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

مولانا محمد اسمٰعیل سنبھلی

مولانا محمد اسمٰعیل سنبھلی
افسوس ہے کہ مولانا محمد اسمٰعیل سنبھلی بھی ہم سے رخصت ہوگئے۔ مولانا دیوبند کے فارغ التحصیل تھے اوربڑے جوش اورجذبہ کے انسان تھے اسی وجہ سے وہ ہمیشہ جمعیۃ علماء کے ساتھ وابستہ رہے اوراس سلسلہ میں قید ومحن کی تکالیف بھی برداشت کیں۔وہ نہایت پُرجوش خطیب ومقرر تھے، ان کی تقریر کی خصوصیت یہ تھی کہ شروع سے لے کر آخیر تک ایک سکینڈ کے وقفہ کے بغیر اورایک ہی لب و لہجہ سے تقریر کرتے تھے۔ تقسیم کے بعد دوسرے حضرات کی طرح انھوں نے بھی عملی سیاسیات سے ترک تعلق کرلیا تھا اوریوپی اورگجرات کے مختلف مدارس میں درس و تدریس کاکام کرتے رہے۔ نہایت مخلص،بے لوث اورمتواضع بزرگ تھے۔اﷲ تعالیٰ ان کو مغفرت و رحمت کی نوازشوں سے سرفراز فرمائے۔
[دسمبر۱۹۷۵ء]

 

Factors Affecting Hospital Service Innovation: Literature Review

Innovation at the hospital as a change in the delivery of patient-focused health services by encouraging healthcare professionals to work smarter, faster and better. Service innovation can provide an effective way to create a sustainable competitive advantage for hospitals. This study aims to analyze and examine the factors that influence service innovation in hospitals using the literature review method. The results were obtained from a literature search that discusses the major factors that influence service innovation, namely in the form of a good management system within the scope of the hospital. This big influence is that human resources, starting from the leaders and employees who work in the hospital, must work together for the advancement and empowerment of the hospital.

Some Representations of the Extended Fermi-Dirac and Bose-Einstein Functions With Applications

The familiar Fermi-Dirac (FD) and Bose-Einstein (BE) functions are of importance not only for their role in Quantum Statistics, but also for their several interesting mathematical properties in themselves. Here, in my present investigation, I have ex- tended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relationship to the family of zeta functions. This thesis gives applications of their transform and distributional representations. The Weyl and Mellin transform representations are used to derive mathematical prop- erties of these extended functions. The series representations and difference equations presented led to various new results for the FD and BE functions. It is demonstrated that the domain of the real parameter x involved in the definition of the FD and BE functions can be extended to a complex z. These extensions are dual to each other in a sense that is explained in this thesis. Some identities are proved here for each of these general functions and their relationship with the general Hurwitz-Lerch zeta function Φ(z, s, a) is exploited to derive some new identities. A closely related function to the eFD and eBE functions is also introduced here, which is named as the generalized Riemann zeta (gRZ) function. It approximates the trivial and non- trivial zeros of the zeta function and shows that the original FD and BE functions are related with the Riemann zeta function in the critical strip. Its relation with the Hurwitz zeta functions is used to derive a new series representation for the eBE and the Hurwitz-Lerch zeta functions. ivThe integrals of the zeta function and its generalizations can be of interest in the proof of the Riemann hypothesis (one of the famous problem in mathematics) as well as in Number Theory. The Fourier transform representation is used to derive various integral formulae involving the eFD, eBE and gRZ functions. These are obtained by using the properties of the Fourier and Mellin transforms. Distributional repre- sentation extends some of these formulae to complex variable and yields many new results. In particular, these representations lead to integrals involving the Riemann zeta function and its generalizations. It is also suggested that the Fourier transform and distributional representations of other special functions can be used to evaluate new integrals involving these functions. As an example, I have considered the gen- eralized gamma function. Some of the integrals of products of the gamma function with zeta-related functions can not be expressed in a closed form without defining the eFD, eBE and gRZ functions. It proves the natural occurrence of these general- izations in mathematics. This study led to various new results for the classical FD and BE functions. Integrals of the gamma function and its generalizations are used in engineering mathematics while integrals of the zeta-related functions are essential in Number Theory. Both classes of integrals have been combined first time in this thesis. This in turn gives integrals of product of the modified Bessel functions and zeta-related functions. Further, whereas complex distributions had been defined ear- lier, and in fact used for different applications, there has been no previous utilization of them for Special Functions in general and for the zeta family in particular. This is provided for the first time in this thesis. An important feature of the approach used is the remarkable simplicity of the proofs by using integral transforms.
Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.