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سر چارلس لایل

سر چارلس لایل

            ماہ گزشتہ میں انگلستان کے ایک مشہور متشرق سر چارلس لایل کی وفات ہوئی موصوف مدت تک ہندوستان میں ممتاز ملکی مناصب پر مامور رہے تھے، ۱۸۹۸؁ء میں چیف کمشنر صوبہ متوسط کے مرتبہ سے پنشن پائی اور اس کے بعد بارہ برس تک انڈیا آفس میں کام کرتے رہے، مسلمانوں کے علوم و السنہ، خصوصاً فارسی، عربی اور اردو کے وہ ایک مستند عالم خیال کئے جاتے تھے اور شعراء عرب کے متعدد دواوین ان کے تحشیہ و مقدمہ کے ساتھ شائع ہوئے، وہ برٹش اکاڈیمی کے فیلو تھے اور ایڈنبرا، آکسفورڈ، اسٹراسبرگ، مختلف یونیورسٹیوں سے ال۔ال۔ڈی، پی۔ایچ۔ ڈی، ڈی۔لٹ وغیرہ کی اعزازی ڈگریاں رکھتے تھے، انسائیکلوپیڈیا برٹانیکا کے آخری ایڈیشن میں ہندوستانی (اردو) لٹریچر پر مضمون انہی کے قلم سے تھا، ان کی عمر ۷۵ سال کی تھی۔ (اکتوبر ۱۹۲۰ء)

 

الحبك النصي وعلاقته بالنص القرآنيدراسة نظرية في ضوء التراث النقدي والبلاغي

The concept of coherence is not only a semantics one that exists within the meaning of text; it refers to grammatical continuity of a text that accurs within surface and deep structure of the discourse، and that define it as a text/discourse. That is why the study of coherence is important in textual linguistics، especially in the Text of Holy Qur’ān. Therefore the ancient researchers have chosen it in different ways in the Qur’ānic textual analysis. The ancient Arab started the study of Coherence to prove the Qur’ānic text as “Moʻjiza” and “iʻjāz” because of its organization and arrangement of text according the “Naẓm” “Insijām” “Ittisāq” “Iltiḥām” and many others. The English term that substitutes these terms is just Cohesion and Coherence. So we can say that the Arab were doing well about the discourse/textual analysis of the texts, especially the Qur’ānic textual coherence was their main goal. The Article aims to explore the main roots، elements and aspects of textual coherence in Arabic language. This work differ from previous works in many aspects as it focuses on the concept of coherence and its various aspects particularly in terms of the coherence in Arabic Language in the light of Qur’ānic text.

Mathematical Modeling of Some Infectious Diseases With Integer and Non-Integer Order Derivatives

Mathematical models play an important role to understand the spread, per sistence and prevention mechanism of infectious diseases. In this thesis, we present some mathematical models and their analysis on the dynamics of Tuberculosis (TB) and Hepatitis B virus (HBV). Firstly, we develop these models with classical integer-order derivative and present a detailed qualita tive analysis including, existence and stability of the equilibria, sensitivity of the model parameters and the existence of the bifurcation phenomena. The threshold quantity also called the basic reproduction numberR0 is presented for each model that shows the disease persistence or elimination for their par ticular cases. Further, we develop some suitable optimal control strategies which would be useful for public health department and other health agen cies, in order to reduce and eradicate TB and HBV from the community. The reported TB infected cases in Khyber Pakhtunkhwa province of Pakistan, for the period 2002-2017 are used to parameterize the proposed TB model and an excellent agreement is shown with the field data. The models are solved numerically using Runge-Kutta order four (RK4) method and numerous nu merical simulations carried out to illustrate the disease dynamics and some of the theoretical results. Mathematical models with fractional differential equations (FDEs) are more realistic and provide comparatively better fit to the real data instead of integer order models. Moreover, FDEs possess the memory effect which plays an essential role in the spreading of a disease. Therefore, the second main mathematical findings of this thesis is that we extend the proposed models using fractional order derivatives considering three different fractional xvi operators namely; Caputo, Caputo-Fabrizio and Atangana-Baleanu-Caputo operators. The proposed fractional models are analyzed rigorously and solved numerically using fractional Adams-Bashforth scheme. The graphical results reveal that the models with fractional derivatives give useful and biologically more feasible consequences.
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