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.

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In this search, we examined the factorial experiments and the study of the significance of the main effects, the interaction of the factors and their simple effects by the F test (ANOVA) for analyze the data of the factorial experience. It is also known that the analysis of variance requires several assumptions to achieve them, Therefore, in case of violation of one of these conditions we conduct a transform to the data in order to match or achieve the conditions of analysis of variance, but it was noted that these transfers do not produce accurate results, so we resort to tests or non-parametric methods that work as a solution or alternative to the parametric tests , these method

        This paper discusses the Sums of Squares of “m” consecutive Woodall Numbers. These discussions are made from the definition of Woodall numbers. Also learn the comparability of Woodall numbers and other special numbers. An attempt to communicate the formula for the sums of squares of ‘m’ Woodall numbers and its matrix form are discussed. Further, this study expresses some more correlations between Woodall numbers and other special numbers.

     Estimating multivariate location and scatter with both affine equivariance and positive break down has always been difficult. Awell-known estimator which satisfies both properties is the Minimum volume Ellipsoid Estimator (MVE) Computing the exact (MVE) is often not feasible, so one usually resorts to an approximate Algorithm. In the regression setup, algorithm for positive-break down estimators like Least Median of squares typically recomputed the intercept at each step, to improve the result. This approach is called intercept adjustment. In this paper we show that a similar technique, called location adjustment, Can be applied to the (MVE). For this purpose we use the Minimum Volume Ball (MVB). In order

It has been shown in ionospheric research that calculation of the total electron content (TEC) is an important factor in global navigation system. In this study, TEC calculation was performed over Baghdad city, Iraq, using a combination of two numerical methods called composite Simpson and composite Trapezoidal methods. TEC was calculated using the line integral of the electron density derived from the International reference ionosphere IRI2012 and NeQuick2 models from 70 to 2000 km above the earth surface. The hour of the day and the day number of the year, R12, were chosen as inputs for the calculation techniques to take into account latitudinal, diurnal and seasonal variation of TEC. The results of latitudinal variation of TE

The acceptance sampling plans for generalized exponential distribution, when life time experiment is truncated at a pre-determined time are provided in this article. The two parameters (α, λ), (Scale parameters and Shape parameters) are estimated by LSE, WLSE and the Best Estimator’s for various samples sizes are used to find the ratio of true mean time to a pre-determined, and are used to find the smallest possible sample size required to ensure the producer’s risks, with a pre-fixed probability (1 - P^*). The result of estimations and of sampling plans is provided in tables.

Key words: Generalized Exponential Distribution, Acceptance Sampling Plan, and Consumer’s and Producer Risks

Consistent "with the thought of tax talk is unified tax natural evolution for him, as the application leads to the inclusion of tax all branches of income and its sources and through truncated part of this entry through the application of price ascending it, it means the procedures of tax reform. Taxes on total income characterized by giving a clear picture of the total income of the taxpayer and its financial situation and its burden family which allows granting exemptions, downloads, and application of prices that fit this case. This requires reconsideration of the structure of the tax system in force and the transition from a system specific taxes to the tax system on the total income of the integration of income from the rental of re

In spite of the disappearing of a clear uniform textbook for teaching ESP at different departments and different colleges in both scientific and humanistic studies, the practitioners at those departments and colleges have to teach translation as one of the important requirements to pass the English language exam. The lack of defined translation activities is a noticeable problem therefore; the problem of teaching translation is diagnosed in that the students lack the ability to comprehend the text in English language and other translation knowledge and skills.

The study aims to suggest a translation strategy and then find out the effect of the translation strategy on ESP learners’ achievement in translation. A sample of 50 stud

This research introduce a study with application on Principal Component Regression obtained from some of the explainatory variables to limitate Multicollinearity problem among these variables and gain staibilty in their estimations more than those which yield from Ordinary Least Squares. But the cost that we pay in the other hand losing a little power of the estimation of the predictive regression function in explaining the essential variations. A suggested numerical formula has been proposed and applied by the researchers as optimal solution, and vererifing the its efficiency by a program written by the researchers themselves for this porpuse through some creterions: Cumulative Percentage Variance, Coefficient of Determination, Variance

This study includes the new methods especially those related to clinical trials non-therapeutic clinical trials and new risks that may be exposed to. The Corna pandemic has raised many repercussions on all levels and fields, and raised many questions, especially in the legal field. Where many responsibilities arise because of the way to deal with this pandemic, exploit it, or neglect some of the obligations imposed to confront this pandemic. Therefore, the legislator had to intervene to organize practice of such clinical trials in order to ensure stability and reassurance, whether to the doctor, researcher or people who subject to such clinical trial in accordance with the Ministerial Resolution No. (730) of (2018). Therefore, such trial