelation coefficient and any subvector of regression coefficient conservative confidence sets for the regression coefficients are then deduced by a projection method for any hypothesis that specifies jointly the value of the autocorrelation coefficient and any set of linear restrictions on the regression coefficients we get exact similar tests for tesing linear hypotheses about the regression coefficients only we suggest bounds type procedures exact confidence sets for the autocorrelation coefficient are built by inverting autocorrelation tests the method is illustrated with two examples copyright 1990 by the econometric society

riemannian curvature on the group of area preserving diffeomorphisms motions of fluid of 2 sphere abstract euler s equation for an incompressible fluid filled in a riemannian manifold d is regarded as a geodesic equation on the group of volume preserving diffeomorphisms of d provided with a one sided invariant metric a negative sectional curvature implies instability of the geodesic with respect to the corresponding flow and perturbation the exponential growth of the perturbation is estimated from the values of the sectional curvatures this paper presents the expression of the components of riemannian curvature tensor of the group of area preserving diffeomorphisms of a 2 sphere in explicit formulas through 3 j coefficients

second order accurate volume of fluid algorithms for tracking material interfaces we introduce two new volume of fluid interface reconstruction algorithms and compare the accuracy of these algorithms to four other widely used volume of fluid interface reconstruction algorithms we find that when the interface is smooth e g continuous with two continuous derivatives the new methods are second order accurate and the other algorithms are first order accurate we propose a design criteria for a volume of fluid interface reconstruction algorithm to be second order accurate namely that it reproduce lines in two space dimensions or planes in three space dimensions exactly we also introduce a second order unsplit volume of fluid advection algorithm that is based on a second order finite difference method for scalar conservation laws due to bell dawson and shubin we test this advection algorithm by modeling several different interface shapes propagating in two simple incompressible flows and compare the results with the standard second order operator split advection algorithm although both methods are second order accurate when the interface is smooth we find that the unsplit algorithm exhibits noticeably better resolution in regions where the interface has discontinuous derivatives such as at corners

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

reconstructing volume tracking a new algorithm for the volume tracking of interfaces in two dimensions is presented the algorithm is based upon a well defined second order geometric solution of a volume evolution equation the method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology a linearity preserving piecewise linear interface geometry approximation ensures that solutions generated retain second order spatial accuracy second order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme we detail our geometrically based solution method in which material volume fluxes are computed systematically with a set of simple geometric tasks we then interrogate the method by testing its ability to track interfaces through large controlled topology changes whereby an initially simple interface configuration is subjected to vortical flows numerical results for these strenuous test problems provide evidence for the algorithm s improved solution quality and accuracy

parachute fluid structure interactions 3 d computation abstract we present a parallel computational strategy for carrying out 3 d simulations of parachute fluid structure interaction fsi and apply this strategy to a round parachute the strategy uses a stabilized space time finite element formulation for the fluid dynamics fd and a finite element formulation derived from the principle of virtual work for the structural dynamics sd the fluid structure coupling is implemented over compatible surface meshes in the sd and fd meshes large deformations of the structure are handled in the fd mesh by using an automatic mesh moving scheme with remeshing as needed

the small sample properties of some preliminary test estimators in a linear model with autocorrelated errors abstract a monte carlo study is used to examine the finite sample relative efficiency of a number of estimators including pre test estimators and the accuracy of asymptotic confidence intervals derived from them for a linear model with ar 1 or ma 1 errors the bias of the ml estimator of the ar 1 parameter and the frequency of ml estimates equal to 1 for the ma 1 parameter have a large bearing on the properties of the estimators of the regression coefficient the traditional ols ar pre test estimator compares relatively favorably even under an ma error specification however the confidence intervals associated with positive autoregressive errors and a trended explanatory variable can be quite inaccurate

problems with the estimation of moving average processes abstract as a consequence of the well known underidentification of the moving average model unless the parameter space is restricted maximum likelihood and other estimators possess properties which can pose problems for estimation when a root of the process is close to the unit circle the behaviour of the estimators is studied both through the analytic properties of their criterion functions and by monte carlo simulation conclusions about the choice of estimator are drawn in particular regarding the treatment of the pre sample residuals

