arXiv subjects

H. J. Haubold

Publications and source records attributed to H. J. Haubold.

At least 19 recordsLinked to original sources

arXiv2025

Mellin Convolutions of Products and Ratios

Usually, convolution refers to Laplace convolution in the literature. But Mellin convolutions can yield very ueeful results. This aspect is illustrated in the coming sections. This paper deals with Mellin convolutions of products and ratios. Functions belonging to the pathway family of functions are considered. Several types of integral representations, their equivalent representations in terms of G and H-functions and their equivalent computable series representations are examined in this paper.

math.CA↗

arXiv2024

Mittag-Leffler Probability Density for Nonextensive Statistics and Superstatistics

It is shown that a Mittag-Leffler density has interesting properties. The Mittag-Leffler random variable has a structural representation in terms of a positive Levy variable and the power of a gamma variable where these two variables are independently distributed. It is shown that several central limit-type properties hold but the limiting forms are positive Levy variable rather than a Gaussian variable. A path is constructed from a Mittag-Leffler function to the Mathai pathway model which also provides paths to nonextensive statistics and superstatistics.

math-ph↗

arXiv2015

United Nations Basic Space Science Initiative (UNBSSI) 1991-2012 and Beyond

This paper contains an overview and summary on the achievements of the United Nations basic space science initiative in terms of donated and provided planetariums, astronomical telescopes, and space weather instruments, particularly operating in developing nations. This scientific equipment has been made available to respective host countries, particularly developing nations, through the series of twenty basic space science workshops, organized through the United Nations Programme on Space Applications since 1991. Organized by the United Nations, the European Space Agency (ESA), the National Aeronautics and Space Administration (NASA) of the United States of America, and the Japan Aerospace Exploration Agency (JAXA), the basic space science workshops were organized as a series of workshops that focused on basic space science (1991-2004), the International Heliophysical Year 2007 (2005-2009), and the International Space Weather Initiative (2010-2012) proposed by the Committee on the Peaceful Uses of Outer Space on the basis of discussions of its Scientific and Technical Subcommittee, as reflected in the reports of the Subcommittee.

physics.space-ph↗

arXiv2015

Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, April 2015

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and more than 25 books on topics in mathematics, statistics, physics, astrophysics, chemistry, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, President of the Mathematical Society of India, and a Member of the International Statistical Institute. He is the founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He is instrumental in the implementation of the United Nations Basic Space Science Initiative. The paper is an attempt to capture the broad spectrum of scientific endeavors of Professor A.M. Mathai at the occasion of his anniversary.

math.HO↗

arXiv2015

Computable Solutions of Fractional Reaction-Diffusion Equations Associated with Generalized Riemann-Liouville Fractional Derivatives of Fractional Order

This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative is derived. In the present paper, computable solutions of distributed order fractional reaction-diffusion equations associated with generalized Riemann-Liouville derivatives of fractional orders as the time-derivative and Riesz-Feller fractional derivative as the space derivative are investigated. The solutions of the fractional reaction-diffusion equations of fractional orders are obtained in this paper. The method followed in deriving the solutions is that of joint Laplace and Fourier transforms. The solutions obtained are in a closed and computable form in terms of the familiar generalized Mittag-Leffler functions. They provide elegant extensions of the results given in the literature.

math-ph↗

arXiv2015

United Nations Human Space Technology Initiative (HSTI)

The Human Space Technology Initiative was launched in 2010 within the framework of the United Nations Programme on Space Applications implemented by the Office for Outer Space Affairs of the United Nations. It aims to involve more countries in activities related to human spaceflight and space exploration and to increase the benefits from the outcome of such activities through international cooperation, to make space exploration a truly international effort. The role of the Initiative in these efforts is to provide a platform to exchange information, foster collaboration between partners from spacefaring and non-spacefaring countries, and encourage emerging and developing countries to take part in space research and benefit from space applications. The Initiative organizes expert meetings and workshops annually to raise awareness of the current status of space exploration activities as well as of the benefits of utilizing human space technology and its applications. The Initiative is also carrying out primary science activities including the Zero-Gravity Instrument Project and the Drop Tower Experiment Series aimed at promoting capacity-building activities in microgravity science and education, particularly in developing countries.

