Manifolds with S 1-category 2 have cyclic fundamental groups

A closed topological n-manifold M ⁿ is of S ¹-category 2 if it can be covered by two open subsets W ₁, W ₂ such that the inclusions W _i → M ⁿ factor homotopically through maps W _i → S ¹. We show that for n > 3 the fundamental group of such an n-manifold is either trivial or infinite cyclic.     

Coverings of 3-manifolds by open balls and two open solid tori

Hempel and McMillan showed that a closed 3-manifold that can be covered by three open balls is a connected sum of S³- and S²-bundles over S¹. In this paper we obtain a classification of all closed 3-manifolds that can be covered by two open balls and one open solid torus or by one open ball and two open solid tori.     

Quantification of Regional Intrapulmonary Oxygen Partial Pressure Evolution during Apnea by He MRI

We present a new method to determine in vivo the temporal evolution of intrapulmonary oxygen concentrations by functional lung imaging with hyperpolarized ³Helium (³ ). Single-breath, single-bolus visualization of ³ administered to the airspaces is used to analyze nuclear spin relaxation caused by the local oxygen partial pressure p_O2(t). We model the dynamics of hyperpolarization in the lung by rate equations. Based hereupon, a double acquisition technique is presented to separate depolarization by RF pulses and oxygen induced relaxation. It permits the determination of p_O2 with a high accuracy of up to 3% with simultaneous flip angle calibration using no additional input parameters. The time course of p_O2 during short periods of breathholding is found to be linear in a pig as well as in a human volunteer. We also measured the wall relaxation time in the lung and deduced a lower limit of 4.3 min.     

Measuring methotrexate polyglutamates in red blood cells: a new LC-MS/MS-based method

The folate antagonist methotrexate (MTX) is the anchor drug in the treatment of rheumatoid arthritis. The therapeutic effects of MTX are attributed to the intracellular levels of MTX, present in the cell as polyglutamates (MTXPGn). We developed a new liquid chromatography-electrospray ionization-tandem mass spectrometry (LC-ESI-MS/MS)-based assay to separately quantitate MTXPGn in red blood cells using stable-isotope-labelled internal standards. Samples were analyzed by LC-ESI-MS/MS using a Waters Acquity UPLC BEH C18 column with a 5–100% organic gradient of 10 mM ammonium bicarbonate (pH 10) and methanol. The analysis consisted of simple sample preparation and a 6-min run time. Detection was done using a Waters Acquity UPLC coupled to a Waters Quattro Premier XE with electrospray ionization operating in the positive ionization mode. Assay validation was performed following recent Food and Drug Administration guidelines. The method was linear from 1–1,000 nM for all MTXPGn (R ²?>?0.99). The coefficient of variation ranged from 1–4% for intraday precision and 6–15% for interday precision. Samples were stable for at least 1 month at ?80 °C. Recovery ranged from 98–100%, and the relative matrix-effect varied from 95–99%. The lower limit of quantitation was 1 nM for each MTXPGn. Fifty patient samples from the tREACH study were analyzed. The MTXPGn concentration and distribution of these samples were comparable with values reported in literature. The developed LC-ESI-MS/MS method for the quantitative measurement of MTXPGn in red blood cells is both sensitive and precise within the clinically relevant range. The method can be easily applied in clinical laboratories due to the combination of simple pre-treatment with robust LC-ESI-MS/MS.

Integral representations of quermassintegrals and Bonnesen-style inequalities

Archiv der Mathematik -     

Fundamental groups of manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-category 2

A closed topological n-manifold M ⁿ is of S ¹-category 2 if it can be covered by two open subsets W ₁,W ₂ such that the inclusions W _i → M ⁿ factor homotopically through maps W _i → S ¹ → M ⁿ . We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic.