M24 is the largest Mathieu sporadic simple group of order 244823040=210.33.5.7.11.23 contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of M24 with respect to the conjugacy classes of all its nonidentity elements.

Rank is a piece of music of the poem and has high Importance in completing music Rhyme and Rhythm and most of its roles and functions are generally ignored. This article tries to evaluate the definitions of the rank and explained some of them and then selects the definition which is comprehensive, simple, complete and extensive in research. Since the rank is successfully used only in Persian language and the frequency is much more significant in the most beautiful and musical kind of Persian lyrics like the lyrics of Hafez, we examine its musical and implicating role while considering lyrics of Hafez. All statistics of verbal substantive multitude pronominal adjective & speech kind of rank will be presented as well.      

Relative to a hereditary torsion theory t we introduce a dimension for a module M, called t -rank of M, which coincides with the reduced rank of M whenever t is the Goldie torsion theory. It is shown that the t -rank of M is measured by the length of certain decompositions of the t -injective hull of M. Moreover, some relations between the t -rank of M and complements to t -torsionfree submodules of M are obtained.

The distinction between existence and quiddity, as well as the link between the two, has been a substantial issue in Islamic philosophy throughout history, having profound effects on other issues. Muslim philosophers argue that contingent beings possess both existence and quiddity in its narrow sense. However, many philosophers believe that Necessary Being (Wājib al-Wujūd) is devoid of quiddity and some deny the quiddity-based reality. Nonetheless, logical reasoning indicates that all ranks of the essence of things (including real and constructed (i‘tibārī), as well as existential and non-existential) are predicated on quiddity. Hence, first and foremost, it is not impossible to put forward an integrated analysis of existence and quiddity for Necessary Being, where quiddity, like existence, is limitless. Second, the copula notions (ma‘ānī rabaṭī) are quiddity-based, even if their quiddity, like their existence, is the quiddity for others. Third, non-existent matters are, in fact, distinct from one another. For example, while the non-existence of a vicious circle and a giant (ghūl) is the same in that they are both non-existent, their distinction stems from their adherence to their quiddity (the whatness of a vicious circle and a giant (ghūl). Fourth, constructed matters (umūr i‘tibārī) are similarly quiddity-based, though their quiddity, like their existence, is constructed (i‘tibārī). As a result, the property of being quiddity-based elevates to an existent qua existent axiom, becoming a direct accident comparable to reality.

In this paper we develop an asymptotic theory for estimation based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and we illustrate the performance of the proposed estimators via a Monte Carlo study.  

Background: The websites of universities by introducing the missions, faculties, departments, courses, educational levels, research and educational facilities, faculty members, students and alumni to the World Wide Web are of great importance. Nowadays webometric ranking of universities is as important as the academic ranking of universities. Webometric ranking of universities reflects the overall web performance of the universities. Analyzing the researches on Iranian academic websites shows many deficiencies in the websites of the Iranian medical universities. These problems are the main causes of low webometric ranks of Iranian medical universities in the "Ranking Web of World Universities". The current study reviews the previous studies on the academic websites of Iran and other countries and suggests several ideas for improving the websites of Iranian medical universities focusing on the structure and content according to the webometric indicators of "Ranking Web of World Universities". The suggested ideas would improve Iranian medical universities ranks in the international level and also affect the major national policies of information management.

Islam meaning submission to God's commandments and prohibitions is of different ranks and stages and since man’s essence changes gradually, the various ranks of Islam are materialized in man over time. To remunerate this submission, God fills man’s heart with peace and tranquility and there is a reciprocal relationship the submission and peace. Allameh Tabatabaei believes Islam is of four ranks and each rank has a corresponding rank of faith. Therefore, man’s material and spiritual life has certain stages and ranks and the holder of each rank has a duty to uplift his rank with the assistance of those residing in higher ranks and to be vigilant and gracious toward those in lower ranks so that they may rise to higher ranks as well. Thus, Muslims have various ranks in understanding religious truths and their realization in their existence and what is of main concern among Muslims is having dialogue, understanding, cooperation and mutual assistance.