on vanishing stability regions in nonlinear systems with high gain feedback when local stabilization of nonlinear systems is achieved by linear feedback the resulting stability region may vanish as the feedback gains increase this is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium as the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium if a feedback linearization design is applied the same instability mechanism may occur when the nonlinearities are not precisely known

goodness of fit tests for kernel regression with an application to option implied volatilities this paper proposes a test of a restrictedspeci cation of regression basedon comparing residual sum of squares from kernel regression our main case is where both the restrictedspeci cation andthe general mod el are nonparametric with our test equivalently viewed as a test of dimension reduction we discuss practical features of implementing the test andvariations applicable to testing parametric mod els as the null hypothesis or semiparametric models that depend on a nite parameter vector as well as unknown functions we apply our testing procedure to option prices we reject a parametric version of the black scholes formula but fail to reject a semiparametric version against a general nonparametric regression 2001 elsevier science s a all rights reserved jel classi cation c12 c14

maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction abstract for second order linear equations and inequalities which are degenerate elliptic but which possess a uniformly elliptic direction we formulate and prove weak maximum principles which are compatible with a solvability theory in suitably weighted versions of l 2 based sobolev spaces the operators are not necessarily in divergence form have terms of lower order and have low regularity assumptions on the coefficients the needed weighted sobolev spaces are in general anisotropic spaces defined by a non negative continuous matrix weight as preparation we prove a poincare inequality with respect to such matrix weights and analyze the elementary properties of the weighted spaces comparisons to known results and examples of operators which are elliptic away from a hyperplane of arbitrary codimension are given finally in the important special case of operators whose principal part is of grushin type we apply these results to obtain some spectral theory results such as the existence of a principal eigenvalue

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

corrections to sub riemannian geometry an error in the proof of corollary 6 2 of 1 has been pointed out by gerard ben arous the computation of m x in the case o 0 on p 243 is incorrect because m x 0 when 0 0 and jg x 0 for all k there is also a factor of missing in the formula as stated for 0 0 but this is not significant thus when applying the pontryagin theorem theorem 6 1 it is necessary to consider one additional case o 0 and m x9 0 along the curve the conditions of the theorem in this case lead to the equations

new properties of convex functions in the heisenberg group we prove some new properties of the weakly h convex functions recently introduced by danielli garofalo and nhieu as an interesting application of our results we prove a theorem of busemann feller alexandrov type in the heisenberg groups h n 1 2

a conditional kolmogorov test this paper introduces a conditional kolmogorov test of model specification for parametric models with covariates regressors the test is an extension of the kolmogorov test of goodness of fit for distribution functions the test is shown to have power against 1 n local alternatives and all fixed alternatives to the null hypothesis a parametric bootstrap procedure is used to obtain critical values for the test

specification test for panel data models with interactive fixed effects abstract in this paper we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model we estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic we show that after being appropriately centered and standardized the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by prakasa rao 2009 to improve the finite sample performance we propose a bootstrap procedure to obtain the bootstrap p value a small set of monte carlo simulations illustrates that our test performs well in finite samples an application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth initial income level and capital accumulation

a central limit theorem under metric entropy with l_2 bracketing let mathbf s rho be a metric space mathbf v mathscr v mu be a probability space and f mathbf s times mathbf v rightarrow mathbb r be a real valued function on mathbf s times mathbf v which has mean zero and is lipschitz in l 2 mu with respect to rho let v be a random variable defined on mathbf v mathscr v mu and let v i i geq 1 be a sequence of independent copies of v the limiting behavior of the process s n s n 1 2 sum n i 1 f s v i is studied under an integrability condition on the metric entropy with bracketing in l 2 mu this metric entropy condition is analogous to one which implies the continuity of the limiting gaussian process a tightness result is derived which in conjunction with the results of andersen and dobric 1987 shows that a central limit theorem holds for the s n process this result generalizes those of dudley 1978 dudley 1981 and jain and marcus 1975

