2015 Abstracts

According to the 2010 US Census, the Hispanic population in Ogden City, Utah has grown by over 36%. This influx of population of Hispanic descent has influenced local businesses to begin advertising in Spanish through multiple mediums. To determine what factors influence a business’s decision to advertise in Spanish, locations of all print advertising in Ogden were determined through personal investigation. Second, neighborhoods and areas were divided according to census divisions that appear on the official website and median household income as well as the population of Hispanic people was recorded to determine if socioeconomic bias was present in the selection of where to advertise in Spanish. A linear regression comparing the total number of Spanish advertisements found in each geographical area was compared first to income, and then to total Hispanic population. The results of the regression illustrate a potential bias based on financial circumstances rather than ethnicity. Further study is needed to determine if this use of Spanish-advertising in the low-income areas affects Spanish-speakers’ access to healthy foods, housing, or other critical aspects of quotidian life.

Jeremiah Rundall, Utah Valley University Physical Sciences The practice in hydrology is to deduce stream discharge from stream stage by creating a rating curve for each stream site from simultaneous measurements of stage and discharge. If a river could be assigned a generic rating curve with a small number of parameters, the cost of developing rating curves could be reduced. The first step has been to classify rivers according to whether there is a unique relationship between stage and discharge. The USGS National Water Information System database of about 3.8 million simultaneous measurements of stage and discharge at15,345 active and historic stream gaging sites was imported into a Python-driven data manipulation script. Linear relationships between z-scores of the logarithms of stage and discharge were developed for each site. A frequency spectrum of the slopes of the linear relationships was created by summing the normal distributions for each site with mean equal to slope and standard deviation equal to uncertainty in slope. There were no stream gaging sites at which discharge changed without a change in stage. At about 70% of stream gaging sites, over 90% of the variation in stage corresponded to a variation in discharge. At the remaining sites, significant variation in stage occurred without a variation in discharge. Current research involves identifying the characteristics of stream sites that lack a unique stage-discharge relationship and creating classes of generic rating curves by considering more complex functional fits.

Amy Fair Brother, Utah Valley University Physical Sciences Results from a 2010 pilot study indicated that multiple parameters in high-frequency (HF) ultrasound spectra (20-80 MHz) correlate to a range of tissue pathologies in surgical margins from breast conservation surgery (BCS). One of these parameters, peak density, was particularly effective at discriminating between normal, atypical, and malignant patholUtah Conference on Undergraduate Research 2015 100 ogies. Subsequently, Utah Valley University and the Huntsman Cancer Institute initiated a follow-up study to further investigate this approach. Objectives: The purpose of this study was to determine the sensitivity and specificity of HF ultrasound for differentiating malignant tissue from normal tissue in BCS surgical margins. Methods: A 73-patient blind study was conducted with conventional pathology used as the gold standard for assessing the HF ultrasound method. Specimens were delivered by the surgeon’s team immediately following resection and ultrasonically tested outside the surgical suite. The margins were approximately 3x20x20 mm, and were oriented using a small staple inserted by the surgeon in one corner and a stitch on one side. The margin was tested at 2-5 locations on the specimens using our methodology and then sent to pathology for their analysis. 498 specimens were tested from 73 patients. That corresponded to 1112 positions collected from the margins. The data was then analyzed for malignancy using peak density, and then correlated with the traditional pathology. Results: Results from the current study indicate that peak density can differentiate between malignant and nonmalignant pathologies with an accuracy of 73.8%. The correlation between pathology and peak density has a high level of statistical significance compared to random chance, with p = 0.000078 (Fisher’s Exact test). The results also provide data for improving the technique. For example, approximately 3 times more false positives were observed than false negatives, indicating the peak density threshold used for identifying malignant pathology is most likely too low and should be adjusted to a higher value. Conclusions: Results from this study showed that HF ultrasound has the potential to provide rapid, intraoperative evaluation of surgical margins, thereby decreasing the number of additional surgeries for patients and thus increasing the quality and efficacy of surgical treatment for breast cancer.

