Sum of Squares of ‘n’ Consecutive Carol Numbers

P. SHANMUGANANDHAM; C. DEEPA

doi:10.21123/bsj.2023.8399

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Publication Date

Wed Mar 01 2023

Journal Name

Baghdad Science Journal

Volume

20

Issue Number

1(SI)

DOI

10.21123/bsj.2023.8399

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Sum of Squares of ‘n’ Consecutive Carol Numbers

Carol Numbers

Cullen Numbers

Fibonacci

Sum of Squares

Woodall Numbers

P. SHANMUGANANDHAM

C. DEEPA

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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 05 2025

Journal Name

Tanmiat Al-rafidain

The Effect of the Strategic Lens in Enhancing Organizational Immunity: An Analytical Study of the Opinions of A Sample of Administrative Leaders in Some Private Banks in Baghdad

Ibtisamah

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Publication Date

Mon Dec 31 2018

Journal Name

Iraqi Journal Of Market Research And Consumer Protection

EFFECT OF PLASTIC WASTES AS LOW COST MATERIAL ON SOME PROPERTIES OF UNSATURATED POLYESTER.: EFFECT OF PLASTIC WASTES AS LOW COST MATERIAL ON SOME PROPERTIES OF UNSATURATED POLYESTER.

Plastic Waste

polymer matrix composite (PMCs)

Polyethylene-terephthalate (PET)

Polyvinyl chloride (PVC).

Awham M.

Ahmed Ali

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In this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after

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Publication Date

Sun Oct 05 2025

Journal Name

Journal Of Physical Education

The Effect of Using Especial Exercises Suggested for Developing of Accuracy Direction by Fencing in Foil for the Players of the National Team of the Young who Handicap

Abdul

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Publication Date

Fri Jun 07 2024

Journal Name

Medicine

Impact of TYMS gene polymorphism on the outcome of methotrexate treatment in a sample of Iraqi rheumatoid arthritis patients – identification of novel single nucleotide polymorphism: Cross-sectional study

Qassim Mahdi

Ali A.

Ali Saleh

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The current work aims to evaluate the association between genetic mutations in thymidylate synthetase (TYMS gene in exon1 and partial regions of promotor and intron 1 [877 bp, 657,220–658,096 bp]) and the therapeutic outcomes for rheumatoid arthritis (RA) Iraqi patients. An observational cross-sectional study involving 95 RA patients with established RA patients based on their methotrexate treatment responsiveness. Genetic sequencing of the TYMS gene was performed for all patients according to the instruction manuals of the sequencing company (Macrogen Inc. Geumchen, South Korea). Four polymorphisms were identified by sequencing 95 randomly selected patients in the noncoding region of TYMS

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(1)

Publication Date

Thu Sep 15 2022

Journal Name

Alustath Journal For Human And Social Sciences

The Degree of Commitment of Social Workers Who Work in the ‎Ministry of Social Development to the Professional Principles of ‎the Social Work Profession under the Corona Pandemic

social workers

professional principles‎

corona pandemic

Dr. Murad Rushdi

Prof. Bassem Ahmed

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The study aimed to identify the degree of commitment of social workers working in the Ministry of Social Development to the professional principles of the social work profession in light of the Corona pandemic, and the sample consisted of (135) specialists. The study reached several results: the most important one is the degree of commitment of social workers working in the Ministry of Social Development to the professional principles of social service was great. The other result is the absence of statistically significant differences according to the variables of sex and place of residence. Moreover, the results also showed the absence of statistically significant differences in the principles of ( Acceptance o

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Publication Date

Sun May 04 2014

Journal Name

Journal Of Physical Education

The effect of developing the strength of the muscles of the arms and shoulders in developing the performance of some floor movements skills in artistic gymnastics for women

Zahra

Suzan

Iyad

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Publication Date

Sun Dec 01 2013

Journal Name

Journal Of Economics And Administrative Sciences

Assess the Reality of the Process of Applying the strategic Innovation In Business organizations : A prospective Study of comparative analysis in anumber of business organizations the Iraqi Industrial

الابداع الاستراتيجي

/ strategic in novation

بشرى هاشم

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Abstract :

The research aims to Estimate the Strength of Strategic Innovation application in terms of application strength , and on the overall level in number of Iraqi Industrial business organizations . After wards determine whether their is differerences among those organizations in application process for the dimensions , and for the overall process .