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

nonparametric estimation of regression functions with both categorical and continuous data abstract in this paper we propose a method for nonparametric regression which admits continuous and categorical data in a natural manner using the method of kernels a data driven method of bandwidth selection is proposed and we establish the asymptotic normality of the estimator we also establish the rate of convergence of the cross validated smoothing parameters to their benchmark optimal smoothing parameters simulations suggest that the new estimator performs much better than the conventional nonparametric estimator in the presence of mixed data an empirical application to a widely used and publicly available dynamic panel of patent data demonstrates that the out of sample squared prediction error of our proposed estimator is only 14 20 of that obtained by some popular parametric approaches which have been used to model this data set

area stationary surfaces in the heisenberg group h1 we consider area stationary surfaces perhaps with a volume constraint in the heisenberg group h1 endowed with its carnot caratheodory distance by analyzing the first variation of area we characterize c2 area stationary surfaces as those with mean curvature zero or constant if a volume preserving condition is assumed and such that the characteristic curves meet orthogonally the singular curves moreover a minkowski type formula relating the area the mean curvature and the volume is obtained for volume preserving area stationary surfaces enclosing a given region as a consequence of the characterization of area stationary surfaces we refine the bernstein type theorem given in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 and nicola garofalo scott pauls the bernstein problem in the heisenberg group arxiv math dg 0209065 to describe all c2 entire area stationary graphs over the xy plane in a calibration argument shows that these graphs are globally area minimizing finally by using the description of the singular set in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 the characterization of area stationary surfaces and the ruling property of constant mean curvature surfaces we prove our main results where we classify area stationary surfaces in with or without a volume constraint and non empty singular set in particular we deduce the following counterpart to alexandrov uniqueness theorem in euclidean space any compact connected c2 surface in area stationary under a volume constraint must be congruent to a rotationally symmetric sphere obtained as the union of all the geodesics of the same curvature joining two points as a consequence we solve the isoperimetric problem in assuming c2 smoothness of the solutions 13 completely reducible hypersurfaces in a pencil pages 672 688 j v pereira s yuzvinsky preview pdf 324 k related articles 14 modules over motivic cohomology pages 689 727 oliver rondigs paul arne ostvaer preview pdf 303 k related articles 15 the fundamental group of period domains over finite fields pages 728 741 sascha orlik preview pdf 154 k related articles articles 1 15

computing the wave kernel matrix functions we derive an algorithm for computing the wave kernel functions cosh sqrt a and mathrm sinhc sqrt a for an arbitrary square matrix a where mathrm sinhc z sinh z z the algorithm is based on pade approximation and the use of double angle formulas we show that the backward error of any approximation to cosh sqrt a can be explicitly expressed in terms of a hypergeometric function to bound the backward error we derive and exploit a new bound for a k 1 k that is sharper than one previously obtained by al mohy and higham siam j matrix anal appl 31 2009 pp 970 989 the amount of scaling and the degree of the pade approximant are chosen to minimize the computational cost subject to achieving backward stability for cosh sqrt a in exact arithmetic numerical experiments show that the algorithm behaves in a forward stable manner in floating point arithmetic and is superior in this respect to the general purpose schur parlett algorithm applied to these functions

lipschitz continuity aleksandrov theorem and characterizations for h convex functions in the geometries of stratified groups we show that h convex functions locally bounded from above are locally lipschitz continuous and that the class of v convex functions exactly corresponds to the class of upper semicontinuous h convex functions as a consequence v convex functions are locally lipschitz continuous in every stratified group in the class of step 2 groups we characterize locally lipschitz h convex functions as measures whose distributional horizontal hessian is positive semidefinite in euclidean space the same results were obtained by dudley and reshetnyak we prove that a continuous h convex function is a e twice differentiable whenever its second order horizontal derivatives are radon measures

