The paper presents the study of the iterations of rational fractions, that is, the behavior of z_0,z_1=f(z_0 ),…,z_(n+1)=f(z_n ),… We illustrate the conditions needed for this function to behave as its linear part and prove the existence of Siegel and Cremer points. The study extends to a description of Fatou and Julia sets.

A denial of service (DoS) attack is an attempt by a person or a group of persons to cripple an online service. This can have serious consequences on companies like Amazon and eBay, which rely on their online availability to do business. Many defense mechanisms have been proposed to thwart DoS attacks. One of these defense mechanisms is called hop-count filtering. Although an attacker can forge any field in the IP header, he or she cannot falsify the number of hops an IP packet takes to reach its destination. This hop-count information can be inferred from the time-to-live value in the IP header. ...

Geographic Information Systems (GIS) have gone a great way since it has started as a science. GIS is making headlines in a number of disciplines and, through its advancement, has improved our ability to model our real world. In the past years the need to support the storage and retrieval of dynamic changes, which occur to our data, has increased which consequently led to the interest in spatio-temporal behavior in GIS. These years have also seen the birth of several spatio-temporal data Models, whose aim is to support this spatio-temporal behavior. The main aim behind Spatio-Temporal support is ...

Abrupt work schedules, such as nightshifts, are prevalent nowadays and are known to cause circadian misalignment and sleep disruption which can have adverse health consequences. Among the well documented pathologies among night workers are cardiometabolic impairments, the effects of which appear to be more disruptive in older adults due to their poorer adaptation to night work schedules. The physiological mechanisms by which night shift work and sleep disruption contribute to increased cardiovascular disease (CVD) risk are poorly understood. Furthermore, the potential role of specific CVD ...

In this thesis, we investigate the use of neural networks for solving the Traveling Salesman Problem (TSP). First, we review the main elements of the theory of NP-completeness. Then, we explain what makes some problems computationally intractable. We review some heuristic approaches used to provide near-optimal solutions to NP-complete problems. Then, we introduce the topic of neural networks and describe some of the most popular neural network models. We pay a special attention to a recent model, named the Hybrid Neural Network model (HNN), used for solving optimization problems and the Hybrid ...

This thesis is an introduction to some of the classical theory and results of Differential Geometry: The geometry of curves and surfaces lying (mostly) in 3-dimensional space. One of the most important tools used to analyze a curve is the Frenet frame, a moving frame that provides a coordinate system at each point of the curve that is adapted to the curve near that point. Given a curve, one can define two quantities: its curvature and torsion. Both quantities are scalar fields and depend on some parameter which parametrizes the curve that is in general the arc length of the curve. The Fundamental ...

In this thesis, we present a new proof of the fundamental theorem of calculus of the Lebesgue Integral [1] and we explore the properties of a new and interesting Lebesgue integrable function [2]. In this thesis, we reveal the main connection between “absolute continuity” and “Lebesgue Integration” that is established from the fundamental theorem of calculus for the Lebesgue integral. And a function which is Lebesgue integrable but not Riemann integrable. In chapter 1, an elementary and simple proof of the fundamental theorem calculus for the Lebesgue integral is given. The proof is based on the ...

From ages to ages there had been expectation of individuals on a specific predictions and future occurrences. So also in a game, different participant that involves in those specified game have their various expectations of the results or the output of the game they are involved in. That is why we need a mathematical theory that helps in prediction of the future expectations in our day to day activities. Therefore the Martingale Theory is a very good theory that explains and dissects the expectation of a gamer in a given game of chance. So in this thesis, we shall talk about the Martin-gale ...

A well known problem with wormhole-routed packet networks is the potentially large amount of blocking that packets can experience due to link contention. Because of the very limited amount of buffering in such networks, blocked packets remain in the network and keep using network resources. Thus, blocked packets may in turn cause other packets to be blocked. This may affect a large number of packets over a large portion of the network. Proper connection management strategies and appropriate protocols must be devised to ensure that blocking of packets due to link contention is bounded. In [3], ...

Vaccination is a preventive measure to reduce death and morbidity against infectious diseases, and has been applied effectively against most of the viral and bacterial infections around the world. Targeted campaigns against children diseases have been very effective in drastically reducing such diseases thanks to national immunization programs in both developed and developing countries. However, many individuals including parents of various ages are still reluctant to commit to vaccination and some recent fears have been increasing when it comes to vaccination more recently, especially due to ...