Semirings, one of the most natural generalization of rings and distributive lattices, were first appeared in the study of ideals of rings, by Dedekind [25] and then Vandiver[78] formally introduced this notion, in 1934. One of the oldest algebraic structure, set of all natural numbers, is also a semiring. Over the years, tremendous applications of the theory of semirings have been recorded [33], from both domains of mathematics. Several types of semirings considered by researchers with respect to their applications in different areas including optimization theory, theoretical physics and computer sciences([1], [26], [30], [32], [77]). One of the most favorite type of semiring which was studied by algebraists during the last few years, is additively inverse semiring. The algebraic structure of inverse semiring was introduced by Karevellas[53] in 1973. In [9], Bandlet and Petrich characterized inverse semirings as a subdirect product of rings and distributive lattices. Sen[76], Ghosh[29] and Mukhopadhyay [74] and many others also considered the structure of inverse semiring. Recently, another class of semirings which appeared in the corpus, is the class of MA-Semirings. Javed, Aslam and Hussain[49] identified this class, as a subclass of additive inverse semirings which satisfies the condition (A-2) stated by Bandlet and Petrich in [9]. They initiated the theory of commutators with its fundamental identities in MA-Semirings, which later proved to be very fruitful in investigating many concepts of ring theory. These include theory of dependent elements and free actions[50], commutativity and centralizing mappings[51] and the theory of derivations of MA-Semirings[49]. Indeed, this algebraic structure is of considerable interest in targeting and generalizing many Lie type results of rings and algebra to semirings. As the name suggests, in this thesis, we will be considering MA-Semirings in regards of various concepts of ring theory. As usual, the first chapter will be devoted to preliminaries that includes some basic concepts of semiring theory. The chapter contains a brief introduction to the class of MA-Semirings and the notion of commutators in MA-Semirings. Chapter 2, deals with the theory of Lie and Jordan ideals of MA-Semirings. We introduce the notion of Jordan ideals of MA-Semiring and investigate famous results of Herstein[35, 40], in the setting of MA-Semirings. Lie ideals of MA-Semiring have been defined, already, by Javed and Aslam *51+. In this chapter, we explore Lanski*56+ and Herstein’s work*43+ on Lie ideals and extend their work to MA-Semirings. Some results of this chapter have accepted for the publication in the Italian Journal of Pure and Applied Mathematics[71]. In Chapter 3, we study the theory of derivation of MA-Semirings. In this regard, we probe the most investigated work of Posner on derivation of prime rings [66]. We also present the proof of one of the famous Posner’s theorem, namely, Posner’s second theorem of derivation, for MA-Semirings. The results of this chapter have accepted for the publication in Hacettepe Journal of Mathematics and Statistics[72]. Chapter 4, will be devoted to the study of Jordan Mappings in MA-Semirings. We formulate the notion of Jordan homomorphism and Jordan triple Homomorphism of MA-Semirings. A few well-known results obtained by Bre s ( ar[15] and Herstein[38], in this subject, are also generalized for MA-Semirings. In last two sections, we define Jordan derivation and Jordan triple derivation of MA-Semirings. In this chapter, we also prove that a Jordan derivation of 2-torsion free prime MA-Semiring is a derivation, which generalizes classical result of Bresar’s [13]. The contents of this chapter have published in the Journal of Open Mathematics[69]. In Chapter 5, we will study the most important concept of left centralizers on MA-Semirings. The work in this chapter, is motivated by the study of Zalar, Vukman and Bres ( ar [19, 79, 80, 84] on left centralizers. Most of the results of this chapter are part of our publication in the Journal of Quasigroups and related systems[70] and in the Journal of Discussiones Mathematicae-General Algebra and Applications[68]. In the last chapter, we will be considering MA-Semiring with the notion of dependent elements and free actions. In his Ph.D. thesis[50], Javed introduced the notions of dependent elements and free actions for the class of MA-Semirings. This chapter is devoted for the development of these notions. Results of this chapter have published in International Mathematical Forum [73].
