Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

Abstract

The prevention of bankruptcy not only prolongs the economic life of the company and increases its financial performance, but also helps to improve the general economic well-being of the country. Therefore, forecasting the financial shortfall can affect various factors and affect different aspects of the company, including dividends. In this regard, this study examines the prediction of the financial deficit of companies that use the logistic regression method and its impact on the earnings per share of companies listed on the Iraqi Stock Exchange. The time period of the research is from 2015 to 2020, where 33 companies that were accepted in the Iraqi Stock Exchange were selected as a sample, and the res

Two- dimensional numerical simulations are carried out to study the elements of observing a Dirac point source and a Dirac binary system. The essential features of this simulation are demonstrated in terms of the point spread function and the modulation transfer function. Two mathematical equations have been extracted to present, firstly the relationship between the radius of optical telescope and the distance between the central frequency and cut-off frequency of the optical telescope, secondly the relationship between the radius of the optical telescope and the average frequency components of the modulation transfer function.

In Production and Operations Management the specialists  have  tried to develop a strategy to counter the risks arising from the activities of the organization and of waste of various types and therefore the risk management in the contemporary framework represents a phenomenon of new quality, and can not be this phenomenon to take practical dimensions, but the development of culture of the organization towards the risks and deal with all aspects and paint ways to address them within an integrated program, and requires new skills and systems provide accurate information capable of coordination between the various parties within the organization.

     The research aims to develop a blu

The study showed that all extracts (aqueous, ethanolic and acetonic) of the leaves of Eucalyptus and Myrtus plants had a inhibitory effect on the growth of all types of yeasts studied, acetone extract recorded the highest inhibition of yeastat 100ppm concentration,The inhibition was 35mm, 34mm, 24mm and 20mm for Candida parapsilosis, Candida glabrata, Candida tropicalis and Candida albicans respectively, The experiments above showed the least significant differences at 0.05 level.The results ofE. Cammldulensis ethanolic tincture analysis has shown the presence of 44 biologically active substances. The main Eucalyptus leaves component was: 2-Bicyclo (2-2.1) heptanol (12.37%), Ledol (8.23%),1,2,4- Benzenetriol (8.45%) and that contain spathul

The European Unit has never been affected by a serious phenomena as the phenomena of the advancing of the far right parties. Though these parties vary in their impact in their original countries, they agree on one important issue which is the deconstruction of the European unit and limiting its supernational powers. These increasing popular parties aim at more national independence in decision making away from the decisions taken by Brussels. Moreover, they criticize the financial and administrative corruption accompanied many of the rescuing procedures directed for example towards countries like Greece and Spain during the international economic crisis. This failure nourishes many of the negative feelings against the European unit which

The article characterizes metaphors and comparisons as a means of rethinking the phenomena of the surrounding world; two directions are named within which metaphors and comparisons are studied: 1) the linguo-classification direction combines several classifications of metaphors and comparisons, which are basically focused on comparing two denotations through the meanings of word forms that are part of the trope; 2) the theoretical and conceptual direction is associated with the concept of conceptual displacement and is the basis of the theoretical and methodological study of metaphor and comparison, i.e. the modern theory of metaphor is being formed; The main attention is focused on the comparative concept of Aristotle, which postul