This paper introduces a relationship between the independence of polynomials associated with the links of the network, and the Jacobian determinant of these polynomials. Also, it presents a way to simplify a given communication network through an algorithm that splits the network into subnets and reintegrates them into a network that is a general representation or model of the studied network. This model is also represented through a combination of polynomial equations and uses Groebner bases to reach a new simplified network equivalent to the given network, which may make studying the ability to solve the problem of network coding less expensive and much easier.

Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

Beta Distribution

Abstract

             Gamma and Beta Distributions has very important in practice in various areas of statistical and applications reliability and quality control of production. and There are a number of methods to generate data behave on according to these distribution. and These methods bassic primarily on the shape parameters of each distribution and the relationship between these distributions and their relationship with some other probability distributions.    &nb

Conditional logistic regression is often used to study the relationship between event outcomes and specific prognostic factors in order to application of logistic regression and utilizing its predictive capabilities into environmental studies. This research seeks to demonstrate a novel approach of implementing conditional logistic regression in environmental research through inference methods predicated on longitudinal data. Thus, statistical analysis of longitudinal data requires methods that can properly take into account the interdependence within-subjects for the response measurements. If this correlation ignored then inferences such as statistical tests and confidence intervals can be invalid largely.

Web application protection lies on two levels: the first is the responsibility of the server management, and the second is the responsibility of the programmer of the site (this is the scope of the research). This research suggests developing a secure web application site based on three-tier architecture (client, server, and database). The security of this system described as follows: using multilevel access by authorization, which means allowing access to pages depending on authorized level; password encrypted using Message Digest Five (MD5) and salt. Secure Socket Layer (SSL) protocol authentication used. Writing PHP code according to set of rules to hide source code to ensure that it cannot be stolen, verification of input before it is s

The utilization of carbon dioxide (CO₂) to enhance wellbore injectivity presents a cost-effective and sustainable strategy for mitigating greenhouse gas emissions while improving reservoir performance. This study introduces an environmentally friendly method employing a water-soluble chitosan salt (CS) that generates a carbonated-rich acid solution upon contact with dry CO₂ at 25 °C and 508 psi. CS solutions (100–2000 ppm) were prepared and evaluated for CO₂ uptake, acid generation, and rheological behavior. Results show that 1000 ppm achieves an optimal CO2 uptake (2612 mg/l), with moderate viscosity increase (from 1.52 to 3.37 cp), while higher concentrations exhibit a sharp rise due to polymer-like network formation. Core floodi

Porous Silicon (PS) layer has been prepared from p-type silicon by electrochemical etching method. The morphology properties of PS samples that prepared with different current density has been study using atom force measurement (AFM) and it show that the Layer of pore has sponge like stricture and the average pore diameter of PS layer increase with etching current density increase .The x-ray diffraction (XRD) pattern indicated the nanocrystaline of the sample. Reflectivity of the sample surface is decrease when etching current density increases because of porosity increase on surface of sample. The photolumenses (PL) intensity increase with increase etching current density. The PL is affected by relative humidity (RH) level so we can use

The work in this paper focuses on the experimental confirming of the losses in photonic crystal fibers (PCF) on the transmission of Q-switched Nd:YAG laser. First HC-PCF was evacuated to 0.1 mbar then the microstructure fiber (PCF) was filled with He gas & gas. Second the input power and output power of Q-switched Nd:YAG laser was measured in hollow core photonic bandgap fiber (HCPCF). In this work loss was calculated in the hollow core photonic crystal fiber (HCPCF) filled with air then N2, and He gases respectively. It has bean observed that the minimum loss obtained in case of filling (HC-PCF) with He gas and its equal to 15.070 dB/km at operating wavelength (1040-1090) nm.