Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

Based on a finite element analysis using Matlab coding, eigenvalue problem has been formulated and solved for the buckling analysis of non-prismatic columns. Different numbers of elements per column length have been used to assess the rate of convergence for the model. Then the proposed model has been used to determine the critical buckling load factor () for the idealized supported columns based on the comparison of their buckling loads with the corresponding hinge supported columns . Finally in this study the critical buckling factor () under end force (P) increases by about 3.71% with the tapered ratio increment of 10% for different end supported columns and the relationship between normalized critical load and slenderness ratio was g

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

Background : The aim of this work is to study the clinical features and causative fungi of tinea pedis in diabetic and non-diabetic patients. Result : Tinea pedis was estimated to be the second most common skin disease in the United States, after acne. Up to 15% of the U.S., population may have tinea pedis. Across Europe and East Asia, prevalence rates reach 20 %. Methods: The Complete history taking regarding: age, sex, occupation, residency, history of diabetes and diabetic profile (fasting blood sugar and post prandial).and Clinical examination of the feet Aim of the study : The aim of this work was to study the clinical features and causative fungi of tinea pedis in diabetic and non-diabetic patients Conclusion : Tinea pedis is more