physics.space-ph↗

arXiv2014

On a Generalized Entropy Measure Leading to the Pathway Model: with a preliminary application to solar neutrino data

An entropy for the scalar variable case, parallel to Havrda-Charvat entropy was introduced by the first author and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper we extend the entropy to cover scalar case, multivariable case, and matrix variate case. Then this measure is optimized under different types of restrictions and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical, physical, and engineering sciences are also pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data is provided.

stat.ME↗

arXiv2014

Threats from space: 20 years of progress

It has been 20 years since planning began for the 1995 United Nations International Conference on Near-Earth Objects. The conference proceedings established the scientific basis for an international organizational framework to support research and collective actions to mitigate a potential near-Earth object (NEO) threat to the planet. Since that time, researchers have conducted telescope surveys that should, within the coming decade, answer many questions about the size, number, and Earth impact probability of these objects. Space explorations to asteroids and comets have been successfully carried out, including sample recovery. Laboratory experiments and computer simulations at Sandia National Laboratories have analyzed the effects of soft X-ray radiation on meteorites - which might help researchers develop a way to redirect an incoming asteroid by vaporizing a thin layer of its surface. An Action Team on NEOs, established in 2001 in response to recommendations of the Third United Nations Conference on the Exploration and Peaceful Uses of Outer Space, identified the primary components of NEO mitigation and emphasized the value of finding potentially hazardous NEOs as soon as possible. Recommendations from the Action Team are meant to ensure that all nations are aware of the NEO danger; and to coordinate mitigation activities among nations that could be affected by an impact, as well as those that might play an active role in any eventual deflection or disruption campaign.

physics.hist-ph↗

arXiv2014

Stochastic processes via the pathway model

After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the input-output type mechanism is considered first, where reaction, diffusion, reaction-diffusion, and production-destruction type physical situations can fit in. Then techniques are described to produce thicker or thinner tails (power law behavior) in stochastic models. Then the pathway idea is described where one can switch to different functional forms of the probability density function) through a parameter called the pathway parameter.

physics.data-an↗

arXiv2014

Space-time fractional reaction-diffusion equations associated with a generalized Riemann-Liouville fractional derivative

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann-Liouville fractional derivative defined in Hilfer et al. , and the space derivative of second order by the Riesz-Feller fractional derivative, and adding a function $ϕ(x,t)$. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of Mittag-Leffler functions. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained earlier by Mainardi et al., and the result very recently given by Tomovski et al.. At the end, extensions of the derived results, associated with a finite number of Riesz-Feller space fractional derivatives, are also investigated.

math-ph↗

arXiv2013

Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -I

In this article we examine the densities of a product and a ratio of two real positive scalar random variables $x_1$ and $x_2$, which are statistically independently distributed, and we consider the density of the product $u_1=x_1x_2$ as well as the density of the ratio $u_2={{x_2}\over{x_1}}$ and show that Kober operator of the second kind is available as the density of $u_1$ and Kober operator of the first kind is available as the density of $u_2$ when $x_1$ has a type-1 beta density and $x_2$ has an arbitrary density. We also give interpretations of Kober operators of the second and first kind as Mellin convolution for a product and ratio respectively. Then we look at various types of generalizations of the idea thereby obtaining a large collection of operators which can all be called generalized Kober operators. One of the generalizations considered is the pathway idea where one can move from one family of operators to another family and yet another family and eventually end up with an exponential form. Common generalizations in terms of a Gauss' hypergeometric series is also given a statistical interpretation and put on a more general structure so that the standard generalizations given by various authors, including Saigo operators, are given statistical interpretations and are derivable as special cases of the general structure considered in this article.

math.CA↗

arXiv2013

Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -II

In this article we examine the densities of a product and a ratio of two real positive definite matrix-variate random variables $X_1$ and $X_2$, which are statistically independently distributed, and we consider the density of the product $U_1=X_2^{1\over2}X_1X_2^{1\over2}$ as well as the density of the ratio $U_2=X_2^{1\over2}X_1^{-1}X_2^{1\over2}$. We define matrix-variate Kober fractional integral operators of the first and second kinds from a statistical perspective, making use of the derivation in the predecessor of this paper for the scalar variable case, by deriving the densities of products and ratios where one variable has a matrix-variate type-1 beta density and the other variable has an arbitrary density. Various types of generalizations are considered, by using pathway models, by appending matrix variate hypergeometric series etc. During this process matrix-variate Saigo operator and other operators are also defined and properties studied.

