Multiplicative inverse in GF (2 m ) is a complex step in some important application such as Elliptic Curve Cryptography (ECC) and other applications. It operates by multiplying and squaring operation depending on the number of bits (m) in the field GF (2 m ). In this paper, a fast method is suggested to find inversion in GF (2 m ) using FPGA by reducing the number of multiplication operations in the Fermat's Theorem and transferring the squaring into a fast method to find exponentiation to (2 k ). In the proposed algorithm, the multiplicative inverse in GF(2 m ) is achieved by number of multiplications depending on log 2 (m) and each exponentiation is operates in a single clock cycle by generating a reduction matrix for high power of two ex

  The content of Furocoumarin derivatives (Psoralens) of Ruta Chalepensis L. (Whole plant) was studied by simple extraction with petroleum ether (b.p. 60-80C^o). The results indicated that the plant contains a total of about (0.015%).

       Investigation of these compounds by thin layer chromatography (TLC) revealed the presence of at least four compounds of which methoxsalen (8-methoxypsoralen) was isolated.     It was identified and authenticated with a standard by spectral method, IR, NMR, Mass spectra and HPLC.This plant could be considered as a good source for supplying this compound, which is widely used in dermatological preparations.

Chemical analysis for evaluation of Nigella sativa L. (black cumin) seeds showed a composition of Fat 39% ; Protein 28% ; Carbohydrate 21% ; Moisture 6% and Ash 4.5% . It was found that the black seed contains the following mineral element : Magnesium 0.26 gm /100gm seed ; Calcium 0.25 gm /100gm seed and Iron 25 ?g / gm /100gm seed ; zinc 4.51?g /gm /100gm seed and Copper 3.60 ?g /gm /100gm seed. The analysis also showed that mineral element I. e. ; lead ; Cobalt ; Nickel ; Chrom ; Cadmium and Aresenic are not present . It was found that the fat of the black seed contains the following fatty acids : Myristic 2.8%; Palmtic 16.6%; Stearic 0.8 % ; Oleic 13.79% ; Linoleic 64.2% and Arachidic 1.9% .

Background: This study compared in vitro the marginal adaptation of three different, low shrink, direct posterior composites Filtekâ„¢ P60 (packable composite), Filtekâ„¢ P90 (Silorane-based composite) and Sonic fillâ„¢ (nanohybrid composite) at three different composite/enamel interface regions (occlusal, proximal and gingival regions) of a standardized Class II MO cavity after thermal changes and mechanical load cycling by scanning electron microscopy. Materials and methods:Thirty six sound human maxillary first premolars of approximately comparable sizes were divided into three main groups of (12 teeth) in each according to the type of restorative material that was used: group (A) the teeth were restored with Filtekâ„¢ P6

This  research aimes to expose the levels of geometrical thinking among the students of mathematic department in Basic Education College at AL-Mustansiriyah University throughout their respondes on the test of  geometrical thinking which consists (50) multi- choice items  distributed on the first four levels of Van Hiele ( recognition – analysis – ordering – deduction ).

The validity and the reliability of the test have been investigated. Besides, the difficulty and its discrimination have been measured. The activity of the wrong variables has been measured.

The test has been applied on (180) male and female students of the first, second and third grades.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

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.

We aimed to examine the potential protective effects of Iraqi H. tiliaceus L. chloroform leaves extract on DEN-induced HCC in male Wistar Albino rats.