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Soft Set Theory Applied to Ordered Semigroups

Thesis Info

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External Link

Author

Khan, Raees

Program

PhD

Institute

Abdul Wali Khan University

City

Mardan

Province

KPK

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12844/1/Raees%20Khan_Maths_2018_AWKU_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727179857

Similar


In mathematics, an ordered semigroup is a semigroup together with a partial order that is compatible with the semigroup operation. Ordered semigroups have many applications in the theory of sequential machines, formal languages, computer arithmetics, and error-correcting codes. In 1999 Molodtsov [71] introduced the notion of a soft subset of a set as a new method for representing uncertainty that is free from the difficulties that have troubled the usual theoretical approaches. In this study, we applied soft set theory to ordered semigroups to obtain the notion of uni-soft left ideals, right ideals, bi-ideals, quasi-ideals, interior ideals and several properties are investigated. Moreover, uni-soft product and complement of soft characteristic function are introduced and the interrelations of them are presented. Characterizations of uni-soft left ideals, right ideals, bi-ideals, quasi-ideals, interior ideals are established. Using the notion of uni-soft left ideals, right ideals, bi-ideals, quasi-ideals, interior ideals, characterizations of semilattices of ordered semigroups are considered. Finally, the concept of uni-soft bi-ideal subsets, uni-soft filters and uni-soft bi-filters are defined and some characterizations of ordered semigroups are given.
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جگر مراد آبادی

جگر مرادآبادی
حضرت جگر مراد آبادی کاحادثۂ وفات جو ۹ستمبر کی صبح کوگونڈہ میں ستربرس کی عمر میں پیش آیا،اردو شعر وسخن کی دنیا کے لیے اس درجہ المناک ہے کہ اس کی تلخی و شدت عرصہ تک محسوس ہوتی رہے گی۔یہی وجہ ہے کہ اُن کا ماتم ہندووپاک میں جیسا ہمہ گیر ہواہے، اقبالؔ مرحوم کے بعد سے آج تک کسی شاعر کاایسا نہیں ہواتھا۔ اردو شاعری کے دور جدیدنے تغزل کے پانچ عظیم المرتبت مجدد پیدا کیے ہیں: اصغرؔ،حسرتؔ،جگرؔ،فانیؔ اورفراق۔ؔانھوں نے اردو غزل کونیا آہنگ، نیا اسلوب دیا اوراُن تصورات سے اسے پاک وصاف کیاجواب تک روایتی ورثہ کی حیثیت سے چلے آرہے تھے۔اس فہرست میں جگرؔ کانمبر اگرچہ فکر وفن کے اعتبار سے اصغرؔوحسرتؔ کے بعد آتاہے لیکن ہردلعزیزی اورعام مقبولیت میں وہ سب سے بلند اورفائق تھے۔ہرشاعر کاکلام تدریجی ارتقا کی منزلوں سے گزر کرپختگی و پائیداری کے مرتبہ تک پہنچتا ہے جہاں اس کو انفرادیت حاصل ہوتی ہے لیکن بڑے شاعروں کے کلام میں تدیجی ارتقا کی مختلف کڑیوں کامعلوم کرلینا اس قدر آسان نہیں ہوتا جتنا کہ مرحوم کے کلام میں ہے۔المجاز قنطرۃ الحقیقہ کا مقولہ اگر صحیح ہے توحضرت جگرؔ کاکلام اس کی سب سے بڑی روشن دلیل ہے۔یہی وجہ ہے کہ اُن کوشہرت ومقبولیت پہلے عوام میں حاصل ہوئی، پھر طبقۂ خواص میں اُن کے فکر وفن کی عظمت وگیرائی کااعتراف پیداہوا۔اُن کے ابتدائی دور شاعری میں حسن وعشق ِمجازی کے طبعی معاملات اوراُن کے رازونیاز کی حقیقی تصویریں پوری آب وتاب اورعریاں شکل وانداز میں پائی جاتی ہیں،اس لیے ان تصویروں نے حسین ودلکش ترنم کے ساتھ مل کر عوام میں اورخصوصاً نوجوانوں میں ایک قیامت برپاکردی اورہرشخص جگر کے اشعار کا مانا ہوانظر آنے لگا۔لیکن وقت کے امتداد اور شعور وتجربہ کی مختلف آزمائشوں سے گزرنے کے ساتھ مرحوم کے فکر میں حسن کا تصور، مقید سے...

Growth in Islamic Economy

A major proof viewed by the Islamic universe today is the proof of re-making and reorganizing the economy in such a way seen as similar to the motivation of Sharia’h work. Money-related new development is one of the topics that in a general sense is termed as a science that offers a technique to show the science of monetary angles. Nevertheless, the standard technique, which has been assembled, is being considered for dissatisfaction in dealing with the issues of the Ummah, for example, despair, backwardness in human resources (HR), and achievement in proper position and life, and even a matter of natural change. Sadly, those conditions are found overwhelmingly in the Muslim world, where they have essentially manifested and represented in Muslim life. Moreover, it seems that the uniqueness of the Muslim world has been challenging, that is, it is typically rich in asset but still weak and poor. As for the path, in Muslim society, there is an ignorance of the achievements of motivation. Thus, there is no possible norm to find the emergence of different methodologies within the Islamic structure, surprisingly in the area of ​​money-related to unforeseen development.

پاکستان میں اردو لسانی تحقیق : تجزیاتی مطالعہ

Language and associated fields have always been favorite topics of discussion among Urdu scholars. Initially these discussions were introductory but gradually they expanded. The grammar had been compiled, dictionaries published and brief discussions ensued about the creation and evolution of Urdu language. During the colonial era in India the socio-linguistics' issues imparted a vital role in these language researches discussions but always remained in the background. There were a number of prominent orientalists who pioneered modern language research in India. Although later on under colonial influence and in the socio-political scenario of India, Muslim and Hindu etymologists also indulged in these language discussions using modern techniques and theories. The growth of English language and the resistance against it, Urdu-Hindi dispute and Hind-Islamic cultural identity are major factors which enhanced the importance of language and helped to establish linguistics as a field of study. So as a result by 1947 many vital and notable works had already emerged. After the establishment of Pakistan, studies in language continued and appreciable efforts can be found in improving existing language studies. In this new scenario modern linguistic theories and discourse has become important and the traditional language-related studies stayed behind as compared to more recognized and scientific methods that had evolved. Not only existing data of language study had been analyzed thoroughly but many new theories and trends discovered as well. The primary purpose of my research is to study, analyze and evaluate the whole language related discourse of Urdu in Pakistan. Through this the scattered material would be collected and easily determined its status, worth and significance. This research would help understand the details of studies in Urdu language.