Physical Sciences and Mathematics Commons^™

Size-Frequency Distribution Of Orbitolina Texana Foraminifera, Jeremy Foote

Undergraduate Review

This study examined size-frequency distributions for an extinct Cretaceous-age benthic foraminifera called Orbitolina Texana in order to determine the health of this foram community during the time of accumulation. Forams were collected from limestone outcrops of the Glen Rose Formation in central Texas. Based on paleontological and sedimentological evidence, Orbitolina Texana are interpreted to be a shallow water (<10 m) benthic organism that was most abundant in back-reef environments. Sizefrequency distributions were generated from the diameters of 4,245 Orbitolina Texana fossils. The results indicate that the Orbitolina Texana population is characterized by a Gaussian (normal) size distribution. Size-frequency distributions of fossilized foraminifera in the stratigraphic record are controlled by two principle variables; environmental controls that affect the biology of the organisms (e.g., environmental stressors, like food availability and ambient conditions) and sedimentological controls that affect how the organisms are distributed (e.g., hydrodynamic parameters, like waves and currents). Based on a sedimentological characterization of the host limestone including lack of high-energy sedimentary structures, high mud content and back-reef position on the depositional profile, hydrodynamic parameters are interpreted to not have exerted a significant effect on the distribution of the forams preserved in the rock record. As such, the biological controls are interpreted to be the dominate control on the foram sizefrequency distribution. Therefore, the Gaussian (normal) size distribution suggests that the mortality rate is independent of size/age, which is classified as Type II survivorship. As this result is consistent with similar taxon, the results indicate that this Orbitolina Texana population was a healthy biologic community, despite the low biologic diversity observed in the Glen Rose Formation.

A Mathematical Analysis Of A Game Of Craps, Yaqin Sun

Undergraduate Review

The game of craps is an extremely popular game offered by casino operators. There are some 40 different types of bets that one can place each time the game is played. One of the best bets from a player’s point of view is the Pass Line bet. The probability of winning a Pass Line bet is almost the same as the probability of losing (²⁴⁴⁄₄₉₅ versus ²⁵¹⁄₄₉₅) as we will derive rigorously in this article. Since the “house” has such a small advantage over the players, many players possess the illusion that they have …

The Archbishop's Odyssey, Leonard Sprague

Undergraduate Review

For centuries, scholars have analyzed a collection of problems that, nowadays, has been defined as NP-complete. Currently, NP-complete problems have no known efficient solutions. The Clay Mathematics Institute has offered a reward of one million dollars for a solution. The problem of finding Hamilton paths and cycles has been shown to be in this category. Knight’s tours, where the knight must visit every square of a chessboard exactly once, are examples of Hamilton paths and cycles.

This research revolves around the creation of a new branch of the tour problems, through a new piece: the Archbishop. Chess Grandmaster Jose Capablanca …

Applying Green Chemistry Principles In The Electrophilic Bromination Of Indole-3-Acetic Acid, Kyle Murphy

Undergraduate Review

The goals of green chemistry are to reduce or eliminate the use of hazardous reagents, prevent the synthesis of toxic products and byproducts, and improve the overall efficiency of chemical reactions. Green chemistry is incredibly important today as chemical products are produced and used around the world, resulting in the use and generation of hazardous chemicals, and unintended consequences to human health and the environment. Figure 1 shows the 12 Principles of Green Chemistry1, developed by Paul Anastas and John Warner, which provide the framework for a sustainable future in the design of more efficient technologies to produce consumer products …

A Strategic Analysis For Small Hydro Power (Shp) Development In Himachal Pradesh, India, Steven Spicer

Undergraduate Review

In addition to India currently being the second most populated country in the world, economists at Goldman Sachs have listed India as one of the five BRICS countries (Brazil, Russia, India, China, and South America) projected to be most dominant economies by 2050. In spite of the rapid growth in India’s economy, there are still many serious issues affecting the majority of its people. The US Energy Information Administration reports that roughly 25% of India’s 1.2 billion people are living without access to electricity; which translates to 300 million citizens without power (EIA, 2013). Various estimates put India’s energy supply …

Research Brief: Applying Green Chemistry Principles Towards The Sustainable Synthesis Of Biodiesel From Waste Vegetable Oil, Brandon Ackley

Undergraduate Review

In 2011, the U.S. consumed over 18 million barrels per day of refined petroleum products and biofuels; almost 22% of global petroleum consumption. This includes oil used for transportation, electricity, and production of consumer products. More than half of this oil was imported from foreign countries, and in his 2006 State of the Union Address President Bush warned that, “We have a serious problem, America is addicted to oil, which is often imported from unstable parts of the world”. With the need for new energy sources more apparent than ever, serious research is needed to further the advancement of alternative …

Who Wants To Play Sadisticube?, Danica Baker

Undergraduate Review

Logic puzzles and games are popular amongst many people for the purpose of entertainment. They also provide intriguing questions for mathematical research. One popular game that has inspired interesting research is Rubik’s Cube. Researchers at MIT have investigated the Rubik’s Cube to find the maximum number of moves, from any starting position, needed to win the game [6]. Another logic puzzle that has recently become very popular is Sudoku. Sudoku is a Japanese number game where a 9x9 grid is set up with a few numbers scattered on the grid. Mathematicians have been investigating Sudoku, exploring questions such as the …

Hydropower Development In Himachal Pradesh: A Stakeholder Equity Analysis, Eliott Rousseau

Undergraduate Review

Seen as the champion of green energy to some and environmentally disastrous to others, hydropower is a multifaceted issue. As it continues to be developed in India, some of the most remote locations and vulnerable people are being affected. This paper holistically examines the process of hydropower development in rural Himachal Pradesh. The locus of this study is tribal region of Bharmour Tehsil within Chamba District of Himachal Pradesh, India. Aspects pertaining to project commission, the consent process, and government sponsored rural development schemes are examined, with emphasis given to equity among rural stakeholders. The nature of this project was …

Environmental Considerations Of Small-Scale Hydroelectric Power Plants In Himachal Pradesh, India, Darwin Werthessen

Undergraduate Review

The need for increased energy production in India is high priority and hydroelectric power has been identified as having the greatest potential for achieving energy independence. The Indian government has continually created more streamlined methods for efficient implementation of hydroelectric facilities with an emphasis on small-scale (<25 MW) and micro (<5 MW) facilities in the more remote regions. Himachal Pradesh has effectively achieved one hundred percent electrification due to these initiatives and realized some of the most successful development in the nation with respect to rural electrification and improved infrastructure such as roads, schools, and hospitals. Hydroelectricity, and especially that produced through run of the river type systems, is generally embraced as a renewable source of energy by many established standards. Small scale run of the river facilities are also heralded for the minimal impact to the environment. However, with increased development and construction in continually industrializing areas, measurable human impacts have increased felt within the environment and ecosystems. Several studies and papers published by the Indian government, as well as the state government of Himachal Pradesh, identify these impacts as low to nonexistent. In contrast, a growing number of studies refute this claim and deserve consideration. There is a diversity of opinion on this subject. Some secondary sources indicate minimal to non-existent environmental impacts stemming from projects less than 25 MW, considered as Small Hydro Power (SHP); while other sources express significant concern. Interviews with government officials and researchers in the Indian states of Himachal Pradesh and Uttarakhand as well as in the capital city of Delhi revealed a wide range of views. This paper presents observations and argues for greater exploration of these issues through future research.