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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.
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