مسٹر رامانجم
اس وقت دنیا کا سب سے بڑا ریاضی دان ایک ہندوستانی تھا، مسٹر رامانجم کی بابت، جس کے کمالات ریاضیہ کا ذکر آج سے ٹھیک ایک سال قبل معارف میں آچکا ہے، بعض علماء فن کا خیال تھا کہ نیوٹن کے بعد سے دنیا میں اس دماغ کا ریاضی دان نہیں پیدا ہوا ہے اور اس کا تو سب کو اعتراف تھا کہ انھوں نے بعض وہ مسائل حل کردیئے جو پوری ایک صدی سے لاینحل چلے آرہے تھے، سخت افسوس ہے کہ ماہ گذشتہ میں اسی ہستی نے دق میں مبتلا ہوکر دنیا کو اپنے فیض سے ہمیشہ کے لئے محروم کردیا، مرحوم کا سن کل ۳۲ سال کا تھا۔
خوش درخشید ولے دولت مستعجمل بود
(جون ۱۹۲۰ء)
مدراس کے نامور ریاضی دان رامانجم کی خبر وفات کسی پچھلے معارف میں درج ہوچکی ہے، یورپ کے اعلیٰ علمی رسائل مدت تک ان کے ماتم میں سوگوار رہے، اور متعدد ماہرین فن کے قلم نے اس حادثہ عظیم پر علم و فن کی جانب سے فریضۂ تعزیت ادا کیا، کیمبرج یونیورسٹی کے مشہور پروفیسر جی،ایچ، ہارڈی نے سائنٹفک ہفتہ وار نیچر میں جو تعزیت نامہ شائع کیا ہے، اس میں بار بار اس قسم کے فقرہ ملتے ہیں۔ ’’یہ بالکل یقینی ہے کہ مرحوم کی مہندسانہ فضیلت اعلیٰ ترین پایہ کی تھی اور وہ ایک استشنائی قوت فکر و اجتہاد کا شخص تھا‘‘۔ اس کے تقریباً بیس مقالات شائع ہوئے، جنھوں نے زمانۂ جنگ ہی میں تمام دنیائے ریاضیات کو اپنی جانب متوجہ کرلیا‘‘۔ اس کے پیش نظر صرف وہ مسائل تھے، جن تک معدددے چند افراد کی رسائی ہوسکتی ہے‘‘۔ اس کی قوت استنباط بالکل حیرت انگیز تھی، جس کی کوئی نظیر کسی یوروپین ریاضی دان میں...
The history of the business and trade is as old as the history of humanity, itself. Different cultures and regions have their own business ethics throughout the times past. With the rise of globalization, the various sets of business ethics are getting common values and forms. While Islam, being a universal religion, provides guidelines for every aspect of life including trade, commerce and business. Islamic business ethics derive from divine revelation and Sunnah of the Prophet (SAW). Business ethics denotes the behavior of trading entity supposed to follow while interacting with society. The Islamic business ethics take care of the all stake holders from production to consumption including employees, trade agreements, quality standards, environment and social responsibilities. The current paper is aiming to elaborate the business ethics in the light of instructions draw from the Seerah of the Prophet (SAW) in order to provide an insight for humanity to follow them, practically
Lead-based electro ceramics like PZT are the most commercially used as sensors, actuators and transducers due to their excellent electromechanical response, however The environmental concerns and the legislation imposed on hazardous materials, lead is considered toxic and its use is banned for many applications. Therefore the alternative lead free electroceramics have become the focus of research in both industry and academia. In our present work among the several families of lead-free, we will focus on the bismuth-based ferroelectric ceramics due to their excellent piezoelectric and ferroelectric properties. In brief this thesis we will emphasize on the improvement of ferroelectric and field-induced strain properties of BNKT-LS ceramic system by different alovilent and isovalent B-site substitutions. The effect of zirconium (Zr+4), niobium (Nb+5) and tantalum (Ta+5) substitution for the B-site in the host perovskite unit cell on the dielectric, electromechanical and piezoelectric properties of lead-free 0.99[Bi1/2(Na0.82K0.18)1/2TiO3]-0.01LiSbO3 (BNKT-LS) piezoceramics has been investigated. The ternary BNKT-LS system was synthesized using low temperature conventional solid state reaction method. Crystal structure, dielectric, ferroelectric and field-induced strain behavior of Zr modified lead-free 0.99[Bi1/2(Na0.82K0.18)1/2(Ti1-xZrx) O3]-0.01LiSbO3 (BNKTZ-LS) ceramics