Valerie Jacobson, Weber State University Physical Sciences This study will compare and contrast the differences between nuclear accidents in Chernobyl and Fukushima. The environmental impacts of the “fall-out” across the two differing landscapes and the displacement of the populations due to radiation contamination, e.g., soil contamination, will be analyzed. Research on health issues, such as the increased numbers of thyroid cancer cases in Ukraine and Belarus in those who were children at the time of the disaster in 1986, will also be reviewed and compared to current health issues in Fukushima. Certain weather patterns distributed the radioactive materials over specific geographic areas that later came to be known as “hot-spots.” The study will evaluate the evacuations handled by the respective governments and the “exclusion zone” measures put in place by each. While the nuclear disasters at Chernobyl and Fukushima have been compared as similar in disaster level, research and data collection of the fallout zones, or hot spots, reveal that the two disasters are not of an equal level. Factors such as air temperature, political and social responses all contributed to the disparity in levels of the two disasters.

Paul Robertson, Utah Valley University Physical Sciences Evaluation of Utah Valley University’s stormwater plan reveals a simple system meant to collect stormwater into the city storm drains as quickly as possible. It is, however, vastly underdeveloped and many unspectacular summer and springtime storms have resulted in property damage, including those of nearby residents. The stormwater runoff has also collected concentrated amounts of hydrocarbons, nitrogen and heavy metals which are being fed directly into Utah Lake, acting as a significant source of pollution for the lake environment. The intentions of this project are to design a stormwater management plan that can withstand a 100 year, 24 hour event and prevent pollutants from entering the Utah Lake system. Mapping and modeling of the University’s storm drains will be accomplished using GIS as well as modeling for efficient retention sites on campus. Captured stormwater will then be used for a variety of functions here on campus and runoff into the adjacent lake will be reduced to insignificant values. Decisions regarding the ultimate implementation of this project will work in concordance with the University’s master plan of future development in order to realistically secure a reliable, low-maintenance system.

Henintsoa Rakotoarisaona, Utah Valley University Physical Sciences The Jordan River is the only outlet of Utah Lake. Historically, this area has been impacted by urbanization, long term mining operations, industrial and agricultural activities resulting in potentially high levels of trace metal pollutants at the headwaters of the Jordan River. Since trace metals are known to be toxic at elevated levels, it is important to evaluate their concentration, distribution and mobility in this sensitive area in order to determine risk to wildlife, humans and downstream users of the Jordan River. Three core samples from 0 cm to 95 cm in depth were collected at the east (industrialized area), west (newly developed area) and north (an island barrier) sides of the outlet of Utah Lake. Each sample was digested in triplicates in the Microwave Accelerated Reaction System (MARS) using US Environmental Protection Agency Method 3052 and analyzed in the Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES) for As, Cd, Cr, Mn, Pb, Cu, Zn, Co, and Ni. A multivariate analysis of variance (MANOVA) was used to analyze the data, with a boneferroni adjustment made for multiple comparisons. The results indicated that the East and North sediments of the Jordan River were significantly (P < 0.5) more heavily impacted by trace metal pollutants than the West side, with the North area accumulating higher levels of the majority of the trace metals or metalloid evaluated. Enrichment of Co, Cr, Pb and Zn was observed on the East sediment at concentrations reaching 10,821, 4.07, 13.7, 12.7, 119.4 mg kg-1, respectively. The most substantial elevation in the concentration of trace metals occurred with Cu in the North section of the lake, increasing from 349 mg kg-1 at 0-15 cm to 1383 mg kg-1 cm depth, showing high mobility, followed by Zn which increased from 46.7 mg kg-1 at 0-15 cm to 592 mg kg-1 30-45 cm depths. The enrichment of these trace metals in the East and North sediments at the outlet of Utah Lake pose a health risk to animals and humans who use these areas for recreational or agricultural purposes.

Melissa Warren, Weber State University Physical Sciences Spot tests are commonly utilized as presumptive qualitative tests for detecting chemical substances. Such tests are the basis for detection of illegal drugs or for cleaning validations in manufacturing systems. In this study we evaluate the use of Scott’s reagent and Mandelin reagent for the detection of trace quantities of diphenhydramine (Benadryl). These reagents have been reported to give false positive tests for illegal drugs such as ketamine (cocaine) when diphenhydramine is present. Our studies were focused on enhancing the detection limits of these reagents and their application of swab tests for diphenhydramine. We report the limits of detection and swab techniques that enhance selectivity and sensitivity for this analyte.

