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
This research’s goal is to restore and to revive the jurisprudence of Mother of Believers (Um alMuaamineen) “Um Salmah” "may God bless her", and to highlight her outstanding assimilation and understanding of religion and her conscious thought. The current research is a comparative scientific theoretical study represented in the comparison of jurisprudence of “Um Salamah” with Hadiths of fasting and pilgrimage rules as well as the duration mentioned in jurisprudence of for doctrines( 4 schools of thought )to identify these hadiths with the inclusion and discussion of their evidence.
The current research included two topics: the first one is to identify and introduce
... Show MoreHighway embankments stability during its service period represents an important factor for the safety of highway users and vehicles. Consequently, the cost of construction of these embankments should be adequate to maintain the safety and durability during this period through proper estimation of the loading on asphalt pavement, slope stability, horizontal and vertical deformation, etc. Slope stability of the embankment mainly depends on the shear strength of the soil layers materials; this shear strength is affected by the water table level through the contribution of the capillary water. Negative pore water pressure above the water table level evolves matric suction in the unsaturated zone above water table; this matric suction increases
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Man was closely associated with nature in its various forms, as it represented the incubator for him in all areas of his life, so writers often made it a material for their literature and a fertile ground for their productions, so it appeared in its various forms and man’s need for it, its good and its bad in literature throughout history, and the Arabs are like Other nations, since the pre-Islamic era, nature was an important outlet and a refuge for poets in the production and creativity of literature and to this day, and when we talk about a poet from the Fatimid state, we find that nature - especially spring and its flowers - in that period took its take from literature and represented a phenomenon for many Among the
... Show MorePraise be to God, Lord of the worlds, and prayers and peace be upon our master and beloved Muhammad, the wise guide and great teacher, the guide to a straight path, the one sent as a mercy to the worlds, and upon his good and chosen family, his chosen companions, the working scholars, and those who follow them in righteousness until the Day of Judgment.
And after:
One of the important controversial topics shared between the sciences of the Noble Hadith and the Fundamentals of God is the issue of the innovator in terms of accepting and rejecting his narration and testimony, and the difference in it leads to disagreement in many branches of jurisprudence that were based on texts narrated by innovated narrators or those accu
... Show MoreAbstract: This article is a comparative analysis of the concept and types of homonyms in Russian and Arabic. Homonyms are lexical units that have the same sound but different meanings. The study of homonymy in different languages can help reveal the features of the semantic structure and syntactic rules of each language. The article discusses the main aspects of homonymy in Russian and Arabic, as well as a comparative analysis of the types of homonyms that exist in both languages. The study includes an analysis of the semantic meanings of homonyms, their use in context, and possible differences in syntactic features that may affect their interpretation and perception by native speakers of these languages. The purpose of the article is to id
... Show MoreThe research problem consisted in answering the question that revolves around whether there is a relationship to the settlement of salaries with the growth of bank deposits? The research also aimed to provide some initial solutions to improve the role of salary localization, in terms of reviewing the concept of electronic payment systems, its tools and channels, and then identifying the concept of salary localization, its importance, objectives and obstacles to its application, and then analyzing the reality of the state of the settlement of salaries and bank deposits for the research sample banks, which are each of the bank (Ashur International, Business Bay, the Iraqi Middle East for Investment, the Iraqi National, Development and the
... Show MoreThe aim of this paper is to know the persuasive methods and public relations strategies in building the reputation of the United Arab Emirates, since the UAE is progressing among the international indicators in good reputation. The researcher used the survey method, using the content analysis tool, to analyze the publications of the UAE Ministry of Foreign Affairs and International Cooperation for the period from 10/1/2021 to 12/31/2021.The researcher reached a set of results, the most important of which are: The UAE Foreign Ministry relied on public relations strategies in order to build a good reputation for the country, as it focused on the media strategy and gave little importance to the consensus-building strategy, as well as focuse
... Show MoreThis paper deals with estimation of the reliability system in the stress- strength model of the shape parameter for the power distribution. The proposed approach has been including different estimations methods such as Maximum likelihood method, Shrinkage estimation methods, least square method and Moment method. Comparisons process had been carried out between the various employed estimation methods with using the mean square error criteria via Matlab software package.
Phytoplankton, as one of the most important primary producers in aquatic ecosystems, has been widely used to indicate the health of ecosystems. Nine physico-chemical parameters of water, as well as the phytoplankton community, of Al-Chibayish marsh were studied. Samples were collected from four sites and analyzed every two months from January to October 2019.
Seasonal variations in physical and chemical properties were observed at all sites during the study period. The results indicated that 154 species of phytoplankton were recorded. The highest percentage of species was recorded to be 64.28% for Bacillariophyceae (diatoms) (Centrales 3.24% and Pennales 61.03%), followed by Chlorophyceae (16.23%), Cyanophyceae
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This research aims to define the roles of auditors by clarifying the concept and risks of cyber security in protecting information and financial data in economic units. Najaf, Babylon and Karbala, then the results were analyzed and the results were presented and analyzed to show that adopting cyber security improves the quality of reports Finance through what it achieves in displaying information with credibility and transparency, in a way that suits the needs of users, and cyber security has a role in managing economic resources more effectively to obtain benefits that would have been lost in the event of an
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