on the minimum of the christoffel function abstract we consider the christoffel function n d associated with a measure d on a compact interval and the question where the minimum of the christoffel function is attained sufficient conditions on the coefficients appearing in the continued fraction expansion of the stieltjes transform are obtained for the n th christoffel function to attain its minimum at the boundary points of the underlying interval in contrary to several monotonicity results for christoffel functions in the literature our approach does not require the absolute continuity of the measure with respect to the lebesgue measure

optimal discrimination designs for multifactor experiments in this paper efficient designs are determined when anderson s procedure is applied in order to identify the degree of a multivariate polynomial regression model it is shown that the optimal designs are very closely related to model robust designs which maximize a weighted p mean of d efficiencies as a consequence we obtain designs with high efficiency for model discrimination and for the statistical analysis in the identified model

iterative learning control for a class of nonlinear systems abstract for precise tracking control of a class of nonlinear systems over a finite time interval an iterative learning control method using the relative degree of a system is proposed the class of nonlinear systems where the iterative learning control is applied can be extended by using the proposed method a sufficient condition is derived for guaranteeing a uniform convergence of the output to the desired output the results obtained for a class of nonlinear systems are shown to be a generalization of the existing results for linear time invariant systems

brief on the equivalence of causal lti iterative learning control and feedback control the goal of iterative learning control ilc is to improve the accuracy of a system that repeatedly follows a reference trajectory this paper proves that for each causal linear time invariant ilc there is an equivalent feedback that achieves the ultimate ilc error with no iterations remarkably this equivalent feedback depends only on the ilc operators and hence requires no plant knowledge this equivalence is obtained whether or not the ilc includes current cycle feedback if the ilc system is internally stable and converges to zero error there exists an internally stabilizing feedback that approaches zero error at high gain since conventional feedback requires no iterations there is no reason to use causal ilc

uniqueness results for inverse robin problems with bounded coefficient in this paper we address the uniqueness issue in the classical robin inverse problem on a lipschitz domain omega subset rr n with l infty robin coefficient l 2 neumann data and isotropic conductivity of class w 1 r omega r n we show that uniqueness of the robin coefficient on a subpart of the boundary given cauchy data on the complementary part does hold in dimension n 2 but needs not hold in higher dimension we also raise on open issue on harmonic gradients which is of interest in this context

optimal designs for comparing curves we consider the optimal design problem for a comparison of two regression curves which is used to establish the similarity between the dose response relationships of two groups an optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions optimal design theory equivalence theorems efficiency bounds is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly the results are illustrated in several examples modeling dose response relationships it is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models in particular it is shown that the use of the optimal designs proposed in this paper instead of commonly used non optimal designs yields a reduction of the width of the confidence band by more than 50

an anisotropic inverse boundary value problem we consider the impedance tomography problem for anisotropic conductivities given a bounded region in space a diffeomorphism from to itself which restricts to the identity on and a conductivity on it is easy to construct a new conductivity which will produce the same voltage and current measurements on we prove the converse in two dimensions i e if 1 and 2 produce the same boundary measurements then 1 2 for an appropriate for conductivities which are near a constant

stability of learning control with disturbances and uncertain initial conditions the authors investigate the effects of state disturbances output noise and errors in initial conditions on a class of learning control algorithms they present a simple learning algorithm and exhibit via a concise proof bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories furthermore these bounds are continuous functions of the bounds on the initial condition errors state disturbances and output noise and the bounds are zero in the absence of these disturbances

experimental designs for model discrimination abstract we present designs that perform well for several objectives simultaneously three different approaches are discussed to augment a given design in an optimal way to evaluate a mixture of the various criteria and to optimize one objective subject to achieving a prescribed efficiency level for the others our sample designs are for the situation of discriminating between a second and third degree polynomial fit under the d criterion and geometric mixtures of d criteria

on g efficiency calculation for polynomial models we study properties of the variance function of the least squares estimator for the response surface for polynomial models we identify a class of approximate designs for which their variance functions are maximized at the extreme points of the design space as an application we examine robustness properties of d optimal designs and d n r optimal designs under various polynomial model assumptions analytic formulas for the g efficiencies of these designs are derived along with their d efficiencies

