Mellin convolutions, statistical distributions and fractional calculus

2018 ◽  
Vol 21 (2) ◽  
pp. 376-398 ◽  
Author(s):  
A. M. Mathai
Keyword(s):  
Fractional Calculus ◽  
Reaction Rate ◽  
Fractional Integrals ◽  
Rate Theory ◽  
Statistical Distributions ◽  
Inverse Gaussian ◽  
Gaussian Density ◽  
Reaction Rate Theory ◽  
Nuclear Reaction Rate

Abstract This paper shows that meaningful interpretations for Mellin convolutions of products and ratios involving two, three or more functions, can be given through statistical distribution theory of products and ratios involving two, three or more real scalar random variables or general multivariate situations. This paper shows that the approach through statistical distributions can also establish connection to fractional integrals, reaction-rate probability integrals in nuclear reaction-rate theory, Krätzel integrals and Krätzel transform in applied analysis, continuous mixtures, Bayesian analysis etc. This paper shows that the theory of Mellin convolutions, currently available for two functions, can be extended to many functions through statistical distributions. As illustrative examples, products and ratios of generalized gamma variables, which lead to Krätzel integrals, reaction-rate probability integrals, inverse Gaussian density etc, and type-1 beta variables, which lead to various types of fractional integrals and fractional calculus in general, are considered.

On Nuclear Reaction Rate Theory

1984 ◽  
Vol 496 (6) ◽  
pp. 380-396 ◽  
Author(s):  
H. J. Haubold ◽  
A. M. Mathai
Keyword(s):  
Nuclear Reaction ◽  
Reaction Rate ◽  
Rate Theory ◽  
Reaction Rate Theory ◽  
Nuclear Reaction Rate

scholarly journals A Versatile Integral in Physics and Astronomy and Fox’s H-Function

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 122 ◽  
Author(s):  
Arak M. Mathai ◽  
Hans J. Haubold
Keyword(s):  
Nuclear Physics ◽  
Reaction Rate ◽  
Inverse Gaussian ◽  
Pathway Model ◽  
Gaussian Distributions ◽  
Generalized Type ◽  
Fox’S H Function ◽  
Nuclear Reaction Rate

This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck–Cohen superstatistics in statistical mechanics, and Mathai’s pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of Fox’s H-function are pointed out.

Thermal Decomposition Kinetics of Glyphosate (GP) and its Metabolite Aminomethylphosphonic Acid (AMPA)

2019 ◽  
Author(s):  
Milad Narimani ◽  
Gabriel da Silva
Keyword(s):  
Thermal Decomposition ◽  
Reaction Rate ◽  
Decomposition Kinetics ◽  
Rate Theory ◽  
Thermal Decomposition Mechanism ◽  
Treatment Processes ◽  
Aminomethylphosphonic Acid ◽  
Reaction Rate Theory ◽  
Decomposition Chemistry ◽  
Kinetics Of

Glyphosate (GP) is a widely used herbicide worldwide, yet accumulation of GP and its main byproduct, aminomethylphosphonic acid (AMPA), in soil and water has raised concerns about its potential effects to human health. Thermal treatment processes are one option for decontaminating material containing GP and AMPA, yet the thermal decomposition chemistry of these compounds remains poorly understood. Here, we have revealed the thermal decomposition mechanism of GP and AMPA by applying computational chemistry and reaction rate theory methods. <br>

Ab Initio Computation of Thermochemistry and Kinetics in the Oxidation of Gas Phase Silicon Species

1992 ◽  
Vol 282 ◽  
Author(s):  
Michael R. Zachariah ◽  
Wing Tsang
Keyword(s):  
Ab Initio ◽  
Gas Phase ◽  
Energy Barrier ◽  
Reaction Rate ◽  
Rate Theory ◽  
Molecular Orbital Calculations ◽  
Activation Energy Barrier ◽  
Ab Initio Computation ◽  
Oxygen Donor ◽  
Reaction Rate Theory

ABSTRACTAb initio molecular orbital calculations coupled to RRKM reaction rate theory have been conducted on some important reactions involved in the oxidation of silane in a high-temperature/high H2O environment. The results indicate thatH2O acts as an oxygen donor to SiH2 to form H3SiOH or SiH2O. Subsequent reactions involve the formation of (HSiOOH, H2Si(OH)2,:Si(OH)2 or SiO). In turn SiO polymerizes into planar rings, without an activation energy barrier. A list of calculated thermochemical data are also presented for a number of equilibrium species.

scholarly journals A Unified Constitutive Model for Creep and Cyclic Viscoplasticity Behavior Simulation of Steels Based on the Absolute Reaction Rate Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Huayan Chen ◽  
Xiangguo Zeng ◽  
Yang Guo ◽  
Fang Wang
Keyword(s):  
Constitutive Model ◽  
Reaction Rate ◽  
Internal State ◽  
Rate Theory ◽  
State Variables ◽  
Absolute Reaction Rate Theory ◽  
Reaction Rate Theory ◽  
Absolute Reaction Rate ◽  
The Absolute ◽  
Absolute Reaction

In this work, the viscoplasticity and creep behavior for modified 9Cr-1Mo and 316 stainless steels were investigated. Based on the absolute reaction rate theory, a unified constitutive model incorporating internal state variables was proposed to characterize the evolution of the back stress. Also, the model was implemented by the ABAQUS system with the semi-implicit stress integration. Compared to the experimental data, the results demonstrated that the proposed approach could effectively simulate the cyclic softening and hardening behavior for such structural steels.

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