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Sum of Squares of ‘n’ Consecutive Carol Numbers
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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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Publication Date
Sun Oct 01 2017
Journal Name
Journal Of Educational And Psychological Researches
The Effect of Caroll’s Pattern on the Second Intermediate Class Pupils' Achievement in Geography
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The present study aims at finding out the (effect of the Caroll’s pattern on the second intermediate class pupils' achievement in geography)

The partial experimental design of two groups, experimental and control, with pre-post tests is used. The sample is represented in (74) female pupils. The sample is divided into two groups (38) experimental group and (36) control one. The sample is selected from first intermediate  class pupils    ( Am Salama Secondary School for girls) \ Baghdad\ Al-karkh-1, for academic year 2015-2016.

The researcher has equalized the two groups in several variables: the previous achievement tests, intelligence, age in months, the scor

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Publication Date
Wed Mar 18 2020
Journal Name
Baghdad Science Journal
The Representaion of Algebraic Integers as Sum of Units over the Real Quadratic Fields: REPRESENTAION OF ALGEBRAIC INTEGERS AS SUM OF UNITS OVER THE REAL QUADRATIC FIELDS
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In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

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Publication Date
Tue Mar 01 2022
Journal Name
Journal Of Engineering
Scheme for Generating True Random Numbers using Electro-mechanical Switches
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This paper proposes a novel method for generating True Random Numbers (TRNs) using electromechanical switches. The proposed generator is implemented using an FPGA board. The system utilizes the phenomenon of electromechanical switch bounce to produce a randomly fluctuated signal that is used to trigger a counter to generate a binary random number. Compared to other true random number generation methods, the proposed approach features a high degree of randomness using a simple circuit that can be easily built using off-the-shelf components. The proposed system is implemented using a commercial relay circuit connected to an FPGA board that is used to process and record the generated random sequences. Applying statistical testing on the exp

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Publication Date
Sat Oct 28 2023
Journal Name
Baghdad Science Journal
Synthesis, Characterization and Theoretical Investigation of Innovative Charge-transfer Complexes Derived from the N-phenyl 3, 4-selenadiazo Benzophenone Imine
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In the current study, a direct method was used to create a new series of charge-transfer complexes of chemicals. In a good yield, new charge-transfer complexes were produced when different quinones reacted with acetonitrile as solvent in a 1:1 mole ratio with N-phenyl-3,4-selenadiazo benzophenone imine. By using analysis techniques like UV, IR, and 1H, 13C-NMR, every substance was recognized. The analysis's results matched the chemical structures proposed for the synthesized substances. Functional theory of density (DFT)
has been used to analyze the molecular structure of the produced Charge-Transfer Complexes, and the energy gap, HOMO surfaces, and LUMO surfaces have all been created throughout the geometry optimization process ut

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Publication Date
Fri Feb 08 2019
Journal Name
Iraqi Journal Of Laser
Random Number Generation for Quantum Key Distribution Systems Based on Shot-Noise Fluctuations in a P-I-N Photodiode
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A simple setup of random number generator is proposed. The random number generation is based on the shot-noise fluctuations in a p-i-n photodiode. These fluctuations that are defined as shot noise are based on a stationary random process whose statistical properties reflect Poisson statistics associated with photon streams. It has its origin in the quantum nature of light and it is related to vacuum fluctuations. Two photodiodes were used and their shot noise fluctuations were subtracted. The difference was applied to a comparator to obtain the random sequence.

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Publication Date
Thu Sep 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
The use of the methods of the lower squares and the smaller squares weighted in the estimation of the parameters and design of the sample acceptance schemesFor general exponential distribution
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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

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Publication Date
Wed Nov 27 2019
Journal Name
Iraqi Journal Of Science
Sum Ideal Graphs Associated to a Given Ideal of a Commutative Ring
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The aim of this paper is to introduce and study a new kind of graphs associated to an ideal of a commutative ring. Let â„› be a commutative ring with identity, and I(â„›) be the set of all non-trivial ideals of â„› with S I(â„›). The sum ideal graph associated to S, denoted by       Î¨(â„›, S), is the undirected graph with vertex set {A I(â„›): S⊂A+B, for some B I(â„›)} where two ideal vertices A and B are adjacent if and only if A B and S⊂A+B. In this paper we establish some of characterizations and results of this kind of graph with providing some examples.

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Publication Date
Mon Sep 23 2019
Journal Name
Baghdad Science Journal
Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields
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In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

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Publication Date
Wed Jan 01 2020
Journal Name
2nd International Conference On Materials Engineering & Science (iconmeas 2019)
New application of pervaporation to enhance the conversion of consecutive reaction
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This study investigates consecutive reaction assisted by pervaporation for the first time. It studies the saponification of diethyladipate DA with sodium hydroxide NaOH solution synchronous with separating ethanol from the reaction mixture through an aqueous – organic membrane. The effect of time on some variables such as: permeated ethanol concentration EtOH wt%, separation factor (α), concentration of NaOH solution CB in the reaction medium and the conversion of DA to monoethyladipate (the intermediate product) was studied. It was shown that EtOH wt% and the conversion increased with increasing time unlike CB but (α) showed the existence of maximum value during the time of experiment. The process of reaction assisted by pervaporation

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Publication Date
Sat Feb 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of some robust methods to estimate parameters of partial least squares regression (PLSR)
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   The technology of reducing dimensions and choosing variables are very important topics in statistical analysis to multivariate. When two or more of the predictor variables are linked in the complete or incomplete regression relationships, a problem of multicollinearity are occurred which consist of the breach of one basic assumptions of the ordinary least squares method with incorrect estimates results.

 There are several methods proposed to address this problem, including the partial least squares (PLS), used to reduce dimensional regression analysis. By using linear transformations that convert a set of variables associated with a high link to a set of new independent variables and unr

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