Convergence in, or with respect to, s-additive measure, in particular, convergence in probability, can be taken as an important notion of the standard measure and probability theory, and as a powerful tool when analyzing and processing sequences of subsets of the universe of discourse and, more generally, sequences of real-valued measurable functions defined on this universe. Our aim is to propose an alternative of this notion of convergence supposing that the measure under consideration is a (complete) non-numerical and, in particular, lattice-valued possibilistic measure, i.e., a set function obeying the demand of (complete) maxitivity instead of that of s-additivity. Focusing our attention to sequences of sets converging in a lattice-valued possibilistic measure, some more or less elementary properties of such sequences are stated and proved.
This paper investigates a split-complex backpropagation algorithm with momentum (SCBPM) for complex-valued neural networks. Convergence results for SCBPM are proved under relaxed conditions and compared with the existing results. Monotonicity of the error function during the training iteration process is also guaranteed. Two numerical examples are given to support the theoretical findings.
In this research, strong convergence properties of the tail probability for weighted sums of negatively orthant dependent random variables are discussed. Some sharp theorems for weighted sums of arrays of rowwise negatively orthant dependent random variables are established. These results not only extend the corresponding ones of Cai \cite{4}, Wang et al. \cite{19} and Shen \cite{13}, but also improve them, respectively.
We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence $(f_n)$ of functions from a measure space to a Banach space. In one result the equi-integrability of $f_n$'s is involved and we assume $f_n\to f$ almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of $(f_n)$ to $f$ is assumed.
We give a definition of uniform PU-integrability for a sequence of /i-measurable real functions defined on an abstract metric space and prove that it is not equivalent to the uniform p-integrability.
Consider the delay differential equation (1) ˙x(t) = g(x(t), x(t − r)), where r > 0 is a constant and g : 2 → is Lipschitzian. It is shown that if r is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.
The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of this paper is a converse Lyapunov Theorem for practical asymptotic stable impulsive systems. Applying our converse Theorem, several criteria on practical asymptotic stability of the solution of perturbed impulsive systems and cascade impulsive systems are established. Finally, some examples are given to show the effectiveness of the derived results.
The aim of this study is to explore the sources of attitude constraints regarding the role of government in the economy, and to find out whether the sources of these constraints are the same as in Western democracies. Use is made of Converse’s approach to conceptualize attitude constraint where an individual’s belief system is seen to be a configuration of attitudes and values characterized by a functional interdependence, or constraint. This constraint may be interpreted in terms of the probability of being able to predict one attitude having knowledge of another. In this study, there is a review of the sources of attitude constraint and related measurement issues. Using ISSP 2006 (Role of Government module) an analysis of attitudinal constraints is presented using two attitudinal scales. This research confirms that the sources of attitude constraint in the Czech Republic are similar to those observed in Western Europe and the USA. Specifically, class, education, and other social-demographic variables are shown to have very limited effects. Moreover, Converse’s contention that attitude constraints are strongly determined by political involvement, political knowledge, or party identification is also shown to be valid for Czech society., Lukáš Linek., 1 obrázek, 4 tabulky, Obsahuje bibliografii, and Anglické resumé
For a pseudo $MV$-algebra $\mathcal A$ we denote by $\ell (\mathcal A)$ the underlying lattice of $\mathcal A$. In the present paper we investigate the algebraic properties of maximal convex chains in $\ell (\mathcal A)$ containing the element 0. We generalize a result of Dvurečenskij and Pulmannová.