Benjamin Finch, Utah Valley University Physical Sciences The Breast Cancer Research Laboratory at Utah Valley University has been using high-frequency ultrasound to test the pathology of surgical margins from breast cancer conservation surgery. Their studies have shown that high-frequency ultrasound may be sensitive to a range of breast pathologies. The ultrasonic parameter that has been shown to be the most sensitive to pathology is the number of peaks (peak density) in the frequency spectra from the captured waveforms. During testing, the ultrasonic transducers apply an amount of force to the tissues that can vary depending on the researcher. The central question of this study was to determine the effect that the applied force has on the final peak density reading, and therefore the reliability of the results. In order to determine the correlation of force and peak density, an experiment was designed to measure the force applied to tissue by the ultrasonic transducer during testing and to simultaneously measure the applied force while collecting ultrasonic waveforms. An Arduino Uno R3 instrument was obtained as well as an Interlink Electronics FSR 406 force sensor pad. The Arduino was programmed to read the voltage from the FSR sensor and use that information to provide force (N) and pressure (N/cm2) data from the stage. Peak density readings from bovine mammary tissue (very similar to human breast tissue) were acquired using varying amounts of force. The results obtained exhibited significant changes in peak density with applied force. The results showed that if the applied force is under 1.18N, the peak density will fluctuate significantly and will therefore give inconsistent results. However, if the force applied is greater than 1.18N, the peak densities will maintain a relatively consistent form. In conclusion, if the force applied during testing is above 1.18N, the waveforms captured from high-frequency ultrasound testing on breast cancer tissues will provide consistent and reliable results, thus improving the quality of the data and accuracy of diagnosis.

Cameran Mecham, Utah Valley University Physical Sciences Introduction:

Monika Miller, Weber State University Physical Sciences Nutritionally important minerals are more readily absorbed by living systems when they are combined with organic acids. These combined metal-organic acid complexes are called chelate metals or chelates. The synthetic processes utilized to prepare these mineral chelates adds significant cost to the final product. Occasionally, manufactures sell cheaper dry blends of unreacted minerals and organic acids to gain an unfair competitive advantage in the market place. There are few if any reliable methods for reliable measurement of the extent of chelation between metals and organic acids. We report our successful application of Fourier-transform Infrared Spectroscopy (FTIR) for the quantitative determination of chelation in solid samples of mineral chelates.

Jennifer Melvin and Wendy Schatzberg, Dixie State University Physical Sciences The general chemistry laboratory can be a dangerous place, and the possible danger is amplified by the fact that general chemistry is frequently a student’s first chemistry laboratory experience. College students come from a variety of backgrounds with only some having had chemistry in high school, and therefore many students will not know beforehand what kind of precautions to take or what kind of action to take in case of an accident in the lab. Safety information is given briefly at the beginning of the semester, but the efficacy of this is uncertain. An online survey was conducted to gauge first- and second-semester general chemistry students’ knowledge about chemistry laboratory safety and the data gathered was analyzed. This survey was conducted at two secondary schools in two different countries. Statistical analysis will be presented. Results will allow discernment of misconceptions held by students over two semesters and between countries, and conclusions can be made about the effectiveness of current laboratory safety instruction methods.

Brett Barton, Dixie State University Physical Sciences Dissolution using ionic liquids has been shown to be an efficient analytical method of dissolving keratin fibers. Using wool and hoof material from livestock, chloride-based ionic liquids were used to break down the hydrogen bonds important for keratin structure, making the extraction of constituent material much easier. Efficient methods of extraction allow for small samples to be analyzed while still providing high yields; efficient dissolution of keratin in a small sample size will be utilized to prevent any harmful effects on the animals. Ionic liquids are nondestructive solvents which allow for the safe extraction of organic substances. Denaturing keratin would help in the process of identifying any constituent radioactive materials. Efficient identification of radioactive material in livestock is crucial for maintaining health and quality of life.

