Global stabilization of a certain class of nonlinear systems

Systems are considered which can be reduced to a regular form and possess an invariant manifold such that the restriction of the system to the manifold is globally asymptotically stable (GAS). We construct a feedback which renders the manifold globally attracting. It was proved that in this situation boundedness of all orbits is necessary and sufficient for the control system to be GAS. A Lyapunov type condition for the latter property adapted to the situation in question is given. Results of Andreini, Bacciotti, and Stefani are shown to be a special case of our result.     

Stability of a certain class of hybrid dynamical systems

In this work we introduce a type of hybrid equation closely related to those that appear when a digital controller or a hybrid controller of a certain class is interconnected with a full non-linear continuous-time system. For these equations we obtain results concerning existence, uniqueness and noncontinuability of solutions. This results are used to study the behaviour of the hybrid dynamical systems associated with those equations. We establish relationships between the stability of these hybrid dynamical systems and the ones corresponding to their associated discretized systems on one hand, and to their associated linearized systems on the other. We also characterize their stability, uniform asymptotic stability and exponential stability. These results are applied to the exponential stabilization of a non-linear control system by digital or hybrid controllers.     

Adaptive finite elements for a certain class of variational inequalities of second kind

In this note, we extend our studies on finite element Galerkin schemes for elliptic variational inequalities of first to the one of second kind. Especially we perform the corresponding a posteriori error analysis for a simple friction problem and a model flow of a Bingham fluid.     

Computing P-values for a class of permutation tests of equal survival functions

Dallas and Rao (Biometrics 56 (2000) 154) proposed a class of permutation tests for testing the equality of two survival distributions based on randomly right censored survival time data consisting of both paired and unpaired observations. Data sets of this type can occur frequently in medical settings. Two members of this class were advocated for use due to their generally high power for detecting scale and location shifts in the exponential and log-logistic distributions for the survival times, and improved power over paired data test procedures that disregard unpaired observations. Because the computations for the tests become quite laborious as the sample sizes increase, computing routines are required for practical implementation of these tests. This paper provides computing routines to execute the tests.     

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard’s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28, 3–32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian Journal of Probability and Statistics 19, 13–31]. We show that, for our model, Skovgaard’s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed.     

A certain class of starlike functions

This paper presents a new class of functions analytic in the open unit disc, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well known classes. The paper deals with several ideas and techniques used in geometric function theory. The order of starlikeness in the class of convex functions of negative order is also considered here.     

Determining optical flow for irregular domains by minimizing quadratic functionals of a certain class

Snyder (1989) has recently classified all smoothness terms which involve first-order derivatives of the flowfield u(x, t) and of the image grey-value function g(x, t). The physically plausible smoothness terms belonging to this class are known from the work of Horn and Schunck (1981) and Nagel (1987).In this paper we discuss the possibilities of approximating the solutions to the minimization problems of Horn & Schunk (1981) and Nagel (1987). In particular, it is shown that these solutions exist, are unique, and depend continuously on the input data. These properties make it possible, while taking into consideration arbitrary models of the grey-value function, to approximate efficiently the (weak) solutions of the associated boundary-value problems in irregularly shaped domains (with a sufficiently smooth boundary) using finite elements.Experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in Nagel's approach influences the results.