Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

To decrease the dependency of producing high octane number gasoline on the catalytic processes in petroleum refineries and to increase the gasoline pool, the effect of adding a suggested formula of composite blending octane number enhancer to motor gasoline composed of a mixture of oxygenated materials (ethanol and ether) and aromatic materials (toluene and xylene) was investigated by design of experiments made by Mini Tab 15 statistical software. The original gasoline before addition of the octane number blending enhancer has a value of (79) research octane number (RON). The design of experiments which study the optimum volumetric percentages of the four variables, ethanol, toluene, and ether and xylene materials leads

A spectrophotometric determination of azithromycin was optimized using the simplex model. The approach has been proven to be accurate and sensitive. The analyte has been reacted with bromothymol blue (BTB) to form a colored ion pair which has been extracted in chloroform in a buffer medium of pH=4 of potassium phthalate. The extracted colored product was assayed at 415 nm and exhibited a linear quantification range over (1 - 20) g/ml. The excipients did not exhibit any interferences with the proposed approach for assaying azithromycin in pharmaceutical formulations.

The ability of Cr (VI) removal from aqueous solution using date palm fibers (leef) was investigated .The effects of pH, contact time, sorbets concentration and initial  metal ions concentration on the biosorption were investigated.

The residual concentration of Cr (VI) in solution was determined colorimetrically using spectrophotometer at wave length 540 nm .The biosorption was pH-dependent, the optimum pH was 7 and adsorption isotherms obtained fitted well with Langmuir isotherms .The Langmuir equation obtained was Ce/Cs = 79.99 Ce-77.39, the correlation factor was 0.908.These results indicate that date palm fibers (leef) has a potential effect for the uptake of Cr (VI) from industrial waste water.

Melanoides tuberculata (O. F. Müller, 1774), a freshwater snail native to eastern Mediterranean, eastern Africa, southeast Asia, southern Asia, India, and Malaysia, it is an effective invader and is now nearly globally distributed. This snail has been studied with interest because of its rapidly distributed, and because of being can serve as compatible intermediate host for many of trematodes in the world. We have summarized information from many articles in order to highlight the most important aspects of this invader snail life.

Thyroid hemiagenesis (THA) is a rare congenital anomaly in which one lobe of thyroid gland fails to develop during embryological stage. Agenesis may be unilateral, total or isthmic. Left thyroid lobe is more commonly involved than right lobe in hemiagenesis. Agenesis of the isthmus was seen in 50% of cases. Left sided hemiagenesis is more common than right sided hemiagenesis with a Left to right ratio of 4:1. Clinically patients can be euthyroid, hypothyroid or hyperthyroid. Often it is diagnosed as an incidental finding during ultrasonography (USG) study of neck, which can easily diagnose this condition.

Actual incidence of THA is unknown; most cases are diagnosed in patients admitted for thyroid scan or thyroid surgery because

       In this work, the fractional damped Burger's equation (FDBE) formula    = 0,