lagrangian navier stokes flows a stochastic model we associate stochastic lagrangian flows with navier stokes deterministic velocities and show their unstable behaviour

a fully eulerian formulation for fluid structure interaction problems in this work we present a fully eulerian framework for fluid structure interaction fsi problems coupling the incompressible navier stokes equations with a hyperelastic solid the fully eulerian framework is a monolithic implicit variational formulation for the coupled problem in contrast to the well established arbitrary lagrangian eulerian ale coordinates the fully eulerian framework formulates both subproblems fluid and solid in eulerian coordinates this concept circumvents various difficulties connected to ale coordinates since no artificial domain mapping is used the formulation is an interface capturing method and uses an extension of the solid s deformation the initial point set to detect the interface location by construction very large deformation as well as topology changes like contact of the solid to the domain boundary or other solid parts are possible

alternative size corrections for some gls test statistics the case of the ar 1 model abstract alternative size corrections are developed for the t and f tests in the ar 1 normal linear model edgeworth corrected critical values are obtained from normal student t chi square and f distributions alternatively we may use cornish fisher corrected test statistics to avoid the problem of negative tail probabilities of an edgeworth distribution the use of the exact distributions student t f results in approximations that are locally exact i e they reduce to the exact formulae for a sufficient simplification of the model monte carlo findings support the theoretical considerations in favour of the locally exact cornish fisher corrections

an edgeworth test size correction for the linear model with ar 1 errors rothenberg s edgeworth size correction is applied to tests of linear hypotheses in the linear regression model with ar 1 errors previous simulation findings on the effect of autocorrelation in the regressors on over rejection are supported when the correction is examined analytically in a special case a simulation study shows that the correction adjusts the size in the right direction but still leaves substantial over rejection when the sample size is small and the original amount of over rejection is large

a penalty projection algorithm for a monolithic fluid structure interaction solver in this paper we propose a new iterative penalty projection algorithm for a monolithic fluid structure interaction solver projection methods that split the computation of the velocity from the pressure are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed however when solid regions are taken into account the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress free conditions and due to the rigidity of the medium the boundary errors propagate deeply in the interior in order to reduce the projection errors we propose a one step penalty projection method in the fluid domain and an iterative penalty projection method in the solid region this technique decouples the pressure velocity degrees of freedom and as a consequence the computational cost in order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity pressure algorithm and the coupled one these numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort a new penalty projection algorithm for a monolithic fsi solver is proposed projection method error is localized where pressure boundary conditions are imposed a one step penalty together with an iterative projection algorithm is used this technique reduces the problem degrees of freedom and the computational cost numerical results show stability and reduction of cpu effort for large problems

ideal magnetohydrodynamics and passive scalar motion as geodesics on semidirect product groups three dimensional ideal magnetohydrodynamic 3d imhd equations are shown to be a geodesic equation on an infinite dimensional lie group the group is the semidirect product of a group of volume preserving diffeomorphisms particle motion and a linear space of divergenceless vector fields current density the present theory includes the work of zeitlin and kambe 1993 for two dimensional imhd flow as a special case passive scalar motion in n dimensional ideal hydrodynamic flow is also generally shown to be described by a geodesic equation

variational principle and conservation laws for nonbarotropic flows a variational formulation for nonbarotropic perfect fluid flow is presented by introducing suitable field variables euler s equations of motion from the variational principles are obtained the conservation laws of energy impulse and angular momenta follow from application of noether s theorem

the sensitivity of ols when the variance matrix is partially unknown we consider the standard linear regression model y xb u with all standard assumptions except that the variance matrix is assumed to be p2x h where x depends on m unknown parameters h 1 2 h m our interest lies exclusively in the mean parameters b or xb we introduce a new sensitivity statistic b1 which is designed to decide whether yl or bk is sensitive to covariance misspeci cation we show that the durbin watson test is inappropriate in this context because it measures the sensitivity of pl 2 to covariance misspeci cation our results demonstrate that the estimator bk and the predictor yl are not very sensitive to covariance misspeci cation the statistic is easy to use and performs well even in cases where it is not strictly applicable 1999 elsevier science s a all rights reserved

