This paper devoted to the analysis of regular singular initial value problems for ordinary differential equations with a singularity of the first kind , we propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the regular singular points and its numerical approximation, two examples are presented to demonstrate the applicability and efficiency of the methods. Finally , we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

    This paper is devoted to the analysis of nonlinear singular boundary value problems for ordinary differential equations with a singularity of the different kind. We propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the singular points and its numerical approximation. Two examples are presented to demonstrate the applicability and efficiency of the methods. Finally, we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

The present studier aims to study the kinetic of reaction at different experimental conditions depending on coliform bacteria concentration and hypochlorite ion. The effects that had been investigated were different of sodium hypochlorite doses, contact time, pH and temperature (20, 29, 37) ^o C. The water samples were taken from Al-Wathba water treatment plant in Risafa side of Tigris River in Baghdad. The biological tests included the most probable number (M.P.N) for indicating the concentration of coliform bacteria with different contact times and the total plate count (T.P.C) for indicating the amount of colonies for general bacteria. The iodimetry method (chemical test) was used for indicating the concentration of hypochlo

in this paper fourth order kutta method has been used to find the numerical solution for different types of first liner

In this paper two modifications on Kuznetsov model namely on growth rate law and fractional cell kill term are given. Laplace Adomian decomposition method is used to get the solution (volume of the tumor) as a function of time .Stability analysis is applied. For lung cancer the tumor will continue in growing in spite of the treatment.

  This paper studies the existence of  positive solutions for the following boundary value problem :-
 
 y(b) 0 α y(a) - β y(a) 0     bta             f(y) g(t) λy    
 
 
The solution procedure follows using the Fixed point theorem and obtains that this problem has at least one positive solution .Also,it determines (  ) Eigenvalue which would be needed to find the positive solution .

The c.orrosion rate of  low carbon  steel  in 4M  hydrochlwic acid with and without  presence of thiourea has b.een studied  by gravimetric ahd gasometric methods  over the temperature range 303-333 K.

The percentage protection of steel increases  vvith the decrease of thimuea concentrations at  various  temperature range  303-333 K and

approaching highest  protection  (86.82%) at 303K  by using  I X 1 o-4 M

of thiourea. The high concentration .of thiourea  ( lxlo-3 M), enl1ances.

the  corrosion rates and  act  as dcpolariser for  the hydrogen  evolution

reaction,&n

Metal enhanced fluorescence (MEF) is an unequaled phenomenon of metal nanoparticle surface plasmons, when light interacts with the metal nanostructures (silver nanoparticles) which result electromagnetic fields to promote the sensitivity of fluorescence. This work endeavor to study the influence of silver nanoparticles on fluorescence intensity of Fluoreseina dye by employment mixture solution with different mixing ratio. Silver nanoparticles had been manufactured by the chemical reduction method so that Ag NP layer coating had been done by hot rotation liquid method. The optical properties of the prepared samples (mixture solution of Fluoreseina dye solutions and colloidal solution with 5 minutes prepared of Ag NPs) tested by using UV-V