Mathematics
The field of Diophantine approximation is a branch of number theory which concerns itself with certain properties of real numbers in relation to the rational numbers. In specific, one may de…
Mathematics
The purpose of this project was to determine if an algorithm could be used to quantitatively analyze paintings. It was hypothesized that there would be a significant difference between the p…
Mathematics
Fourth Award
In an era of rapid growth in information technology, a significant danger threatens digital security: cyber-attacks. Public-key cryptosystems are used to overcome virtual vulnerabilities. Th…
Mathematics
Given a triangle and a set of three angles, celebrated geometrical theorem of Jacobi (1825) produces a new triangle and a point (Jacobi point) in perspective with the first. Different proper…
Mathematics
In the research we study the systems of tangent circles inscribed in generalized Archimedes arbeloses and its properties. By the generalized Archimedes arbelos we mean one of the following m…
Mathematics
A method of solving of the Diophantine equations of the first degree, that lets us to solve these equations in general already exists. But there are no such methods for the Diophantine equat…
Mathematics
Language is the lens through which humans see the entire world. The purpose of this research project is to observe how the language in which a message is written impacts the time required fo…
Mathematics
In their study of generalized covering maps in categorical Galois theory, Borceux and Janelidze analyzed topological properties of the coproduct completions of small categories. Up to equiva…
Mathematics
In this paper, we focus on the dynamical behaviors of the non-monotone points and the periodic points of the tent mappings under iteration. We first discuss the variation of the number and l…
Mathematics
In this project, we defined a mid-tangent point with respect to a fixed point X and a tangent at a point P on planar curve C as a point on the tangent that is equidistant from X and P. We st…
Mathematics
In many cases of Land Search and Rescue the search for individuals that are believed to be unconscious or in need of medical attention are time critical. However, due to the shortage of reso…
Mathematics
This puzzle was first mentioned in Dudeney’s book “Puzzles of Canterbury” in 1907. Since then an optimal algorithm in the general case has not been obtained despite many attempts from people…
Mathematics
There are numerous mathematical systems that are implemented in the process of archaeological seriation. Archeological seriation is a relative dating process in which assemblages are placed…
Mathematics
The burning number of a graph was introduced by Bonato-Janssen-Roshanbin [Lecture Notes in Computer Science 8882 (2014)] for measuring the speed of the spread of contagion in a graph. Today,…
Mathematics
Third Award
Appel and Haken (1977) proved that four colors suffice to color any map by using the discharging method. While the original problem required the same four colors, but what if each country ha…
Mathematics
I. Purpose: To determine the most effective acne medication in inhibiting bacterial growth II. Hypothesis: If I treat three bacteria cultures with three different acne medications, then mino…
Mathematics
Antimicrobial resistance is a worldwide epidemic that continues to spread out of control. With the emergence of superbugs such as Methicillin-resistant Staphylococcus aureus and Carbapenem-r…
Mathematics
In this project I established the Lis1 gene as a potential novel target for pharmaceutical treatment of schizophrenia. 80% of schizophrenics currently comply poorly with medication regimens,…
Mathematics
Purpose: Type II diabetes, along with obesity increasing in prominence in the United States and other countries, is characterized by hyperglycemia and insulin resistance to glucose uptake in…
Mathematics
Background. Prostate cancer is the 2nd most common cancer in men and affects nearly 240,000 males annually in the United States with about 29,700 deaths each year. Androgen blocking is the m…
Mathematics
Since the discovery of Alzheimer’s disease by Dr. Alois Alzheimer in 1906, little attempt has been made to understand this disease spatially. In year 1 of this study, a correlation between A…
Mathematics
Arb1 is an essential yeast protein associated with the protein production machinery in the cell known as the ribosome. This study will help to determine the ability to dynamically balance pr…
Mathematics
This experiment focused on the effect Curcuma Longa, commonly known as Turmeric, on a HeLa cervical cancer cell line. It was conducted with the purpose to optimize an in-vitro model using a…
Mathematics
Third Award
Multidrug resistance is a major obstacle in the treatment of cancer. One of the major causes of resistance is P-glycoprotein, an ATP binding cassette transporter that binds and removes toxin…
Mathematics
Saponins are foaming glycosides, consisting of a polycyclic aglycone that is either a choline steroid or triterpenoid attached to one or more sugar side chains. Saponins have received a numb…
Mathematics
Alzheimer’s disease is the 5th leading cause of mortality in the elderly population. The disease progresses through the formation of plaques in neuronal synapses, leading to neuronal death.…
Mathematics
One prominent treatment for prostate cancer is androgen deprivation therapy, which slows tumor growth by targeting the androgen receptor signaling pathway. Unfortunately, most tumors progres…
Mathematics
Nosocomial infections, along with hospital errors, are one of the leading causes of death in America, resulting in 99,000 deaths annually. The problem being addressed is the prevalence of ba…
Mathematics
Currently, organ transplantation is the best treatment available for patients experiencing end-stage heart and kidney failure. Unfortunately, the ten-year survival rate of a transplanted org…
Mathematics
The egg timer test is a novel test that allows women to know how fast their biological clock is ticking. The test measures anti-Mullerian Hormone/Mullerian inhibiting substance (AMH/MIS), a…