sub riemannian geometry of the coefficients of univalent functions abstract we consider coefficient bodies m n for univalent functions based on the lowner kufarev parametric representation we get a partially integrable hamiltonian system in which the first integrals are kirillov s operators for a representation of the virasoro algebra then m n are defined as sub riemannian manifolds given a lie poisson bracket they form a grading of subspaces with the first subspace as a bracket generating distribution of complex dimension two with this sub riemannian structure we construct a new hamiltonian system to calculate regular geodesics which turn to be horizontal lagrangian formulation is also given in the particular case m 3

existence of weak solutions to degenerate p laplacian equations and integral formulas abstract we study the problem of solving some general integral formulas and then apply the conclusions to obtain results about the existence of weak solutions of various degenerate p laplacian equations we adapt variational calculus methods and the mountain pass lemma without the palais smale condition and we use an abstract version of lions concentration compactness principle ii

area stationary surfaces inside the sub riemannian three sphere we consider the sub riemannian metric gh on mathbb s 3 given by the restriction of the riemannian metric of curvature 1 to the plane distribution orthogonal to the hopf vector field we compute the geodesics associated to the carnot caratheodory distance and we show that depending on their curvature they are closed or dense subsets of a clifford torus we study area stationary surfaces with or without a volume constraint in mathbb s 3 g h by following the ideas and techniques by ritore and rosales area stationary surfaces in the heisenberg group mathbb h 1 arxiv math dg 0512547 we introduce a variational notion of mean curvature characterize stationary surfaces and prove classification results for complete volume preserving area stationary surfaces with non empty singular set we also use the behaviour of the carnot caratheodory geodesics and the ruling property of constant mean curvature surfaces to show that the only c2 compact connected embedded surfaces in mathbb s 3 g h with empty singular set and constant mean curvature h such that h sqrt 1 h 2 is an irrational number are clifford tori finally we describe which are the complete rotationally invariant surfaces with constant mean curvature in mathbb s 3 g h

uniform consistency of kernel estimators of a regression function under generalized conditions abstract in this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data in addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous we consider the cases that some regressors are discrete and the data are either stationary mixing themselves or generated by a class of functions of one sided infinite stationary mixing sequences moreover we demonstrate the performance of the kernel estimation method under these generalized conditions by a numerical example

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

regression discontinuity designs with unknown discontinuity points testing and estimation abstract the regression discontinuity design has become a common framework among applied economists for measuring treatment effects a key restriction of the existing literature is the assumption that the discontinuity point is known which does not always hold in practice this paper extends the applicability of the regression discontinuity design by allowing for an unknown discontinuity point first we construct a unified test statistic to check whether there are selection or treatment effects our tests are shown to be consistent and local powers are derived also a bootstrap method is proposed to obtain critical values second we estimate the treatment effect by first estimating the nuisance discontinuity point it is shown that estimating the discontinuity point does not affect the efficiency of the treatment effect estimator simulation studies illustrate the usefulness of our procedures in finite samples

lq l holder continuity for quasilinear parabolic equations associated to sobolev derivations abstract let x be a locally compact metrizable space endowed with a couple of equivalent finite radon measures m and and let e be a hilbert c monomodule over c0 x we consider a class of abstract nonlinear parabolic equations defined as follows let be a closed derivation from l2 x m to l2 e and tt be the strongly continuous nonlinear semigroup naturally associated in the sense of brezis 1973 to the convex l s c functional e u x u x p d x where is the natural modulus function associated to e the generator of the semigroup considered is a natural generalization of the usual p laplacian operator we suppose that a suitable sobolev like inequality of the form u l2d d 2 x m c u l2 e holds true for some d 2 with p 2 d then tt is a nonlinear markov semigroup in the sense that it is order preserving and nonexpansive on each lq x m for any q 2 and moreover it satisfies ttu ttv l x m cm x t u v lq x m for all q 2 and suitable constants depending only on p q d examples include the semigroup generated by the p laplacian on finite measure manifolds with boundary and homogeneous dirichlet boundary conditions as well as by p laplacian like operators associated both to regular sub riemannian structures and to systems of possibly singular or degenerate vector fields satisfying the appropriate sobolev inequalities

