Search from the Journals, Articles, and Headings
Advanced Search (Beta)
Loading...
Loading...
Loading...
Loading...
Loading...
Loading...

ڈاکٹر مختار احمد انصاری

ڈاکٹر مختار احمدانصاری مرحوم
۹؍ مئی ۱۹۳۶؁ء کی شام کو سات بجے کے قریب میں ڈیرہ دون کی ایک سڑک سے گزر رہا تھا کہ پیچھے سے ایک موٹر تیزی سے آئی اور نکل گئی، میں نے دیکھا کہ اس پر ڈاکٹر انصاری بیٹھے ہیں، سرکھلا تھا اور چہرہ سے بے حد تکان معلوم ہوتا تھا، رات گزر گئی اور صبح کو ان کی قیام گاہ کی تلاش کی، معلوم ہوا کہ وہ رات ہی دلّی چلے گئے، لیکن جب شام ہوئی تو معلوم ہوا کہ وہ رات دلّی نہیں گئے، راستہ سے سیدھے جنت کو سدھارے، دل دھڑکا آنکھیں پرنم ہوئیں اور سینہ سے آہ کا ایک شعلہ اٹھا، جس نے صبر و تمکین کی متاع کو جلا کر خاکستر بنادیا۔
ڈاکٹر مختار احمد انصاری گو نسب و وطن کے لحاظ سے ضلع غازی پور کے ایک ممتاز قصبہ یوسف پور کے ایک نہایت شریف خاندان سے تھے، مگر در حقیقت ان کا تعلق پورے ہندوستان سے تھا، اس یوسف کا کنعان، وہ محدود مقام نہ تھا، جس کو یوسف پور کہتے ہیں، بلکہ پورا ہندوستان تھا، اسی لئے آج پورے ہندوستان نے ان کی موت کا ماتم کیا، کیا مسلمان، کیا ہندو، کیا سکھ، کیا عیسائی سب نے یہی جانا کہ آج ان کا حقیقی بھائی اس دنیا سے چل بسا۔
میں نے ڈاکٹر انصاری کو سب سے پہلے ۱۹۱۲؁ء میں اس وقت دیکھا جب وہ بلقان کی جنگ میں طبی وفد لے کر ترکی جارہے تھے اور اس تقریب سے لکھنؤ اسٹیشن سے گزر رہے تھے، مولانا شبلی اور بہت سے لوگ لکھنؤ اسٹیشن پر ڈاکٹر صاحب کو الوداع کہنے گئے تھے، اس وقت ڈاکٹر صاحب کی عمر ۳۰، ۳۲ برس کی تھی، کھلتا ہوا رنگ، دُبلا پتلا چھریرا بدن کشیدہ قامت، ہنستا چہرہ، انوری یا قیصری مونچھیں، جسم پر چست خاکی وردی،...

عہد نبوی میں نوجوان صحابہ کرام کا بطور معلم تقرر اور اصلاح معاشرہ میں ان کا کردار

It is above-board that teachers play an important role in forming, formulating, molding and developing the society as individuals and as a whole. The youth has ever been an icon to lead the community in every sphere of life. The young stuff has played the pivotal role in preaching, scribing, teaching, political, economic and even diplomatic fields. The present research article explores the role of various companions of Holy Prophet (r) in these fields. Firstly, the Holy Prophet (r) groomed his companions, stormed their brains and paved them on the Divine way, then sent them to the said fields to work. Among those companions, Ḥaḍrat Muṣ‘ab bin ‘Umayr, Mu‘ādh bin Jabal, ‘Abdullāh ibn e Maktūm, Rāfi‘ bin Mālik, ‘Abdullāh ibn e Mas‘ūd, ‘Abdullāh ibn e ‘Abbās, Abū Sa‘īd Khudrī (y) as well as from females Ḥaḍrat ‘Āyshah, Ḥaḍrat Ḥafṣah, Shifā bint-e-‘Abdullah etc. Were appointed as preachers. Their task was not only to teach and educate the community rather to present themselves before them as paragon for their particular fields. The research concludes that the Prophet (r) laid down a criteria for selection of the teachers of Muslim Ummah. The selection criteria of the Prophet (r) was based not only on contingent variables but also on some special characteristics like teaching and training, potential empathy for the learners and a passion for social reformation. As a result, these preachers, after practicing their ideal and best performance, produced numerous educations, merchants, facilitators and reformers in the society. The present research paper will explore the companions’ efforts for the reformation of the society.

