In the last twenty years, the work was done on the different problems related to the Qualitative Theory of differential equations. But during the last few years, the interest surrounded around the well-known Hilbert's Sixteenth Problem which he posed at Paris Conference of International Congress of Mathematicians in 1900, together with other twenty-two problems 17]. In this book we are mainly concerned in the second part of Hilbert's sixteenth Problem, which poses the question of maximal number and relative position of limit cycles of the polynomial system of the form: (A) in which P and Q are polynomials in x and y. We write the system A in the form of (B) Where, and, are homogeneous quadratic and cubic polynomials in x and y. Chapter No. 1 comprises the basic concepts for general theory of limit cycles and Hilbert's Sixteenth Problem. Chapter No. 2 contains an Algorithm for determining so called focal basis. This can be implemented on the computer to get the estimate for the number of small-amplitude limit cycles. Chapter No. 3 deals with some classes of system (B) with several small-amplitude limit cycles.

Residue analysis of chlorpyrifos (an organophosphate pesticide) was investigated in different water samples. Analysis was carried out in collaboration with pesticide residue laboratory Kala Shah Kaku due to the availability of latest chromatographic techniques. Chlorpyrifos was analyzed in different samples of water collected from different sites of Lahore. Sample preparation was done by using Solid Phase Extraction (SPE) technique. Analysis was carried out using High Performance Liquid Chromatography (HPLC). Acetonitrile, methanol solvents were used as mobile phase to achieve the best separation. Chlorpyrifos was detected in 0.161 mg/L-1.912mg/L concentration ranges. Maximum residue limit of chlorpyrifos in drinking water established by either World Health Organization (WHO) or European Union (EU) is 0.040mg/L. The highest concentration of chlorpyrifos residue was 1.912mg/L in water sample collected from Kala Shah Kaku. Study of residue analysis of chlorpyrifos in water has the significant role to solve the environmental problems related to pesticides.