Questions concerning matrix algebras and invariance of spectrum

Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$. Denote the algebra of all $n\times n$ matrices with entries from $A$ by $M_{n}(A)$. In this paper we prove some results concerning the open question: If $A$ is inverse closed in $B$, then is $M_{n}(A)$ inverse closed in $M_{n}(B)$? We also study related questions in the setting where $A$ is a symmetric Banach *-algebra.Comment: 6 pages, no figures, no table

Binding the Diproton in Stars: Anthropic Limits on the Strength of Gravity

We calculate the properties and investigate the stability of stars that burn via strong (and electromagnetic) interactions, and compare their properties with those that, as in our Universe, include a rate-limiting weak interaction. It has been suggested that, if the diproton were bound, stars would burn ~10^{18} times brighter and faster via strong interactions, resulting in a universe that would fail to support life. By considering the representative case of a star in our Universe with initially equal numbers of protons and deuterons, we find that stable, "strong-burning" stars adjust their central densities and temperatures to have familiar surface temperatures, luminosities and lifetimes. There is no "diproton disaster". In addition, strong-burning stars are stable in a much larger region of the parameter space of fundamental constants, specifically the strength of electromagnetism and gravity. The strongest anthropic bound on stars in such universes is not their stability, as is the case for stars limited by the weak interaction, but rather their lifetime. Regardless of the strength of electromagnetism, all stars burn out in mere millions of years unless the gravitational coupling constant is extremely small, \alpha_G < 10^{-30}.Comment: 16 pages, 4 figures. Accepted for publication in JCA

Testing the Multiverse: Bayes, Fine-Tuning and Typicality

Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to provide a deeper explanation for some aspect of our models (in this case, the standard model of cosmology) that seem unnatural or fine-tuned. In particular, I will consider how cosmologists can test the multiverse using observations of this universe.Comment: 19 pages, 3 figures. Conference proceedings: to appear in "The Philosophy of Cosmology", edited by Khalil Chamcham, Joseph Silk, John D. Barrow, and Simon Saunders. Cambridge University Press, 201

Lightweight helmet-mounted eye movement measurement system

The helmet-mounted eye movement measuring system, weighs 1,530 grams; the weight of the present aviators' helmet in standard form with the visor is 1,545 grams. The optical head is standard NAC Eye-Mark. This optical head was mounted on a magnesium yoke which in turn was attached to a slide cam mounted on the flight helmet. The slide cam allows one to adjust the eye-to-optics system distance quite easily and to secure it so that the system will remain in calibration. The design of the yoke and slide cam is such that the subject can, in an emergency, move the optical head forward and upward to the stowed and locked position atop the helmet. This feature was necessary for flight safety. The television camera that is used in the system is a solid state General Electric TN-2000 with a charged induced device imager used as the vidicon

Augmentation of Mind-body Therapy and Role of Deep Slow Breathing

Mind-body therapies have been shown to be effective in clinical treatment of disorders such as high blood pressure and stress. Significant differences in the effectiveness of mind–body therapies have been shown and a common link among the therapies has yet to be defined. This article overviews the role of slow rhythmic breathing in physiological as well as therapeutic effects of mind-body therapies. Slow deep breathing practice has important implications as it may underlie the basic mechanism that synchronizes the brain with the autonomic response. This article reviews studies that include the effect of deep slow breathing with or without mind-body therapy exercises. In utero studies that monitor patterns of fetal breathing reveal sympathetic activation with irregular, shallow fast breathing movements compared to slow deep breathing. Recognition of respiratory mechanisms in mind-body therapies can lead to development of more effective relaxation exercises that may incorporate deep slow breathing in clinical applications

Some services of the Time and Frequency Division of the National Bureau of Standards

The Time and Frequency Division of the National Bureau of Standards (NBS) provides several services to the general public. The radio broadcasts of WWV, WWVH, and WWVB supply reliable, unambiguous time signals to many users. The NBS telephone time-of-day service attracts several hundreds of thousands of calls each year. Periodically, the NBS provides courses on specific topics relating to time and frequency technology. In addition to numerous technical papers published each year, the NBS has prepared the first volume of a comprehensive monograph on time and frequency. The results of research in the Time and Frequency Division of the NBS have had significant impact. An active TV time system capable of serving most of the U.S. currently awaits a ruling by the FCC on a petition filed last year on behalf of the NBS by the Department of Commerce. Three more recent developments are: (1) a TV frequency comparator (patent applied for); (2) a method to perform an independent (absolute) frequency evaluation of commercial cesium beam oscillators; and (3) a method of removing one source of frequency drift in commercial cesium beam oscillators

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetised, turbulent plasma---and, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion discs around black holes. In the context of discs, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfv\'enic turbulence: collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, $\beta_\mathrm{i}$: it ranges from $\sim0.05$ at $\beta_\mathrm{i}=0.1$ to at least $30$ for $\beta_\mathrm{i} \gtrsim 10$. This energy partition is approximately insensitive to the ion-to-electron temperature ratio $T_\mathrm{i}/T_\mathrm{e}$. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfv\'enic turbulence will tend towards a nonequilibrium state in which one of the species is significantly hotter than the other, viz., hotter ions at high $\beta_\mathrm{i}$, hotter electrons at low $\beta_\mathrm{i}$. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high $\beta_i$ and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when $\beta_\mathrm{i}\lesssim1$ and by linear phase mixing (Landau damping) when $\beta_\mathrm{i}\gg1

Final Portfolio - SPARC Open Education Leadership Program, 2017-18

Final portfolio of work completed for the SPARC Open Education Leadership Program, 2017-18, including the Capstone Project Final Report, the Community Resource entitled “Piloting Faculty OER Grant Programs: A Practical Guide for Librarians,” and the blog Opening Up Liberal Arts Colleges (linked). “Piloting Faculty OER Grant Programs is also available separately in The Cupola