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

The need to create the optimal water quality management process has motivated researchers to pursue prediction modeling development. One of the widely important forecasting models is the sessional autoregressive integrated moving average (SARIMA) model. In the present study, a SARIMA model was developed in R software to fit a time series data of monthly fluoride content collected from six stations on Tigris River for the period from 2004 to 2014. The adequate SARIMA model that has the least Akaike's information criterion (AIC) and mean squared error (MSE) was found to be SARIMA (2,0,0) (0,1,1). The model parameters were identified and diagnosed to derive the forecasting equations at each selected location. The correlation coefficien

The need to create the optimal water quality management process has motivated researchers to pursue prediction modeling development. One of the widely important forecasting models is the sessional autoregressive integrated moving average (SARIMA) model. In the present study, a SARIMA model was developed in R software to fit a time series data of monthly fluoride content collected from six stations on Tigris River for the period from 2004 to 2014. The adequate SARIMA model that has the least Akaike's information criterion (AIC) and mean squared error (MSE) was found to be SARIMA (2, 0, 0) (0,1,1). The model parameters were identified and diagnosed to derive the forecasting equations at each selected location. The correlat

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

The first aim in this paper is to introduce the definition of fuzzy absolute value on the vector space of all real numbers  then basic properties of this space are investigated. The second aim is to prove some properties that finite dimensional fuzzy normed space have.

Purpose: The concept of complete street is one of the modern trends concerned with diversifying means of transportation and reducing the disadvantages of mechanical transportation modes. This paper discusses the role of complete streets can play in developing the urban environment in the Alyarmok District of Baghdad.   Method/design/approach: The linear regression method used to analyze the opinions of 100 respondents surveyed in the study area in order to find the relationship between the urban environment and the complete street elements.   Theoretical framework: The Modern trends in urban planning aim to find alternatives to the policies of traditional transportation planning that focus on vehicular mobi

        Vitamin K is a fundamental enzymatic co-factor implicated in the carboxylation of several vitamin K dependent proteins involved in the pathogenesis of certain age – related diseases. Inflammation is realized as an important factor in such diseases. Vitamin K is recognized to play an anti-inflammatory behavior that is distinct of its action as an enzymatic co- factor by suppressing many signaling pathways mainly the nuclear factor κB (NF-κB) signal transduction pathway. As well as to play a role as an antioxidant versus the generation of reactive oxidative species (ROS). The purpose of this review is to focus on the protective function of vitamin K as an anti-inflammatory agent

Introduction and Aim: Graves ophthalmopathy is one of the pandemic public health disorders in Iraq. The current investigation attempts to determine the variation in the complete total blood cells on the recovery of individuals with Graves' ophthalmopathy following low and high-dose Radioactive Iodine 131 (RI-131) exposures.   Materials and Methods: The complete blood CBC level in people with Graves' illness and healthy, normal controls were quantitatively identified using the CBC counter. Thyroid stimulating hormone was utilized to compare the recovery of ophthalmopathy patients in comparison to a control group.    Results: In comparison to healthy controls, patients with Graves' ophthalmopathy disease who received 10 mci of RAI-