were investigated in composition range x = 0 - 0.040. XRD patterns revealed the formation of pure perovskite phase with no apparent structural phase transition with pseudo cubic symmetry for the compositions at low concentration of dopants although there were some traces of secondary phases at higher concentrations. The temperature-dependent dielectric peaks of the BNKTZ-LS ceramics broadened and ferroelectric polarizations decreased with increasing Zr concentration. Ferroelectric and bipolar field induced-strain curves indicated a disruption of ferroelectric order upon Zr addition into BNKT-LS ceramics. This destabilization of the ferroelectric order was accompanied by an enhanced field-induced strain. A high field-induced strain (S = 0.30%) with a normalized strain (d*33 = Smax/Emax = 500 pm/V) was observed at an applied electric field of 6 kV/mm at x = 0.020. The Ta-modified 0.99[(Bi0.82Na18)TiO3-(Bi1/2K1/2)TiO3]- 0.01LiSbO3 (BNKTT-LS) piezoceramics were also synthesized by a conventional solid-state reaction method. The effect of Ta addition into the BNKT-LS ceramics were studied through X-ray diffraction, dielectric, temperature dependent ferroelectric and field-induced strain characterizations. As the Ta content was increased, the maximum dielectric constant as well as the depolarization temperature (Td) decreased. The polarization and strain hysteresis loops indicate that the addition of Ta significantly disrupts the ferroelectric order of the BNKT-LS ceramics leading to a degradation of the remnant 14 polarization and coercive field. However, the destabilization of the ferroelectric order is accompanied by a significant enhancement in the unipolar strain. A large unipolar field-induced strain of 0.38% with a normalized (d*33 = Smax/Emax = 650 pm/V) at a driving field of 6 kV/mm was obtained at room temperature for x = 0.013. This significant strain enhancement is a result of the reversible phase transition between a NP phase in a zero field and a field-induced ferroelectric phase. Finally the effect of Nb-substitution on the dielectric, electromechanical and piezoelectric properties of Pb-free 0.99[Bi1/2(Na0.82K0.18)1/2Ti1-xNbxO3]-0.01LiSbO3 (BNKT-LS) piezoelectric ceramics has been investigated. X- ray diffraction analysis reveals pseudo-cubic symmetry for the compositions with x = 0 - 0.030. Both the dielectric constant εr and depolarization temperature Td decreased with an increase in Nb content. An analysis of the electric field induced polarization and strain hysteresis loops indicated that Nb substitution disrupted the long range ferroelectric order of BNKT-LS ceramics. This degraded the remnant polarization, coercive field and piezoelectric coefficient d33 while the electric field induced strain increased (peaked at x=0.015) to 0.43% corresponding to a normalized strain (d33* = 614 pm/V) at a deriving field of 7 kV/mm. This abnormal strain enhancement may be attributed to the reversible phase transition between the polar and non-polar phases. At high Nb concentrations, BNKNb-LS ceramics shows a typical relaxor behavior. So for all dopants the increase in concentration results in a decrease in the maximum dielectric constant as well as the depolarization temperature Td, the disruption of the long range ferroelectric order, the degradation of remnant polarization, coercive field and piezoelectric coefficient d33. This was also accompanied by enhancement in the electric field induced strain. This abnormal strain enhancement could be attributed to a reversible phase transition between polar and non-polar phase for all systems. For high doping level BNKT-LS ceramics showed a typical relaxor behaviour.