wave equation for sums of squares on compact lie groups in this paper we investigate the well posedness of the cauchy problem for the wave equation for sums of squares of vector fields on compact lie groups we obtain the loss of regularity for solutions to the cauchy problem in local sobolev spaces depending on the order to which the hormander condition is satisfied but no loss in globally defined spaces we also establish gevrey well posedness for equations with irregular coefficients and or multiple characteristics as in the sobolev spaces if formulated in local coordinates we observe well posedness with the loss of local gevrey order depending on the order to which the hormander condition is satisfied

the union non union wage differential an application of semi parametric methods here we use a large sample of uk manual workers and compare estimates of the union wage differential obtained from a conventional heckman two step method of controlling for the potential endogeneity of union status with semi parametric estimates the semi parametric methodology yields slope coefficients very close to heckman two step and least squares that is much of the the difference in differentials between least squares and heckman semi parametric methods arises from the magnitude of the constant terms this is the source of the large union wage differentials obtained when self selection is taken into account all of our attempts to control for selection generate very different constant terms from ols so that despite our misgivings about identification of the constants we doubt the validity of the ols differentials

global behavior of the heat kernel associated with certain sub laplacians on semisimple lie groups abstract we prove global sharp estimates for the heat kernel related to certain sub laplacians on a real semisimple lie group from which we deduce an estimate for the corresponding green function

growth and convergence a profile of distribution dynamics and mobility in this paper we focus primarily on the dynamic evolution of the world distribution of growth rates in per capita gdp we propose new concepts and measures of convergence or divergence that are based on entropy distances and dominance relations between groups of countries over time we update the sample period to include the most recent decade of data available and we offer traditional parametric and new nonparametric estimates of the most widely used growth regressions for two important subgroups of countries oecd and non oecd traditional parametric models are rejected by the data however using robust nonparametric methods we find strong evidence in favor of polarization and within group mobility

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

isoholonomic problems and some applications we study the problem of finding the shortest loops with a given holonomy we show that the solutions are the trajectories of particles in yang mills potentials theorem 4 or equivalently the projections of kaluza klein geodesics theorem 2 applications to quantum mechanics berry s phase sect 3 and the optimal control of deformable bodies sect 6 are touched upon

on nonparametric multivariate binary discrimination aitchison aitken 1976 introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space the technique is designed for use in multivariate binary discrimination their estimator depends crucially on an unknown smoothing parameter a and aitchison aitken proposed a maximum likelihood method for determining a from the sample unfortunately this leads to an adaptive estimator which can behave very erratically when there are a number of empty or near empty cells present we demonstrate this both theoretically and by example to overcome these difficulties we introduce another method of estimating a which is designed to minimize a global function of the mean squared error

non minimality of corners in subriemannian geometry we give a short solution to one of the main open problems in subriemannian geometry namely we prove that length minimizers do not have corner type singularities with this result we solve problem ii of agrachev s list and provide the first general result toward the 30 year old open problem of regularity of subriemannian geodesics

on a class of semilinear evolution equations for vector potentials associated with maxwell s equations in carnot groups abstract in this paper we prove existence and regularity results for a class of semilinear evolution equations that are satisfied by vector potentials associated with maxwell s equations in carnot groups connected simply connected stratified nilpotent lie groups the natural setting for these equations is provided by the so called rumin s complex of intrinsic differential forms

nonlinear internal models for output regulation in this note we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems this result provides a significant enhancement of the nonequilibrium theory for output regulation which we have presented in a recent paper

