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.
A thioredoxin-like protein (txl) gene was cloned from the bumblebee, Bombus ignitus. The B. ignitus txl (Bitxl) gene spans 1777 bp and consists of three introns and four exons coding for 285 amino acid residues with a conserved active site (CGPC). The deduced amino acid sequence of the Bitxl cDNA was 65% similar to the Drosophila melanogaster txl. Northern blot analysis revealed the presence of Bitxl transcripts in all tissues examined. When H2O2 was injected into the body cavity of B. ignitus workers, Bitxl mRNA expression was up-regulated in the fat body tissue. In addition, the expression levels of Bitxl mRNA in the fat body greatly increased when B. ignitus workers were exposed to low (4°C) or high (37°C) temperatures, or injected with lipopolysaccharide (LPS), which suggests that the Bitxl possibly protects against oxidative stress caused by extreme temperatures and bacterial infection.
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.
Small bowel obstruction is a common clinical problem presenting with abdominal distention, colicky pain, absolute constipation and bilious vomiting. There are numerous causes, most commonly attributed to an incarcerated hernia, adhesions or obstructing mass secondary to malignancy. Here we present an unusual cause of a small bowel obstruction secondary to an incarcerated incisional hernia in association with an acute organoaxial gastric volvulus. and N. R. Kosai, H. S. Gendeh, M. Noorharisman, P. A. Sutton, S. Das