Recognizing Graph Theoretic Properties with Polynomial Ideals

Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Groebner bases, toric algebra, convex programming, and real algebraic geometry.Comment: 20 pages, 3 figure

Vapor Phase Adsorption of Water on Hydroxyapatite

Water vapor adsorption isotherms were determined gravimetrically on three hydroxyapatite samples differing in preparation and with surface areas of 70.4, 22.5, and 3.0 M 2/gm, respectively. Heats of adsorption for the first layer of water were found to be 13.3, 13.2, and 13.9 kcallmole on these hydroxyapatites. From repeated thermal desorption and adsorption cycles of water, stepwise adsorption was observed which diminished with each outgassing cycle until it disappeared after the fourth cycle. Cross-sectional area of adsorbed water molecule on hydroxyapatite surface was estimated at 11.5 Å2. Standard free energies, isosteric heats, changes in enthalpy, and entropy of adsorption of water on HAP samples outgassed at 300 C were determined.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67213/2/10.1177_00220345770560120101.pd

X chromosomes Aneuploidy Lymphocytes Centromeres Chromosomal translocations Sex chromosomes Etiology Fluorescent in situ hybridiz

Humans, birds, and some primates do not express the uric acid degrading enzyme urate oxidase (UOX) and, as a result, have plasma uric acid concentrations higher than UOX expressing animals. Although high uric acid concentrations are suggested to increase the antioxidant defense system and provide a health advantage to animals without UOX, knockout mice lacking UOX develop pathological complications including gout and kidney failure. As an alternative to the knockout model, RNA interference was used to decrease UOX expression using stable transfection in a mouse hepatic cell line (ATCC, FL83B). Urate oxidase mRNA was reduced 66% (p \u3c 0.05) compared to wild type, as measured by real time RT-PCR. To determine if UOX knockdown resulted in enhanced protection against oxidative stress, cells were challenged with hexavalent chromium (Cr(VI)) or 3-morpholinosydnonimine hydrochloride (SIN-1). Compared to wild type, cells with UOX knockdown exhibited a 37.2 ± 3.5% reduction (p \u3c 0.05) in the electron spin resonance (ESR) signal after being exposed to Cr(VI) and displayed less DNA fragmentation (p \u3c 0.05) following SIN-1 treatment. Cell viability decreased in wild type cells (p \u3c 0.05), but not cells with UOX knockdown, after treatment with SIN-1. These results are consistent with an increased intracellular uric acid concentration and an increased defense against oxidative stress

Urate oxidase knockdown decreases oxidative stress in a murine hepatic cell line

Humans, birds, and some primates do not express the uric acid degrading enzyme urate oxidase (UOX) and, as a result, have plasma uric acid concentrations higher than UOX expressing animals. Although high uric acid concentrations are suggested to increase the antioxidant defense system and provide a health advantage to animals without UOX, knockout mice lacking UOX develop pathological complications including gout and kidney failure. As an alternative to the knockout model, RNA interference was used to decrease UOX expression using stable transfection in a mouse hepatic cell line (ATCC, FL83B). Urate oxidase mRNA was reduced 66% (p < 0.05) compared to wild type, as measured by real time RT-PCR. To determine if UOX knockdown resulted in enhanced protection against oxidative stress, cells were challenged with hexavalent chromium (Cr(VI)) or 3-morpholinosydnonimine hydrochloride (SIN-1). Compared to wild type, cells with UOX knockdown exhibited a 37.2 ± 3.5% reduction (p < 0.05) in the electron spin resonance (ESR) signal after being exposed to Cr(VI) and displayed less DNA fragmentation (p < 0.05) following SIN-1 treatment. Cell viability decreased in wild type cells (p < 0.05), but not cells with UOX knockdown, after treatment with SIN-1. These results are consistent with an increased intracellular uric acid concentration and an increased defense against oxidative stress

Determination of Phase Transitions in Gutta-Percha by Differential Thermal Analysis

Pure gutta-percha was heat-treated in a differential thermal analyzer. The high melting form crystallized on cooling when gutta-percha was heated to 70 C or less. Above 74 C, crystallization into the low melting form predominated. Either polymorph can be selectively crystallized by control of the heat-treatment temperature before cooling.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67076/2/10.1177_00220345770560120301.pd

Characterization of the compaction and sintering of hydroxyapatite powders by mercury porosimetry

Mercury porosimetry was used to measure the bulk and real densities, pore volumes and pore size distributions of compacts of hydroxyapatite before and after sintering. The hydroxyapatites were prepared by two different methods and had widely different surface areas. The properties were determined as a function of compaction force and sintering temperature. Densities from porosimetry were in good agreement with geometric densities. A linear relation was found between pore volume and log of the applied force. There was also a linear relationship between bulk volume and pore volume of the compacts. A bimodal pore size distribution was observed for the high surface area hydroxyapatite which disappeared with increasing compaction loads. Pressurization and depressurization measurements indicated that the main body of the pores in the compacts attained a more regular "spherical" shape with increasing compaction force than did the "necks". The pore volume, percent porosity, and bulk density of the compacts remained unchanged up to 600[deg]C; however, the surface area and the average pore diameter changed at 400[deg]C. The distribution of pores became more uniform, narrower in distribution, and larger in size as the sintering temperature increased. The change in pore area with pore volume indicated that two mechanisms were operating during sintering. The pore area proved to be the most sensitive indicator of changes during sintering.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22375/1/0000824.pd