a class of nonholonomic kinematic constraints in elasticity we propose a first example of a simple classical field theory with nonholonomic constraints our model is a straightforward modification of a cosserat rod based on a mechanical analogy we argue that the constraint forces should be modelled in a special way and we show how such a procedure can be naturally implemented in the framework of geometric field theory finally we derive the equations of motion and we propose a geometric integration scheme for the dynamics of a simplified model

euler lagrange and hamilton equations for non holonomic systems in field theory a generalization of the concept of a system of non holonomic constraints to fibred manifolds with n dimensional bases is considered motion equations in both lagrangian and hamiltonian settings for systems subjected to such constraints are investigated regularity conditions for the existence of a non holonomic legendre transformation and the corresponding formulae for hamiltonian and momenta are found in particular lagrangian constraints and semi holonomic constraints and simplifications arising in this case are discussed

on the construction of some complete metrics with exceptional holonomy on construit explicitement trois metriques completes distinctes d holonomie egale a g 2 une metrique complete d holonomie egale a spin 7 et diverses metriques incompletes d holonomie exceptionnelle

lagrangian systems with constraints a geometric approach to the method of lagrange multipliers a geometric approach to the method of lagrange multipliers is presented using the framework of the tangent bundle geometry the nonholonomic systems with constraint functions linear in the velocities are studied in the first place and then and using this study of the nonholonomic mechanical systems as a previous result the holonomic systems are considered the lagrangian inverse problem is also analysed and finally the theory is illustrated with several examples

a geometrical framework for the study of non holonomic lagrangian systems a geometrical framework is presented for the treatment of a class of dynamical systems which are modelled by a system of second order differential equations coupled with first order equations linear in the derivatives such problems in particular make their appearance in the study of lagrangian systems with non holonomic constraints among other things we discuss the concepts of symmetry and adjoint symmetry for such systems and identify for that purpose an appropriate notion of dynamical covariant derivative and jacobi endomorphism the intrinsic tools which are being developed further allow a direct geometrical construction of the dynamics of non holonomic systems the vertically rolling disc is chosen as an illustrative example for the newly proposed formalism and results

einstein matrices on s3 r3 and r4 bundles on construit a partir d un espace de base de kahler quaternionique 4n dimensionnel des metriques de cohomogeneite 1 en dimensions 4n 3 dont les surfaces de niveau sont l espace fibre s 2 des structures presque complexes sur la variete de base on obtient les conditions sur les fonctions metriques qui proviennent du fait qu on impose l equation d einstein et on obtient des solutions pour des espaces de dimension 4n 3 compactes et non compactes deux metriques 7 dimensionnelles ricci plates avec holonomie g 2 sont incluses dans les solutions non compactes

on the geometry of non holonomic lagrangian systems we present a geometric framework for non holonomic lagrangian systems in terms of distributions on the configuration manifold if the constrained system is regular an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics if the constrained system is singular we develop a constraint algorithm which is very similar to that developed by dirac and bergmann and later globalized by gotay and nester special attention to the case of constrained systems given by connections is paid in particular we extend the results of koiller for caplygin systems an application to the so called non holonomic geometry is given

regression with covariates and outcome calculated from a common set of variables measured with error estimation using the simex method in medical research a situation commonly arises where new variables are calculated from a common set of directly measured variables when the directly measured variables each contain an error component the relationship between the observed calculated variables can often be distorted a source of this distortion is the presence of common measurement error in the observed calculated variables often known as coupled error it is still possible to estimate the relationship between the calculated variables when measurement error is present this paper presents two general methodologies that account for the presence of correlated measurement error when working with calculated variables the equivalence of the methods will be established for one case while the general advantage of the simulation extrapolation technique will be shown for more complicated situations the performance of the estimators will be examined with examples arising from the medical literature

