Physical Sciences and Mathematics Commons^™

Generalized Markoff Equations, Euclid Trees, And Chebyshev Polynomials, Donald Joseph Mcginn

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Markoff equation is x^2+y^2+z^2 = 3xyz, and all of the positive integer solutions

of this equation occur on one tree generated from (1, 1, 1), which is called the

Markoff tree. In this paper, we consider trees of solutions to equations of the form

x^2 + y^2 + z^2 = xyz + A. We say a tree of solutions satisfies the unicity condition

if the maximum element of an ordered triple in the tree uniquely determines the

other two. The unicity conjecture says that the Markoff tree satisifies the unicity

condition. In this paper, we show that there exists …

Beryllium Is A Potent And Unique Gsk-3Β Inhibitor With Potential To Differentially Regulate Glycogen Synthase And Β-Catenin, Ata Ur Rahman Mohammed Abdul

UNLV Theses, Dissertations, Professional Papers, and Capstones

Glycogen Synthase Kinase-3β (GSK-3β) is an important serine/threonine kinase that phosphorylates/regulates diverse and metabolically important proteins. Some of the important substrates of GSK-3β are glycogen synthase, tau, β-catenin, cyclin D1, axin, c-jun, c-myc, Heat Shock Factor–1, BCL-3, CREB, Histone H1.5, mdm2, p21 (CIP1), pyruvate dehydrogenase and many more. De-regulation of GSK-3β has been implicated in diseases like cancer, Alzheimer’s disease, bipolar disorder and type 2 diabetes mellitus. Currently, GSK-3β is one of the most widely studied proteins and there is a great interest in developing potent and efficient GSK-3β-inhibitors for research as well as therapeutic purposes. We demonstrate that beryllium …

Modeling Studies And Numerical Analyses Of Coupled Pdes System In Electrohydrodynamics, Yuzhou Sun

UNLV Theses, Dissertations, Professional Papers, and Capstones

Electrohydrodynamics (EHD) is the term used for the hydrodynamics coupled with electrostatics, whose governing equations consist of the electrostatic potential (Poisson) equation, the ionic concentration (Nernst-Planck) equations, and Navier-Stokes equations for an incompressible, viscous dielectric liquid. In this dissertation, we focus on a specic application of EHD - fuel cell dynamics - in the eld of renewable and clean energy, study its traditional model and attempt to develop a new fuel cell model based on the traditional EHD model. Meanwhile, we develop a series of ecient and robust numerical methods for these models, and carry out their numerical analyses on …

Carbon Isotope Variations Associated With A Middle Ordovician Karstic Unconformity, Patricia Suzanne Williams

UNLV Theses, Dissertations, Professional Papers, and Capstones

Large negative carbon isotope (δ¹³C) excursions have been documented from late Neoproterozoic-Paleozoic successions. These δ¹³C excursions have been widely used for regional and global stratigraphic correlation, particularly in strata with limited paleontological and radiometric age controls. Recent studies, however, argued that some negative δ¹³C excursions from stratigraphic record may have been resulted from meteoric/burial diagenesis, which commonly shifts both carbon and oxygen isotopes toward lower values. Testing the diagenetic origin of δ¹³C excursions in stratigraphic successions without independent stratigraphic framework has been difficult because it evolves into circular arguments about stratigraphic completeness …