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.
In this study, investigations of structural properties of n-type porous silicon prepared by laser assisted-electrochemical etching were demonstrated. The Photo- electrochemical Etching technique, (PEC) was used to produce porous silicon for n-type with orientation of (111). X-ray diffraction studies showed distinct variations between the fresh silicon surface and the synthesized porous silicon surfaces. Atomic force microscopy (AFM) analysis was used to study the morphology of porous silicon layer. AFM results showed that root mean square (RMS) of roughness and the grain size of porous silicon decreased as etching current density increased. The chemical bonding and structure were investigated by using fourier transformation infrared spec
... Show MoreShiranish formation has been divided into two microfacies units: 1 - Many biowackestone facies and 2 - maly packstone using planktonic foraminifera and other carbonate components in the rock cutting and core slides. Microfacies reflect marin deep shelf margin in the lower part of the formation, the upper part was deeper. The thickness of the formation is determined, depending on addition to the presence of echinoderm framents debris and spines. This is in disagreement with the 195 ft thickness reported by the Oil Exploration Company The age of the formation is estimated depending on the recognized biostratigraphic zone using the index fossils to be Upper - Middle Mastrichtion.
The charge density distributions of 10 B nucleus are calculated using the
harmonic oscillator wave functions. Elastic and inelastic electron scattering
longitudinal form factors have been calculated for the similar parity states of 10B
nucleus where a core of 4He is assumed and the remaining particles are
distributed over 3/ 2 1p and 1/ 2 1p orbits which form the model space.
Core-polarization effects are taken into account. Core-polarization effects are
calculated by using Tassie model and gives good agreement with the measured
data.
Abstract
The logistic regression model is one of the nonlinear models that aims at obtaining highly efficient capabilities, It also the researcher an idea of the effect of the explanatory variable on the binary response variable. &nb
... Show MoreNovel derivatives of 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole and 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole carrying Schiff bases moiety were synthesised and fully characterised. The protection of D- fructose using benzoyl chloride was synthesized, followed by nucleophilic addition/elimination between benzotria- zole and chloroacetyl chloride to give 1-(1- chloroacetyl)- 1H-benzotriazole. The next step was condensation reaction of protected fructose and 1-(1-chloroacetyl)-1H- benzotriazole producing a new nucleoside analogue. The novel nucleoside analogues underwent a second conden- sation reaction with different aromatic and aliphatic amines to provide new Schiff b
... Show MoreIn this study, we investigate about the run length properties of cumulative sum (Cusum) and The exponentially weighted moving average (EWMA) control charts, to detect positive shifts in the mean of the process for the poisson distribution with unknown mean. We used markov chain approach to compute the average and the standard deviation for run length for Cusum and EWMA control charts, when the variable under control follows poisson distribution. Also, we used the Cusum and the EWMA control charts for monitoring a process mean when the observations (products are selected from Al_Mamun Factory ) are identically and independently distributed (iid) from poisson distribution i
... Show MoreAbstract
The research aimed to test the relationship between the size of investment allocations in the agricultural sector in Iraq and their determinants using the Ordinary Least Squares (OLS) method compared to the Error Correction Model (ECM) approach. The time series data for the period from 1990 to 2021 was utilized. The analysis showed that the estimates obtained using the ECM were more accurate and significant than those obtained using the OLS method. Johansen's test indicated the presence of a long-term equilibrium relationship between the size of investment allocations and their determinants. The results of th
... Show MoreThe new type of paranormal operators that have been defined in this study on the Hilbert space, is paranormal operators. In this paper we introduce and discuss some properties of this concept such as: the sum and product of two paranormal, the power of paranormal. Further, the relationships between the paranormal operators and other kinds of paranormal operators have been studied.
Let m ≥ 1,n ≥ 1 be fixed integers and let R be a prime ring with char (R) ≠2 and
(m+n). Let T be a (m,n)(U,R)-Centralizer where U is a Jordan ideal of R and T(R)
⊆ Z(R) where Z(R) is the center of R ,then T is (U,R)- Centralizer.
The purpose of this work is to construct complete (k,n)-arcs in the projective 2-space PG(2,q) over Galois field GF(11) by adding some points of index zero to complete (k,n–1)arcs 3  n  11. A (k,n)-arcs is a set of k points no n + 1 of which are collinear. A (k,n)-arcs is complete if it is not contained in a (k + 1,n)-arc