The discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.

Blastocystosis is symptomatic infection caused by the protozoal parasite Blastocystis , which resides in the intestinal tract of its hosts and it is one of the most common parasites reported in humans. It’s prevalence ranges between (30 - 50%) of the population in developing countries. This genus has a worldwide distribution and often the most commonly reported human intestinal protozoan in children and adults, even infect infants

Urban land uses are in a dynamic state that varies over time, the city of Karbala in Iraq has experienced functional changes over the past 100 years, as the city is characterized by the presence of significant tourist and socio-economic activity represented by religious tourism, and it occur due to various reasons such as urbanization. The purpose of this study is to apply a Markov model to analyze and predict the behavior of transforming the use of land in Karbala city over time. This can include the conversion of agricultural land, or other areas into residential, commercial, industrial land uses. The process of urbanization is typically driven by population growth, economic development, based on a set of probabilities and transitions bet

The Multiple Signal Classification (MUSIC) algorithm is the most popular algorithm to estimate the Angle of Arrival (AOA) of the received signals. The analysis of this algorithm (MUSIC) with typical array antenna element ( ) shows that there are two false direction indication in the plan
aligned with the axis of the array. In this paper a suggested modification on array system is proposed by using two perpendiculars crossed dipole array antenna in spite of one array antenna. The suggested modification does not affect the AOA estimation algorithm. The simulation and results shows that the proposed solution overcomes the MUSIC problem without any effect on the performance of the system.

A winglet is devices attached at the wing tips, used to improve aircraft wing efficiency by reduction influence wing tips vortices and induct drag, increasing lift force at the wing tips and effective aspect ratio without adding greatly to the structural stress and weight in the wing structure. This paper is presented three-dimensional numerical analysis to proposed modification swept back wing by adding Raked winglets devices at the main wing tips belong the two seat trainer aircraft type Aermacchi Siai S211 by using Fluent ANSYS 13 software. CFD numerical analysis process was performed at the same flight boundary conditions indifferent wing angle of attacks with constant air flow velocity V∞ =50 (m/sec), ambient pressure Po=101325 (P

         The varied thermal conductivity (insulation) of silica aerogel with heating for different pH has been investigated, it has been depended on ambient pressure drying method in the preparing silica aerogel samples, also six different pH of samples (1, 2, 3, 7, 8 and 9) were treated under five degree of heating with (50,100,150,200 and 250) ᴼC. This technique is important to test the carry-outs hydrophobic silica to temperature without high-quality material changes in the basic characteristics. The hot-wire technique is used in this work to examine the thermal conductivity, Fourier Transform Infrared Spectroscopy (FTIR) depended to characterize the bonds and their artificial by heating. Resu

In this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control

Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

Roller compacted concrete (RCC) is a material with no slumps and is made from the same raw materials as conventional concrete. The roller compacted dam method, the high paste technique, the corps of engineers method, and the maximum density method are all ways of designing RCC. The evolution of RCC has resulted in a substantial change in construction projects, most notably in dams, because of the sluggish pace of conventional placement, consolidation, and compacting. The construction process was accelerated by incorporating RCC into dams, resulting in a shorter construction period. Research shows that the dams that used RCC had completed one to two years sooner than the dams that used regular concrete (Bagheri an

In this research we assumed that the number of emissions by time (𝑡) of radiation particles is distributed poisson distribution with parameter (𝑡), where  < 0 is the intensity of radiation. We conclude that the time of the first emission is distributed exponentially with parameter 𝜃, while the time of the k-th emission (𝑘 = 2,3,4, … . . ) is gamma distributed with parameters (𝑘, 𝜃), we used a real data to show that the Bayes estimator 𝜃 ∗ for 𝜃 is more efficient than 𝜃̂, the maximum likelihood estimator for 𝜃 by using the derived variances of both estimators as a statistical indicator for efficiency