the determination of the surface impedance of an obstacle from measurements of the far field pattern we consider the problem of determining the surface impedance of an obstacle from measurements of the far field pattern of a scattered time harmonic acoustic wave it is shown that this problem can be stabilized by assuming that the impedance is holder continuous with an a priori bound given on the impedance and its holder coefficient a constructive method for determining the impedance is given through the use of the backus gilbert method for solving improperly posed moment problems

bayesian d optimal designs on a fixed number of design points for heteroscedastic polynomial models summary we consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially however this dependence is not known precisely and additional parameters are required in the model our design criteria permit various subsets of the parameters to be estimated with different emphasis bayesian d optimal designs on a compact interval with the number of support points restricted to be one more than the degree of the polynomial are found analytically for a large class of priors these designs may or may not be optimal within the class of all designs depending on the prior distribution

optimal designs for identifying the degree of a polynomial regression if an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations anderson showed that the following method is optimal starting with the highest specified degree the procedure is to test in sequence whether the coefficients are 0 in this paper optimal designs for anderson s procedure are determined explicitly the optimal design maximizes the minimum power of a given set of alternatives

hardy spaces of the conjugate beltrami equation we study hardy spaces of solutions to the conjugate beltrami equation with lipschitz coefficient on dini smooth simply connected planar domains in the range of exponents 1 infty we analyse their boundary behaviour and certain density properties of their traces we derive on the way an analog of the fatou theorem for the dirichlet and neumann problems associated with the equation mbox div sigma nabla u 0 with l p boundary data

the neumann problem for elliptic equations with non smooth coefficients in this paper we study the neumann and regularity problems for divergence form symmetric elliptic operators l div av where a aifix is a matrix of bounded measurable functions and ellipticity is the existence of a 0 such that 2 114 2 ais ir 21412 for all i r we assume that l is defined in the unit ball b but the methods of proof are sufficiently general to allow b to be a bounded starlike lipschitz domain the neumann problem lu 0 in b avun q f

optimal designs for a class of polynomials of odd or even degree prior y y1 v y d where the numbers yj correspond to the models of degree 2j 1 2j for j 1 r for a special class of priors optimal designs of a very simple structure are calculated generalizing the d1 optimal design for polynomial regression of degree 2r 1 2r the support of these designs splits up in three sets and the masses of the optimal design at the support points of every set are all equal the results are derived in a general context using the theory of canonical moments and continued fractions some applications are given to the d optimal design problem for polynomial regression with vanishing coefficients of odd or even powers

predictive optimal iterative learning control a new optimization based iterative learning control algorithm is proposed and its properties derived an important characteristic of this algorithm is that it uses present and future predicted errors to compute the current control in a similar manner to model based predictive control using a receding horizon in particular it enables the algorithm designer to achieve good control over convergence rate the actual implementation has a multimodel structure but uses standard linear quadratic regulator methods for a causal formulation in the iterative learning sense of what is originally a non causal algorithm the results are illustrated by simulations

an iterative learning control theory for a class of nonlinear dynamic systems abstract an iterative learning control scheme is presented for a class of nonlinear dynamic systems which includes holonomic systems as its subset the control scheme is composed of two types of control methodology a linear feedback mechanism and a feedforward learning strategy at each iteration the linear feedback provides stability of the system and keeps its state errors within uniform bounds the iterative learning rule on the other hand tracks the entire span of a reference input over a sequence of iterations the proposed learning control scheme takes into account the dominant system dynamics in its update algorithm in the form of scaled feedback errors in contrast to many other learning control techniques the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes external input perturbations as a prerequisite the convergence proof of the proposed learning scheme is given under minor conditions on the system parameters

c1 domains and unique continuation at the boundary it is shown that the square of a nonconstant harmonic function u that either vanishes continuously on an open subset v contained in the boundary of a dini domain or whose normal derivative vanishes on an open subset v in the boundary of a c1 1 domain in d satisfies the doubling property with respect to balls centered at points q v under any of the above conditions the module of the gradient of u is a b2 d weight when restricted to v and the hausdorff dimension of the set of points q v u q 0 is less than or equal to d 2 these results are generalized to solutions to elliptic operators with lipschitz second order coefficients and bounded coefficients in the lower order terms 1997 john wiley sons inc