Estimation of static and dynamic petrophysical properties of multi-layer hydrocarbon reservoirs is crucial for the assessment of storage and flow capacities, compartmentalization, and for best primary or enhanced recovery practices. Interactive numerical simulation to reproduce field logs and core data is a reliable procedure to estimate static and dynamic petrophysical properties of complex rock formations. Previously, Voss et al. (2009) introduced the concept of Common Stratigraphic Framework (CSF) to construct and cross-validate multi-layer static/dynamic petrophysical models by invoking the interactive, numerical simulation of well logs both before and after invasion. This thesis documents the successful implementation of the CSF concept to examine and quantify the effects of mud-filtrate invasion on apparent resistivity, nuclear, and magnetic resonance logs acquired in San Martin, Cashiriari and Pagoreni gas fields in Camisea, Peru. Conventional petrophysical interpretation methods yield abnormally high estimates of water saturation in some of the reservoir units that produce gas with null water influx. This anomalous behavior is due to relatively low values of deep apparent electrical resistivity, and has otherwise been attributed to the presence of clay-coating grains and/or electrically conductive grain minerals. On the other hand, electrical resistivity logs exhibit substantial invasion effects as evidenced by the separation of apparent resistivity logs (both LWD and wireline) with multiple radial lengths of investigation. In extreme cases, apparent resistivity logs “stack” because of very deep invasion. We diagnose and quantify invasion effects on resistivity and nuclear logs with interactive numerical modeling before and after invasion. The assimilation of such effects in the interpretation consistently decreases previous estimates of water saturation to those of irreducible water saturation inferred from core data. It is shown that capillary pressure effects are responsible for the difference in separation of resistivity curves in some of the reservoir units. The final multi-layer CSF is in agreement with gas production measurements and permits reliable flow predictions to assist in reservoir engineering and production studies. / text

Introduction: Proton pump inhibitors (PPI) may impair the biotransformation of clopidogrel leading to increased major adverse cardiac events (MACE). Available studies have focused solely on patients receiving clopidogrel following a cardiac event. Given the widespread use of this combination, (about 64% in a recent study), this represents a major interaction that deserves further study. The objective of this thesis was to determine if the potential interaction between PPIs and clopidogrel leads to an increase in MACE in high-risk atherosclerotic patients receiving clopidogrel and PPIs as compared to clopidogrel alone. Methods: We conducted a retrospective chart review of patients in the University Hospital System who received clopidogrel between January 1, 2007 and April 30, 2009. Patients were included if they were hospitalized for acute coronary syndromes, stroke/TIA, revascularization (coronary, cerebral or peripheral arteries), or aspirin allergy. The primary outcome was the composite of myocardial infarction (MI), stroke/transient ischemic attack (TIA), coronary artery revascularization, or death (all cause) during the first year following discharge. Secondary outcomes included the composite of MI, stroke /TIA, revascularization (coronary, cerebral or peripheral arteries), or death. Bivariate analyses were conducted using Student’s t test, Mann Whitney U and Chi-square tests where appropriate. Multivariate analysis was conducted to adjust for baseline differences. Results: Overall, 1700 charts were reviewed and 572 patients met study criteria. The median follow-up was 332 days. The most common indication for clopidogrel use was coronary artery revascularization (66%). There were 201 patients in the clopidogrel with PPI group and 371 patients in the clopidogrel without PPI group. Baseline characteristics were evenly matched between both groups except for smoking, liver disease, and prior receipt of a PPI. The primary endpoint occurred in 21 patients in the clopidogrel with PPI group and 38 patients in the clopidogrel without PPI group (10% vs. 10%, p = 0.9, OR 1.02, 95% CI 0.58 – 1.80). The primary endpoint was unchanged after multivariate adjustments for baseline differences (adjusted OR 0.98, 95% CI 0.54 – 1.75). Likewise, there was no difference in the secondary endpoint (14% vs. 15%, p = 0.8, OR 1.02; 95% CI 0.58 – 1.80). The secondary endpoint was also unchanged after multivariate adjustments for baseline differences (adjusted OR 1.04, 95% CI (0.61 – 1.75) Conclusion: Patients receiving clopidogrel with a PPI demonstrated similar rates of MACE when compared to patients receiving clopidogrel without a PPI. / text