the nonholonomic variational principle a variational principle for mechanical systems and fields subject to nonholonomic constraints is found providing chetaev reduced equations as equations for extremals investigating nonholonomic variations of the chetaev type and their properties we develop foundations of the calculus of variations on constraint manifolds modelled as fibred submanifolds in jet bundles this setting is appropriate to study general first order nonlinear nonitegrable constraints that locally are given by a system of first order ordinary or partial differential equations we obtain an invariant constrained first variation formula and constrained euler lagrange equations both in intrinsic and coordinate forms and show that the equations are the same as chetaev equations without lagrange multipliers introduced recently by other methods we pay attention to two possible settings first when the constrained system arises from an unconstrained lagrangian system defined in a neighbourhood of the constraint and second more generally when an internal constrained system on the constraint manifold is given in the latter case a corresponding unconstrained system need not be a lagrangian nor even exist we also study in detail an important particular case nonholonomic constraints that can be alternatively modelled by means of co distributions in the total space of the fibred manifold in nonholonomic mechanics this happens whenever constraints affine in velocities are considered it becomes clear that and why if the distribution is completely integrable the constraints are semiholonomic the principle of virtual displacements holds and can be used to obtain the constrained first variational formula by a more or less standard procedure traditionally used when unconstrained or holonomic systems are concerned if however the constraint is nonintegrable no significant simplifications are available among others some properties of nonholonomic systems are clarified that without a deeper insight seem rather mysterious

segmented regression with errors in predictors semi parametric and parametric methods we consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors with a focus on linear and logistic regression in epidemiologic studies segmented regression models often occur as threshold models where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold furthermore in occupational and environmental studies the exposure typically cannot be measured exactly ignoring this measurement error leads to asymptotically biased estimators of the threshold it is shown that this asymptotic bias is different from that observed for estimating standard generalized linear model parameters in the presence of measurement error being both larger and in different directions than expected in most cases considered the threshold is asymptotically underestimated two standard general methods for correcting for this bias are considered regression calibration and simulation extrapolation simex in ordinary logistic and linear regression these procedures behave similarly but in the threshold segmented regression model they operate quite differently the regression calibration estimator usually has more bias but less variance than the simex estimator regression calibration and simex are typically thought of as functional methods also known as semi parametric methods because they make no assumptions about the distribution of the unobservable covariate x the contrasting structural parametric maximum likelihood estimate assumes a parametric distributional form for x in ordinary linear regression there is typically little difference between structural and functional methods one of the major surprising findings of our study is that in threshold regression the functional and structural methods differ substantially in their performance in one of our simulations approximately consistent functional estimates can be as much as 25 times more variable than the maximum likelihood estimate for a properly specified parametric model structural parametric modelling ought not be a neglected tool in measurement error models an example involving dust concentration and bronchitis in a mechanical engineering plant in munich is used to illustrate the results 1997 by john wiley sons ltd

partial differential equations with differential constraints a geometric setting for constrained exterior differential systems on fibered manifolds with n dimensional bases is proposed constraints given as submanifolds of jet bundles locally defined by systems of first order partial differential equations are shown to carry a natural geometric structure called the canonical distribution systems of second order partial differential equations subjected to differential constraints are modeled as exterior differential systems defined on constraint submanifolds as an important particular case lagrangian systems subjected to first order differential constraints are considered different kinds of constraints are introduced and investigated lagrangian constraints constraints adapted to the fibered structure constraints arising from a co distribution semi holonomic constraints holonomic constraints

spin c manifolds and complex contact structures in this paper we extend our notion of projectable spinors 9 ch 1 to the framework of spin c manifolds and deduce the basic formulas relating spinors on the base and the total space of riemannian submersions with totally geodesic one dimensional fibres some geometric applications concerning positive kahler einstein complex contact manifolds e g their characterisation as twistor spaces over positive quaternionic kahler manifolds are also given