Tim Beach, Utah State University Physical Sciences Successful management of the arid West requires a basic knowledge of available water resources, withdrawals, and existing management efforts. Utah, the second driest state in the country, is continuing its efforts to restore impaired water systems and teach the next generation to conserve water. Because of a fast-growing population, the diversity of Utah’s landscape, and strict regulations that govern water throughout the state, understanding the region’s current water condition can be difficult. Historically, the majority of this information has been stored in databases, represented by only numbers and statistics. In an effort to better conceptualize this data and increase the spatial understanding of Utah’s water, a set of maps have been produced. These maps were created using ESRI’s ArcMap software and Adobe Illustrator. Included are major lakes and rivers, average annual precipitation, average annual streamflow, total urban withdrawals per county, total agricultural withdrawals per county, and water management. Viewing visual representations of this information in multiple maps can aid in creating spatial inferences, and raise additional questions regarding aquatic restoration and management throughout the state. This set of maps can also be used to supplement physical science education at all school levels. Future work includes distributing these maps as posters to schools and water managers, as well making it a resource for teachers via websites and fact sheets.

Melinda Hurlbut, Dixie State University Physical Sciences A newly discovered plant fossil locality in the Chinle Formation (Upper Triassic) in Washington County broadens the distribution of known Late Triassic plant fossil localities to include southwestern Utah. Previously reported plant localities in the Chinle Formation are known from southeastern Utah, Arizona, New Mexico, and equivalent strata from the Dockum Group in Texas. The majority of the known plant fossil localities are from higher stratigraphic units of the Chinle Formation. However, the new Washington County locality is from the older, basal unit, the Shinarump Member. The plant fossils identified from the new locality include fronds of the fern Phlebopteris sp., fertile leaves of the fern Cynepteris sp., and leaves of the bennettitalean Zamites sp. Undetermined species of conifers are represented by a partial branch and a three- dimensionally preserved cone containing well preserved seeds. The diversity of species found at the Washington County plant fossil locality correlates with other known floral assemblages from the Chinle Formation, suggesting general homogeneity of Chinle Formation floras. These plant fossil assemblages support interpretations of basal Chinle Formation paleoclimates as humid and warm.

Eric Johnson, University of Utah Physical Sciences The ability to reduce O2 in mild conditions holds many important implications such as: use as an economical fuel cell, pharmaceutical synthesis, biomass degradation and conversion of small molecules to fuels. We are building the [M(μ-OH) (oxapyme)M(H2O)]+ molecules and symmetrical counterparts for use in O2 reduction reactions (M = Cobalt, Nickel, Iron). The precursors to the [M(μ-OH)(oxapyme)M(H2O)]+ have been synthesized as follows. 2-[5-(2-Nitro-phnyl)-[1,3,4]oxadiazol- 2-yl]-phenylamine serves as the backbone of the complex, allowing for two distinct ligands to be attached to each side. Initial yields for this synthesis averaged at 6%. To be able to complete the synthesis this needed to be significantly raised. The literature procedure was modified in various ways until new reaction conditions were found that allowed for 40% yield. Other precursors include 2,2’-(1,3,4)Oxadiazole-2,5-diyl-bis-aniline which also serves as a ligand backbone but differs in that it allows for preparation of a symmetrical ligand have been synthesized with a 51% yield. The first ligand Bis-pyridine-2-ylmethyl-amino has been produced with a 60% yield. The second ligand Methyl-pyridine-2-ylmethyl-amino has been synthesized with an approximate yield of 75%. These yields are high enough to finish the synthesis of the ligand and subsequently coordinate the metals. Upon completion, the electrochemical properties of the compounds that differ in the metal composition and the ligand (symmetrical versus asymmetrical) will be determined using studies such as cyclic voltammetry. Once the metal and ligand that are most apt at oxygen reduction is determined, more advanced studies will be undertaken to identify the reaction mechanism and intermediates.