Solvability of Systems of Differential Equations by Complex Symmetry Analysis

Complex symmetry analysis (CSA) establishes a connection between a class of n and 2n, dimen- sional complex and real systems of ordinary/partial differential equations (ODEs/PDEs), respec- tively. Similarly, another class of systems of PDEs is extractable from the base complex systems of ODEs by CSA. The equivalence of the base complex systems under an invertible transforma- tion of the dependent and independent variables has been exploited to study the corresponding real systems. Of particular interest is the extension of Lie groups of transformations developed to solve scalar and systems of non-linear second order ODEs, to two and four dimensional systems of the same order, respectively. For scalar equations, they may be used to either reduce them to the free particle equation (linearize) or integrate them. The former requires an 8-dimensional algebra while a 2-dimensional solvable algebra is sufficient to apply the latter. In this thesis, those two and four dimensional systems are characterized that arise from linearizable or integrable scalar and two dimensional systems of second order ODEs, respectively. Further, invariance of systems of PDEs under equivalence transformations is studied with CSA by employing the invariance properties of the base complex PDEs. Three linearizable classes of two dimensional systems of cubically semi-linear (in the first deriva- tive) second order ODEs has appeared so far in the literature. A comparison of two of the classes, obtainable from geometric methods and CSA, is presented. Both these classes are transformable to the system of free particle equations subject to certain linearization conditions, even though their general (cubic) semi-linear forms are proved to be inequivalent under point transformations. There are five equivalence classes of two dimensional linearizable systems of second order ODEs namely, those with 5, 6, 7, 8 and 15-dimensional Lie algebras. For those systems that arise from a scalar complex linearizable second order ODE, treated as a pair of real ODEs, a reduced optimal canonical form is established. Of the five only three equivalence classes with 6, 7 or 15-dimensional algebras are recovered by this procedure. Both the equations of these systems are found to sat- isfy Cauchy-Riemann (CR) equations with respect to the dependent variables. Therefore, here as elsewhere in this thesis, such systems are called CR-structured systems. A class of non-linearizable two dimensional CR-structured systems of second order ODEs is presented to show that the linearizability of the scalar complex equations is not sufficient to map ii iii the emerging systems to linear forms. A general system of n second order ODEs with 2n symmetry generators may not be amenable to quadratures by real symmetry analysis. However, it is shown that the CR-structured systems may be solvable by a procedure called complex-linearization even if they have fewer symmetries than required to linearize or integrate them. A symmetry generator of the base complex ODE associates a pair of Lie-like operators with the CR-structured systems. It is proved that all such operators are not necessarily real symmetries of the emerging system. A criterion has been developed which shows when and how the real symme- try generators of the CR-structured systems of two second order ODEs are extractable from the associated complex Lie symmetries of the base ODEs. The most general complex-linearizable form and the complex-linearization criteria for four di- mensional systems of second order ODEs are derived by extending the geometric linearization criteria presented for two dimensional systems of cubically semi-linear second order ODEs. Two canonical forms of such systems have been derived by employing CSA on a system of dimension two once and a scalar equation twice. A specific form of the complex linearizing transformations associated with the base two dimensional systems is shown to furnish the reduction of the corresponding four dimensional complex-linearizable systems to the free particle Newtonian systems. Semi-invariants for a class of systems of two linear parabolic type PDEs in two independent variables under equivalence transformations of the dependent variables have been deduced. This class of systems of two linear parabolic type PDEs and the real transformations that map such systems into themselves with different coefficients in general, are shown to correspond to complex scalar linear parabolic equations and associated complex transformations, respectively. Moreover, the semi-invariants for such systems of PDEs also correspond to complex Ibragimov invariants of the complex scalar linear parabolic PDEs. Particular cases of systems of parabolic type equations, i.e., when they are uncoupled or coupled in a special manner, have been studied with CSA.
Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.