some tests for the constancy of regressions under heteroscedasticity abstract for testing the equality of coefficients of a linear regression model under heteroscedasticity we suggest an f criterion conditioned on the posterior mean of the ratio of standard deviations of error terms in two subsamples for pairable subsamples and exact f test is derived sampling experiments show that the chow test differs substantially from the nominal significance level when the two subsample sizes are unequal and that the f test conditioned on the posterior mean is superior to other tests when sample sizes are small

complex trkalian fields and solutions to euler s equations for the ideal fluid we consider solutions to the complex trkalian equation vec nabla times vc vc where vc is a 3 component vector function with each component in the complex field and may be expressed in the form vc e ig vec nabla f with g real and f complex we find there are precisely two classes of solutions one where g is a cartesian variable and one where g is the spherical radial coordinate we consider these flows to be the simplest of all exact 3 d solutions to the euler s equation for the ideal incompressible fluid the novel approach we use in solving for these classes of solutions to these 3 dimensional vector pdes involves differential geometric techniques one may employ the method to generate solutions to other classes of vector pdes

a projection method for coupling two phase vof and fluid structure interaction simulations abstract the study of multiphase fluid structure interaction mfsi is becoming of great interest in many engineering applications in this work we propose a new algorithm for coupling a fsi problem to a multiphase interface advection problem an unstructured computational grid and a cartesian mesh are used for the fsi and the vof problem respectively the coupling between these two different grids is obtained by interpolating the velocity field into the cartesian grid through a projection operator that can take into account the natural movement of the fsi domain the piecewise color function is interpolated back on the unstructured grid with a galerkin interpolation to obtain a point wise function which allows the direct computation of the surface tension forces

a new test for fourth order autoregressive disturbances abstract this paper proposes a new test for simple fourth order autoregressive disturbances in the linear regression model the test is shown to be most powerful invariant in a given neighourhood of the alternative hypothesis for all design matrices an empirical power comparison suggests that the test is generally more powerful than the wallis test the difference in power probably being slight for most economic applications although for certain design matrices the power advantage of the new test is very real selected bounds for the test s significance points are tabulated

differential geometry on diffeomorphism groups and lagrangian stability of viscous flows a differential geometrical formulation of the motion of an incompressible viscous fluid is presented the geodesic equation on a manifold is extended with an additional term consisting of an endomorphism of the tangent space and a class of curves defined by the resultant equation is introduced based on this extension the motion of an incompressible viscous fluid is formulated as curves of this class in a diffeomorphism group and the expression for the variational equation of the curves is derived the expression is then shown to coincide with the governing equations for the lagrangian displacement which interprets the physical meaning of variation vector fields of the curves the variational equation is reduced to a more simplified form which can be used to study evolution of the distances between fluid particles advected by a given basic flow

maximum likelihood estimation of regression models with first order moving average errors when the root lies on the unit circle1 this paper considers the maximum likelihood estimator of the first order moving average process when the true value of the coefficient is one the results are also extended to regression analysis it is shown that there is a local maximum of the likelihood function within an interval of o t 1 of the true value and also that the probability that the maximum occurs exactly at the true value can be calculated in finite samples in this paper we consider the maximum likelihood estimator mle of the coefficient p of a first order moving average ma 1 process when the true value of the coefficient is plus or minus one the results are also extended to regression equations with errors generated by the ma 1 process our study has been motivated chiefly by two factors first it has been sometimes suggested that the occurrence of a maximum near or at p 1 could be interpreted as evidence for over differencing 4 13 while this does not present any difficulty for exact maximum likelihood estimation procedures 12 we need to consider the properties of the maximum likelihood estimates of p when true p 1 in order to apply conventional test procedures e g the likelihood ratio test second kang 9 has shown that the likelihood function is stationary at p 1 and simulation studies on the behavior of the mle of p reveal that the global maximum can occur at p 1 even if the true p is within the invertibility region 9 5 there are two main results in this paper first we show that there is a local maximum of the likelihood function p such that p 1 is of o t 1 but p is not asymptotically normally distributed second it is shown possible to calculate the exact probability that p 1 is a local maximum of the likelihood function in finite samples although we focus only on local maxima near or at p 1 by constructing arguments similar to those of jennrich 8 or sargan 14 it can be shown that the global maximum has probability limit one in large samples so that the properties of these maxima would seem to be of primary interest asymptotically in considering the global mle

