Abstract:
The norm concept of elastic compliance tensor and its irreducible parts and their ratios are used to study the anisotropy of the alloys Au-Cd at different percentages of Cd at different temperatures, Aux Cu53-x Zn47 for different values of x and Au-Ni at different percentages of Ni is given.

Abstract:
The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of Zn structure semiconductors are calculated. The relation of the scalar parts norm and the other parts norms and the anisotropy of the material are presented. The norm ratios are used as a criterion to present the anisotropy degree of the properties of the material. The ratio (N / C°) is calculated, where N is the norm of elastic constant tensor of the material and C° is the elastic constant of the crystal in the order of magnitude e2 / r4, where e is the charge of the electron, and r is the distance between the nearest neighbor atom. Also the comparison of (N / C° ) with Zinc Blender lattice parameter, Zinc Blende density and Energy Gap at 300 K are given in (Radwan, 2001).

Abstract:
Reduction procedure of decomposing a Cartesian tensor of rank n into its irreducible parts is given. The numbers of different irreducible parts of the sixth rank Cartesian tensor are calculated. The number of independent components of sixth rank Cartesian tensor is computed. The scalar normalized irreducible parts of sixth rank Cartesian tensor are presented. Examples of different symmetry of sixth rank tensors are given.

Abstract:
The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of Lithium compounds are calculated. The relation of the scalar parts norm and the other parts norms and the anisotropy of the material are presented. The norm ratios are used as a citerion to present the anisotropy degree of the properties of the material.

Abstract:
Decomposition of elastic constant tensor into irreducible parts is given. Elastic constant tensor norm and norm ratios for various anisotropic materials of the same or different symmetry are calculated. The norm of a tensor is used as criterion for comparing the overall effect of the properties of anisotropic materials and the norm ratios are used as criterion to represent the anisotropy degree of the properties of materials.

Abstract:
Excel spreadsheet is used in solving optimization problems of one variable and several variable without constraints and it is stated that the Solver of Tools menu can be used to solve the constrained optimization problems.

Abstract:
Fifht order Runge – Kutta method (Bucher’s method) is used in solving initial value problems of the form by the aid of Excel Spread Sheet for different values of step size h, and the true relative percent error εt is calculated for every case.

Abstract:
The paper shows that how powerful of excel spreadsheet in solving mathematical problems numerically. The numerical solutions of many initial value problems with boundary conditions of partial differential equations using excel are given and the effect of changing the parameters of the equations is treated.