American Journal of Applied Mathematics and Statistics

It is already known the appearance of time advance (due to distortion by the non-resonant background) instead of the expected time delay in the region of a compound-nucleus resonance in the center-of-mass (C-) system. Here at the same conditions we study cross sections and durations of the neutron-nucleus scattering in the laboratory (L-) system. Here it is shown that such time advance is a virtual paradox but in the L-system the time-advance phenomenon does not occur and only the trivial time delay is observed. At the same time the transformations from C-system into the L-system appeared to be different from the standard kinematical transformations because in the C-system the motion of a compound nucleus is absent but it is present in the L-system. We analyze the initial wave-packet motion (after the collision origin) and the cross section in the laboratory (L-) system. Also here (as physical revelations of profound general methodic and in very good consistent accordance with the experiment) several results of the calculated cross sections for the neutron-nucleus in comparison with the experimental data in the L-system at the range of one or two overlapped compound resonances are presented. It is shown in the space-time approach that the standard kinematical transformations of cross sections from the C-system to the L-system are not valid because it is necessary to consider the center-of-mass motion in the L-system. Finally on a correct self-consistent base of the space-time description of the nuclear processes in the laboratory system with 3 particles in the final channel, it is shown the validity of the former approach, obtained for the space-time description of the nuclear processes with 2-particle channels earlier.

American Journal of Applied Mathematics and Statistics. 2015, 3(3), 131-141. DOI: 10.12691/ajams-3-3-6
Pub. Date: July 06, 2015

Full-Text PDF

17760 Views5187 Downloads1 Likes

On Theoretical Methodology of Nuclear Reactions and Outcome of Certain Physical Phenomena from Them. I. What Follows from the Analytical Properties of the One-channel and the Multichannel S-matrix?

by V.S. Olkhovsky

Review Article

Analytical structure of the non-relativistic unitary and non-unitary S-matrix are investigated for he cases of any interactions with any motion equations inside a sphere of radius a, enclosed by the centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials. Some kinds of the symmetry conditions are imposed. The Schroedinger equation for r > a for the particle motion and the condition of the completeness of the correspondent wave functions are assumed. The connection of the obtained results with the causality is examined. Partially some analytical properties for the multi-channel S-matrix are investigated and the sum rules for mean compound-nucleus time delays and the density of compound-nucleus levels. Sometimes (as physical revelations of profound general methodic and in very good consistent accordance with the experiment) observable physical effects, such as parity violation enhancement and time resonances or explosions, are manifested. Finally a scientific program of future search is presented as a clear continuation and extension of the obtained results.

American Journal of Applied Mathematics and Statistics. 2015, 3(3), 111-130. DOI: 10.12691/ajams-3-3-5
Pub. Date: July 06, 2015

Full-Text PDF

17356 Views4762 Downloads1 Likes

Semi-Markov Model of a Standby System with General Distribution of Arrival and Failure Times of Server

by R.K. Bhardwaj and Ravinder Singh

Original Research

The aim of this paper is to develop a stochastic model of a cold standby system consisting of two identical units and a service facility, called server. This paper considers the failure of server during operation. The semi-Markov approach is explored to develop the probabilistic model and regenerative point technique is used to derive expressions for system’s performance measures such as mean time to system failure, availability, profit etc. In the model the server takes some time to arrive at the system. The server, while on job, may fail. Upon failure it goes for treatment and rejoins thereafter. Both the arrival and failure times follow general distribution with different probability distribution functions. The numerical illustration, for a particular case, points out that both the server arrival and failure times significantly affect the system performance.

American Journal of Applied Mathematics and Statistics. 2015, 3(3), 105-110. DOI: 10.12691/ajams-3-3-4
Pub. Date: July 02, 2015

Full-Text PDF

10102 Views2909 Downloads33 Likes

A Unified Formula for The nth Derivative and The nth Anti-Derivative of the Bessel Function of Real Orders

by Mhenni M. Benghorbal

Original Research

A complete solution to the problem of finding the nth derivative and the nth anti-derivative of elementary and special functions has been given. It deals with the problem of finding formulas for the nth derivative and the nth anti-derivative of elementary and special functions. We do not limit n to be an integer, it can be a real number. In general, the solution is given through unified formulas in terms of the Fox H-function and the Miejer G-function which, in many cases, can be simplified to less general functions. This, in turn, makes the first real use of these two special functions in the literature and shows the need of such functions. In this talk, we would like to present the idea on the Bessel function which is a well known special function. One of the key points in this work is that the approach does not depend on integration techniques. We adopt the classical definitions for generalization of differentiation and integration. Namely, the nth order of differentiation is found according to the Riemann-Liouville definition

where (k − 1 < n < k) and

. The generalized Cauchy n-fold integral is adopted for the nth order of integration

American Journal of Applied Mathematics and Statistics. 2015, 3(3), 100-104. DOI: 10.12691/ajams-3-3-3
Pub. Date: June 16, 2015

Full-Text PDF

11973 Views5096 Downloads6 Likes

Financial Modeling for Investment through Anticipated Annuities in Scenarios with Floating Interest Rate

by Arturo García-Santillán, Lizette Gutiérrez-Delgado, Celia Cristóbal-Hernández and Virginia Catalayud-Gutiérrez

Case Study

The aim of this work focuses on showing, through a hypothetical scenario with financial calculations, how to develop an investment with constant one-year deposit and reinvestment of dividends earned. To this end, the financial model includes a type of floating interest rate throughout the year, depending on the reference interest rate indicated by the "Banco de Mexico". For this reason in the hypothetical scenario we are considering changes in interest rates at the moment of reinvestment. Therefore, to make financial calculus, we utilized as reference interest rate, the interest rate TIIE (for its acronym in Spanish) Interest rate of Internal equilibrium, which is set by the “Banco de Mexico”. We utilized the formula of an annuity anticipated with cohorts, depending on the changes in the interest rate TIIE. The results obtained show the behavior of the investment over a year in which the interest earned at all times is reinvested, generating an effect known in Mexico as “anatocismo” or compounded interest.

American Journal of Applied Mathematics and Statistics. 2015, 3(3), 93-99. DOI: 10.12691/ajams-3-3-2
Pub. Date: May 17, 2015

Full-Text PDF

11730 Views3447 Downloads9 Likes

A Method for Solving a Class of Boundary Value Problems of Laguerre Equation

by Li Ren, Shunchu Li and Dongdong Gui

Original Research

Based on the analysis of the boundary value problem of Laguerre equation, this paper studies the similar structure of its solution expression. This paper is found that its solution can be obtained by combining similar kernel function with coefficients of left boundary condition. While the similar kernel function is constructed by both the function of guide solution and coefficients of right boundary condition. Hence, we proposed a method for solving this class of boundary value problems: the similar constructing method.

American Journal of Applied Mathematics and Statistics. 2015, 3(3), 89-92. DOI: 10.12691/ajams-3-3-1
Pub. Date: May 06, 2015

Full-Text PDF

9518 Views2868 Downloads10 Likes