geometrical analysis of free rotation of a rigid body rotational motion of a free rigid body without action of external torque is governed by the euler equation which is reformulated as a geodesic equation by introducing a riemannian metric and connection on the lie group so 3 the aim of this work is to investigate the stability of the motion from the viewpoint of geodesic variation and also to study the relationship between the instability and the riemannian sectional curvatures of variable signs the stability theorem of steady rotations known in the mechanics dynamical property is recovered by solving the jacobi equation for the variational field y a geometrical field existence of a conjugate point for the rigid body of any shape is confirmed and the condition for any jacobi field concerning the steady rotations such that to have a conjugate time is derived the sectional curvatures k s are calculated for the stable steady rotation the curvatures k s take either positive definite values or both positive and negative values in oscillatory manner depending on the inertia tensor however the time averages s are always positive for any y in the linearly stable case while there exist y s which make negative in the case of linear instability

finite mode analogs of 2d ideal hydrodynamics coadjoint orbits and local canonical structure abstract the algebraic finite mode hydrodynamic type systems that have o n integrals of motion for o n n modes and are intrinsically connected with two dimensional ideal fluid flows are studied special emphasis is given on the structure of their phase space and the problem of finding proper dynamical variables for its description in connection with appropriate problems for the original hydrodynamic equations various possibilities for embedding in the space of canonical variables are demonstrated on the simplest example of the su 3 model giving the finite dimensional analogs of clebsch variables

efficiency of iterative estimators in the regression model with ar 1 disturbances abstract the mean square error approximation method of nagar is applied to the iterated prais winsten and iterated maximum likelihood estimators of regression coefficients in the model with ar 1 disturbances their mean square errors are found to equal that of the two stage prais winsten estimator at the second order level of approximation

the beltrami spectrum for incompressible fluid flows recently v yakhot s orszag and their co workers have suggested that turbulent flows in various regions of space organize into a coherent hierarchy of weakly interacting superimposed approximate beltrami flows a mathematical framework is developed here to study organized beltrami hierarchies in a systematic fashion this framework is applied to several important classes of examples with universal beltrami hierarchies an analysis of the persistence of such beltrami hierarchies is also presented for general solutions of the navier stokes equations

bootstrapping cointegrating regressions abstract in this paper we consider bootstrapping cointegrating regressions it is shown that the method of bootstrap if properly implemented generally yields consistent estimators and test statistics for cointegrating regressions for the cointegrating regression models driven by general linear processes we employ the sieve bootstrap based on the approximated finite order vector autoregressions for the regression errors and the first differences of the regressors in particular we establish the bootstrap consistency for ols method the bootstrap method can thus be used to correct for the finite sample bias of the ols estimator and to approximate the asymptotic critical values of the ols based test statistics in general cointegrating regressions the bootstrap ols procedure however is not efficient for the efficient estimation and hypothesis testing we consider the procedure proposed by saikkonen 1991 asymptotically efficient estimation of cointegration regressions econometric theory 7 1 21 and stock and watson 1993 a simple estimator of cointegrating vectors in higher order integrating systems econometrica 61 783 820 relying on the regression augmented with the leads and lags of differenced regressors the bootstrap versions of their procedures are shown to be consistent and can be used to do asymptotically valid inferences a monte carlo study is conducted to investigate the finite sample performances of the proposed bootstrap methods