Kyle Marcus, Cami McKellar, Riley Pearce, Shay Beck, and Zenja Draca, Dixie State University Physical Sciences Invasive marine and freshwater species have a detrimental impact on aquatic ecosystems and are easily transferred between bodies of water as a result of unregulated settlement and attachment to commercial and recreational watercraft. This results in infestation of waterways and disruption of native organisms throughout an ecosystem. The quagga mussel (Dreissena rostriformis bugensis) is one example of such invasive species that has called for a focus on cross-contamination prevention. The goal is to use aquatic paint suitable for watercraft that prevents the settlement and/or attachment of various aquatic species such as algae, snails (Physa sp.), anemones (Aiptasia sp.), and quagga mussels. The paint is integrated with newly developed surfactants that act as an inhibitor to the adherence ability of invasive aquatic species. The surfactants are added to provide a barrier between the paint surface and the organisms creating an undesirable surface area for the organisms to attach. This barrier disrupts the specific naturally occurring chemical and physical processes that allow organisms to adhere to surfaces. The most innovative characteristic of the surfactant-based paint is its effectiveness on adherence inhibition without degradation, dissociation, or toxicity to the environment. Preventing adherence of invasive organisms to surfaces could have significant positive effects on the efficiency and cost of operations in marine environments and waterways.

Mattie Jones, Dixie State University Physical Sciences Current techniques for isolating components of samples found at crime scenes by their unique chemical properties are lengthy and often destroy important forensic evidence. New methods aimed at forensic analysis of sensitive, minute samples are critical to the intelligence community. In particular, successful extraction of dyes from materials found at crime scenes will provide innumerable benefits for matching, identifying, and finding origins of these materials and dyes. Ionic liquids possess the necessary chemical properties to ensure efficient extractions while maintaining the forensic signatures of the original materials. Ionic liquids, which are organic salts that are room temperature, provide a versatile solvent to achieve single-component extraction-separation-identification of forensic analytes. Following extraction, successful identification by infrared, absorption, and fluorescence spectroscopy has provided evidence of preserved quality and complete separation of material and dye. This novel approach to forensic analysis is advantageous particularly when sample sizes are extremely limited, but it can be readily scaled to larger applications. Developing a simple and affordable method of achieving specific molecular interactions provides a solution for often unidentifiable evidence in crimes. Harnessing the versatility of ionic liquids in a high-yielding recovery and efficient single-pot methods will enhance forensic abilities for the intelligence community and forensic investigators.

Madeline Parson, Travis Bulloch, and Tyler Argyle, Southern Utah University Physical Sciences Lipid bilayers have many important purposes in living cells. A lipid bilayer forms a barrier which separates the fluid inside the cell from the fluid surrounding the cell. The arrangement of components within cell membranes can be extremely important, particularly in cell communications. For example, when our immune system attacks certain pathogens, it recognizes them by specific proteins in the inner and outer regions. This can be thought of as forming a “bull’s-eye” shape. The ability to generate such patterns in bilayers might see applications in many areas of biology. Our goal is to take an initially un-patterned supported lipid bilayer (model cell membrane) and use magnetic tweezers as a delivery system to generate patterns. We hope to show pattern formation using fluorescent-labeled lipids within our bilayer. In the past, we have used streptavidin and biotinylated lipids with Oregon Green. Currently, we are pursuing a fluorescein/anti-fluorescein system that has been yielding much more promising results. We are currently using a fluorescent microscope to confirm that patterns are forming within the bilayer.

Michael Kutschke and Niccolo Fiorentino University of Utah Measurements of joint angles, moments, and forces can be sensitive to positional changes in the center of a joint. Due to its deep location, the hip joint center (HJC) can be difficult to determine. Regression equations and functional methods use skin markers and are commonly used to measure the HJC, yet introduce sources of error such as bony landmark identification, soft tissue artifact, and system resolution. Additionally, the accuracy of said methods cannot be established in-vivo without a reference standard. The purpose of this study was to implement a dual fluoroscopy (DF) and model-based tracking technique to quantify the subject-specific HJC position in-vivo. This reference standard (DF-HJC) was then compared to the HJC defined by regression equations (CODA) and a functional method (FHJC) using skin markers. Five subjects with normal hip anatomy provided informed consent to participate in this IRB approved study. A gait marker set was applied to the subject’s skin. The subject performed various activities involving the inferior limb while a 10-camera Vicon system measured the position of the skin markers. From these data, the CODA and FHJCs were identified. Simultaneously, the hip was visualized using a DF system, and the DF-HJC was identified using model-based tracking. The DF-HJC was then transformed to the Vicon coordinate system for comparison with the CODA and FHJCs. The average Euclidean distance (and standard deviation) for the five subjects from the DF-HJC was 2.0 (0.6) cm for CODA and 1.3 (0.4) cm for the FHJC. To our knowledge this is the first study to use DF and model-based tracking to measure the in-vivo position of the HJC. This technique affords greater accuracy in determining subject-specific bone geometry and visualization of deep hip anatomy, thus may be considered a reference standard for identifying the HJC.

