Ordering results for series and parallel systems comprising heterogeneous exponentiated Weibull components

In this paper, we discuss the usual stochastic and reversed hazard rate orders between the series and parallel systems from two sets of independent heterogeneous exponentiated Weibull components. We also obtain the results concerning the convex transform orders between parallel systems and obtain necessary and sufficient conditions under which the dispersive and usual stochastic orders, and the right spread and increasing convex orders between the lifetimes of the two systems are equivalent. Finally, in the multiple-outlier exponentiated Weibull models, based on weak majorization and p-larger orders between the vectors of scale and shape parameters, some characterization results for comparing the lifetimes of parallel and series systems are also established, respectively. The results of this paper can be used in practical situations to find various bounds for the important aging characteristics of these systems.     

Internal Migration of Ethno‐national Minorities: The Case of Arabs in Israel

Recent scholarship emphasizes differences among ethnic groups' internal migration patterns. Yet, with few exceptions, research has focused on the Anglo‐American world, neglecting experiences from other regions. This paper is part of a larger research project that studies mobility among the Arab minority in Israel and its driving forces. In this paper we examine patterns of internal migration by analysing the propensity to migrate as well as migrants' individual and social characteristics. First, we survey the theoretical backdrop that is suggested by recent geographic literature on internal migration among ethnic and racial minorities, including native groups. Second, we contextualize the group studied, providing necessary background information on the political, socio‐economic and demographic conditions of Arabs in Israel. We briefly discuss attributes that are – or have been – potential hindering factors to Arab mobility in the Jewish state. Finally, we analyse 1995 national census data at the micro scale and provide a basis for future explanations of the phenomenon. We conclude by outlying some future directions in the study of internal migration of minorities in Israel.     

An Agent‐Based Model for Pathogen Persistence and Cross‐Contamination Dynamics in a Food Facility

We used an agent‐based modeling (ABM) framework and developed a mathematical model to explain the complex dynamics of microbial persistence and spread within a food facility and to aid risk managers in identifying effective mitigation options. The model explicitly considered personal hygiene practices by food handlers as well as their activities and simulated a spatially explicit dynamic system representing complex interaction patterns among food handlers, facility environment, and foods. To demonstrate the utility of the model in a decision‐making context, we created a hypothetical case study and used it to compare different risk mitigation strategies for reducing contamination and spread of Listeria monocytogenes in a food facility. Model results indicated that areas with no direct contact with foods (e.g., loading dock and restroom) can serve as contamination niches and recontaminate areas that have direct contact with food products. Furthermore, food handlers’ behaviors, including, for example, hygiene and sanitation practices, can impact the persistence of microbial contamination in the facility environment and the spread of contamination to prepared foods. Using this case study, we also demonstrated benefits of an ABM framework for addressing food safety in a complex system in which emergent system‐level responses are predicted using a bottom‐up approach that observes individual agents (e.g., food handlers) and their behaviors. Our model can be applied to a wide variety of pathogens, food commodities, and activity patterns to evaluate efficacy of food‐safety management practices and quantify contamination reductions associated with proposed mitigation strategies in food facilities.     

Goodness-of-fit tests based on Verma Kullback–Leibler information

In this article, a new consistent estimator of Veram’s entropy is introduced. We establish the entropy test based on the new information namely Verma Kullback–Leibler discrimination methodology. The results are used to introduce goodness-of-fit tests for normal and exponential distributions. The root of mean square errors, critical values, and powers for some alternatives are obtained by simulation. The proposed test is compared with other tests.     

Some Results Based on a Version of the Generalized Dynamic Entropies

We propose new dynamic measures of uncertainty based on the notion of generalized dynamic entropy introduced in Di Crescenzo and Longobardi (2006). These can uniquely determine distribution functions in continuous and discrete cases, and the characterizations of some well-known distributions are provided. We also define some orderings and aging notions based on the generalized dynamic measures, and prove some of their properties, obtaining as corollaries results that have recently appeared in the literature.     

