On the Unit Graph of a Noncommutative Ring

Let $R$ be a ring (not necessary commutative) with non-zero identity. The unit graph of $R$, denoted by $G(R)$, is a graph with elements of $R$ as its vertices and two distinct vertices $a$ and $b$ are adjacent if and only if $a+b$ is a unit element of $R$. It was proved that if $R$ is a commutative ring and \fm is a maximal ideal of $R$ such that |R/\fm|=2, then $G(R)$ is a complete bipartite graph if and only if (R, \fm) is a local ring. In this paper we generalize this result by showing that if $R$ is a ring (not necessary commutative), then $G(R)$ is a complete $r$-partite graph if and only if (R, \fm) is a local ring and $r=|R/m|=2^n$, for some $n \in \N$ or $R$ is a finite field. Among other results we show that if $R$ is a left Artinian ring, $2 \in U(R)$ and the clique number of $G(R)$ is finite, then $R$ is a finite ring.Comment: 6 pages. To appear in Algebra Colloquiu

Exploring field scale salinity using simulation modeling, example for Rudasht area, Esfahan Province, Iran

Salinity / Simulation models / Soil-water-plant relationships / Soil properties / Climate / Irrigated farming / Water quality / Iran / Esfahan Province / Rudasht Area

Effect of different levels of dietary betaine on growth performance, food efficiency and survival rate of pike perch (Sander lucioperca) fingerlings

A 6-week feeding experiments were carried out to determine the effects of different levels of dietary betaine on growth performance, food efficiency and survival rate of pike perch which has a critical period during transition feeding. Fingerlings of pike perch were fed with live food (treatment A), without betaine added to biomar (treatment B), 1% betaine added to biomar (treatment C) and 2% betaine added to biomar (treatment D) in 1000 l concreted tanks. 200 fingerlings (1.50 g, mean weight) were stocked in each tank and fed up to 7 meals per day. Higher increment in body weight (4.99 ± 0.73 g), specific growth rate (3.90 ± 0.06) and food efficiency (104.42 ± 4.27) were obtained with treatment D (2% betaine added to biomar). This treatment also showed significant (P<0.05) decrease in food conversion ratio (0.93 ± 0.04) in comparison with other treatments. Highest survival rate was observed in treatment B (biomar without betaine) with a 34.5 % rate and greatest cannibalism (1.03 ± 0.01) was found in treatment D, respectively. It was concluded that betaine could increase the palatability and acceptability of food and could be suitable to weaning the pike perch fingerlings to artificial diet

Intensity Separation based Iris Recognition Method using Curvelets and PCA

This paper presents a PCA-based iris recognition method called Intensity Separation Curvelet based PCA (ISCPCA). The proposed method uses Canny Edge detection and the Hough transform to extract and rectangularize the iris from the input eye image. The second generation Fast Digital Curvelet Transform (FDCT) is then applied to the resulting image, dividing it into its subbands. The resulting complex subbands coefficients within the same level are concatenated, generating two single frames. The coefficients in each resulting frame are then normalized and evenly divided into a preselected number of bands. The coefficient matrices within each frame are then vectorized and concatenated, generating a single 2D matrix. Conventional PCA is then performed on the resulting 2D matrix extracting its eigenvectors which are used for iris matching. The Euclidean distance is used as a measure to quantify the closeness of different iris images. Experimental results on images from the CASIA-Iris-Interval benchmark eye image dataset show that the proposed ISC-PCA technique significantly outperforms the state of the art PCA based methods, and achieves competitive results to those of the learning based techniques

Sharing your assets? A holistic review of the sharing economy

Even though academics and practitioners extensively apply the notion of the sharing economy (SE), the conceptualization and the literature construction remained disjointed and dispersed due to the lack of a rigorous attempt to understand the core concept of the SE. This concept is multidimensional, which makes its investigation essential for practitioners and academics. Based on a 15-year data set collected from the Web of Science database, our paper seeks to provide a pervasive science plot of the intellectual structure of the SE field. A bibliometric review method was used by studying documents published from 2005 to 2020, using the VOSviewer, Bibexcel, SPSS, and GunnMap2 software. Providing an overview of articles, authors, the most influential journals, and themes of research, we contribute to the literature on the SE by identifying and proposing six research groups in MDS analysis, six research clusters in HCA analysis, and future study directions. Eventually, the research acknowledges the theoretical contribution, the limits of the present study, and recommends further study directions

Trees with a large Laplacian eigenvalue multiplicity

In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than $1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order $n$ that have a multiplicity that is close to the upper bound $\frac{n-3}{2}$, and emphasize the particular role of the algebraic connectivity.Comment: 11 pages, 5 figure

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.Comment: 19 pages, 4 figure

CFA optimizer: A new and powerful algorithm inspired by Franklin's and Coulomb's laws theory for solving the economic load dispatch problems

Copyright © 2018 John Wiley & Sons, Ltd. This paper presents a new efficient algorithm inspired by Franklin's and Coulomb's laws theory that is referred to as CFA algorithm, for finding the global solutions of optimal economic load dispatch problems in power systems. CFA is based on the impact of electrically charged particles on each other due to electrical attraction and repulsion forces. The effectiveness of the CFA in different terms is tested on basic benchmark problems. Then, the quality of the CFA to achieve accurate results in different aspects is examined and proven on economic load dispatch problems including 4 different size cases, 6, 10, 15, and 110-unit test systems. Finally, the results are compared with other inspired algorithms as well as results reported in the literature. The simulation results provide evidence for the well-organized and efficient performance of the CFA algorithm in solving great diversity of nonlinear optimization problems