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.
Abstract
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 hydroisomerization of n-decane was studied on SAPO-11 catalyst. Catalyst of 0.25wt.%Pt/SAPO-11 was prepared locally and used in the present work. The hydroconversion performed in a continuous fixed-bed laboratory reaction unit. Experiments of n-decane isomerization were performed in a temperature range of 200 to 275°C,LHSV range of 0.5-2 h-1, and hydrogen to decane mole ratio of 2.1-8.2. The results show that the n-decane conversion increases with increasing temperature and decreasing LHSV , the maximum conversion 56.77 % was achieved at temperature 275°C and LHSV of 0.5 h-1. The kinetic of n-decane isomerization was also studied and the reaction was first order. The kinetic analysis also showed that the
... Show MoreThe hydroisomerization of n-decane was studied on SAPO-11 catalyst. Catalyst of 0.25wt.%Pt/SAPO-11 was prepared locally and used in the present work. The hydroconversion performed in a continuous fixed-bed laboratory reaction unit. Experiments of n-decane isomerization were performed in a temperature range of 200 to 275°C,LHSV range of 0.5-2 h-1, and hydrogen to decane mole ratio of 2.1-8.2. The results show that the n-decane conversion increases with increasing temperature and decreasing LHSV , the maximum conversion 56.77 % was achieved at temperature 275°C and LHSV of 0.5 h-1. The kinetic of n-decane isomerization was also studied and the reaction was first order. The kinetic analysis also showed that the activation energy eq
... Show MoreThe organation ⁄monomer N-naphthylacrylamide (NAA) was prepared; subsequently the synthesized monomer was successfully copolymerized with acrylicacid (AA) and methylacrylate (MA) by free radical technique using dry benzene as solvent and benzoyl peroxide (BPO) as initiator. The overall conversion was kept low (≤ 10% wt/wt) for all studies copolymers samples. The synthesized monomer and copolymers were characterized using Fourier transform infrared spectroscopy (FT-IR), and their thermal properties were studied by DSC and TGA. The copolymers compositions were determined by elemental analysis. Kelen-Tudes and Finmman-Ross graphical procedures were employed to determine
... Show MoreThe organation ⁄monomer N-naphthylacrylamide (NAA) was prepared; subsequently the synthesized monomer was successfully copolymerized with acrylicacid (AA) and methylacrylate (MA) by free radical technique using dry benzene as solvent and benzoyl peroxide (BPO) as initiator. The overall conversion was kept low (≤ 10% wt/wt) for all studies copolymers samples. The synthesized monomer and copolymers were characterized using Fourier transform infrared spectroscopy (FT-IR), and their thermal properties were studied by DSC and TGA. The copolymers compositions were determined by elemental analysis. Kelen-Tudes and Finmman-Ross graphical procedures were employed to determine the monomers reactivity ratios. The der
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