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.

The one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical
function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant the

The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal con

Estimation of the unknown parameters in 2-D sinusoidal signal model can be considered as important and difficult problem. Due to the difficulty to find estimate of all the parameters of this type of models at the same time, we propose sequential non-liner least squares method and sequential robust  M method after their development through the use of sequential  approach in the estimate suggested by Prasad et al to estimate unknown frequencies and amplitudes for the 2-D sinusoidal compounds but depending on Downhill Simplex Algorithm in solving non-linear equations for the purpose of obtaining non-linear parameters estimation which represents frequencies and then use of least squares formula to estimate

The life on earth is driven by energy, supplied by the tiny organelles of the cell called mitochondria and they are usually stated as the powerhouses of the cell.  In population genetics, Mitochondrial DNA (mtDNA) is used extensively to categorize individuals or populations.  The mutation sites observed in human mtDNA by comparing with the reference sequence (rCRS) are termed into definite human mtDNA haplogroups. Previous studies showed that mtDNA specific haplogroups and polymorphisms were established to be linked with various human diseases, including cancer in numerous populations. Furthermore, it is also known that several mitochondrial DNA polymorphisms are implicated in enhanced production of Reactive Oxygen Species (ROS

     A reliable differential pulse polarographic (DPP) method has been developed and applied for the determination of ibuprofen IBU in dosage form with dropping mercury electrode (DME) versus Ag/AgCl. The best peak was found at cathodic peak of -1.18 V in phosphate buffer at pH=4 and 0.025M of KNO₃ as supporting electrolyte. In order to obtaine the highest sensitivity, instrumental and experimental parameters were examined including the type and concentration of supporting electrolyte, pH of buffer solution, pulse amplitude and voltage step time. Diffusion current showed a direct linear relationship to ibuprofen concentration in the range of (5 – 30) μg. mL^-1 (2.43× 10^-5

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

This experiment was conducted in the orchard of the Department of Horticulture,college of Agriculture,Baghdad University during the growing season of 2007 To study the effects of spray with three concentration of cultar(0,500,1000 mg.L-1) ,tow concentration of K2SO4(0,5g.L-1), and salinity of irrigation water with three concentration (1,2,3dS.m-1) on some characteristics of vegetative growth of two cultivars of apricot trees (Labib1 and Zienni).The age of trees was four years .The tree grafted on original of seed apricot . Afactorial trail was carry out according to randomized complete block design with arrangement of split-split with three replications. Salinity of irrigation water took main plot, potassium took sub plot and cultar took s