The generalized order k–Pell sequences in some special groups of nilpotency class 2

2021 ◽  
pp. 1-17
Author(s):  
M. Hashemi ◽  
E. Mehraban
Author(s):  
Maulana Akbar Shah @ U Tun Aung

Abstract In addition to compliance with the five pillars of Islam, Da’wah Islamiyyah is an indispensable act for Muslims who view their life missions as to propagate Islam. The act of da’wah is a mission only undertaken by those who are selected to do so, as Allah SWT said: “You are the best of peoples, taken out for mankind, you enjoin what is right, forbid what is wrong…,” (Al-Qur’an, Al- `Imran, 3:110). The phrase “you are taken out for mankind” is a very clear phrase which refers to a special group. Many du’at propagate Islam through regular procedures. In this contemporary day and age, it would be more successful if creative da’wah methodologies are used to special groups where special talent is required. Examples of these special target groups are individuals such as [1] pregnant mothers, [2] mothers of new born babies, [3] parents of toddlers, [4] parents of children [5] youth, teenagers and adolescents, [6] married couples, [7] elderly or aged individuals and [8] non-Muslims.  They are good targets to promote Islam. Thus, du’at must have special talents and knowledge to do so. In this regard, du’at must be equipped with exceptional knowledge of the target groups to propagate Islam effectively. The present paper attempts to highlight the distinctive natures of the above mentioned categories of individuals and explores how du’at should approach them when he or she encounters them for the purpose of promoting Islam.        Keywords: Call to Islam, Da’wah Islamiyyah, creative da’wah, creative da’ie, enjoin good, forbid evil.   Abstrak Selain mematuhi 5 rukun Islam, dakwah Islamiyyah tidak dapat diasingkan daripada seseorang Muslim yang bermatlamat untuk menyebarkan ajaran Islam. Berdakwah adalah suatu tugas yang hanya dijalankan oleh mereka yang terpilih. Seperti yang diwahyukan oleh Allah SWT “Kamu adalah sebaik-baik umat yang dilahirkan bagi umat manusia, kerana kamu menyuruh berbuat segala perkara yang baik dan melarang daripada segala perkara yang buruk dan keji...” (Al-Quran, Al-Imran, 3:110). Frasa “umat yang dilahirkan bagi umat manusia”  jelas dinyatakan di mana ia merujuk kepada satu golongan yang istimewa. Kebanyakan pendakwah menyebarkan Islam melalui metodologi yang sudah menjadi kebiasaan. Bagaimanapun, pada zaman ini, pendakwahan akan lebih berjaya jika kaedah yang kreatif digunakan kepada beberapa golongan yang tertentu. Antara contoh golongan yang dimaksudkan adalah [1] wanita yang mengandung, [2] ibu kepada bayi yang baru lahir, [3] ibu bapa kepada anak-anak kecil, [4] ibu bapa kepada kanak-kanak, [5] golongan belia dan remaja, [6] pasangan suami isteri, [7] warga emas, dan [8] golongan bukan Islam. Mereka merupakan sasaran yang sempurna untuk mempelajari Islam. Oleh hal demikian, para pendakwah mesti mempunyai bakat yang istimewa dan ilmu yang mencukupi untuk berdakwah. Para pendakwah juga harus memahami kumpulan sasaran dengan menyeluruh supaya penyebaran ajaran Islam akan lebih berkesan. Tujuan penulisan ini adalah untuk menggariskan sifat unik golongan yang dinyatakan di atas dan menerokai bagaimana para pendakwah harus mendekati mereka dengan niat untuk menyebarkan Islam.   Kata Kunci: Panggilan kepada Islam, dakwah Islamiyyah, dakwah kreatif, da’ie kreatif, menyuruh kepada kebaikan, menghalang daripada kejahatan.  


Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 335
Author(s):  
Mohamed A. Abd Elgawad ◽  
Haroon M. Barakat ◽  
Shengwu Xiong ◽  
Salem A. Alyami

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,⋯,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.


2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.


2021 ◽  
Vol 53 (1) ◽  
pp. 107-132
Author(s):  
Tomasz Rychlik ◽  
Fabio Spizzichino

AbstractWe study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.


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