scholarly journals On A Logarithmic Mittag-Leffler Function, its Properties and Applications

2021 ◽  
Author(s):  
M.A. Pathan ◽  
Hemant Kumar
Keyword(s):  
Infectious Diseases ◽  
Hypergeometric Functions ◽  
Point Of View ◽  
Integral Representations ◽  
Contour Integral ◽  
Application Point

In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions. 

scholarly journals On the integral representations for the confluent hypergeometric function

2016 ◽  
Vol 472 (2193) ◽  
pp. 20160421 ◽  
Author(s):  
Bujar Xh. Fejzullahu
Keyword(s):  
Integral Representation ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Contour Integral ◽  
Confluent Hypergeometric Functions ◽  
Special Cases

In this paper, we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases. Consequently, we derive expansions of the confluent hypergeometric function in terms of functions of the same kind. Furthermore, we obtain a new identity involving integrals and sums of confluent hypergeometric functions. Our results generalized several well-known results in the literature.

Rough Sets and Approximate Reasoning

2014 ◽  
pp. 180-228 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Approximate Reasoning ◽  
Human Reasoning ◽  
Intuitionistic Fuzzy ◽  
Application Point ◽  
Future Work

Several models have been introduced to capture impreciseness in data. Fuzzy sets introduced by Zadeh and Rough sets introduced by Pawlak are two of the most popular such models. In addition, the notion of intuitionistic fuzzy sets introduced by Atanassov and the hybrid models obtained thereof have been very fruitful from the application point of view. The introduction of fuzzy logic and the approximate reasoning obtained through it are more realistic as they are closer to human reasoning. Equality of sets in crisp mathematics is too restricted from the application point of view. Therefore, extending these concepts, three types of approximate equalities were introduced by Novotny and Pawlak using rough sets. These notions were found to be restrictive in the sense that they again boil down to equality of sets and also the lower approximate equality is artificial. Keeping these points in view, three other types of approximate equalities were introduced by Tripathy in several papers. These approximate equalities were further generalised to cover the approximate equalities of fuzzy sets and intuitionistic fuzzy sets by him. In addition, considering the generalisations of basic rough sets like the covering-based rough sets and multigranular rough sets, the study has been carried out further. In this chapter, the authors provide a comprehensive study of all these forms of approximate equalities and illustrate their applicability through several examples. In addition, they provide some problems for future work.

scholarly journals Implicit max-stable extremal integrals

Extremes ◽  
2020 ◽  
Author(s):  
D. Kremer
Keyword(s):  
Loss Function ◽  
Open Problem ◽  
Stochastic Integral ◽  
Extreme Values ◽  
Stable Distributions ◽  
Extreme Value ◽  
Point Of View ◽  
Extreme Value Distributions ◽  
Application Point ◽  
Deterministic Function

Abstract Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function f ≥ 0. From an application point of view, one is rather interested in extreme loss events that occur relative to f than in the corresponding extreme values itself. In this context, so-called f -implicit α-Fréchet max-stable distributions arise and have been used to construct independently scattered sup-measures that possess such margins. In this paper we solve an open problem in Goldbach (2016) by developing a stochastic integral of a deterministic function g ≥ 0 with respect to implicit max-stable sup-measures. The resulting theory covers the construction of max-stable extremal integrals (see Stoev and Taqqu Extremes 8, 237–266 (2005)) and, at the same time, reveals striking parallels.

scholarly journals Integral representations of generalized Lauricella hypergeometric functions

1992 ◽  
Vol 15 (4) ◽  
pp. 653-657 ◽  
Author(s):  
Vu Kim Tuan ◽  
R. G. Buschman
Keyword(s):  
Integral Representation ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Appell Function

The generalized hypergeometric function was introduced by Srivastava and Daoust. In the present paper a new integral representation is derived. Similarly new integral representations of Lauricella and Appell function are obtained.

Channeling in 4H-SiC from an Application Point of View

2019 ◽  
Vol 963 ◽  
pp. 386-389 ◽  
Author(s):  
Peter Pichler ◽  
Tomasz Sledziewski ◽  
Volker Häublein ◽  
Anton Bauer ◽  
Tobias Erlbacher
Keyword(s):  
Monte Carlo ◽  
Ion Implantation ◽  
Monte Carlo Simulations ◽  
Electronic Devices ◽  
Point Of View ◽  
Power Electronic ◽  
Application Point ◽  
Doping Profiles

During ion implantation into monocrystalline semiconductors, some of the implanted atoms will be deflected to crystal directions along which they may penetrate deeply into the crystal. We investigate such channeling effects for Al and N implantation into 4H-SiC by Monte Carlo simulations. The focus of the work is on the effects of channeling on doping profiles, the relevance for the net doping of typical power electronic devices, and the influence of scattering oxides.

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