مزاح کے انسانی نفسیات پر اثرات اسلامی تعلیمات کی روشنی میں Effects of humor on human psychology in the light of Islamic teachings

Every branch of art leaves a deep impact on the human psyche, but the immortal fact is that the reason for their creation is also to reduce the tension of the human mind. The most representative theory of humor in philosophy and psychology and even in physics. Is the idea of ​​well-being, comfort or well-being? Broadly speaking, this suggests that humor (which has an obvious physiological effect) has effects on the nervous system and allows different levels of stress to be released. In other words, laughter and good humor have the ability to release stored nervous energy. Humor is included in human nature and man has a strong desire for this thing that there should be such means for him to express joy and expansion. Because through them, man is blessed with mental and physical peace and comfort. In these things, he considers the survival of his self-respect. Islam not only allows humor, sports and entertainment, but also sets rules and regulations within which human beings can fulfill their natural needs. Its cultural traditions should also be propagated. As the head and governor of the Islamic state, the Holy Prophet (ﷺ) made the best arrangements for his state, the taste of the people and their entertainment, and set an example for the rulers that, like other matters, oppression in this not to be taken for granted, fun and humor are part of human nature. He (ﷺ) allowed fun and laughter and He (ﷺ) himself used to be cheerful. Islam admires cheerfulness and cheerfulness, and encourages it so that people can be refreshed and perform their duties in an auspicious manner. Through this paper, it will be clarified that what are the effects of humor on human psychology and what are the teachings of Islam and the Prophet of Islam in this regard. Key Word:    Fine Arts, Humor, Human terms, Human humor

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.