We investigate a generalization of Fubini numbers. We present the combinatorial interpretation as barred PREFERENTIAL arrangements with some additional conditions on the blocks. We provide a proof for a generalization of Nelsen's Theorem. We consider these numbers from a probabilistic view point and demonstrate how they can be written in terms of the expectation of random descending factorial involving the negative binomial process.

The gallbladder stone is a common disease; its best management is cholecystectomy with surgical operation. Since 1882 cholecystectomy is a conventional procedure, but Laparascopic cholecystectomy procedure initially begins in France (1978) and quickly spreads in USA, European countries, and other counties around the world. Its popularity was because reducing postoperative pain, abdomen aesthetics, patients quick return to normal daily activity, shortening hospitalization and reducing costly hospital expenses. In some private hospital in Iran since nearly 10 years ago laparascopic procedures - mainly cholecystectomy- usually are done, although it was not initially welcomed. It gradually spreads on nearly all training hospitals.Since 1373 (1994) in Razi hospital 380 laparascopic procedures including 90 Cholecystectomies and others was diagnostic or cancer stagings. There were four general surgeons in Razi hospital, all in some way engaged in different Laparascopic procedures.For first 15 Laparascopic cholecystectomy operations we faced with many problems; all due our limited experiences; since then we had more experiences, and our next patients were as follow: Acute cholecystitis (12) chronic cholecystitis (shrinked gallbladders (four patients) and gallbladder empyems (two patients)).Mean of hospitalization was two days.In one case patient did not believe his/her management and repeatedly returned complaining of limited incision.In eight cases we forced to perform Conversion procedures; due to visceral perforations (three cases), hemorrhagia (one case), sever adhesions, and bad anatomical positions (four cases). It is noteworthy that four complications were in first 15 patients, and three in men.As described above we suggest Laparascopic cholecystectomy with an experienced team is a PREFERENTIAL procedure; limited incision and quickly return to normal daily activity are its advantages.

Introduction: Nurses have a special position in hospitals due to their specialized, valuable and stressful job. Gender inEQUALITY together with the concerns about health inequalities need attention. Therefore, this study aimed to investigate gender EQUALITY among nurses in Fars province of Iran and to provide solutions to improve gender EQUALITY. Methods: This quantitative-qualitative study was conducted in 2020. In the quantitative phase, the study population included all nurses employed in public and private hospitals of Fars province as well as all nursing students at Fars universities during 2011-2018. In the qualitative phase, 16 semi-structured interviews were conducted. Using SPSS version 23. 0, the quantitative data was analyzed by applying descriptive statistics and Chi-squared test. Qualitative data were analyzed with Max QDA by using the framework method. Results: The majority of hospital nurses (79. 81%) and nursing students (65. 86%) were female. There were statistically significant relationships between gender and hospital, the type of employment, university, and the type of degree (P=0. 00). In addition, 3 main themes including culture building, nursing education and employment as well as 17 sub-themes were identified to improve gender EQUALITY among nurses. Conclusion: Fars province faces challenges such as gender inEQUALITY among nurses and the shortage of male nurses. It is essential to invest in the development and implementation of strategies and executive solutions for raising and maintaining the prestige of nursing profession and training qualified nurses with a focus on creating healthcare job opportunities for men and women equally.

The notion of a positive implicative EQUALITY algebras are defined, and related properties are studied. Characterizations of a positive implicative EQUALITY algebra is investigated. Conditions for an EQUALITY algebra to be positive implicative are provided. EQUALITY algebra with some types is considered, and several properties are investigated. Using EQUALITY algebra with some types, we characterize a commutative EQUALITY algebra and a positive implicative algebra.

In this paper we study a representation of a fuzzy subgroup  m of a group  G, as a product of indecomposable fuzzy subgroups called the components of m. This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and some of their properties to prove this theorem. We illustrate with some examples.

In this paper, first we define the notion of involutive operator on bounded involutive EQUALITY algebras and by using it, we introduce a new class of EQUALITY algebras that we called it a tense like EQUALITY algebra. Then we investigate some properties of tense like EQUALITY algebra. For two involutive bounded EQUALITY algebras and an EQUALITY homomorphism between them, we prove that the tense like EQUALITY algebra structure can be transfer by this EQUALITY homomorphism. Specially, by using a bounded involutive EQUALITY algebra and quotient structure of it, we construct a quotient tense like EQUALITY algebra. Finally, we investigate the relation between tense like EQUALITY algebras and tense MV-algebras.

In this paper, by using the notion of ordinal sum of EQUALITY algebras which is defined in [4], we investigate some related properties and different kinds of filters of it such as prime and maximal. In addition, by focusing on chain EQUALITY algebra, we define the concept of a cut of an EQUALITY algebra and use it to introduce a new ordinal sum of them. By defining a relation relative to a cut, we show that the family of classes is made a cone algebra. Finally, we prove that every chain EQUALITY algebra can be represented as an ordinal sum of chain cone algebras.

In this paper, we apply the concept of similarity operations to EQUALITY algebras and introduce similarity EQUALITY algebras. We investigate some related properties of them. In particular, we prove that there is a one to one correspondence  between similarity filters and similarity congruence relations on a similarity EQUALITY algebra. Furthermore, we prove the  first isomorphism theorem on similarity EQUALITY algebras. We use the similarity filters to establish the uniform structure  on similarity EQUALITY algebras and obtain some properties of this topology. In addition, we introduce and study a  corresponding propositional logic for similarity EQUALITY algebras and prove the soundness and completeness of this  propositional logic based on similarity EQUALITY algebras.

This article is an attempt to deal with gender EQUALITY, on a theoretical level, in the political domain. First the basic approaches towards gender EQUALITY in the political domain are presented for discussion. Following that, three approaches: gender EQUALITY, difference and inEQUALITY as three perspectives of EQUALITY-orientation, difference-orientation and inEQUALITY-orientation are selected. Then the political domain is divided into three parts: citizens’ rights, political participation and the tenure of political posts. Afterwards, the attitudes of 210 members of the University of Tehran’s students are recorded in a survey. For this purpose the statistical methods, one-variable analysis, variation analysis, co-efficiency and path analysis are used. The results of the research findings indicate the impact of external factors. For example an individual’s attitude towards gender EQUALITY is conditioned by the social adjustment of the individual in the family, his personal opinions, and his behavior. In general, most of the students have difference-oriented attitudes towards gender in the political domain and they are less in favor of gender inEQUALITY on gender EQUALITY. But men have a higher tendency towards gender inEQUALITY than women