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Intersectional Soft Set Theory Applied to Ordered Semihypergroups

Thesis Info

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Author

Farooq, Muhammad

Program

PhD

Institute

Abdul Wali Khan University

City

Mardan

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11536/1/Muhammad%20Farooq%20PhD%20%28Maths%29%202019.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726494705

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Throughout this thesis, which contains seven chapters, Z will denote an ordered semihypergroup, unless otherwise stated.Chapter one, which is of introductory nature provides basic definitions and reviews some of the background materials which are needed for the subsequent chapters.In chapter two, definition of int-soft subsemihypergroup and int-soft left (resp., right) hyperideals are introduced. Characterizations of different classes (regular, intra-regular, right weakly regular and weakly-regular) ordered semihypergroups in terms of int-soft hyperideals are given. In this respect, discuss the study of semisimple ordered semihypergroups and characterize it in terms of int-soft hyperideals. The notions of convex soft set and critical soft point are also given. Moreover introduce the notions of (?,?)-int-soft hyperideals and their basic properties are discussed in this chapter.In chapter three, give the concept of int-soft interior hyperideals and characterize simple ordered semihypergroups in terms of int-soft interior hyperideals and int-soft hyperideals. Moreover characterize semisimple ordered semihypergroups in terms of int-soft interior hyperideals. Furthermore, introduce the notion of (?,?)-int-soft interior hyperideals of ordered semihypergroups. Finally, introduce the notion of (?,?)-int-soft simple ordered semihypergroups and characterize it in terms of (?,?)-int-soft hyperideals and (?,?)-int-soft interior hyperideals.In chapter four, the notion of int-soft bi-hyperideals is introduced. Moreover give the characterization of (regular, right weakly regular, intra-regular and right weakly regular, intraregular and left weakly regular) ordered semihypergroups in terms of int-soft bi-hyperideals. Furthermore definitions of prime, strongly prime, semiprime, irreducible and strongly irreducible int-soft bi-hyperideals are given. Finally, characterize ordered semihypergroups by the properties of these notions.In chapter five, definition of int-soft generalized bi-hyperideals is given and the related properties are discussed. Furthermore, characterize some classes in terms of int-soft generalized bi-hyperideals.In chapter six, definition of int-soft quasi-hyperideals is given and discuss some basic properties of int-soft quasi-hyperideals. Characterize (weakly regular, intra-regular and left weakly regular) ix ordered semihypergroups in terms of int-soft quasi-hyperideals. Moreover characterize regular, left (resp., right) simple ordered semihypergroups in terms of int-soft quasi-hyperideals.In chapter seven, the notion of int-soft left (resp., right) hyperfilters is introduced. Numerous related properties are investigated. Moreover, define completely prime int-soft hyperideals of ordered semihpergroups. Finally, characterize int-soft hyperfilters in terms of completely prime int-soft hyperideals.
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نیا ز احمد صدیقی

آہ! جناب نیاز احمد صدیقی
اسی مہینہ یعنی مارچ ۱۹۸۳؁ء میں جناب نیاز احمد صدیقی تقریباً ۸۴ سال کی عمر میں اﷲ کو پیارے ہوئے، وہ کوئی ادیب شاعر، نقاد اور مصنف نہ تھے، شروع سے آخر تک انگریزی زبان کے قابل قدر استاذ رہے، وطن مریاہو ضلع جونپور تھا، اردو زبان کے مایہ ناز ادیب اور نقاد جناب رشید احمد صدیقی کے چھوٹے بھائی تھے، مسلم یونیورسٹی علی گڑھ سے ایم اے، ایل ایل بی اور بی ٹی کی ڈگریاں حاصل کرکے شبلی اسکول اعظم گڑھ میں انگریزی کے استاد ہوئے، پھر جب یہ اسکول انٹر اور ڈگری کالج بنا، تو اس کے انگریزی کے لکچرر مقرر کئے گئے، آخر میں محمد حسن انٹر کالج کے پرنسپل بنے، وہاں سے ریٹائر ہونے کے بعد دارالعلوم ندوۃ العلماء میں کچھ دنوں انگریزی پڑھاتے رہے، یہی ان کی زندگی کی مختصر روداد ہے، مگر وہ ان چند شریف انسانوں میں تھے، جو حدیث سوزو ساز زندگی کے حامل، اخوت کے بیان اور محبت کی زبان بن کر اپنے گھر والوں، دوستوں اور معاصروں کے ساتھ رہے، اپنی اس طویل زندگی کے سولہ برس دارالمصنفین کے احاطہ میں گزارے اور اس کے شب و روز کو پر کیف بنانے میں کوئی کسر اٹھا نہیں رکھی، کوئی مسئلہ ہوتا، کوئی نازک وقت آتا، یا کوئی تقریب ہوتی، تو ہر موقع پر اپنے مخلصانہ، مشفقانہ اور ناصحانہ مشوروں سے سب کی دل داری، دلنوازی اور رہنمائی کرتے، وہ یہاں کی زندگی کے جزولاینفک ہوگئے تھے، اپنے شریفانہ برتاؤ، اخلاقی بلندی اور روزمرہ کی زندگی کے لین دین کی طہارت اور صاف باطنی میں قرونِ اولیٰ کی روایت کو تازہ کرتے، ان کی پاک اور طاہر زندگی پر اس وقت رشک آتا جب دارالمصنفین کے احاطہ کے اندر بعض لوگوں کی زبان سے یہ سننے میں آتا کہ ایک صحابی کی زندگی...

