Projectively Solid Sets and an N-dimensional Piccard's Theorem

We discuss functions f : X × Y → Z such that sets of the form f (A × B) have non-empty interiors provided that A and B are non-empty sets of second category and have the Baire property

The Optical Gravitational Lensing Experiment. Variable Stars in Globular Clusters - IV. Fields 104A-E in 47 Tuc

Five fields located close to the center of the globular cluster NGC 104=47 Tuc were surveyed in a search for variable stars. We present V-band light curves for 42 variables. This sample includes 13 RR Lyr stars -- 12 of them belong to the Small Magellanic Cloud (SMC) and 1 is a background object from the galactic halo. Twelve eclipsing binaries were identified -- 9 contact systems and 3 detached/semi-detached systems. Seven eclipsing binaries are located in the blue straggler region on the cluster color-magnitude diagram (CMD) and four binaries can be considered main-sequence systems. One binary is probably a member of the SMC. Eight contact binaries are likely members of the cluster and one is most probably a foreground star. We show that for the surveyed region of 47 Tuc, the relative frequency of contact binaries is very low as compared with other recently surveyed globular clusters. The sample of identified variables also includes 15 red variables with periods ranging from about 2 days to several weeks. A large fraction of these 15 variables probably belong to the SMC but a few stars are likely to be red giants in 47 Tuc. VI photometry for about 50 000 stars from the cluster fields was obtained as a by product of our survey.Comment: Latex file, l-aa style, 10 pages, 7 ps figures included. Submitted to A&A. Figure 8 available from ftp://sirius.astrouw.edu.pl/pub/jka/47Tuc/fig8.ps.

Oil, Gas, and Mineral Law

This article is a survey of the relevant developments in oil, gas, and mineral law from December 1, 2019, through November 30, 2020. The article focuses on law likely to be influential to Texas practitioners

Nano ES GEMMA and PDMA, New Tools for the Analysis of Nanobioparticles—Protein Complexes, Lipoparticles, and Viruses

Differential mobility analysis (DMA) is a technique suited for size analysis as well as preparative collection of airborne nanosized airborne particles. In the recent decade, the analysis of intact viruses, proteins, DNA fragments, polymers, and inorganic nanoparticles was possible when combining this method with a nano-electrospray charge-reduction source for producing aerosols from a sample solution/suspensions. Mass analysis of high molecular weight noncovalent complexes is also possible with this methodology due to the linear correlation of the electrophoretic mobility diameter and the molecular mass. In this work, we present the analysis (size and molecular mass) of high molecular weight multimers (noncovalent functional homocomplex) of Jack bean urease in a mass range from 275 kDa up to 2.5 MDa, with mainly present tri- and hexamers but also higher oligomers of the 91 kDa monomer subunit. In a second experiment, the size analysis of intact very-low-density (∼35 nm), low-density (∼22 nm) and high-density lipoparticles (∼10 nm), which are heterocomplexes consisting of cholesterol, lipids, and proteins in different ratios, is presented. Results from mobility analysis were in excellent agreement with particle diameters found in literature. The last presented experiment demonstrates size analysis of a rod-like virus and selective sampling of a selected size fraction of electrosprayed, singly-charged tobacco mosaic virus particles. Sampling and subsequent transmission electron microscopic investigations of a specific size fraction (40 nm electrophoretic mobility diameter) revealed the folding of virus particles during the electrospray and charge reduction (electrical stress) as well as solvent evaporation (mechanical stress) process, leading to an observed geometry of 150 (length) × 35 (width) nm (average cylindrical geometry of unsprayed intact virus 300 × 18 nm)