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حد کا اصطلاحی مفہوم

حد کا اصطلاحی مفہوم
ایسے امور جن کی حلت و حرمت اللہ تعالیٰ نے خود بیان فرما ئی ہے اور ان سے تجاوز کرنے سے منع فرما دیا ہے۔ یہ امور " حدود اللہ " کہلاتے ہیں۔ اہل علم نے حد کی اصطلاحی تعریفیں مندرجہ ذیل بیان کی ہیں:
ایسے کام جن کی حلت و حرمت اللہ تعالیٰ نے بیان فرمائی ہو، جیسا کہ ابن منظور افریقی تحریر کرتے ہیں
"وحُدُود الله تعالى الأَشياء التي بيَّن تحريمها وتحليلها وأَمر أَن لا يُتعدى شيء منها۔"8
"حدود اللہ سے مراد ایسی اشیاء ہیں کہ جن کی حلت و حرمت اللہ تعالیٰ نے بیان فرما دی ہے اور یہ حکم دیا ہے کہ ان سے آگے نہ بڑھا جائے۔ "
علامہ زبیدی ؒ (م:1205ھ)حدود کی اقسام اور اس کا مفہوم بیان کرتے ہیں
"فَحُدُودُ ا الله عزّ وجلّ ضَرْبَانِ : ضَرْبٌ منها حُدودٌ!حدَّها للنّاسِ في مَطَاعِمِهم ومَشارِبِهم ومَنَاكِحِهِم وغيرها ممّا أَحَلّ وحَرَّم،وأَمَرَ بالانتِهَاءِ عمّا نَهَى عنه منها ونَهَى عن تَعَدِّيهَا ، والضَّرْب الثانِي عُقوباتٌ جُعِلَتْ لمنْ ركِبَ ما نَهَى عنْه ، كحَدّ السّارِق۔"9
"حدود اللہ کی دو اقسام ہیں: ایک تو ایسی حدود جو لوگوں کے لیے ان کے ماکولات ، مشروبات اور مناکحات وغیرہ میں بسبب حلال اور حرام متعین کی گئی ہیں یہ ان اشیاء سے رکنے کا سبب ہیں جن سے تجاوز کرنے سے روکا گیا ہےاور دوسری قسم وہ سزائیں ہیں جو ممنوع کام کرنے والوں کو دی جاتی ہیں جیسا کہ چور کی حد ۔ "
امام سرخسی ؒ (م:483ھ)حد کی اصطلاحی تعریف کرتے ہوئے لکھتے ہیں
"في الشرع الحد اسم لعقوبة مقدرة تجب حقا لله تعالى ولهذا لا يسمى به التعزير لأنه غير مقدر ولا يسمي به القصاص لأنه حق العباد وهذا لأن وجوب حق العباد۔"10
"شریعت میں حد اس مقررہ سزا کا نام ہے جو بطور حق اللہ...

افتاء كے فضائل قرآن و حدیث كی روشنی میں

To derive and discover the hidden solution to problems regarding every walk of life, according to the teachings of Islam is called Ijtihad and to convey this solution (answer) to the people concerned is called Ifta. Answers to some queries have been directly given by ALLAH ALMIGHTY Himself Then Allah gave the responsibility to his beloved Prophet Muhammad (SA W) to explain & enlighten the people according to the will of ALMIGHTY ALLAH as Quran And then the same responsibility transfers to the eminent religious scholars (Muftis) who are the true inheritors of the Holy Prophet (SAW) Mufti acts as the deputy of the Holy Prophet (SA W) and holds a very high, important & sensitive position of guiding the people towards Islamic teachings. That is why it needs high care, piety & skill. In the given article the reality, importance and virtues of this highly important position have been enlightened

Power Digraphs in Number Theory

The modular exponentiation is considered to be one of the renowned problems in number theory and is of paramount importance in the field of cryptography. Now a days many security systems are based on powerful cryptographic algorithms. Most of them are designed by using the exponentiation x k ≡ y (mod n) as in RSA, Diffie- Hellman key exchange, Pseudo-random number generators etc. For the last two decades, this problem is being studied by associating the power digraphs with modular exponentiation. For the fixed values of n and k, a power digraph G(n, k) is formed by taking Z n as the set of vertices and the directed edges (x, y) from x to y if x k ≡ y (mod n) for the vertices x and y. These digraphs make a novel connection between three disciplines of discrete mathematics namely number theory, graph theory and cryptography. The objective of this dissertation is to generalize the results on symmetry, heights, isolated fixed points, the number of components of a power digraph and the primality of Fermat numbers. To obtain the desired goal, a power digraph is decomposed into the direct product of smaller power digraphs by using the Chinese Remainder Theorem. The method of elimination is adopted to discard those values of n and k which do not provide desired results. During the entire course of research, the Carmichael lambda-function λ(n) is used for developing the relations between the properties of a power digraph and the parameters n, k. For any prime divisor p of n, the concept of equivalence classes has been used to discuss the symmetry of order p of G(n, k). The general rules to determine the heights are formulated by comparing the prime factorizations of k, λ(n) and the orders of vertices. Some necessary and sufficient conditions for the existence of symmetric power digraphs G(n, k), where n = p α q 1 q 2 · · · q m such that p, q i are distinct primes and α > 1, of order p are established. Explicit formulae for the determination of the heights of the vertices and components of a power digraph in terms of n, k, λ(n) and the orders of vertices are formulated. An expression for the number of vertices at a specific height is established. The power digraphs in which each vertex of indegree 0 of a certain subdigraph is at height q ≥ 1 are characterized. The necessary and sufficient conditions on n and k for a digraph to have at least one isolated fixed point are obtained. The work ends with the complete classification of the power digraphs with exactly two components.
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