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

on nonparametric discrimination using density differences summary we propose a technique for nonparametric discrimination in which smoothing parameters are chosen jointly according to a criterion based on the difference between two densities the approach is suitable for categorical continuous and mixed data and uses information from both populations to determine the smoothing parameter for any one population in the case of categorical data optimal performance is sometimes achieved using negative smoothing parameters a property which does not emerge if the smoothing parameters are chosen individually

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

robust output regulation with nonlinear exosystems for over a decade the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neutrally stable thus the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions in this paper we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems an example with the well known van der pol oscillator as the exosystem is given to illustrate our approach

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

smoothness of subriemannian isometries we show that the group of isometries i e distance preserving homeomorphisms of an equiregular subriemannian manifold is a finite dimensional lie group of smooth transformations the proof is based on a new pde argument in the spirit of harmonic coordinates establishing that in an arbitrary subriemannian manifold there exists an open dense subset where all isometries are smooth

duality on gradient estimates and wasserstein controls abstract we establish a duality between l p wasserstein control and l q gradient estimate in a general framework our result extends a known result for a heat flow on a riemannian manifold especially we can derive a wasserstein control of a heat flow directly from the corresponding gradient estimate of the heat semigroup without using any other notion of lower curvature bound by applying our result to a subelliptic heat flow on a lie group we obtain a coupling of heat distributions which carries a good control of their relative distance

path planning on compact lie groups using a homotopy method abstract in this paper we address the issue of solving the motion planning problems mpp for short for a class of left invariant control systems whose state spaces are semisimple compact lie groups the sub riemannian metrics induced by the dynamics of admit nontrivial abnormal extremals this fact a priori represents an obstruction for the procedure we use to tackle the mpp which consists of a homotopy or continuation method we are however able to provide complete answers for the mpp

sub riemannian calculus on hypersurfaces in carnot groups we develop a sub riemannian calculus for hypersurfaces in graded nilpotent lie groups we introduce an appropriate geometric framework such as horizontal levi civita connection second fundamental form and horizontal laplace beltrami operator we analyze the relevant minimal surfaces and prove some basic integration by parts formulas using the latter we establish general first and second variation formulas for the horizontal perimeter in the heisenberg group such formulas play a fundamental role in the sub riemannian bernstein problem

boundedness and regularity of solutions of degenerate elliptic partial differential equations abstract we study quasilinear degenerate equations with their associated operators satisfying sobolev and poincare inequalities our problems are similar to those in sawyer and wheeden 2006 20 but we consider more general integral equations on abstract sobolev spaces indeed we provide a unified approach via abstract setting our main tool is moser iteration we obtain boundedness assuming a weighted sobolev embedding of weak solutions and also harnack inequalities for nonnegative solutions assuming further that a weighted poincare inequality holds for their logarithm and existence of a sequence of cutoff functions and hence holder s continuity of solutions our assumption is weaker than the above mentioned paper and other existing papers even in the case where the setting is on r n for example we do not assume any doubling condition and we are able to deal with weighted estimates our results are new even when the leading term in the equations are vector fields that satisfy hormander s conditions

semi global robust output regulation of minimum phase nonlinear systems based on high gain nonlinear internal model we consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum phase nonlinear systems with rth degree r 2 the robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high gain nonlinear internal model perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system which satisfies some general immersion assumption the state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold furthermore the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high gain observer to robustly estimate the derivatives of the regulated output error the stabilisation analysis of the resulting closed loop systems leads to regional as wel

consistent specification tests for semiparametric nonparametric models based on series estimation methods abstract this paper considers the problem of consistent model specification tests using series estimation methods the null models we consider in this paper all contain some nonparametric components a leading case we consider is to test for an additive partially linear model the null distribution of the test statistic is derived using a central limit theorem for hilbert valued random arrays the test statistic is shown to be able to detect local alternatives that approach the null models at the order of op n 1 2 we show that the wild bootstrap method can be used to approximate the null distribution of the test statistic a small monte carlo simulation is reported to examine the finite sample performance of the proposed test we also show that the proposed test can be easily modified to obtain series based consistent tests for other semiparametric nonparametric models

