scholarly journals Evaluation of inverse integral transforms for undergraduate physics students

2012 ◽  
Vol 90 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Aaron Farrell ◽  
Brandon P. van Zyl ◽  
Zachary MacDonald
Keyword(s):  
Nuclear Physics ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Simple Approach ◽  
General Representation ◽  
Central Idea ◽  
Physics Students ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Inverse Transform

We provide a simple approach to the analytical evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind our method is to reduce the inverse transform to the solution of an ordinary differential equation. We illustrate the utility of our approach by providing examples of the evaluation of transforms without the use of tables. We also demonstrate how the method may be used to obtain a general representation of a function in the form of a series involving the Dirac delta distribution and its derivatives, which has applications in quantum mechanics, semiclassical, and nuclear physics.

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

scholarly journals Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hansol Park
Keyword(s):  
Influence Function ◽  
Equilibrium Solution ◽  
Phase Locking ◽  
Small Diameter ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Sphere Model ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Winfree Model

<p style='text-indent:20px;'>We present a high-dimensional Winfree model in this paper. The Winfree model is a mathematical model for synchronization on the unit circle. We generalize this model compare to the high-dimensional sphere and we call it the Winfree sphere model. We restricted the support of the influence function in the neighborhood of the attraction point to a small diameter to mimic the influence function as the Dirac delta distribution. We can obtain several new conditions of the complete phase-locking states for the identical Winfree sphere model from restricting the support of the influence function. We also prove the complete oscillator death(COD) state from the exponential <inline-formula><tex-math id="M1">\begin{document}$ \ell^1 $\end{document}</tex-math></inline-formula>-stability and the existence of the equilibrium solution.</p>

scholarly journals On the Convolution Equation Related to the Diamond Klein-Gordon Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Amphon Liangprom ◽  
Kamsing Nonlaopon
Keyword(s):  
Convolution Equation ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Singular Distribution ◽  
Klein Gordon ◽  
The Relationship

We study the distributioneαx(♢+m2)kδform≥0, where(♢+m2)kis the diamond Klein-Gordon operator iteratedktimes,δis the Dirac delta distribution,x=(x1,x2,…,xn)is a variable inℝn, andα=(α1,α2,…,αn)is a constant. In particular, we study the application ofeαx(♢+m2)kδfor solving the solution of some convolution equation. We find that the types of solution of such convolution equation, such as the ordinary function and the singular distribution, depend on the relationship betweenkandM.

Superstatistics of the Klein–Gordon equation in deformed formalism for modified Dirac delta distribution

2018 ◽  
Vol 33 (10n11) ◽  
pp. 1850060 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Deformation Parameter ◽  
Gordon Equation ◽  
Wave Functions ◽  
Boltzmann Factor ◽  
Dirac Delta ◽  
Cornell Potential ◽  
Delta Distribution ◽  
Klein Gordon ◽  
Aharonov Bohm ◽  
Klein Gordon Equation

The Klein–Gordon equation is extended in the presence of an Aharonov–Bohm magnetic field for the Cornell potential and the corresponding wave functions as well as the spectra are obtained. After introducing the superstatistics in the statistical mechanics, we first derived the effective Boltzmann factor in the deformed formalism with modified Dirac delta distribution. We then use the concepts of the superstatistics to calculate the thermodynamics properties of the system. The well-known results are recovered by the vanishing of deformation parameter and some graphs are plotted for the clarity of our results.

scholarly journals On regularizations of the Dirac delta distribution

2016 ◽  
Vol 305 ◽  
pp. 423-447 ◽  
Author(s):  
Bamdad Hosseini ◽  
Nilima Nigam ◽  
John M. Stockie
Keyword(s):  
Dirac Delta ◽  
Delta Distribution

scholarly journals Superstatistics of Diatomic Molecules with the Shifted Deng-Fan Potential Model

2021 ◽  
Vol 12 (3) ◽  
pp. 4126-4139
Keyword(s):  
Partition Function ◽  
Short Range ◽  
Deformation Parameter ◽  
Potential Model ◽  
Diatomic Molecules ◽  
Thermal Fluctuations ◽  
Boltzmann Factor ◽  
Molecular Systems ◽  
Dirac Delta ◽  
Delta Distribution

In this article, we discuss the thermodynamic properties of the shifted Deng-Fan potential for HCl, CrH, CuLi, and ScF diatomic molecules using the q-deformed superstatistics approach. The partition function is obtained with the help of the generalized Boltzmann factor from the modified Dirac delta distribution. In addition, thermodynamic functions such as entropy, specific heat capacity, free energy, and mean energy are obtained using the partition function. Our results are presented graphically, and the ordinary statistical quantities are recovered when the deformation parameter tends to zero. Our results may be useful in the study of thermal fluctuations in atomic and molecular systems involving short-range interactions.

scholarly journals Violence today

2006 ◽  
Vol 11 (2) ◽  
pp. 261-267
Author(s):  
Michel Wieviorka
Keyword(s):  
Cold War ◽  
Labor Movement ◽  
Nuclear Physics ◽  
Industrial Structure ◽  
Historical Context ◽  
Central Idea ◽  
New Approaches ◽  
The World ◽  
Recent Developments ◽  
The Cold War

In this paper, the author seeks to approach contemporary violence in its most different expressions, including the use of the most recent developments in biology, bacteriology, chemistry and nuclear physics. The central idea is that violence changes, and with it the way it is perceived and how we react to it. The text, besides putting violence into a historical context, analyzes 1) the big transformation(s) in the world: the end of the cold war, the new industrial structure and its consequences for the decline of the labor movement, globalization and the new forms of victimization; 2) in the second part, the author points to new approaches and characterizes novel contemporary subjects.

Sign in / Sign up

Export Citation Format

Share Document