math.CA↗

arXiv2013

Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -III

In this article we define Kober fractional integral operators in the multivariable case. First we consider one sequence of independent random variables and an arbitrary function, which can act as the joint density of another sequence of random variables. Then we define a concept, analogous to the concept of Kober operators in the scalar variable case. This extension is achieved by using statistical techniques and the representation gives an interpretation in terms of a joint statistical density. Then we look at two sets of random variables where between the sets they are independently distributed but within each set they are dependent. Again extensions of Kober fractional integral operator are considered. Several such statistical interpretations are given for Kober operators in the multivariable case.

math.CA↗

arXiv2013

Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -IV

In the preceding articles we considered fractional integral transforms involving one real scalar variable, one real matrix variable and real scalar multivariable case. In the present paper we consider the multivariable case when the arbitrary function is a real-valued scalar function of many $p\times p$ real matrix variables $X_1,...,X_k$. Extension of all standard fractional integral operators to the cases of many matrix variables is considered, along with interesting special cases and generalized matrix transforms.

math.CA↗

arXiv2013

A Pathway Idea in Model Building

The pathway idea is a way of going from one family of functions to another family of functions and yet another family of functions through a parameter in the model so that a switching mechanism is introduced into the model through a parameter. The advantage of the idea is that the model can cover the ideal or stable situation in a physical situation as well as cover the unstable neighborhoods or move from unstable neighborhoods to the stable situation. The basic idea is illustrated for the real scalar case here and its connections to topics in astrophysics and non-extensive statistical mechanics, namely superstatistics and Tsallis statistics, Mittag-Leffler models, hypergeometric functions and generalized special functions such as the H-function etc are pointed out. The pathway idea is available for the real and complex rectangular matrix variate cases but only the real scalar case is illustrated here.

cond-mat.stat-mech↗

arXiv2013

Fractional Operators in the Matrix Variate Case

Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric function with the argument being a rectangular matrix. Subsequently some fractional integral operators are introduced which complement these results available on fractional operators in the matrix variate cases. Several properties and limiting forms are derived. Then the pathway idea is incorporated to move among several different functional forms. When these are used as models for problems in the natural sciences then these can cover the ideal situations, neighborhoods, in between stages and paths leading to optimal situations.

math-ph↗

arXiv2012

The United Nations Human Space Technology Initiative (HSTI): Science Activities

The United Nations Human Space Technology Initiative (HSTI) aims at promoting international cooperation in human spaceflight and space exploration-related activities; creating awareness among countries on the benefits of utilizing human space technology and its applications; and building capacity in microgravity education and research. HSTI has been conducting various scientific activities to promote microgravity education and research. The primary science activity is called 'Zero-gravity Instrument Distribution Project', in which one-axis clinostats will be distributed worldwide. The distribution project will provide unique opportunities for students and researchers to observe the growth of indigenous plants in their countries in a simulated microgravity condition and is expected to create a huge dataset of plant species with their responses to gravity.

physics.pop-ph↗

arXiv2012

The United Nations Human Space Technology Initiative (HSTI): Activity Status in 2012

In 2010, the Human Space Technology Initiative (HSTI) was launched by the United Nations Office for Outer Space Affairs (UNOOSA) within the United Nations Programme on Space Applications. The Initiative aims at promoting international cooperation in human spaceflight and space exploration-related activities, creating awareness among countries on the benefits of utilizing human space technology and its applications, and building capacity in microgravity education and research. HSTI has conducted a series of outreach activities and expert meetings bringing together participants from around the world. HSTI will also be implementing science and educational activities in relevant areas to raise the capacities, particularly in developing countries, in pursuit of the development goals of the United Nations, thus contributing to promoting the peaceful uses of outer space.

physics.pop-ph↗