Neuer Beweis eines Satzes von Taussky und Geiringer

Ohne ZusammenfassungDiese Untersuchung wurde ausgefÜhrt unter Kontrakt Nr. DA-04-200-ORD-340 zwischen dem Office of Ordnance Research, Abt. der US Army und dem State College of Washington.     

Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz functions

We describe the possible restrictions of the cotangent bundle to an elliptic curve . We apply this in positive characteristic to the computation of the Hilbert-Kunz function of a homogeneous R₊-primary ideal in the graded section ring .     

Diffusion on a self-assembled monolayer: molecular modeling of a bound + mobile lubricant

The diffusion of tricresyl phosphate molecules on an octadecyltrichlorosilane self-assembled monolayer (SAM) was characterized using molecular dynamics simulations. The simulations predict that when placed on the top of a close-packed SAM, the molecules remain mobile on the surface with an isotropic diffusion activation energy of approximately 9 kJ/mol. In contrast, an anisotropic barrier that results from chain tilt within the SAM is predicted for diffusion into a defect created by reducing the alkane chain length within a cylinderical region of the surface. Once in the defect, the molecules become trapped by embedding part of the molecule into the side of the SAM.     

An additive analysis of multiplicative Schwarz methods

We present an analysis of multiplicative Schwarz methods for symmetric positive definite problems that is based on the theory of additive Schwarz preconditioners and discuss applications to multigrid methods and domain decomposition methods.     

The Hilbert–Kunz Function in Graded Dimension Two

Let R denote a two-dimensional normal standard-graded K-domain over the algebraic closure K of a finite field of characteristic p, and let I ? R denote a homogeneous R ₊-primary ideal. We prove that the Hilbert–Kunz function of I has the form ? (q) = e _HK (I)q ² + γ(q) with rational Hilbert–Kunz multiplicity e _HK (I) and an eventually periodic function γ(q).     

Cellular properties and population asymptotics in the population balance equation

Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.     

Hemispherical-rod microlens as a variant fractional Fourier transformer

It is shown that a hemispherical-rod microlens can act as a fractional Fourier transform device with a continuously varying degree of fractionality. It is believed to be the first proposed device to perform such a task; its most immediate applications include optical tomography.     

The protective role of melanin against UV damage in human skin

Human skin is repeatedly exposed to UVR that influences the function and survival of many cell types and is regarded as the main causative factor in the induction of skin cancer. It has been traditionally believed that skin pigmentation is the most important photoprotective factor, as melanin, besides functioning as a broadband UV absorbent, has antioxidant and radical scavenging properties. Besides, many epidemiological studies have shown a lower incidence for skin cancer in individuals with darker skin compared to those with fair skin. Skin pigmentation is of great cultural and cosmetic importance, yet the role of melanin in photoprotection is still controversial. This article outlines the major acute and chronic effects of UVR on human skin, the properties of melanin, the regulation of pigmentation and its effect on skin cancer prevention.