Continuous Dependence of Bounded Φ-variation Solutions on Parameter for a Class of Discontinuous Systems

The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.

Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations

The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.

On Second Riesz Φ-Variation of Normed Space Valued Maps

In this article we present a Riesz-type generalization of the concept of second variation of normed space valued functions defined on an interval [a,b]R. We show that a function f [a,b], where X is a reflexive Banach space, is of bounded second Φ-variation, in the sense of Riesz, if and only if it can be expressed as the (Bochner) integral of a function of bounded (first) $\Phi$-variation. We provide also a Riesz lemma type inequality to estimate the total second Riesz-Φ-variation introduced.

The Space of Bounded p(·)-Variation in Wiener’s Sense with Variable Exponent

In this paper, we proof some properties of the space of bounded p(·)-variation in Wiener’s sense. We show that a functions is of bounded p(·)-variation in Wiener’s sense with variable exponent if and only if it is the composition of a bounded nondecreasing functions and h?lderian maps of the variable exponent. We show that the composition operator H, associated with , maps the spaces into itself if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable.

The Space of Bounded p(·)-Variation in the Sense Wiener-Korenblum with Variable Exponent

In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.

Functions of Bounded （p（·), 2)-Variation in De la Vallee Poussin-Wiener’s Sense with Variable Exponent

In this paper we establish the notion of the space of bounded ?(p(⋅), 2)variation in De la Vallée Poussin-Wiener’s sense with variable exponent. We show some properties of this space and we show that any uniformly bounded composition operator that maps this space into itself necessarily satisfies the so-called Matkowski’s conditions.

Construction of <i>k</i>-Variate Survival Functions with Emphasis on the Case <i>k</i>= 3

The purpose of this paper is to present a general universal formula for k-variate survival functions for arbitrary k = 2, 3, ..., given all the univariate marginal survival functions. This universal form of k-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case k = 2 and the main results for the case k = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general k ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the k = 3 and k ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the k-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the copula methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.

A new control law based on characteristic exponent assignment for libration point orbit maintenance

A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.

Locally Defined Operators and Locally Lipschitz Composition Operators in the Space WBVp(·)([a, b])

We give a neccesary and sufficient condition on a function such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(&#183;)-variation with variable exponent functions into itself is a Nemytskij com-position operator.