on the properties and limitations of the height function method in two dimensional cartesian geometry in this study we define the continuous height function to investigate the approximation of an interface line and its geometrical properties with the height function method we show that in each mixed cell the piecewise linear interface reconstruction and the approximation of the derivatives and curvature based on three consecutive height function values are second order accurate we also discuss the quadratic reconstruction and fourth order accurate expressions of the normal and curvature we present a hierarchical algorithm to compute the normal vector and curvature of an interface line with the height function method that switches automatically between second and fourth order approximations and that can be applied also when the local radius of curvature is of the order of the grid spacing

some notes on periodic beltrami fields in cartesian geometry some mathematical facts about beltrami fields which are time independent solutions of the three dimensional incompressible euler equations with nontrivial helicity are assembled the linearization about an arbitrary fixed beltrami field is studied in a hamiltonian framework a factorization of this linearization is introduced and used to characterize null spaces for beltrami fields with ergodic streamlines an interesting property of unstable modes is noticed and its consequences concerning the nature of potential instabilities are discussed

joint one sided tests of linear regression coefficients abstract the main example of the class of problems considered below is that of testing whether a subset of regression coefficients are jointly zero assuming knowledge of the coefficients signs if this knowledge is ignored the likelihood ratio wald and lagrange multiplier tests are each equivalent to the f test we propose a new test which can be applied as a one sided t test and which is umpi in a subspace of the parameter space empirical power comparisons with the power envelope the f test and the exact one sided likelihood ratio test show that the new test can have exceptionally good power over a wide range of the parameter space

vof evaluation of the surface tension by using variational representation and galerkin interpolation projection abstract in this work we propose a variational approach with cell to point galerkin projections for studying two phase interface advection problems dominated by surface tension a volume of fluid vof algorithm is used for tracking and locating the evolution of the two phase interface on a cartesian grid and a finite element numerical scheme for solving the velocity pressure state the velocity field that drives the evolution of this interface is computed from the weak form of the navier stokes equation where the surface tension force is represented in variational form by the continuous surface force csf and continuous surface stress css methods standard numerical approaches solve the strong form of the navier stokes equations and define the css term by taking the divergence of the surface tension tensor this computation of the divergence term results in a singular force which is difficult to compute when the grid is refined since the tensor is computed in a discontinuous cell by cell way in this work we use the variational formulation of the navier stokes equation and avoid differentiation the tensor which is a function of the unit normal is evaluated over regular sobolev spaces by using a cell to point galerkin projection this allows a regular piece wise continuous representation of the surface tensor and the unit normal based on the vof reconstruction in standard approaches the csf surface force is computed by using the curvature which is the divergence of the unit normal in this paper we recover the curvature with point wise galerkin projection avoiding direct differentiation tests on convergence for two and three dimension in the static and dynamical cases are reported to show the correct representation in the desired spaces this method is also natural for coupling non uniform grid computation of the fluid with cartesian grid of the vof algorithm

on the sensitivity of the usual t and f tests to covariance misspecification we consider the standard linear regression model with all standard assumptions except that the disturbances are not white noise but distributed n 0 p2x h where x 0 i n our interest lies in testing linear restrictions using the usual f statistic based on ols residuals we are not interested in nding out whether h 0 or not instead we want to nd out what the e ect is of possibly nonzero h on the f statistic itself we propose a sensitivity statistic for this purpose discuss its distribution and obtain a practical and easy to use decision rule to decide whether the f test is sensitive or not to covariance misspeci cation when h is close to zero some nite and asymptotic properties of u are studied as well as its behaviour in the special case of an ar 1 process near the unit root 2000 elsevier science s a all rights reserved jel classixcation c12 c22 c51 c52

the optimal size of a preliminary test of linear restrictions in a misspecified regression model abstract when the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model it is well known that a minimax risk regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value regardless of the degrees of freedom we show that this result no longer holds in the likely event that relevant regressors are excluded from the model at the outset