On the odd girth and the circular chromatic number of generalized Petersen graphs

A class \(\mathcal{G}\) of simple graphs is said to be girth-closed (odd-girth-closed) if for any positive integer g there exists a graph \(\mathrm {G} \in \mathcal{G}\) such that the girth (odd-girth) of \(\mathrm {G}\) is \(\ge g\). A girth-closed (odd-girth-closed) class \(\mathcal{G}\) of graphs is said to be pentagonal (odd-pentagonal) if there exists a positive integer \(g^*\) depending on \(\mathcal{G}\) such that any graph \(\mathrm {G} \in \mathcal{G}\) whose girth (odd-girth) is greater than \(g^*\) admits a homomorphism to the five cycle (i.e. is \(\mathrm {C}_{_{5}}\)-colourable). Although, the question “Is the class of simple 3-regular graphs pentagonal?” proposed by Ne?et?il (Taiwan J Math 3:381–423, 1999) is still a central open problem, Gebleh (Theorems and computations in circular colourings of graphs, 2007) has shown that there exists an odd-girth-closed subclass of simple 3-regular graphs which is not odd-pentagonal. In this article, motivated by the conjecture that the class of generalized Petersen graphs is odd-pentagonal, we show that finding the odd girth of generalized Petersen graphs can be transformed to an integer programming problem, and using the combinatorial and number theoretic properties of this problem, we explicitly compute the odd girth of such graphs, showing that the class is odd-girth-closed. Also, we obtain upper and lower bounds for the circular chromatic number of these graphs, and as a consequence, we show that the subclass containing generalized Petersen graphs \(\mathrm {Pet}(n,k)\) for which either k is even, n is odd and \(n\mathop {\equiv }\limits ^{k-1}\pm 2\) or both n and k are odd and \(n\ge 5k\) is odd-pentagonal. This in particular shows the existence of nontrivial odd-pentagonal subclasses of 3-regular simple graphs.     

A note on the mean residual life of a coherent system with a cold standby component

In this paper, we investigate the effect of a cold standby component on the mean residual life (MRL) of a system. When the system fails, a cold standby component is immediately put in operation. We particularly focus on the coherent systems in which, after putting the standby component into operation, the failure of the system is due to the next component failure. For these systems, we define MRL functions and obtain their explicit expressions. Also some stochastic ordering results are provided. Such systems include k-out-of-n systems. Hence, our results extend some results in literature.     

Barriers to Remarriage Among Older People: Viewpoints of Widows and Widowers

We conducted this research based on a qualitative approach to describe the opinions of older widows and widowers on remarriage obstacles. Based on purposive sampling and inclusion criteria, we chose 48 participants on maximum diversity of sex, age, education, employment, and socioeconomic status. Two thirds of the participants were female, 40% had spent more than 10 years widowed, and 65% were living with their children. We collected data individually through semistructured, face-to-face interviews. Based on conventional content analyses, 2 independent researchers implemented data analysis manually. Barriers to remarriage were finally categorized into 4 main themes: personal, normative, interactive, and financial factors. Results of this study showed that older people are more concerned about public opinions and social norms surrounding remarriage. As long as these thoughts and norms are not changed, the concept of remarriage among widows and widowers remains a vital taboo and concern.     

Pluralistic media ignorance: Presence and causes

This study examines the presence and causes of pluralistic media ignorance - incorrect estimation of media content in a way that creates the impression that popular broadcasting is overabundant with morally controversial material. Using the appearance of sexual content in television advertising in Israel as a case study, we compare survey estimates (N = 305) of the prevalence of this material with its actual level according to the findings of a content analysis of commercials (N = 752). Pluralistic media ignorance emerges as a predominant norm, when viewers are requested to estimate the prevalence of “soft core” content like kissing and partial nudity, but it is a minor phenomenon, when estimating the share of more explicit material such as intercourse, homosexuality and rape. The most prominent predictors of pluralistic media ignorance are disapproval of the inclusion of objectionable content in popular media and extended recall of media exemplars that contain such content. Religiosity, ethnicity and sex are only partly predicting the emergence of pluralistic media ignorance. Media consumption, fear of media influence and other demographics are not predicting it at all. Public policy implications are discussed and suggestions for future research are given.