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سپ تے فقیر

سپ تے فقیر

کسے پنڈ وچ اک فقیر رہندا سی۔ بہت غریب سی، اوہدا تے اوہدے گھر والی دا گزارہ خیرات والیاں چیزاں اتے ای ہوندا سی۔ اک دن اوہناں کول کھاون لئی کجھ وی نئیں سی۔ ایس لئی اوہ سویرے سویرے ای بھیک منگن ٹر پیا۔ فقیر کول اک کپڑے دا تھیلہ سی جس وچ اوس نے اک لوٹا تے اک کجہ رکھیا ہویا سی۔ کجے وچ وی اوہ لوکاں ولوں ملیا سالن پاندا تے لوٹے وچ پانی پا کے ضرورت ویلے پیندا سی۔ ہتھ وچ اوہ ہمیشہ سوٹی رکھدا سی۔ رستے وچ جاندے ہویاں اوس نوں اک سپ نظر آیا۔ اوس نے بہت تیزی نال سپ نوں کجے وچ بند کیتا۔ اوس دا منہ کپڑے نال بند کر کے اپنی بیوی نوں دے دتا۔ اوس نوں یقین سی کہ جدوں اوہدی بیوی کجہ کھولے گی تاں سپ اوس نوں ڈنگ مارے گا تے انج اوہ مر جاوے گی۔ جدوں اوس دی بیوی نے کجے دا منہ کھولیا تاں اوس نوں اندروں اک بہت قیمتی ہار ملیا۔ ایہہ ویکھ کے دونویں بہت حیران ہوئے۔

ایس خوبصورت ہار دی شہرت جدوں شہزادی تائیں اپڑی تاں اوس نے ہار ویکھن دی خواہش دا اظہار کیتا۔ ہار ویکھ کے شہزادی نے اوہناں نوں منہ منگے پیسے دے کے ہار خرید لیا۔ شہزادی ہار خرید کے بہت خوش سی۔ اک دن اوس ہار اپنے میز اتے رکھیا تے آپ کسے کم محل توں باہر چلے گئی۔ واپس آئی تاں اوس نوں حیرت ہوئی کہ میز اتے ہار نئیں بلکہ اک سوہنا جیہا بال منہ وچ انگوٹھا پا کے ستا ہویا اے۔ پہلاں تاں شہزادی بہت ڈری۔ وزیر نے آکھیا کہ تہاڈا ہار جادو دا ہار سی۔ دراصل اوہ ایہو بچہ سی جس نوں ظالم جادوگر نے ہار بنا دتا سی۔ ہن ایہہ دوبارہ اپنی...

اسلامی ریاست میں قیادت کے راہنما اصول اسلامی تعلیمات کی روشنی میں

Islamic state is responsible to provide the means of protection for its inhabitants. It is the religious and spiritual duty of Islamic state to protect the Islamic culture and civilization as well so that the Muslims could perform their religious and social duties freely. Likewise, an Islamic state is supposed to ensure justice into the society. It indicates that establishing an Islamic state is core responsibility of Muslims so that they could practice their religion in free atmosphere and religious leadership. In this connection, the purpose of this research paper was to explore the principles of leadership in an Islamic state. The qualitative and descriptive research methodology was employed for the collection and analysis of data. The review of literature revealed that Muslim scholars have given particular emphasized on establishing the Islamic state. Moreover the jurists have counted the essential qualities in Islamic leadership. In this context, this article has dealt with the ideal principles which are necessary for the Islamic leadership. These principles are extracted from Qur’ān, Sunnat and. (صلى الله عليه وسلم) Prophet Holy of life

Majoriztion and its Applications

The notion of majorization arose as a measure of the diversity of the components of an n-dimensional vector (an n-tuple) and is closely related to convexity. Many of the key ideas relating to majorization were discussed in the volume entitled Inequalities by Hardy, Littlewood and Polya (1934). Only a relatively small number of researchers were inspired by it to work on questions relating to majorization. After the volume entitled Theory of Majorization and its Applications (Marshall and Olkin, 1979), they heroically had shifted the literature and endeavored to rearrange ideas in order, often provided references to multiple proofs and multiple viewpoints on key results, with reference to a variety of applied fields. For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometime extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations. Majorization theory is a key tool that allows us to transform complicated non-convex constrained optimization problems that involve matrix-valued variables into simple problems with scalar variables that can be easily solved. In this PhD thesis, we restrict our attention to results in majorization that directly involve convex functions. The theory of convex functions is a part of the general subject of convexity, since a convex function is one whose epigraph is a convex set. Nonetheless it is an important theory, which touches almost all branches of mathe- matics. In calculus, the mean value theorem states, roughly, that given a section of a smooth curve, there is a point on that section at which the derivative (slope) of the viiviii curve is equal (parallel) to the ”average” derivative of the section. It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval. In the first chapter some basic results about convex functions, some other classes of convex functions and majorization theory are given. In the second chapter we prove positive semi-definite matrices which imply exponen- tial convexity and log-convexity for differences of majorization type results in discrete case as well as integral case. We also obtain Lypunov’s and Dresher’s type inequalities for these differences. In this chapter both sequences and functions are monotonic and positive. We give some mean value theorems and related Cauchy means. We also show that these means are monotonic. In the third chapter we prove positive semi-definite matrices which imply a surprising property of exponential convexity and log-convexity for differences of additive and multiplicative majorization type results in discrete case. We also obtain Lypunov’s and Dresher’s type inequalities for these differences. In this chapter we use mono- tonic non-negative as well as real sequences in our results. We give some applications of majorization. Related Cauchy means are defined and prove that these means are monotonic. In the fourth chapter we obtain an extension of majorization type results and ex- tensions of weighted Favard’s and Berwald’s inequality when only one of function is monotonic. We prove positive semi-definiteness of matrices generated by differ- ences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality. This implies a surprising property of exponen- tial convexity and log-convexity of these differences which allows us to deduce Lya- punov’s and Dresher’s type inequalities for these differences, which are improvements of majorization type results and weighted Favard’s and Berwald’s inequalities. Anal- ogous Cauchy’s type means, as equivalent forms of exponentially convexity and log- convexity, are also studied and the monotonicity properties are proved. In the fifth chapter we obtain all results in discrete case from chapter four. Weix give majorization type results in the case when only one sequence is monotonic. We also give generalization of Favard’s inequality, generalization of Berwald’s inequal- ity and related results. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality which implies exponential convexity and log-convexity of these differences which allow us to deduce Lyapunov’s and Dresher’s type inequalities for these differences. We introduce new Cauchy’s means as equiva- lent form of exponential convexity and log-convexity. In the sixth chapter we prove positive semi-definiteness of matrices generated by dif- ferences deduced from Popoviciu’s inequalities which implies a surprising property of exponential convexity and log-convexity of these differences which allows us to deduce Gram’s, Lyapunov’s and Dresher’s type inequalities for these differences. We intro- duce some mean value theorems. Also we give the Cauchy means of the Popoviciu type and we show that these means are monotonic.
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