Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

The aim of this paper is to determine the feasibility of using fluorometric methods as an indicator for quality and contamination of milk with E.coli bacteria, and selection the suitable wavelength to be used with laser induced auto fluorescence. Three groups of milk samples were used in this study: Fresh pasteurized milk samples, milk samples containing different concentration of E.coli bacteria which were added artificially, and milk samples that were kept in refrigerator for 3-5 days. Thirteen excitation wavelengths were used to get the emission spectra for all milk samples using spectroflourometer .The results showed that the emission spectra at 275nm excitation wavelength gave a good differentiation between these three groups.

In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach contraction principle to include metric space with modular spaces has been included in some recent research, the aim of study proves some pro

the main of this paper is to give a comprehensive presentation of estimating methods namely maximum likelihood bayes and proposed methods for the parameter

Biological Activity of Complexes of Some Amino Acid

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.

That the possibility of imposing a tax on electronic commerce is increasing interest in it by governments in developed and developing countries alike, and there is interest in a logical by governments and bodies of taxation, in particular in developing countries erosion potential tax in the tax base resulting from the adoption of e-commerce if not mutation rules and tax legislation, local and international to take into account this important economic developments and how to keep up, said the combination of the taxation system is the only way to increase revenue needed to finance government spending on goods and services needed by society.

The most important conclusions reached by the rese

The housing sector in Iraq has suffered from multiple problems, the most prominent of which is the failure of the housing market to achieve housing production that faces population increases and a high number of households.

The research aims to foresight the future of the housing sector,  and to identify the expectations of experts in the development of the housing sector and housing production, in order to overcome the obstacles and problems.

Foresight does not mean forecasting about future events, but rather it is a process and skill aimed at familiarity with providing sufficient knowledge to achieve the desired future goals, Accordingly, adopting a method of future foresight will reduce error,  surprise and s

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

Thermal pyrolysis kinetics of virgin high-density polyethylene (HDPE) was investigated. Thermal pyrolysis of HDPE was performed using a thermogravimetric analyzer in nitrogen atmosphere under non-isothermal conditions at different heating rates 4, 7, 10 °C/min. First-order decomposition reaction was assumed, and for the kinetic analysis Kissinger-Akahira-Sunose(KAS), Flynn-Wall-Ozawa(FWO) and Coats and Redfern(CR) method were used. The obtained values of  average activation energy by the KAS and FWO methods were equal to137.43 and 141.52 kJ/mol respectively, these values were considered in good agreement, where the  average activation energy value obtained by CR equation methods was slightly different which equal to 153.16 kJ/