the alternative durbin watson test an assessment of durbin and watson s choice of test statistic abstract this paper examines durbin and watson s 1950 choice of test statistic for their test of first 0order autoregressive regression disturbances attention is focused on an alternative statistic d theoretical and empirical power properties of the d test are compared with those of the durbin watson test the former is found to be locally best invariant while the latter is approximately locally best invariant the d test is also found to be more powerful than its counterpart against negative autocorrelation and for small values of the autocorrelation coefficient against positive autocorrelation selected bounds for significance points of d are tabulated

second order properties of estimators of serial correlation from regression residuals abstract second order properties of estimators and tests offer a way of choosinf among aymptotically equivalent procedures this paper studies the second order terms of two estimators of serial correlation in the linear model using these second order approximations the maximum likelihood estimator is judge to be superior in terms of bias and variance a small monte carlo experiment is done to assess the accuracy of the results

two dimensional ideal magnetohydrodynamics and differential geometry it is shown that equations of two dimensional ideal magnetohydrodynamics may be regarded as geodesic equations on appropriate infinite dimensional lie group the physical interpretation of such a geometric picture is given using an analogy with two and a half dimensional ideal hydrodynamics the sectional curvature responsible for the separation of neighbouring geodesics and hence for stability is calculated

a point optimal test for autoregressive disturbances abstract this paper is concerned with testing for first order autoregressive disturbances in the linear regression model and recommends an alternative test to the durbin watson test the new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space an empirical power comparison indicates that the test is generally more powerful than the durbin watson test the comparison also suggests that for many economic applications the difference in power will be small although circumstances do exist in which the power advantage of the new test is very real selected bounds for the test s significance points are tabulated

a newton raphson pseudo solid domain mapping technique for free and moving boundary problems an implicit pseudo solid domain mapping technique is described that facilitates finite element analysis of free and moving boundary problems the technique is based on an implicit full newton strategy free of restrictions on mesh structure this leads to many advantages over existing domain mapping techniques the fully coupled approach using newton s method is particularly effective for problems with strong coupling between the internal bulk physics and the governing physics at unknown free boundary locations it is also useful when the distinguishing conditions which constrain the free boundary shape provide only an implicit dependence on the boundary location unstructured meshes allow for efficient resolution of internal and boundary layers and other regions of strong local variations in the solution and they also reduce the amount of user interaction required to define a problem since the meshes may be generated automatically the technique is readily applied to steady or transient problems in complex geometries of two and three dimensions examples are shown that include free and moving boundary problems from solidification and capillary hydrodynamics

geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid motion of an ideal fluid is represented as geodesics on the group of all volume preserving diffeomorphisms an explicit form of the geodesic equation is presented for the fluid flow on a three torus riemannian connection commutator and curvature tensor are given explicitly and applied to a couple of simple flows with the beltrami property it is found that the curvature is non positive for the section of two abc flows with different values of the constants a b and c the study is an extension of the arnold s results 1989 in the two dimensional case to three dimensional fluid motions

lin constraints clebsch potentials and variational principles the poisson bracket formulation of fluid plasma and rigid body type systems has undergone considerable recent development using techniques of symmetry group reduction the relationship between this approach and that using lin constraints and clebsch potentials is established the connection is made in the setting of abstract clebsch variables as well as that of variational principles on reduced spaces variational principles for both the clebsch and reduced form such as fluids in spatial representation are derived from the standard variational principle of hamilton in material lagrangian representation using reduction theory

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

autocorrelation pre testing in the linear model estimation testing and prediction abstract this paper explores by means of a monte carlo experiment the consequences of autocorrelation pre testing on estimation hypothesis testing and prediction in the linear regression model with first order autoregressive disturbances we find that overall pre testing is preferable to pure ols regression techniques and generally compares favourably with the strategy of always correcting for possible autocorrelation more surprising findings include the degree to which the regression matrix affects the relative performance of the various strategies and the degree to which the familiar ols based t test can lose power in the presence of autocorrelation

