Estimates for the volume of a Lorentzian manifold

We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.Comment: 8 pages, a pdf version of the preprint can also be retrieved from http://www.math.uni-heidelberg.de/studinfo/gerhardt/LM-Volume.pdf v2: A further estimate has been added covering the case when the mean curvature is merely non-negative resp. non-positive (Theorem 1.1

The changing face of cancer therapeutics improved : outcome and decreased toxicity with Molecular Targeted Drugs

The treatment of patients with cancer has largely involved the administration of cytotoxic drugs with narrow therapeutic indices, with little selectivity for cancer cells over normal proliferating cells. The primary exception to this has been the successful administration of hormonal manipulation to treat breast and prostate malignancies. The development of hormonal manipulation arose from the observation by Sir George Beatson that breast carcinomas improved after bilateral oophorectomy. This led to the use of Tamoxifen and more recently aromatase inhibitors and oestrogen receptor antagonists. These targeted therapeutics are characterised by their ability to induce selective tumour cell death and achieve patient benefit with low toxicity, and have had a significant impact on the outcome of patients with early and advanced oestrogen receptor positive breast cancer. Further advances in the understanding of tumour cell biology, the sequencing of the human genome, and the characterisation of the molecular differences between malignant and normal cells have, over the past two decades, resulted in the identification of a large number of critically important molecular targets. As with the identification of the importance of oestrogens and the oestrogen receptor, this has accelerated the development of molecularly targeted therapeutics and is rapidly revolutionising cancer medicine (Table 1). This brief review will describe some of the most important advances achieved and will attempt to predict what future cancer therapeutics will entail.peer-reviewe

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Tribology of Skin: Review and Analysis of Experimental Results for the Friction Coefficient of Human Skin

In this review, we discuss the current knowledge on the tribology of human skin and present an analysis of the available experimental results for skin friction coefficients. Starting with an overview on the factors influencing the friction behaviour of skin, we discuss the up-to-date existing experimental data and compare the results for different anatomical skin areas and friction measurement techniques. For this purpose, we also estimated and analysed skin contact pressures applied during the various friction measurements. The detailed analyses show that substantial variations are a characteristic feature of friction coefficients measured for skin and that differences in skin hydration are the main cause thereof, followed by the influences of surface and material properties of the contacting materials. When the friction coefficients of skin are plotted as a function of the contact pressure, the majority of the literature data scatter over a wide range that can be explained by the adhesion friction model. The case of dry skin is reflected by relatively low and pressure-independent friction coefficients (greater than 0.2 and typically around 0.5), comparable to the dry friction of solids with rough surfaces. In contrast, the case of moist or wet skin is characterised by significantly higher (typically >1) friction coefficients that increase strongly with decreasing contact pressure and are essentially determined by the mechanical shear properties of wet skin. In several studies, effects of skin deformation mechanisms contributing to the total friction are evident from friction coefficients increasing with contact pressure. However, the corresponding friction coefficients still lie within the range delimited by the adhesion friction model. Further research effort towards the analysis of the microscopic contact area and mechanical properties of the upper skin layers is needed to improve our so far limited understanding of the complex tribological behaviour of human ski

Quantum cosmological Friedman models with a massive Yang-Mills field

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a massive Yang-Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang-Mills field. In the latter case the mass of the Yang-Mills field assumes the role of the eigenvalue.Comment: 16 pages, v3: typos corrected, final version, to appear in CQ

“ENDOTROPHIC” SPORULATION

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72259/1/j.1749-6632.1963.tb13674.x.pd

Simple method for temporal study of subpicosecond distributed feedback dye lasers.

The spectral and temporal behaviour of subpicosecond DFDLs are studied. A simple and sensitive spectral diagnostic method is proposed to exhibit the presence and determine the temporal separation and relative amplitude of any following pulse. The measurements were performed in a hybrid excimer-dye laser system generating less than 100 fs pulses at 248 nm

Intensity-dependent loss properties of window materials at 248 nm.

Transmission of fused silica, CaF2, LiF, and MgF2 is measured using 450-fsec, 248-nm pulses in the range 10–120 GW/cm2. Different loss mechanisms such as scattering of transmitted radiation, color-center formation, and multiphoton absorption were studied separately. For fused silica a two-photon absorption mechanism is found, while for CaF2, LiF, and MgF2 three-photon absorption and absorption due to color-center formation are found as dominant absorption mechanisms