Some contractible open manifolds and coverings of manifolds in dimension three

AbstractMcMillan has shown that every irreducible, contractible, open 3-manifold is the monotone union of handlebodies (only 0- and 1-handles) and that there are uncountably many such manifolds. Work by Myers and Wright shows that no irreducible, contractible, open 3-manifold different from R3 can nontrivially cover any 3-manifold when the handlebodies all have genus one or have bounded genus. We describe a family of irreducible, contractible, open 3-manifolds that we call composite Whitehead manifolds. These manifolds have the property that when written as the monotone union of handlebodies, the handlebodies must have unbounded genus. We show that there are uncountably many composite Whitehead manifolds that nontrivially cover open 3-manifolds but do not cover a compact 3-manifold. We also show that there exist uncountably many composite Whitehead manifolds which cannot nontrivially cover any 3-manifold. It is a famous unsolved problem if any irreducible, contractible, open 3-manifold different from R3 can cover a compact 3-manifold. It is unlikely that any composite Whitehead manifold covers a compact manifold, but our techniques are not strong enough to answer this question

Pharmaconutrition in the clinical management of COVID-19: a lack of evidence-based research but clues to personalized prescription

A scientific interest has emerged to identify pharmaceutical and nutritional strategies in the clinical management of coronavirus disease 2019 (COVID-19). The purpose of this narrative review is to critically assess and discuss pharmaconutrition strategies that, secondary to accepted treatment methods, could be candidates in the current context of COVID-19. Oral medicinal doses of vitamin C (1–3 g/d) and zinc (80 mg/d elemental zinc) could be promising at the first signs and symptoms of COVID-19 as well as for general colds. In critical care situations requiring parenteral nutrition, vitamin C (3–10 g/d) and glutamine (0.3–0.5 g/kg/d) administration could be considered, whereas vitamin D3 administration (100,000 IU administered intramuscularly as a one-time dose) could possess benefits for patients with severe deficiency. Considering the presence of n-3 polyunsaturated fatty acids and arginine in immune-enhancing diets, their co-administration may also occur in clinical conditions where these formulations are recommended. However, despite the use of the aforementioned strategies in prior contexts, there is currently no evidence of the utility of any nutritional strategies in the management of SARS-CoV-2 infection and COVID-19. Nevertheless, ongoing and future clinical research is imperative to determine if any pharmaconutrition strategies can halt the progression of COVID-19

Population Synthesis and the Diagnostics of High-redshift Galaxies

The effect of redshift on the observation of distant galaxies is briefly discussed emphasizing the possible sources of bias in the interpretation of high-z data. A general energetic criterion to assess physical self-consistency of evolutionary population synthesis models is also proposed, for a more appropriate use of this important tool to investigate distinctive properties of primeval galaxies.Comment: 8 pages and 6 color figures. Invited talk at the conference "New Quests in Stellar Astrophysics: The link between Stars and Cosmology", 26-30 March, 2001, Puerto Vallarta, Mexico, eds. M. Chavez et al., to be published by Kluwe

Dust-to-Gas Ratio and Metallicity in Dwarf Galaxies

We examine the dust-to-gas ratio as a function of metallicity for dwarf galaxies [dwarf irregular galaxies (dIrrs) and blue compact dwarf galaxies (BCDGs)]. Using a one-zone model and adopting the instantaneous recycling approximation, we prepare a set of basic equations which describes processes of dust formation and destruction in a galaxy. Four terms are included for the processes: dust formation from heavy elements ejected by stellar mass loss, dust destruction in supernova remnants, dust destruction in star-forming regions, and accretion of heavy elements onto preexisting dust grains. Solving the equations, we compare the result with observational data of nearby dIrrs and BCDGs. The solution is consistent with the data within the reasonable ranges of model parameters constrained by the previous examinations. This means that the model is successful in understanding the dust amount of nearby galaxies. We also show that the accretion rate of heavy element onto preexisting dust grains is less effective than the condensation of heavy elements in dwarf galaxies.Comment: 14 pages LaTeX, 4 figures, to appear in Ap

Does the Number Density of Elliptical Galaxies Change at z<1?

We have performed a detailed V/Vmax test for a sample of the Canada-France Redshift Survey (CFRS) for the purpose of examining whether the comoving number density of field galaxies changes significantly at redshifts of z<1. Taking into account the luminosity evolution of galaxies which depends on their morphological type through different history of star formation, we obtain \sim 0.5 in the range of 0.3<z<0.8, where reliable redshifts were secured by spectroscopy of either absorption or emission lines for the CFRS sample. This indicates that a picture of mild evolution of field galaxies without significant mergers is consistent with the CFRS data. Early-type galaxies, selected by their (V-I)_{AB} color, become unnaturally deficient in number at z>0.8 due to the selection bias, thereby causing a fictitious decrease of . We therefore conclude that a reasonable choice of upper bound of redshift z \sim 0.8 in the V/Vmax test saves the picture of passive evolution for field ellipticals in the CFRS sample, which was rejected by Kauffman, Charlot, & White (1996) without confining the redshift range. However, about 10% of the CFRS sample consists of galaxies having colors much bluer than predicted for irregular galaxies, and their \avmax is significantly larger than 0.5. We discuss this population of extremely blue galaxies in terms of starburst that has just turned on at their observed redshifts.Comment: 11 pages including 3 figures, to appear in ApJ Letter

Consequences of a Change in the Galactic Environment of the Sun

The interaction of the heliosphere with interstellar clouds has attracted interest since the late 1920's, both with a view to explaining apparent quasi-periodic climate "catastrophes" as well as periodic mass extinctions. Until recently, however, models describing the solar wind - local interstellar medium (LISM) interaction self-consistently had not been developed. Here, we describe the results of a two-dimensional (2D) simulation of the interaction between the heliosphere and an interstellar cloud with the same properties as currently, except that the neutral H density is increased from the present value of n(H) ~ 0.2 cm^-3 to 10 cm^-3. The mutual interaction of interstellar neutral hydrogen and plasma is included. The heliospheric cavity is reduced considerably in size (approximately 10 - 14 AU to the termination shock in the upstream direction) and is highly dynamical. The interplanetary environment at the orbit of the Earth changes markedly, with the density of interstellar H increasing to ~2 cm^-3. The termination shock itself experiences periods where it disappears, reforms and disappears again. Considerable mixing of the shocked solar wind and LISM occurs due to Rayleigh-Taylor-like instabilities at the nose, driven by ion-neutral friction. Implications for two anomalously high concentrations of 10Be found in Antarctic ice cores 33 kya and 60 kya, and the absence of prior similar events, are discussed in terms of density enhancements in the surrounding interstellar cloud. The calculation presented here supports past speculation that the galactic environment of the Sun moderates the interplanetary environment at the orbit of the Earth, and possibly also the terrestrial climate.Comment: 23 pages, 2 color plates (jpg), 3 figures (eps

Decoupling 802.11B From the Partition Table in Erasure Coding

Many cyberneticists would agree that, had it not been for extensible epistemologies, the evaluation of superblocks might never have occurred. In this paper, authors disprove the improvement of context-free grammar, demonstrates the technical importance of distributed systems. In our research, we concentrate our efforts on showing that IPv4 and erasure coding are never incompatible