Michaelle Cadet, Utah Valley University Physical Sciences Breast cancer is the most common cancer among women in the United States. Tumor angiogenesis and its inhibition is an important aspect of oncology and the treatment of cancer. High-frequency ultrasound (10-100 MHz) is particularly sensitive to small vascular structures that are close in size to the ultrasound wavelength (15-150 _m). The ability to rapidly determine the degree of vascularization in small animals in vivo would provide a useful characterization tool for breast cancer studies. The objective of this study was to determine if direct ultrasonic measurements in the 10-100 MHz range could be used as a vascularization assay for breast tumors and other tissues. To accomplish this, six mice from the Huntsman Cancer Institute (Salt Lake City, Utah) with grafted breast cancer tumors (three control and three treated with an angiogenesis inhibitor called Avastin) were tested in vivo using through-transmission ultrasonic measurements. A second study was also performed at the Ludwig Boltzmann Institute for Experimental and Clinical Traumatology (Vienna, Austria), where the femoral artery in one hind leg of each of sixteen mice was ligated and tested over the time period of eight days. Eight of the ligated limbs were treated with vascular endothelial growth factor (VEGF) while the remaining eight ligated limbs were allowed to grow ischemic. The unligated limbs were controls. Results from the Huntsman Cancer Institute study indicated that breast tumors in Avastin-treated mice showed higher ultrasound velocities than control tumors. This can be ascribed to the vasculature in the nontreated tumors creating greater wave scattering in the tissue, thus decreasing the velocity. Results from the Boltzmann Institute study indicated that in mice with ligated femoral arteries, ultrasonic signals from ischemic limbs displayed a decrease in wave velocity over the test period as compared to the VEGF-treated limbs. However, both the ischemic and VEGF-treated limbs showed decreases in ultrasonic attenuation during the entire test period. Results from Avastin-treated mouse tumors and mouse limbs with ligated femoral arteries revealed that high-frequency ultrasound holds potential for measuring angiogenesis in vivo.

Nicole Cowan, Utah Valley University Physical Sciences Breast cancer is the second most prevalent cancer among women, affecting one out of eight women in their lifetime. The ability to differentiate between malignant and normal tissues during breast cancer surgery would enable the surgeon to remove all of the cancer from the affected region in the breast, thereby reducing the risk of recurrence and the need for subsequent surgeries. A pilot study conducted at the Huntsman Cancer Institute showed that high-frequency ultrasound (20-80 MHz), and in particular the ultrasonic parameter peak density, was sensitive to breast tissue pathology. The objective of this study was to determine the effect of tissue microstructure on peak density using phantoms that mimic the histology of breast tissue. Phantoms were created from a mixture of distilled water, Knox gelatin, and Metamucil fiber. In order to simulate breast tissue histology and terminal ductal lobular units, polyethylene microspheres were embedded into the phantoms in layers, totaling 4 layers per phantom. The volume percent of polyethylene microspheres was kept constant in each phantom while varying microsphere sizes (58-925 μm diameter). Pitch-catch and pulse-echo measurements were acquired using 50-MHz transducers (Olympus NDT, V358-SU, 50 MHz, 0.635-cm diameter active element), a HF pulsar-receiver (UTEX, UT340), and a 1-GHz digital oscilloscope (Agilent DSOX3104A). Glycerol (Genesis Scientific) was used as a coupling agent between the transducers and the phantoms. Spectra were derived from the data, giving peak density (the number of peaks and valleys in a specified spectral range) and attenuation values. In a previous study, histology- mimicking phantoms were fabricated where the weight percent of polyethylene microspheres was kept constant, but the microsphere diameter was varied. The former study showed a clear trend of higher peak density values for smaller diameters, but no trend for attenuation. In contrast, the phantoms from this study showed no trend in peak density, but a clear trend of higher attenuation values for larger microspheres. The results show that specific changes in tissue microstructure affect the parameters of peak density and attenuation differently. Changes in the number of scatterers and in their size, as in the previous study, affected peak density most significantly. In contrast, changes solely in the size of the scatterers, but not in their number, affected attenuation most significantly. These results are consistent with attenuation results for lobular carcinoma in the pilot study. These results show that peak density and attenuation are complementary parameters, and could be used together to characterize a variety of tissue pathologies

