Economics--Mathematical models

One of the limiting factors restricting aircraft landings at maJor airports is the
minimum spacing requirements due to vortex wake avoidance. If it can be shown that the
separation requirements are too conservative, then it may be possible to increase the rate
of landings on a given runway. During August/September 2003, NASA and the (United
States Department of Transportation) USDOT sponsored a wake acoustics test at the
Denver International Airport. The central instrument of the test was a large microphone
phased array. Different types of aircrafts were recorded during landing and the acoustic
data obtained was stored. From acoustic data the spectrograms were generated using the
technique of AutoRegressive (AR) spectral estimation from multitaper autocorrelation
estimates.
Several sources of sound that are recorded in the audio files can be observed in the
spectrograms. Some these signals, such as the noise generated from the aircraft engine can be identified easily because of their strength and the Doppler shift they undergo. In
contrast to this, the wake vortex signal is weaker and does not exhibit a Doppler shift
because it's stationary in space. Therefore it may not be identified easily because of the
existence of stronger signals. The motive in our research is to develop methods to
determine these strong signals that appear as spectral lines in the spectrogram. In the
future, the results obtained in this work can be used to eliminate these strong signals from
the spectrogram thus allowing us to see and identify wake vortex signal which is more
important to us.

This thesis examines as well as compares four essential issues of the Cournot oligopoly model--existence, uniqueness, and stability of the equilibrium solution, and the competitive property of the model. A Cournot equilibrium solution exists for the market when the marginal revenue of each firm declines due to an output expansion by all other firms. The existing Cournot solution is unique when a non-zero Jacobian determinant of the marginal profit functions exist. The equilibrium solution is stable when two conditions are simultaneously satisfied: (i) each firm's marginal cost does not fall faster than the market demand curve, and (ii) on the aggregate the marginal profit of the firms decreases as all the firms expand their outputs. The existence, uniqueness, and stability are necessary properties for the Cournot equilibrium solution to become quasi-competitive. However, the Cournot solution will converge towards the competitive solution only in absence of economies of scale. These results have an important policy implication that, allowing entry into an oligopolistic market will improve the market performance.

This thesis discusses the locational theories and their implications and
applications on the Turkish Consulate. Chapters I and II analyzes the theories of
Von Thunen, Jsard, and Hoover. Chapter III discuses Weber's theories and an
application on the Turkish Consulate. Chapter IV summarizes the conclusions.