In this research the natural frequency of a cracked simple supported beam (the crack is in many places and in different depths) is investigated analytically, experimentally and numerically by ANSYS program, and the results are compared. The beam is made of iron with dimensions of L*W*H= (0.84*0.02* 0.02m), and density = 7680kg/m³, E=200Gpa. A comparison made between analytical results from ANSYS with experimental results, where the biggest error percentage is about (7.2 %) in crack position (42 cm) and (6 mm) depth. Between Rayleigh method with experimental results the biggest error percentage is about (6.4 %) for the same crack position and depth. From the error percentages it could be concluded that the Rayleigh method gives

The effect of insecticide lamda cyhalothrin on Allium cepa L.root meristem were studied cytogenetically .Using three concentrations of the insecticide 5%, 7.5%, 10% at 6,12,24hours treatments . The insecticide significantly reduced the mitotic index at all concentrations. Moreover showed its ability to induced C – metaphase in 10% .The effects were also caused chromosome aberration like stickness in anaphase, telophase, binucleated cells, Micronuclei formation. These alternations indicating that this insecticide was effective in producing disturbance of spindle fibers.

This study was carried out to find out the effect of germination of broad beans and chickpeas seeds for different periods on their antinutritional factors content ( Trypsin inhibitor and Phytic acid ) and the chemical constituents of germination seeds compared with the control samples (ungerminated seeds) . The results indicated asignificant increase (P<0.05) in crude protein content as germination period proceeded.The highest values of 28.0% and 24.0% were reached on the sixth and fourth day for germinated broad beans and chickpeas respectively, The intial values were 25.6% and 23.5% for control samples, respectively. The content of raffinose,stachyose and verbascose were reduced as germination period proceeded, Stachyose and verbascose we

The numerical response of Chrysoperla mutata MacLachlan was achieved by exposing the larvae of the predators to various densities of dubas nymphs Ommatissus lybicus DeBerg. Survival rate of predators’ larvae and adults emergence increased with increasing consumption . Repriductive response of predator was highly correlated with the amount of food consumed (+0.996).

In this paper an eco-epidemiological system has been proposed and studied analytically as well as numerically. The boundedness, existence and uniqueness of the solution are discussed. The local and global stability of all possible equilibrium point are investigated. The global dynamics is studied numerically. It is obtained that system has rich in dynamics including Hopf bifurcation.

      Let S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.