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- Creator:
- LaGrange, Thomas L.
- Description:
- Markov Chains are a category of stochastic processes with an associated dependence structure. Their inception resulted from A. A. Markov’s desire to disprove a rival’s assertion concerning the application of the Law of Large Numbers (LLN) to dependent variables. Markov’s use of a classic Russian novel to illustrate a dependent relationship between vowels and consonants serves as motivation for investigating the extent to which the properties of these processes can be applied to other means of communication. This work summarizes a history of the Law of Large Numbers and the Markovian properties associated with three different aspects of communication.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands
- Creator:
- Costa, Matthew
- Description:
- Derivations of wave equations, various presentations of their solutions and MATLAB models are presented. Thereafter, basic ocean wave forecasting will be discussed along with it’s applications.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands
- Creator:
- Zechlin, Mollie J.
- Description:
- Public key cryptography, is the basis of m odem cryptography, allows us to send and receive messages over public channels secretly, without requiring a meeting beforehand. Most public key cryptosystems, such as the Diffie- Hellman Key Exchange, rely on the difficulty of solving the Discrete Logarithm Problem (DLP). We can translate public key cryptosystems that rely on the DLP to Elliptic Curve cryptosystems as the Elliptic Curve Discrete Logarithm Problem (ECDLP) is believed to be more difficult and therefore harder
to break. There are certain precautions we need to take when using Elliptic Curve Cryptography to safeguard against particular attacks on the cryptosystem.
Therefore, picking a curve that is secure enough is crucial to a good cryptosystem.
Unfortunately, there are only a handful of secure elliptic curves that are publicly known and used. The goal of this thesis is to generate more elliptic curves that are useful for our security systems.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands
- Creator:
- Lee, Seungju
- Description:
- Packaging/repackaging is essential to ensure pharmaceutical product’s stability (i.e. efficacy and safety). Before processing to package/repackage products into container/closures, there must be evidence to verify its stability. The most common verification methods are real-time study and statistical analysis. Real-time study can be very accurate, but it is also timeconsuming, which is inadequate for industry use. On the other hand, statistical analysis is appropriate for industry use since it can take short-term data and obtain the results quickly. In particular, we apply regression analysis on pharmaceutical product container/closure data along its decision-making framework to determine a container height 95% confidence interval and estimate the shelf life. Using a freeware program R, we are able to conduct the analysis more quickly and efficiently.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands
- Creator:
- Chen, Vickie V.
- Description:
- Recent progress has been made toward understanding the density that k integers are G-wise relatively prime as a limiting form of a uniform distribution motivate this work. Fix a positive integer k and let G be a simple graph with k vertices that are arbitrary integers. We say that these integers are G-wise relatively prime if for any pair of vertices joined by an edge, the corresponding integers are relatively prime. Observe that if G is a complete graph, then this reduces to the notion of integers being pairwise relatively prime. From this
foundation, we can compute the density that k integers are G-wise relatively prime. The main objective of this thesis is to extend the notion of G-wise relative primality to rings of algebraic integers and to rings of polynomials over a finite field.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands
- Creator:
- Ferguson, Vincent
- Description:
- Exploring the Effects of Wolbachia-infected Mosquitoes on the Spread of the Zika Virus
by Vincent Ferguson
Recent efforts to stop the spread of Zika, a vector-borne disease, through pesticides and insecticides have not been successful. Research has shown that Zika can be spread via the Aedes aegypti mosquito and human sexual contact. We examine how the use of Wolbachia as a form of control can reduce the transmission rate between infectious mosquitoes and susceptible humans. Through analysis of our mathematical model, we find the reproductive number of Zika before and after including Wolbachia into our calculations. With this model, we are able to run simulations to show how fast Zika can spread in a population. Using local sensitivity analysis, we study how changes in different parameter values affect the reproductive number.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands
- Creator:
- Lieberman, David A.
- Description:
- This paper aims to generalize results on single variable polynomial rings over commutative rings with zerodivisors to the case of polynomial rings in arbitrarily many variables. Given a commutative ring R, we give necessary and sufficient conditions for the ring of polynomials with coefficients in R in arbitrarily many variables to be a PVMR and Krull ring. In answering these questions, we make use of the t and v operations on ideals as a means of characterizing these rings. We also give conjectures on necessary and
sufficient conditions for an arbitrary polynomial ring to be a Dedekind ring, a UFR, and integrally closed.
- Resource Type:
- Thesis
- Campus Tesim:
- Channel Islands