Reading in a report: the French National Gendarmerie, on the reasons for the cargo train coup between the cities of Ain Sefra and Bashar in 1957

It is no coincidence that the researcher in history, especially the history of the Algerian revolution, finds a missing link in the history of the Algerian revolution, which we call the history of what history has neglected. Intentionally, or unintentionally, the archives of Algeria in France, Pax- Provence, or others, or even with some Algerian families, who still hide their archives from researchers? a question that the Algerian researcher will answer to show the truth with documents. Similar to this document, which deals with a topic, in which scientific material was scarce, which is related to the revolution’s strategy to abort and eliminate French projects, the strategy of the National Liberation Army to adapt to the situation consisted in sabotaging French transportation routes, especially railways, in order to destroy France’s economy as well as When she wanted to isolate the people from their revolution, by building barbed wire at the level of the East and West.

Influence of Different Protein Sources on Growth Performance and Carcass Characteristics of Kajli Male Lambs

Three independent studies using male Kajli lambs at post-weaning, growing and finishing stages were designed and undertaken to examine the effect of different protein sources with or without probiotics on growth performance and carcass characteristics. In the trial I, 32 male Kajli lambs at three months age were randomly divided into eight groups of four animals each in a 4×2 factorial arrangement. Four iso-caloric (70% TDN) and iso- nitrogenous (22% CP) diets were formulated with four different protein sources i.e. corn gluten meal 30% (CGM), canola meal (CM), cotton seed meal (CSM) and sunflower meal (SFM) containing either 0 or 50g of probiotics (Protexin®)/ ton of feed. In trial II and III, lambs were again randomized and given the same treatment as in trial I. However, crude protein (CP) content of diets was reduced from 22 to 18% in trial II and 18 to14% in trial III. In trial I, higher (P<0.05) dry matter (DM) and CP intake, DM, CP, neutral detergent fibre (NDF) and acid detergent fibre (ADF) digestibility, blood glucose, N-balance and total weight gain were observed in lambs fed CM diet than those fed CGM, CSM and SFM diets. However, blood urea nitrogen (BUN), creatinine and serum minerals remained unaltered (P>0.05) in lambs fed diets containing different protein sources. Neutral detergent fibre and ADF digestibility and blood glucose was higher (P<0.05) in lambs fed diets containing probiotics. Dry matter and CP intake and their digestibility, BUN, creatinine, serum minerals, N-balance and total weight gain remained unaltered (P>0.05). In trial II, higher (P<0.05) DM and CP intake, blood glucose, N-balance and total weight gain were noticed in lambs fed CM diet than those fed CGM, CSM and SFM diets. However, diets containing different protein source didn’t affect (P>0.05) the DM, CP, NDF and ADF digestibility, BUN, creatinine and serum minerals. Neutral detergent fibre and ADF digestibility and total weight gain was higher (P<0.05) in lambs fed diets containing probiotics. However, diets containing probiotics didn’t influence (P>0.05) DM and CP intake, DM and CP digestibility, BUN, blood glucose, creatinine, serum minerals and N-balance. In trial III, higher (P<0.05) DM and CP intake, N-balance and total weight gain were observed in lambs fed CM diet than those fed CGM, CSM and SFM diets. However, DM, CP, NDF and ADF digestibility, BUN, blood glucose, creatinine and serum minerals remained unaltered (P>0.05) in lambs fed diets containing different protein source. Acid detergent fibre digestibility and total weight gain was higher (P<0.05) in lambs fed diets containing probiotics however, DM and CP intake, DM, CP and NDF digestibility, BUN, blood glucose, creatinine, serum minerals and N- balance remained unaffected (P>0.05). Hot carcass weights of lambs differed significantly (P<0.05) in lambs fed diets containing different protein sources with or without probiotics. However, dressing percentage (DP) and skin, feet, heart, liver and lungs weight remained unaltered (P>0.05) across all the treatments. The higher DP was observed in lambs fed CM diets, whereas it was lower in lambs fed SFM diet. Leg, loin, shoulder, breast and neck weights of the half carcass of the lambs remained unaffected (P>0.05) across all the treatments. Crude protein content of carcass was different (P<0.05) in lambs fed diets containing different protein source with or without probiotics, while moisture, ether extract and ash contents remained unaltered (P>0.05) across all treatments. The ratio of lean, fat and bone in primal cuts of half carcass (neck, shoulder, breast, loin and leg) remained unchanged (P>0.05) across all the treatments, except for the proportion of lean in shoulder, bone in loin and fat in legs, which was affected (P<0.05) by the diets containing different protein sources. In short, the lambs fed CM diets performed better than those fed CGM, CSM and SFM diets in all the three trials. Diets containing probiotics improved weight gain in trial II and III but not in trial I.