ایک مکمل کہانی جو تمام اجزائے ترکیبی کے ساتھ بیان کی جاتی ہے ناول کہلاتی ہے۔یہ وہ صنف سخن ہے جس میں جذبات،خیالات،واقعات اور ثقافت کو حصہ بنایاجاسکتا ہے۔ناول معاشرے میں نسل در نسل چلنے والی کہانیوں کا عکاس ہے کیونکہ یہ ایک طویل کہانی ہوتا ہے اس لیے معاشرے کی مکمل ترجمانی کرتا ہے۔
ادبی اصطلاح میں دیکھا جائے تو ناول سے مراد ایک ایسی کہانی ہے جس میں پوری زندگی بیان کی جاتی ہے۔ناول ادب کی ایک صنف ہے لغت میں ناول کے معنیٰ’’نادر‘‘نئی بات یانئی چیز کے ہیں۔یہ اطالوی زبان کے لفظ’’ناولا‘‘سے نکلا ہے ناول کے ،معنی بھی’’نیا ‘‘کے ہیں۔
معاشی ،مذہبی،سیاسی،سماجی،نفسیاتی چاہے زندگی کا کوئی بھی موڑ ہو ناول میں ہر پہلو کو کھل کر بیان کیا جاسکتا ہے۔قدیم زمانے میں داستان کا عروج تھا اور زمانے کی ترقی کے ساتھ ساتھ عصر جدید میں ادب کی نئی صورتیں سامنے آئیں۔ناول داستان کی ہی ترقی یافتہ شکل ہے۔
دوسرے اصناف ادب کی نسبت اردو ناول کی عمر کم ہے۔مگر ناول نے اپنا راستہ طے کرتے ہوئے منزل کو پالیا۔طویل داستان جس کے لیے نشستیں درکار ہوتی ہیں اس میں تبدیلیاں کرنے کے بعد مختصر کیا گیا اور ناول کا نام دیا گیا۔اردو ناول عروج وزوال کی منزلیں طے کرتا ہوا عصر حاضر میں جدید ناول کی طرف گامزن ہے۔
ناول دراصل عصر حاضر میں اس زمانے اور معاشرے کی سچی تصویر پیش کر رہا ہے بہر کیف ناول کے تمام عناصر کو نہایت ہی خوبصورتی اور ہم آہنگی ،تخلیقی و فنی دلکشی ، توازن اور فن کارانہ سلیقہ مندی کے ساتھ منظر عام پر لے آنا ہی ناول نگارکے لیے کامیابی کی دلیل ہے...
Every year heads of different states make their speeches in the general debate of United Nations General Assembly (UNGA). They address national and international issues and suggest measures to resolve them with the help of international community and the United Nations. Muhammad Nawaz Sharif also made speeches in the UNGA. In 2013, he was newly elected prime minister and was enthusiastic to resolve issues with India. There was no internal political pressure on him at that time and the government in India was hostile towards Pakistan. But one year in power and embattled with domestic issues and international pressure, the prime minster approached the issues differently in his 2014 speech. The aim of this paper is to compare his two speeches and see what changes occurred in his stance towards India. The main focus of the analysis is: Who is the addressee of these speeches? How confident did Nawaz feel about the solution of the issues that he raised. The Corpus tool Wmatrix has been used to analyze the data. The results show significant differences in his two speeches with regard to his stance towards India.
Syllabus Designing for Teaching of English at Intermediate Level in Pakistani Colleges The present study aimed at identifying weak areas of the syllabus of English for Intermediate level that hamper the teaching and learning process, and to suggest changes to align it with teaching and learning requirements and needs of the students in an age of science, technology and commerce. Giving rationale of the study, the researcher discussed the need of evaluating the syllabus. He established the necessity of the research work in perspective of the phenomenon of change, mass failure of students, lack of skills and intellectual and creative incapacity of the students. He set the research questions and objectives of the study. The researcher discussed various aspects of syllabus design and evaluation of syllabus in literature review. They include: basic concept of syllabus; needs analysis; impact of situational factors; aims and objectives; concept of proficiency; learning styles; various approaches to syllabus design; methodology; role and design of instructional materials; selection and grading; and tools of evaluation of syllabus. The researcher adopted quantitative and qualitative techniques. The population comprised Intermediate students, Graduation students, teachers of English, parents and members of the Curriculum Committee. The choice was made by convenient sampling technique. The size of the population was 1000 Intermediate students, 500 Graduation students, 600 teachers and 1000 parents. The questionnaires were sent to every segment of population in numbers exceeding the actual population size of each segment. The questionnaires returned from Intermediate students, Graduation students, teachers and parents were 1040, 460, 340 and 480 respectively. The research tools used were questionnaires, group discussion, and evaluation tools selected from certain linguists. The data analysis manifested that almost all the respondents from all categories of population criticised the present syllabus in perspective of its aims and objectives, needs, contents, methodology, and styles of learning. The application of evaluation tools also demonstrated gross level flaws in the syllabus contents and textbooks. The researcher gave his finding derived from the data analysis and the evaluation. They included these observations: the evaluation of the syllabus had not been carried out since 1972; needs analysis was never conducted. Listening and speaking skills were never included in the syllabus. The syllabus was failing in producing proficiency of language in the students. On the basis of the analysis and the finding, the researcher gave recommendations for an effective syllabus. They included: periodical evaluation of the syllabus and needs analysis process; shifting of contents from literature based to skills based; making the syllabus dominantly communicative and task based; and inclusion of certain contents in the syllabus. He also suggested syllabus contents for Intermediate level of education. The researcher concluded the research with a note of optimism and best wishes for the future of ELT in Pakistan.