a tulczyjew triple for classical fields the geometrical structure known as the tulczyjew triple has proved to be very useful in describing mechanical systems even those with singular lagrangians or subject to constraints starting from basic concepts of the variational calculus we construct the tulczyjew triple for first order field theory the important feature of our approach is that we do not postulate ad hoc the ingredients of the theory but obtain them as unavoidable consequences of the variational calculus this picture of field theory is covariant and complete containing not only the lagrangian formalism and euler lagrange equations but also the phase space the phase dynamics and the hamiltonian formalism since the configuration space turns out to be an affine bundle we have to use affine geometry in particular the notion of the affine duality in our formulation the two maps and which constitute the tulczyjew triple are morphisms of double structures of affine vector bundles we also discuss the legendre transformation i e the transition between the lagrangian and the hamiltonian formulation of the first order field theory

7 dimensional compact riemannian manifolds with killing spinors using a link between einstein sasakian structures and killing spinors we prove a general construction principle of odd dimensional riemannian manifolds with real killing spinors in dimensionn 7 we classify all compact riemannian manifolds with two or three killing spinors finally we classify nonflat 7 dimensional riemannian manifolds with parallel spinor fields

real killing spinors and holonomy we give a description of all complete simply connected riemannian manifolds carrying real killing spinors furthermore we present a construction method for manifolds with the exceptional holonomy groupsg2 and spin 7

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

kahlerian twistor spinors on a kahler spin manifold kahlerian twistor spinors are a natural analogue of twistor spinors on riemannian spin manifolds they are defined as sections in the kernel of a first order differential operator adapted to the kahler structure called kahlerian twistor penrose operator we study kahlerian twistor spinors and give a complete description of compact kahler manifolds of constant scalar curvature admitting such spinors as in the riemannian case the existence of kahlerian twistor spinors is related to the lower bound of the spectrum of the dirac operator

regularity aspects and hamiltonization of non holonomic systems we discuss various aspects of the transition from lagrangian to hamiltonian equations for systems with general nonlinear non holonomic constraints the emphasis is first on constructing the reduced dynamics on the constraint submanifold and then trying to start a hamiltonization procedure from there we prove a theorem concerning the regularity which is required to obtain a unique second order dynamics on the constraint submanifold and we show that the same condition allows the transition to a hamiltonian picture throughout the analysis different degrees of generality are discussed

chetaev versus vakonomic prescriptions in constrained field theories with parametrized variational calculus starting from a characterization of admissible chetaev and vakonomic variations in a field theory with constraints we show how the so called parametrized variational calculus can help to derive the vakonomic and the nonholonomic field equations we present an example in field theory where the nonholonomic method proved to be unphysical

mechanical systems with nonholonomic constraints a geometric setting for the theory of first order mechanical systems subject to general nonholonomic constraints is presented mechanical systems under consideration are not supposed to be lagrangian systems and the constraints are not supposed to be of a special form in the velocities as e g affine or linear a mechanical system is characterized by a certain equivalence class of 2 forms on the first jet prolongation of a fibered manifold the nonholonomic constraints are defined to be a submanifold of the first jet prolongation it is shown that this submanifold is canonically endowed with a distribution this distribution resp its vertical subdistribution has the meaning of generalized possible resp virtual displacements the concept of a constraint force is defined and a geometric version of the principle of virtual work is proposed from the principle of virtual work a formula for a workless constraint force is obtained a mechanical system subject nonholonomic constraints is modeled as a deformation of the original unconstrained system a direct characterization of a constrained system by means of a class of 2 forms along the canonical distribution is given and constrained equations of motion in an intrinsic form are found a geometric definition of regularity for systems under nonholonomic constraints is provided in particular the case of lagrangian systems is discussed also systems subject to holonomic constraints and nonholonomic constraints affine in the velocities are investigated within the range of the general scheme

metrics with exceptional holonomy it is proved that there exist metrics with holonomy g2 and spin 7 thus settling the remaining cases in berger s list of possible holonomy groups we first reformulate the holonomy h condition as a set of differential equations for an associated h structure on a given manifold we collect the needed algebraic facts about g2 and spin 7 we then apply the machinery of over determined partial differential equations in the form of the cartan kahler theorem to prove the existence of solutions whose holonomy is g2 or spin 7 we also provide explicit examples and some information about the generality of the space of

