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.
The current environment is witnessing several developments as a result of the changes taking place in all areas of economic, social , political and legal that led to the transformation of the industrial economy , which depends based on quantitative production to a knowledge economy which relies based on information and knowledge , as the central pillar of this economy during the trading of these information and knowledge between all individuals in general and decision makers , in particular, through information and communication technology of computers and the Internet to achieve sustainable human development in the social dimension. &
... Show MoreOxazepine [1] is non – nomologous seven –member ring that contain two netroatoms (oxygen and nitrogen ). Meanwhile diazepine [2] contains to nitrogen atoms in seven – member ring.
Diazepam (valium) [3] is used to relive anxiety tension associated with anxiety disorder and muscle spasms (1, 2, 3
... Show MoreThe chemical composition of wastes of pressed grapes and found that the main components of wastes of pressed grapes, represented by the percentage of moisture was 6.47%, and the proportions are 3.71%. Either carbohydrates amounted to 85.77 %, either in fat models using petroleum ether Petroleum ether) was the increase of 0.27%. estimated the percentage of ash in the sampls was 3.78%, either fiber reached 69.47 %,, in addition to the test extracts towards the growth of seven types of bacteria, which included Bacillus subtilis, Bacillus cereus, Bacillus stearothermophilus, Escherishia coli, Staphylococcus aureus, Salmonella typhimurium and Pseudomonas fluorescens and yeast Candida albicans and Kluyveromyces marxianus, ( diffusion method ).
... Show MoreMany of the signs that the global energy system indicate the start of a period of transition from total dependence on fossil energy sources, especially oil, into a new era in which alternative energy sources play an important role in meeting the growing needs of energy demand, so sought many of the developed countries through research the studies carried out to try to bring renewable energy sources and non-renewable (shale oil, oil sands, solar energy, wind energy .... etc) replace traditional fossil energy sources (oil, gas, coal) and despite the recent availability dramatically and spread throughout the the world, but they are going to dry up in the foreseeable future. So many countries, especially the developed sought to find
... Show MoreThis research aim at finding out the impact of using the strategy of shape V on the achievement of the students of the Department of Artistic Education in the subject of "Principles of scientific Research ". This strategy is one of the cognitive strategies used in this topic . To verify the aim of the research ,the two researchers have put the following null hypothesis:-There are no significant differences on the level of 0,05 among the average degrees of the students of the experimental group in their answers on the topics of the pre and post cognitive achievement tests of the subject of "principles of scientific Research " . The two researchers have adopted the experimental approach which consists of one group . the population of the r
... Show MoreThe study aims at studying and analyzing the subject of marketing vigilance as it is one of the modern approaches in the marketing field that can be used to face changes in the competitive and strategic environment and that represents quick reactions on the part of the institution to ensure its survival and distinctiveness other aims are: Consolidating the strength of the marketing organization and its success continuously, represented by changes in the market share, awareness of the institution's position in the market and its relations with competing tourism companies, diversification of tourism services, as well as an analysis of the competitive strategic position of tourism institutions for the purpose of conducting a r
... Show MoreStudied the effect of foliar fertilizers Alaongrin results showed that spraying fertilizer Alaongrin and Fertilizers and Ministry of Agriculture and rack licorice extract every three weeks after thirty days from planting seedlings
An experiment in the semester, the second semester of the academic year (2022-2023), and the data used was not processed (the second test for two independent, inaccurate samples, the Bermon correlation coefficient, and the Spearman correlation coefficient), and the following results were reached: There is a statistically significant difference at the level of ( 0) average, 05) between the third grade who studied the plan for asking cluster questions, and between the average of those who studied the special feature according to the traditional method of selecting achievement, and enjoyed completing the specialization, choosing the experimental group, because the strategy of asking cluster questions is one of the externalities that... Lear
... Show MoreThis research after financial ratios in the detection of fraud to the financial statements published which enables specialists from the work of their studies and their conclusions to obtain the information they seek on the activities of the entity. Has provided researchers what these relics They then field study to test the validity and sincerity of the findings of the suggestions that have been upheld the need to study all financial ratios extracted in general, organized and used in decision-making processes necessary administrative.And that the financial management attention more financial analysis and extraction of financial ratios and compare them with industry standards taken from historical norms