International Journal of Trend in Scientific Research and Development

In this paper, a new generalization of the mean value theorem is firstly established. Based on the Rolle’s theorem, a simple proof is provided to guarantee the correctness of such a generalization. Some corollaries are evidently obtained by the main result. It will be shown that the mean value theorem, the Cauchy’s mean value theorem, and the mean value theorem for integrals are the special cases of such a generalized form. We can simultaneously obtain the upper and lower bounds of certain integral formulas and verify inequalities by using the main theorems. Finally, two examples are offered to illustrate the feasibility and effectiveness of the obtained results. 

by Yeong-Jeu Sun "A Note on the Generalization of the Mean Value Theorem" 

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, 

URL: https://www.ijtsrd.com/papers/ijtsrd38258.pdf

Paper URL : https://www.ijtsrd.com/mathemetics/calculus/38258/a-note-on-the-generalization-of-the-mean-value-theorem/yeongjeu-sun

callforpapermedicalscience, medicalsciencejournal, manuscriptsubmission

In this paper, the generalized gamma functions of the first and second types are firstly introduced and investigated. It can be proven that the traditional gamma function is a special case of the first type of generalized gamma function. Besides, the iterative formula of the generalized gamma function will be fully derived. Finally, a numerical example is provided to illustrate the validity and effectiveness of our main result. 

by Yeong-Jeu Sun "A Note on the Generalized Gamma Function" 

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, 

URL: https://www.ijtsrd.com/papers/ijtsrd38259.pdf

Paper URL : https://www.ijtsrd.com/mathemetics/calculus/38259/a-note-on-the-generalized-gamma-function/yeongjeu-sun

callforpaperlifesciences, lifesciencesjournal, researchpapers

Obscuration is the phenomenon of covering of a certain percentage of area of an object by another. It can be a governing variable in radiation heat transfer, fluid dynamics and so on. Although modern day analytical tools allow determination of area of obscuration, the non availability of handy formulae for theoretical calculations has lead to this study. In this study, the method of integration shall be used to determine the area of obscuration for various cases. Two circles of different radii shall be considered for this study. Various positions shall be considered and based on the combinations obtained, expressions for the area of obscuration shall be derived. This study aims at enumerating and exploring various cases so as to pave way towards a further study of general formulae to arrive at required expressions. Thus the theoretically obtained area can be used in various calculations as and when found of necessity. 

BY Gourav Vivek Kulkarni "Determination of Area of Obscuration between Two Circles by Method of Integration" 

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, 

URL: https://www.ijtsrd.com/papers/ijtsrd35863.pdf

Paper URL : https://www.ijtsrd.com/mathemetics/calculus/35863/determination-of-area-of-obscuration-between-two-circles-by-method-of-integration/gourav-vivek-kulkarni

ugcjournallist, listofugcapprovedjournals, researchpublication

In a number of Engineering applications, there are certain governing variables that bear the potential to possess a major part of the control towards the success of the process. Some of these variables may be independent while others are dependent on each other is some or the other manner. In applications involving metered quantity of fluid flow, radiation heat transfer and so on, one of such governing variables is the flow rate. Flow rate may refer to that of any fluid or radiation or solids in certain cases. As flow rate depends on the area of opening that is available for flow, it is customary to either determine the area of opening or that of obscuration. In this paper, initially the physical significance of area of obscuration in applications related to fluid flow, radiation heat transfer, packaging applications and photo sensors shall be elaborated to establish a premise for the later derived general expression for determination of the area of obscuration for a combination of two circles with different radii, with one placed at any arbitrary point in space. This general expression shall be deemed to be applicable for provided certain necessary condition is met with respect the relation between the radii of the two circles and the distance between their centres. The derived general formula shall be verified towards the end to confirm the validity for any arbitrary case. 

BY Gourav Vivek Kulkarni "Significance of Area of Obscuration and Derivation of General Expression by Method of Integration" 

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, 

URL: https://www.ijtsrd.com/papers/ijtsrd35869.pdf

Paper URL : https://www.ijtsrd.com/mathemetics/calculus/35869/significance-of-area-of-obscuration-and-derivation-of-general-expression-by-method-of-integration/gourav-vivek-kulkarni

callforpaperarts, artsjournal, peerreviewedjournal