This paper presents an alternative method for developing effective embedded optimized Runge-Kutta (RK) algorithms to solve oscillatory problems numerically.   The embedded scheme approach has algebraic orders of 5 and 4. By transforming second-order ordinary differential equations (ODEs) into their first-order counterpart, the suggested approach solves first-order ODEs. The amplification error, phase-lag, and first derivative of the phase-lag are all nil in the embedded pair. The alternative method’s absolute stability is demonstrated. The numerical tests are conducted to demonstrate the effectiveness of the developed approach in comparison to other RK approaches. The alternative approach outperforms the current RK methods

The dental amalgam of radioactive materials in the restoration of teeth because of its readily adaptable to existing materials in the oral cavity in addition to mechanical properties such as hardness mechanical resistance Alndgat and others in this study were prepared Almlagm used Guy dental restoration of silver alloy tin plus some elements to improve the characteristicsmechanical such as copper, zinc or indium in addition to mercury

Copulas are very efficient functions in the field of statistics and specially in statistical inference. They are fundamental tools in the study of dependence structures and deriving their properties. These reasons motivated us to examine and show  various types of copula functions and their families. Also, we separately explain each method that is used to construct each copula in detail with different examples. There are various outcomes that show the copulas and their densities with respect to the joint distribution functions. The aim is to make copulas available to new researchers and readers who are interested in the modern phenomenon of statistical inferences.

الاستثمار الاجنبي المباشر في العراق ودوره في تحقيق التنمية الاقتصادية

     Let S be an inverse semiring, and U be an ideal of S. In this paper, we introduce   the concept of U-S Jordan homomorphism of inverse semirings, and extend the result  of  Herstein on Jordan homomorphisms in inverse semirings.

Since the inflammatory factor IL-6 known by its critical role in different metabolic reactions in the
body, therefore, this study was designed to detect it is effect in the thyroid gland function by
injecting three groups of rats, the first with IL-6 , the second with carbimazole (antithyroid drug) and
the third with normal saline (Control).The experiment included three groups of rat; each was injected
with recombinant human interleukin-6 (rhIL-6), Carbimazole, or normal saline (Control). The results
of experiments showed that both IL-6 and carbimazole caused a decrease in the levels of thyroid
hormones (T3 and T4) in animal sera, and a significant decrease in animal body weight, but had no
effect on the liver weight

The best optimum temperature for the isolate was 30○C while the pH for the maximum mineral removal was 6. The best primary mineral removal was 100mg/L, while the maximum removal for all minerals was obtained after 8 hrs, and the maximum removal efficiency was obtained after 24 hrs. The results have proved that the best aeration for maximum removal was obtained at rotation speed of 150 rpm/ minute. Inoculums of 5ml/ 100ml which contained 106 cell/ ml showed maximum removal for the isolate.

In this paper we define and study new concepts of fibrwise totally topological spaces over B namely fibrewise totally compact and fibrwise locally totally compact spaces, which are generalization of well known concepts totally compact and locally totally compact topological spaces. Moreover, we study relationships between fibrewise totally compact (resp, fibrwise locally totally compact) spaces and some fibrewise totally separation axioms.