intrinsic random walks and sub laplacians in sub riemannian geometry on a sub riemannian manifold we define two type of laplacians the macroscopic laplacian as the divergence of the horizontal gradient once a volume is fixed and the microscopic laplacian as the operator associated with a geodesic random walk we consider a general class of random walks where all sub riemannian geodesics are taken in account this operator depends only on the choice of a complement c to the sub riemannian distribution and is denoted l c we address the problem of equivalence of the two operators this problem is interesting since on equiregular sub riemannian manifolds there is always an intrinsic volume e g popp s one p but not a canonical choice of complement the result depends heavily on the type of structure under investigation on contact structures for every volume there exists a unique complement c such that l c on carnot groups if h is the haar volume then there always exists a complement c such that h l c however this complement is not unique in general for quasi contact structures in general p l c for any choice of c in particular l c is not symmetric w r t popp s measure this is surprising especially in dimension 4 where in a suitable sense p is the unique intrinsic macroscopic laplacian a crucial notion that we introduce here is the n intrinsic volume i e a volume that depends only on the set of parameters of the nilpotent approximation when the nilpotent approximation does not depend on the point a n intrinsic volume is unique up to a scaling by a constant and the corresponding n intrinsic sub laplacian is unique this is what happens for dimension smaller or equal than 4 and in particular in the 4 dimensional quasi contact structure mentioned above

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

output regulation of uncertain nonlinear systems with nonlinear exosystems an adaptive control algorithm is proposed for output regulation of uncertain nonlinear systems in output feedback form under disturbances generated from nonlinear exosystems a new nonlinear internal model is proposed to generate the desired input term for suppression of the disturbances the proposed internal model design is based on boundedness of the disturbance high gain design and saturation it is capable to tackle disturbances in any specified initial conditions some uncertainties in the systems are allowed provided that they do not affect the desired feedforward control term and they are tackled by using nonlinear dominant functions and an adaptive control coefficient the proposed control algorithm ensures the global convergence of the state variables to the invariant manifold which implies that the measurement or the tracking error approaches to zero asymptotically

decay estimates for the linear damped wave equation on the heisenberg group abstract this paper is devoted to the derivation of l 2 l 2 decay estimates for the solution of the homogeneous linear damped wave equation on the heisenberg group h n for its time derivative and for its horizontal gradient moreover we consider the improvement of these estimates when further l 1 h n regularity is required for the cauchy data our approach will rely strongly on the group fourier transform of h n and on the properties of the hermite functions that form a maximal orthonormal system for l 2 r n of eigenfunctions of the harmonic oscillator

curvature in sub riemannian geometry we study curvature problems on a nearly riemannian manifold which is a sub riemannian manifold m hm g vm whose adapted tensor field given by 2 2 vanishes identically first we prove the existence and uniqueness of what we call horizontal riemannian connection which is a torsion free and metric linear connection on the horizontal distribution hm then we define the horizontal sectional curvature of m and study nearly riemannian space forms which are nearly riemannian manifolds of constant horizontal sectional curvature several horizontal geometric objects are introduced and studied for example horizontal ricci tensor horizontal scalar curvature horizontal laplacian finally as a prelude to applications to kaluza klein theories we define the horizontal einstein gravitational tensor field and show that its horizontal divergence vanishes identically on m some examples are presented to illustrate the theory developed in the paper

a consistent model specification test with mixed discrete and continuous data in this paper we propose a nonparametric kernel based model specification test that can be used when the regression model contains both discrete and continuous regressors we employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross validation cv methods the test statistic is shown to have an asymptotic normal null distribution we also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic the bootstrap being our preferred method for obtaining the null distribution in practice simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency based nonparametric estimators that require sample splitting to handle the presence of discrete regressors