On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua

Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density of the sum of two gamma random variables is derived. Then a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed. An explicit expression for the error bound is obtained. The proposed technique is shown to be computationally efficient, i.e. only polynomial in growth in the number of terms compared to the exponential growth of most other methods. It provides a vast improvement in accuracy and shows only logarithmic growth in the required precision. In addition, it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms. As an application, the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with N scalar fields is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio

On the implications of a dilaton in gauge theory

Some recent work on the implications of a dilaton in 4d gauge theories are revisited. In part I of this paper we see how an effective dilaton coupling to gauge kinetic term provides a simple attractive mechanism to generate confinement. In particular, we put emphasis on the derivation of confining analytical solutions and look into the problem how dilaton degrees of freedom modify Coulom potential and when a confining phase occurs. In part II, we solve the semi-relativistic wave equation, for Dick interquark potential using the Shifted l-expansion technique (SLET) in the heavy quarkonium sector. The results of this phenomenological analysis proves that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism.Comment: 8 pages. Talk given at CTP Symposium on Supersymmetry at LHC: Theoretical and Experimental Prospectives, Cairo, Egypt, 11-14 Mar 200

Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with variable coefficient

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Taylor & Francis.In this paper, a numerical implementation of a direct united boundary-domain integral equation (BDIE) related to the Neumann boundary value problem for a scalar elliptic partial differential equation with a variable coefficient is discussed. The BDIE is reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretization of the BDIEs with quadrilateral domain elements leads to a system of linear algebraic equations (discretized BDIE). Then, the system is solved by LU decomposition and Neumann iterations. Convergence of the iterative method is discussed in relation to the distribution of eigenvalues of the corresponding discrete operators calculated numerically.The work was supported by the grant EP/H020497/1 "Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK

Isotope and noble gas study of three aquifers in central and southeast Libya

2013 Summer.Includes bibliographical references.To view the abstract, please see the full text of the document

Chemical compositions and heavy metal contents of Oreochromis niloticus from the main irrigated canals (rayahs) of Nile Delta

AbstractThe present study aimed to assess the seasonal variations of the proximate chemical composition, physicochemical, microbiological aspects and heavy metal concentrations of Oreochromis niloticus muscles collected from The Nile rayahs from spring 2014 to winter 2015. Rayahs are the main irrigated canals of Nile Delta, Egypt and represent El Tawfiki, El Menoufy, El Behery, and El Nasery rayahs. Results showed a spatial and temporal significant difference (p<0.01) in the proximate composition and Physicochemical aspects of O. niloticus muscles. The moisture, protein, fat, ash, carbohydrates and calorific values varied between (78.55–80.77%), (16.10–17.88%), (1.10–1.95%), (0.55–1.50%), (0.10–0.94%) and (78.37–89.73%), respectively. Heavy metal accumulation in the O. niloticus muscles showed irregular distributions with descending order of: Fe>Zn>Mn>Cu>Pb>Cd. Generally, heavy metals, TVB-N, TMA, TBA and TVC did not exceed the maximum permissible limits in the tissues of O. niloticus. The values of Hazard Index (HI) and Hazard Quotient (HQ) are lower than the acceptable limits, which indicate that the metals in O. niloticus in the Nile rayahs, Egypt, do not pose any particular human health risk concern. Therefore, O. niloticus muscles collected from four rayahs are safe for human consumption and could be used as a source of healthy diet for humans

On the Application of Data Clustering Algorithm used in Information Retrieval for Satellite Imagery Segmentation

This study proposes an automated technique for segmenting satellite imagery using unsupervised learning. Autoencoders, a type of neural network, are employed for dimensionality reduction and feature extraction. The study evaluates different segmentation architectures and encoders and identifies the best performing combination as the DeepLabv3+ architecture with a ResNet-152 encoder. This approach achieves high performance scores across multiple metrics and can be beneficial in various fields, including agriculture, land use monitoring, and disaster response

Optical study of the vibrational and dielectric properties of BiMnO3

BiMnO3 (BMO), ferromagnetic (FM) below Tc = 100 K, was believed to be also ferroelectric (FE) due to a non-centro-symmetric C2 structure, until diffraction data indicated that its space group is the centro-symmetric C2/c. Here we present infrared phonon spectra of BMO, taken on a mosaic of single crystals, which are consistent with C2/c at any T > 10 K, as well as room-temperature Raman data which strongly support this conclusion. We also find that the infrared intensity of several phonons increases steadily for decreasing T, causing the relative permittivity of BMO to vary from 18.5 at 300 K to 45 at 10 K. At variance with FE materials of displacive type, no appreciable softening has been found in the infrared phonons. Both their frequencies and intensities, moreover, appear insensitive to the FM transition at Tc