Conics and Geometry is a report that focuses on the development of new approaches in mathematics by breaking from the accepted norm of the time. The conics themselves have their beginning in this manner. The author uses three ancient problems in geometry to illustrate this trend. Doubling the cube, squaring the circle, and trisecting an angle have intrigued mathematicians for centuries. The author shows various approaches at solving these three problems: Hippias’ Quadratrix to trisect an angle and square the circle, Pappus’ hyperbola to trisect an angle, and Little and Harris’ simultaneous solution to all three problems. After presenting these approaches, the focus turns to the conic sections in the non-Euclidean geometry known as Taxicab geometry. / text

Currently, there exist several methods for finding roots of polynomial functions. From elementary processes such as the quadratic formula and the Rational Root Theorem to calculus-based ideas, choosing an appropriate means of solving often depends on the conditions of the given polynomial. This report will explore several solving methods and discuss their advantages as well as their limitations. / text

This report focuses on the discovery of Fermat numbers as well as the subsequent innovations in processes for finding factors of Fermat numbers. The property of the prime factors of Fermat numbers, as well as the connections between Fermat numbers and other areas of mathematics, is also discussed. / text

In 1990’s, the circumstances of being a contestant on a popular game show were published in a trendy question and answer column in Parade Magazine. If contestant switched from the initial choice to a second choice offer by the host, would the chances of winning the desired prize be increase? The columnist’s response to the reader sparked a good deal of controversy among mathematicians. Shortly after the publication of this answer, articles appeared in various mathematical publications some supporting and some refuting the columnist’s answer. This document reports the results of research into the controversy generated by some of the probability problems used on Let’s Make a Deal game show. Using a variety of approaches and assumption, the author attempts to formulate mathematical proof to explain the correct answer to the contestant’s question, “Should I switch?” / text

The aim of this paper is to summarize Professor McAdam’s course on the applications of calculus by showing how calculus can be applied within mathematical situations by understanding concepts in physics. Aside from using calculus to assist in maximizing or minimizing situational problems, it is important to understand how the rules of calculus came to be. This paper shows origins of a few of the many rules used in calculus, applications in economics, plane flight, dogs fetching sticks, and relativity in space. / text

Daily advancements in technology influence many aspects of society. In today’s political and economic era, the need for secure, computerized convenience is apparent. Cryptosystems play a major role for everyone, from an individual making an online purchase to the government communicating with an ally during wartime. As technology advances, so do cryptosystems. The author of this paper discusses different types of cryptosystems, from substitution ciphers to public key cryptography, and introduces the mathematical foundations of such systems. / text

This paper will outline some of the key parts of the Statistics course offered through the UTeach Summer Master’s Program as taught by Dr. Martha K. Smith. The paper begins with the introduction of the normal probability density function and is proven with calculus techniques and Euclidean geometry. Probability is discussed at great length in Smith’s course and the importance of understanding probability in statistical analysis is demonstrated through a reference to a study on how medical doctors confuse false positives in breast cancer testing. The frequentist perspective is concluded with a proof that the normal probability density function is zero. The shift from traditional to Bayesian inference begins with a brief introduction to the terminology involved, as well as an example with patient testing. The pros and cons of Bayesian inference are discussed and a proof is shown using the normal probability density function in finding a Bayes estimate for µ. It will be argued that a Statistics course moving from traditional to Bayesian analysis, such as that offered by the UTeach Summer Master’s Program and Smith, would supplement the traditional Statistics course offered at most universities. Such a course would be relevant for the mathematics major, mathematics educator, professionals in the medical industry, and individuals seeking to gain insights into how to understand data sets in new ways. / text

Machine learning methods have been employed in data mining to discover useful, valid, and beneficial patterns for various applications of which, the domain encompasses areas in business, medicine, agriculture, census, and software engineering. Focusing on software engineering, this report presents an investigation of machine learning techniques that have been utilized to predict programming faults during the verification and validation of software. Artifacts such as traces in program executions, information about test case coverage and data pertaining to execution failures are of special interest to address the following concerns: Completeness for test suite coverage; Automation of test oracles to reduce human intervention in Software testing; Detection of faults causing program failures; Defect prediction in software. A survey of literature pertaining to the verification and validation of software also revealed a novel concept designed to improve black-box testing using Category-Partition for test specifications and test suites. The report includes two experiments using data extracted from source code available from the website (15) to demonstrate the application of a decision tree (C4.5) and the multilayer perceptron for fault prediction, and an example that shows a potential candidate for the Category-Partition scheme. The results from several research projects shows that the application of machine learning in software testing has achieved various degrees of success in effectively assisting software developers to improve their test strategy in verification and validation of software systems. / text