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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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کوئی دھوکا سا ہوا ہو جیسے

کوئی دھوکا سا ہوا ہو جیسے
اشک ہونٹوں کو چھوا ہو جیسے

ایک خوشبو تھی ہوا میں ہر سو
دل نے اک نام لیا ہوا جیسے

آگ ہی آگ ہے اب چاروں طرف
دل کہ جلتا سا دیا ہوا جیسے

جا کے کنعاں میں ہوا کہنے لگی
شاہ ، بے مول بکا ہو جیسے

آ کے اب دیکھ مسیحا میرے
درد کا نام فضاؔ ہو جیسے

معاصر نظام ہائے معیشت میں تقسیم دولت کے تصورات کا تقابلی جائزہ

One of the core issues in contemporary economic trends is the fair and just distribution of wealth into the society. In this research, a comparative study of ‘distribution of wealth’ in Capitalism, Communism and Islam has been conducted. Qualitative research method is adopted for the analysis of data. The review of literature reveals that central ideas of Capitalism, Communism and Islam are ‘liberty’, ‘equality’ and ‘justice’ respectively. After evaluating the basic infrastructure, methodological framework and practical consequences of these three systems, it has been established that Capitalism and Communism have badly failed in maintaining fair distribution of wealth. Both (Capitalism and Communism) enhanced global inequality which could be assessed from the present economic condition of world as half the world’s wealth is now in the hands of just 1% of the population. On the other hand, Islam has ensured the just distribution of wealth by taking two revolutionary steps: by giving 18 compulsory and 6 optional commandments about circulation of wealth and by overruling all means of hoarding. Moreover, unlike Capitalism and Communism, Islam has given special instructions to distribute wealth among poor, disable, and helpless persons of society who are incapable of participating in the process of production. These measures promote peace and prosperity in society and reduce the ratio of poverty. In the light of above findings, it is concluded that only Islamic economic system can guarantee the just and fair distribution of wealth. It is, therefore, recommended that Islamic countries should implement the Islamic economic system in order to get rid of economic instability.

Response Modification Factors for Reinforced Concrete Buildings in Pakistan

Response modification factors in building codes are an essential part of all seismic building codes. These factors are used in the denominator of the base shear equation in the simplified method of seismic design to reduce the base shear in order to encompass non-linear seismic resistance potential of buildings. The selection of response modification factor for a specific class of structural system has, therefore, serious implications on the safety and economy of structural designs. Keeping in view the importance of response modification factor, a large number of researchers around the world, have made attempts to evaluate this factor for different types of structural systems. In all the cases, however, these factor have been evaluated considering a particular design code and local construction practices. Therefore, these factors are not universal and hence cannot be used in every region. Response modification factors that are part of building code of Pakistan have been adopted from an American code. Variation and uncertainties in construction practices and quality of construction in Pakistan are different from those in the US which renders the response modification factors inapplicable to design of buildings in Pakistan, until verified. There is a need for development of response modification factors for forthcoming edition of building code of Pakistan that are reflective of the true seismic building performance in Pakistan. This research was carried out to compute response modification factors for Special Moment Resisting Frame (henceforth referred to as SMRF) buildings in Pakistan This research work was initiated through a building stock survey that was conducted in five main cities of Pakistan to study contemporary construction practices. Several disparities were found to exist between design specifications and construction practices. These included reduced compressive strength of concrete as compared to specified xi compressive strength, haphazard and increased spacing of ties and stirrups, improper location of lap splices and smaller diameter of reinforcement as compared to nominal diameter, amongst others. Experimental models of RC beam-column connections were built incorporating these deficiencies. These models were then subjected to reverse cyclic loading in quasi-static experiments. The experimental results obtained from quasi-static tests were used to calibrate numerical models of the connections and were consequently integrated into numerical building models. Numerical simulations were carried out on reinforced concrete frames to compute response modification factors. Response modification factor was computed for a total of 256 twodimensional hypothetical reinforced concrete buildings based on experimental response of beam-column connections. The set of hypothetical frames considered varying span lengths and number of storys. The frames were designed based on BCP-SP 07 and analyzed using non-linear pushover analysis for computation of response modification factor. The disparity between design specifications and actual construction was accounted for in non-linear constitutive law for structural members derived from the experimental work. The computed response modification factors showed a wide dispersion with building span lengths, number of storys and detailing deficiencies. As a general trend, the values of response modification factors decreased with increasing period of vibration of the buildings and increasing span lengths. Based on the extensive experimental and numerical work, response modification factor value of 8.5 is recommended for RC SMRFs for standard quality control environments, where a full compliance between design specifications and construction practices is ensured. The overall range of the computed response modification factors for fullycode- compliant SMRF buildings is from 6.0 to 12.0 which signifies a large scatter in the values based on varying span lengths and building heights. This necessitates the use of period-dependent response xii modification factors in the forthcoming editions of the Building Code of Pakistan. For buildings with construction deficiencies pertaining to concrete quality and reinforcement detailing, the values of response modification factors range from 4.0 to 6.1 for buildings with varying span lengths and height. The determination of quality control environment and subsequent use of response modification factor is left to the discretion of design engineers. It is, however, emphasized that a judicious selection of response modification factor, based on ground realities, should be made by design engineers to avoid a compromise on the safety and economy of structural designs. A minimum requirement of 20.db should be adopted in the building code for proportioning the column depth in exterior beam-column connections to ensure hinging in beams rather than joints.