The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

        The present article studies the specific cultural features contained in phraseological units. The problem is approached through three different levels:

1. The modern linguistic meaning.
2. Lexical components of phraseological units.
3. The first variables of linguistic units.

  The paper emphasizes the gradual process of the cultural charge in the semantic structure of phraseological units.      

       Наша Статья посвящена вопросам анализа национ-ально - культурной сп

Atorvastatin calcium (ATR) is an antihyperlipidemic agent used for lowering blood cholesterol levels. However, it is very slightly soluble in water with poor oral bioavailability, which interferes with its therapeutic action. It is classified as a class II drug according to Biopharmaceutical Classification System (low solubility and high permeability).

The research aims to identify the reasons that lead to asymmetry of information between economic unity administration and the parties that use accounting information such as shareholders, So,  the ability to reach to the solutions that would reduce this problem, these factors have been divided into two types: the first one is the internal factors which represent the administration's desire   in order to expand the self-interest of getting the profits and increase the value and competitive entity and investors to obtaining greater returns for their shares, so the second type is the external factors, which represent the failer that occurs ​​in the laws and regula

Abstract

That the reduction of costs for products and services provided by economic units is one of the main concerns at the present time to keep pace with competition in the markets, economic units are always striving to stay competitive in a modern business environment and achieve a competitive advantage, (TDABC) in the General Company for Electrical and Electronic Industries / Air cooler engine plant to reduce the costs facing the economic units under the circumstances of the Iraqi environment, especially the industrial, and the need for development events in traditional methods (TDABC) as a technology for reducing costs by relying on time guidelines. The research also concluded that the financial and non-financ

The analysis of the classic principal components are sensitive to the outliers where they are calculated from the characteristic values and characteristic vectors of correlation matrix or variance Non-Robust, which yields an incorrect results in the case of these data contains the outliers values. In order to treat this problem, we resort to use the robust methods where there are many robust methods Will be touched to some of them.

   The robust measurement estimators include the measurement of direct robust estimators for characteristic values by using characteristic vectors without relying on robust estimators for the   variance and covariance matrices. Also the analysis of the princ

Abstract

      In this study, we compare between the autoregressive approximations (Yule-Walker equations, Least Squares , Least Squares ( forward- backword ) and Burg’s (Geometric and Harmonic ) methods, to determine the optimal approximation to the time series generated from the first - order moving Average non-invertible process, and fractionally - integrated noise process, with several values for d (d=0.15,0.25,0.35,0.45) for different sample sizes (small,median,large)for two processes . We depend on figure of merit function which proposed by author Shibata in 1980, to determine the theoretical optimal order according to min

Estimation of the unknown parameters in 2-D sinusoidal signal model can be considered as important and difficult problem. Due to the difficulty to find estimate of all the parameters of this type of models at the same time, we propose sequential non-liner least squares method and sequential robust  M method after their development through the use of sequential  approach in the estimate suggested by Prasad et al to estimate unknown frequencies and amplitudes for the 2-D sinusoidal compounds but depending on Downhill Simplex Algorithm in solving non-linear equations for the purpose of obtaining non-linear parameters estimation which represents frequencies and then use of least squares formula to estimate

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

Maulticollinearity is a problem that always occurs when two or more predictor variables are correlated with each other. consist of the breach of one basic assumptions of the ordinary least squares method with biased estimates results, There are several methods which are proposed to handle this problem including the  method To address a problem  and  method To address a problem , In this research a comparisons are employed between the biased   method and unbiased   method with Bayesian   using Gamma distribution  method  addition to Ordinary Least Square metho