Abstract:
Solar energy has become a promising alternative to conventional fossil fuel sources. Solar panels are used to collect solar radiation and convert it into electricity. One of the techniques used to maximize the effectiveness of this energy alternative is to maximize the power output of the solar collector. In this project the maximum power is calculated by determining the voltage and the current of maximum power. These quantities are determined by finding the maximum value for the equation for power using differentiation. After the maximum values are found for each time of day, each individual quantity, voltage of maximum power, current of maximum power, and maximum power is plotted as a function of the time of day.

Abstract:
A conjecture of Sendov states that if a polynomial has all its roots in the unit disk and if $\beta$ is one of those roots, then within one unit of $\beta$ lies a root of the polynomial's derivative. If we define $r(\beta)$ to be the greatest possible distance between $\beta$ and the closest root of the derivative, then Sendov's conjecture claims that $r(\beta) \le 1$. In this paper, we assume (without loss of generality) that $0 \le \beta \le 1$ and make the stronger conjecture that $r(\beta) \le 1-(3/10)\beta(1-\beta)$. We prove this new conjecture for all polynomials of degree 2 or 3, for all real polynomials of degree 4, and for all polynomials of any degree as long as all their roots lie on a line or $\beta$ is sufficiently close to 1.

Abstract:
Define $S(n,\beta)$ to be the set of complex polynomials of degree $n \ge 2$ with all roots in the unit disk and at least one root at $\beta$. For a polynomial $P$, define $|P|_\beta$ to be the distance between $\beta$ and the closest root of the derivative $P'$. Finally, define $r_n(\beta)=\sup \{|P|_\beta : P \in S(n,\beta) \}$. In this notation, a conjecture of Bl. Sendov claims that $r_n(\beta) \le 1$. In this paper we investigate Sendov's conjecture near the unit circle, by computing constants $C_1$ and $C_2$ (depending only on $n$) such that $r_n(\beta) \sim 1 + C_1 (1-|\beta|) + C_2 (1-|\beta|)^2$ for $|\beta|$ near 1. We also consider some consequences of this approximation.

Abstract:
Epidemiological
surveillance for microbes is currently based on either agar culture followed by
identification, or genetic amplification. Both techniques are highly
skilled-labor intensive, costly, and must be done in central laboratories. The
Defined Substrate Utilization^{®} (DSU^{®}) format provides an
epidemiological series of specific screening formulations that obviate these
limitations. All reagents are present in optimized stable powder form in a test
tube—add water, inoculate, and incubate. A specific color change provides a
sensitive and specific detection of the target microbe. Two DSU^{®} methods for Staphylococcus aureus (S. aureus) are presented: aureusAlert^{®} for all S. aureus and EPI-M^{®} for methicillin-resistant S. aureus (MRSA). Both aureusAlert

Abstract:
Define a subset of the complex plane to be a Rolle's domain if it contains (at least) one critical point of every complex polynomial P such that P(-1)=P(1). Define a Rolle's domain to be minimal if no proper subset is a Rolle's domain. In this paper, we investigate minimal Rolle's domains.

Abstract:
The arguments of Cannon, Floyd, Grayson and Thurston showing that solve geometry groups are not almost convex also show that solvable Baumslag-Solitar groups are not almost convex.

Abstract:
Let S(n) be the set of all polynomials of degree n with all roots in the unit disk, and define d(P) to be the maximum of the distances from each of the roots of a polynomial P to that root's nearest critical point. In this notation, Sendov's conjecture asserts that d(P)<=1 for every P in S(n). Define P in S(n) to be locally extremal if d(P)>=d(Q) for all nearby Q in S(n), and note that maximizing d(P) over all locally extremal polynomials P would settle the Sendov conjecture. Prior to now, the only polynomials known to be locally extremal were of the form P(z)=c(z^n+a) with |a|=1. In this paper, we determine sufficient conditions for real polynomials of a different form to be locally extremal, and we use these conditions to find locally extremal polynomials of this form of degrees 8, 9, 12, 13, 14, 15, 19, 20, and 26.

Colorectal cancer (CRC) results from the progressive accumulation of genetic and epigenetic
alterations that lead to the transformation of normal colonic epithelium to
colon adenocarcinoma. From the analysis of the molecular genesis of colon
cancer, four central tenets concerning the pathogenesis of cancer have been
established. The first is that the genetic and epigenetic alterations that
underlie colon cancer formation promote the cancer formation process because
they provide a clonal growth advantage to the cells that acquire them. The
second tenet is that cancer emerges via a multi-step progression at both the molecular and the morphologic level. The third is that loss of genomic stability
is a key molecular step in cancer formation. The fourth is that hereditary cancer syndromes frequently correspond to germ line forms of key genetic defects
whose somatic occurrences drive the emergence of sporadic colon cancers.

Despite the developments in the diagnostic and management strategies, a considerable number
of colorectal cancer (CRC) patients
present with disease recurrence after curative surgery. Moreover; there are no
reliable indicators to determine the prognosis and response of CRC patients to
therapy. By harnessing recent
technological advances in molecular profiling techniques, it is anticipated
that greater insight to the various
combinations of genetic events or alternative pathways underlying
carcinogenesis will be gained. By carrying out literature search, we were able
to identify a comprehensive list of genes with high differential expression patterns in colorectal cancer that
could serve as molecular markers to complement existing histopathological factors in diagnosis, follow up and
therapeutic strategies for individualized care of patients.

Abstract:
This article reviews the current status of cardiovascular disease (CVD) on the international scale. Presently viewed as an epidemic that has migrated from westernized societies to developing countries, several important issues are elaborated upon. They include the basis for the increasing prevalence of CVD and the associated societal implications. The challenges related to lack of resources and infrastructure support may also impede successful implementation of proven strategies to reduce CVD. In addition to traditional risk factors such as cigarette smoking, hypertension, obesity, hyperlipidemia, diabetes mellitus and insulin resistance, many developing countries must also contend with other risk biomarkers. Included in this grouping are human immunodeficiency virus/acquired immunodeficiency syndrome and other infectious/inflammatory processes as well as nutritional and vitamin deficiencies that make preventive measures more difficult to prioritize. Taken together, greater partnering between local governments, affiliated hospitals and international societies is needed to enhance and facilitate efforts aimed at optimizing standard of care measures in developing countries in order to reduce cardiovascular risk.