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

integrability conditions for killing spinors the conditions for the existence of solutions ofd c are discussed in general it is not sufficient to consider only the first integrability condition d dv 2c2 v in particular the second integrability condition is needed to explain why in certain cases only for one choice of sign does a solution exist the killing spinor tensors as defined by walker and penrose are shown to be the spinorial equivalent of conformal killing tensors their relationship to the killing spinors and spinor vectors used in supergravity is given

spin c geometry of kahler manifolds and the hodge laplacian on minimal lagrangian submanifolds from the existence of parallel spinor fields on calabi yau hyper kahler or complex flat manifolds we deduce the existence of harmonic differential forms of different degrees on their minimal lagrangian submanifolds in particular when the submanifolds are compact we obtain sharp estimates on their betti numbers which generalize those obtained by smoczyk in 49 when the ambient manifold is kahler einstein with positive scalar curvature and especially if it is a complex contact manifold or the complex projective space we prove the existence of kahlerian killing spinor fields for some particular spin c structures using these fields we construct eigenforms for the hodge laplacian on certain minimal lagrangian submanifolds and give some estimates for their spectra these results also generalize some theorems by smoczyk in 50 finally applications on the morse index of minimal lagrangian submanifolds are obtained

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

einstein manifolds of dimension five with small first eigenvalue of the dirac operator soit m n une variete de spin compacte d einstein a courbure scalaire positive r 0 et on note par d t s t s l operateur de dirac agissant sur des sections du fibre spinoriel on etudie le probleme de la classification des varietes pour le cas a 5 dimensions

jet methods in nonholonomic mechanics classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle m r the framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly for systems with linear constraints a new interpretation is given of appell s equations as first order differential equations associated with a suitable vector field the d alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints the equivalence between the equations of motion arising from this generalization the ones set up on gauss principle of least constraint and hertz s principle of least curvature is established

einstein metrics on s 3 r 3 and r 4 bundles starting from a 4n dimensional quaternionic kahler base space we construct metrics of cohomogeneity one in 4n 3 dimensions whose level surfaces are thes 2 bundle space of almost complex structures on the base manifold we derive the conditions on the metric functions that follow from imposing the einstein equation and obtain solutions both for compact and non compact 4n 3 dimensional spaces included in the non compact solutions are two ricci flat 7 dimensional metrics withg 2 holonomy we also discuss two other ricci flat solutions one on ther 4 bundle overs 3 and the other on anr 4 bundle overs 4 these haveg 2 and spin 7 holonomy respectively

the dirac operator on generalized taub nut spaces we find sufficient conditions for the absence of harmonic l2 spinors on spin manifolds constructed as cone bundles over a compact kahler base these conditions are fulfilled for certain perturbations of the euclidean metric and also for the generalized taub nut metrics of iwai katayama thus proving a conjecture of visinescu and the second author

non holonomic lagrangian systems in jet manifolds a geometrical setting in terms of jet manifolds is developed for time dependent non holonomic lagrangian systems an almost product structure on the evolution space is constructed in such a way that the constrained dynamics is obtained by projection of the free dynamics a constrained poincare cartan 2 form is defined if the non holonomic system is singular a constraint algorithm is constructed special attention is devoted to caplygin systems and a reduction theorem is proved

non holonomic lagrangian and hamiltonian mechanics an intrinsic approach a geometrical approach to lagrangian and hamiltonian non holonomic dynamics is proposed the construction relies on a revisitation of the poincare cartan 1 form leading to the introduction of the concepts of lagrangian and hamiltonian pairs and to the implementation of a non holonomic legendre map the relationship with the standard extrinsic approach is outlined a unified canonical framework joining both lagrangian and hamiltonian aspects is proposed