The Research revealed number of conclusions including that the process of strategic innovation is applied in a good Level , and demonstrates the desier of the industrial companies Leaders to Launch beyond the familiar products , and to provide new products that

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(2)

Publication Date

Mon Nov 05 2018

Journal Name

Iraqi Journal Of Market Research And Consumer Protection

EFFECT OF PLANT DENSITIES ON THE GROWTH AND YIELD OF SUNFLOWER Helianthus annuus L.: EFFECT OF PLANT DENSITIES ON THE GROWTH AND YIELD OF SUNFLOWER Helianthus annuus L.

كثافات نباتية

زهرة الشـمس

صفات زراعية

حاصل.

أروى عبد الكريـم

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A field experiment was conducted at the experimental field of botanical garden, faculty of science, university of Baghdad, in order to study the effect of plant density on growth and yield of two local cultivars of sunflower (Sin Althieb and Shumose). The densities used were 4.4 and 8.8 plant/m². The results showed difference between cultivars in their agronomic traits and their yields. There was a significant increase in plant height and leaf area index by increasing the plant density, while head diameter, number of seeds and leaf area decreased. But the most significant effect was the increasing in yield and biological yield by increasing the plant density. There was an increase by 72% and 58% in the yield and 79% an

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Publication Date

Tue Nov 22 2022

Journal Name

College Of Islamic Sciences

The issues of illusion to Ibn hisham AI- Ansari( H 761T) on grammarian

Questions of Ibn Hisham Al-Ansar

M. M Mahdi Khazal Mugheer

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This research shows the issues of Ibn Hisham's illusion in its leadership of the grammarians; As Ibn Hisham attributed - during his presentation of grammatical issues - grammatical opinions to a number of grammarians claiming them in them, and after referring to the main concepts that pertain to those grammarians, we found that Ibn Hisham had delusional in those allegations, in addition to that clarifying the terms illusion and claim in the two circles of language And the terminology, and perhaps the most prominent result in this research is that he worked to investigate these issues by referring to their original sources, with an explanation of the illusions of Ibn Hisham in his attribution to these issues.

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Publication Date

Mon Apr 06 2020

Journal Name

August

INFLUENCE OF SOME FACTOR ON SOMATIC EMBRYOS INDUCTION AND GERMINATION OF DATE PALM CV BARHI BY USING CELL SUSPENSION CULTURE TECHNIQUE

This study was done to examine different concentrations of mercuric chloride (Hgcl2) for Explants sterilization and different concentration of NAA) mg/L with 2iP for their effect on initiation primary callus and subsequent embryogenesis in Phoenix dactyliferae cultivar Barhi. Leaf primordial and shoot tips were excised from 2-3 years old offshoot. The result showed that contamination percentage decreased with an increase in concentration of Hgcl2 for two explants where in the control (0.0)% gave highest value 75% and 62.5% of contamination for leaf primordial and shoot tip respectively while the addition (0.1)% gave a significant decrease 37.5 and 0% for explants respectively. The Explants were inoculated onto Murashiege and Skoog

1962 (MS) medium supplemented with 2iP 3mg/L and containing 0

25

50 or 100 mg/L of NAA

the addition (50) mg/L of NAA gave highest value 68.8% in percentage of callus initiation with significant difference from addition 0% gave lowest value (18.8)%

as well Explants of shoot tip gave significant difference was 53.1% while leaf primordial gave 28.1%

Primary callus was transferred to fresh MS medium containing (0

5

10 and 20) mg/L of NAA with 3mg/L 2iP

Results were recorded after 12 weeks. A highest value of embryonic callus induction percentage or fresh weight and dry weight 87.5% or 1.56g and 0.47g for the character respectively for the treat 20 mg/L while control treatment 0.0 gave the lowest value 12.5% or 0.37g and 0.14g for same character respectively. Inoculated 1g fresh biomass into a 250 ml Erlenmeyer flask containing 50 ml MS liquid medium supplemented with NAA 20mg/L and agitated at 150 rpm by shaker to making suspension culture the measurements of packed cell volume ( pcv) or fresh and dry weight taken weekly for 12 weeks

maximum values were reached in the eighth week of PCV and fresh weight but the dry weight reached to highest value in seventh week

then the curve began to decline gradually until it reached stability in the last two weeks. The cell suspension was Diluted to different initial cell density of 100

500

10000

50000 and 100000 cells /ml with hemocytometer. The initial cell number of (10000) cells gave significant different of plating efficiency PE (11.6)% while (100) cells gave lowest value 1.8% of PE.

Ali A.

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