a semi implicit level set method for multiphase flows and fluid structure interaction problems in this paper we present a novel semi implicit time discretization of the level set method introduced in 8 for fluid structure interaction problems the idea stems from a linear stability analysis derived on a simplified one dimensional problem the semi implicit scheme relies on a simple filter operating as a pre processing on the level set function it applies to multiphase flows driven by surface tension as well as to fluid structure interaction problems the semi implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost it is validated through comparisons with the original explicit scheme and refinement studies on two dimensional benchmarks

on estimating and testing in a linear regression model with autocorrelated errors abstract in this paper we examine the small sample properties of feasible gls estimators and tests of individual regression coefficients bayesian and non bayesian estimators for an autocorrelation coefficient denoted by are examined by monte carlo experiments it is shown that when the value of is large the bayesian estimator for performs better than non bayesian estimators for when the value of is large and the sample size is 20 none of the feasible gls estimators performs well in hypothesis testing however when the sample size is 40 the feasible bayesian gls estimator performs much better that the feasible non bayesian gls estimators in hypothesis testing

poisson brackets and clebsch representations for magnetohydrodynamics multifluid plasmas and elasticity abstract poisson brackets are constructed by the same mathematical procedure for three physical theories ideal magnetohydrodynamics multifluid plasmas and elasticity each of these brackets is given a simple lie algebraic interpretation moreover each bracket is induced to physical space by use of a canonical poisson bracket in the space of clebsch potentials which are constructed for each physical theory by the standard procedure of constrained lagrangians

testing ar 1 against ma 1 disturbances in an error component model this paper derives three lm statistics for an error component model with first order serially correlated errors the first lm statistic jointly tests for zero first order serial correlation and random individual effects the second lm statistic tests for zero first order serial correlation assuming fixed individual effects and the third lm statistic tests for zero first order serial correlation assuming random individual effects in all three cases the corresponding lm statistic is the same whether the alternative is ar 1 or ma 1 this paper also derives two extensions of the burke godfrey and termayne 1990 test from the time series to the panel data literature the first tests the null of ar 1 disturbances against ma 1 disturbances and the second tests the null of ma 1 disturbances against ar 1 disturbances in an error component model these tests are computationally simple requiring only ols or within residuals the small sample performance of these tests are studied using monte carlo experiments

a fixed grid sharp interface method for bubble dynamics and phase change abstract a numerical method has been developed for direct simulation of bubble dynamics with large liquid to vapor density ratio and phase change the numerical techniques are based on a fixed grid finite volume method capable of treating the interface as a sharp discontinuity the unsteady axisymmetric navier stokes equations and energy equation in both liquid and vapor phases are computed the mass momentum and energy conditions are explicitly matched at the phase boundary to determine the interface shape and movement the cubic b spline is used in conjunction with a fairing algorithm to yield smooth and accurate information of curvatures nondimensional parameters including reynolds weber and jakob numbers are varied to offer insight into the physical and numerical characteristics of the bubble dynamics based on the present sharp interface approach bubble dynamics for density ratio of 1600 or higher with and without phase change can be successfully computed

fredholm properties of riemannian exponential maps on diffeomorphism groups we prove that exponential maps of right invariant sobolev h r metrics on a variety of diffeomorphism groups of compact manifolds are nonlinear fredholm maps of index zero as long as r is sufficiently large this generalizes the result of ebin et al geom funct anal 16 2006 for the l 2 metric on the group of volume preserving diffeomorphisms important in hydrodynamics in particular our results apply to many other equations of interest in mathematical physics we also prove an infinite dimensional morse index theorem settling a question raised by arnold and khesin topological methods in hydrodynamics springer new york 1998 on stable perturbations of flows in hydrodynamics finally we include some applications to the global geometry of diffeomorphism groups

fighting the teflon factor comparing classical and bayesian estimators for autocorrelated errors abstract this paper claims on the basis of a monte carlo study that current estimators employed in the context of first order autocorrelated errors should be abandoned in favor of a bayesian alternative frequentists are confronted on their own playing field the bayesian estimator employs an ignorance prior and the criterion adopted is the mean square error of the competing estimators with the predictable exception of the ols estimator when the autocorrelation parameter is close to zero the bayesian estimator dominates the competition by a substantive margin