Sergio Arellano, Snow College Mathematical Sciences Why is music so pleasant to? In Western music, we have used what is called the “tempered scale” for centuries, and even though it has gone through changes, it is still largely based around the mathematical principles that Pythagoras created two thousand years ago. Is it possible that the explanation to this phenomenon has to do with the mathematical basis of music, which is unconsciously perceived by the brain? The human brain is known for detecting the underlying mathematical patterns present in many non-music related disciplines, such as visual arts. Independent of the music world, there is a proportion called the Golden Ratio or Phi. It is found in art and geometry, because human eyes tend to find that this proportion produces beauty. This is not a coincidence; this proportion is found everywhere around us, especially in nature. With this in mind, it makes sense to search for the Golden Ratio in the tempered scale to explain the mind’s intuitive appreciation of music. This research discovered the surprising fact that there is a Phi relationship between the first and third degree of the major scale, in terms of the frequency of sounds. The relationship is this: the sum of the frequencies of the notes of the minor III chord divided by the sum of the frequencies of the major I chord in any given major key, tends to be Phi. Another very surprising result was the importance of the number 24 in the frequencies of the major scale. These two particularities help to shed light on why human ears have an untaught comprehension of music; the underlying perception of mathematical relationships by the mind are related to the natural appreciation of it.

Amy Gifford and Brennon Bauer, Southern Utah University Mathematical Sciences Mutualism is the way two organisms of different species exist in a relationship in which each individual benefits from the activity of the other. We study a mathematical model of mutualism. The stability of the steady state solutions of this system will be analyzed. Also, we give some numerical experiments that verify the theoretical results for those steady solutions.

Jason Adams, Nathan Jewkes and Tyrell Vance, Southern Utah University Mathematical Sciences We will study the divisibility of p^(n)-1 where p is a prime number larger than 5 and n is a positive integer. We will generalize the result by considering the case where n is odd and two cases where n is even. We show that when n=2^(k), k an integer greater than 1, 2^(k+2)∙3∙5 is a factor of p^(n)-1. We also show that when n=2^(m)∙l for m a positive integer greater than 1 and l an odd positive integer greater than 1, 2^(m+2)∙3∙5 is a factor of p^(n)-1.

Christopher Vander Wilt and Daniel Gulbrandsen Utah Valley University Let nP denote the polytope obtained by expanding the convex integral polytope P⊂R^d by a factor of n in each dimension. Ehrhart [1] proved that the number of lattice (integer) points contained in nP is a rational polynomial of degree d in n. What happens if the polytope is expanded by not necessarily the same factor in each dimension? In this talk a partial answer to this question will be provided, using powers of n as different factors to expand the polytope. It will be shown that the number of lattice points contained in the polytope formed by expanding P by multiplying each vertex coordinate by such a factor is a quasi-polynomial in n. Quasi-polynomials are a generalization of polynomials, where the coefficients of the quasi-polynomials are periodic functions with integral period. Furthermore, particular cases where the number of such lattice points is a polynomial will be presented. In addition, the period of these quasi-polynomials as well as the Law of Reciprocity will be addressed. At the end, future work will be discussed. [1] E. Ehrhart, “Sur les Poly`edres Rationnels Homoth ´etiques `a n Dimensions,” C. R. Acad. Sci. Paris 254 (1962)