We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.
Let $G$ be a graph with vertex set $V(G)$, and let $k\ge 1$ be an integer. A subset $D \subseteq V(G)$ is called a {\it $k$-dominating set} if every vertex $v\in V(G)-D$ has at least $k$ neighbors in $D$. The $k$-domination number $\gamma _k(G)$ of $G$ is the minimum cardinality of a $k$-dominating set in $G$. If $G$ is a graph with minimum degree $\delta (G)\ge k+1$, then we prove that $$\gamma _{k+1}(G)\le \frac {|V(G)|+\gamma _k(G)}2.$$ In addition, we present a characterization of a special class of graphs attaining equality in this inequality.
Fuzzy transform is a new type of function transforms that has been successfully used in different applications. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.
Let $\mathbb N$ be the set of nonnegative integers and $\mathbb Z$ the ring of integers. Let $\mathcal B$ be the ring of $N \times N$ matrices over $\mathbb Z$ generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of $\mathcal B$ yields that the subrings generated by them coincide. This subring is the sum of the ideal $\mathcal F$ consisting of all matrices in $\mathcal B$ with only a finite number of nonzero entries and the subring of $\mathcal B$ generated by the identity matrix. Regular elements are also described. We characterize all ideals of $\mathcal B$, show that all ideals are finitely generated and that not all ideals of $\mathcal B$ are principal. Some general ring theoretic properties of $\mathcal B$ are also established.
The increasing availability of computing power in the past two decades has been used to develop new techniques for optimizing the solution of estimation problem. Today's computational capacity and the widespread availability of computers have enabled the development of a new generation of intelligent computing techniques, such as the algorithm of our interest. This paper presents a new member of the class of stochastic search algorithms (known as Canonical Genetic Algorithm "CGA") for optimizing the maximum likelihood function ln (L(θ, σa2 )) of the first order moving average MA(1) model. The presented strategy is composed of three main steps: recombination, mutation, and selection. The experimental design is based on simulating the CGA with different values of (θ), and sample size n. The results are compared with those of moment method. Based on MSE value obtained from both methods, one can conclude that CGA can give estimators (\hat \theta) for MA(1) parameter which are good and more reliable than those estimators obtained by moment method.
The Cantor-Bernstein theorem was extended to $\sigma $-complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to $\sigma $-complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.
We continue in the direction of the ideas from the Zhang's paper \cite{Z} about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči \cite{K1}): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity properties with mapping defining generalized concept lattice as fuzzifications of Zhang's ones.
Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis., Hongfen Yuan., and Obsahuje bibliografické odkazy