Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

A review of recent activities in the NASA CELSS program

A CELSS (Controlled Ecological Life Support System) is a device that utilizes photosynthetic organisms and light energy to regenerate waste materials into oxygen and food for a crew in space. The results of studies with the CELSS program suggest that a bioregenerative life support system is a useful and effective method of regenerating consumable materials for crew sustenance. The data suggests that the operation of a CELSS in space is practical if plants can be made to behave predictably in the space environment. Much of the work centers on the biological components of the CELSS system. Ways of achieving high efficiency and long term stability of all components of the system are examined. Included are explorations of the conversion of nonedible cellulose to edible materials, nitrogen fixation by biological and chemical methods, and methods of waste processing. A description is provided of the extent to which a bioregenerative life support system can meet the constraints of the space environment, and the degree is assessed to which system efficiency and stability can be increased during the next decade

Engineering verification of the biomass production chamber

The requirements for life support systems, both biological and physical-chemical, for long-term human attended space missions are under serious study throughout NASA. The KSC 'breadboard' project has focused on biomass production using higher plants for atmospheric regeneration and food production in a special biomass production chamber. This chamber is designed to provide information on food crop growth rate, contaminants in the chamber that alter plant growth requirements for atmospheric regeneration, carbon dioxide consumption, oxygen production, and water utilization. The shape and size, mass, and energy requirements in relation to the overall integrity of the biomass production chamber are under constant study

Triple-wavelength fiber ring laser based on a hybrid gain medium actively mode-locked at 10 GHz

A fiber ring laser based on a hybrid gain medium that produces three simultaneously mode-locked wavelength channels is presented. The lithium niobate based modulator used to actively mode-lock the laser cavity at 10 GHz is birefringence compensated to reduce its polarization sensitivity. A Lyot filter defines the lasers multiwavelength spectrum which has a wavelength spacing of 1 nm. The polarization sensitive nature of the laser cavity and its affect on the performance of the laser is discussed

Ethics and Deep Learning

This article appears as chapter 21 of Prince (2023, Understanding Deep Learning); a complete draft of the textbook is available here: http://udlbook.com. This chapter considers potential harms arising from the design and use of AI systems. These include algorithmic bias, lack of explainability, data privacy violations, militarization, fraud, and environmental concerns. The aim is not to provide advice on being more ethical. Instead, the goal is to express ideas and start conversations in key areas that have received attention in philosophy, political science, and the broader social sciences.Comment: Copyright in this Work has been licensed exclusively to The MIT Press, https://mitpress.mit.edu, which will be releasing the final version to the public in 2023. All inquiries regarding rights should be addressed to The MIT Press, Rights and Permissions Departmen

Discovery of Pulsed X-ray Emission from the SMC Transient RX J0117.6-7330

We report on the detection of pulsed, broad-band, X-ray emission from the transient source RX J0117.6-7330. The pulse period of 22 seconds is detected by the ROSAT/PSPC instrument in a 1992 Sep 30 - Oct 2 observation and by the CGRO/BATSE instrument during the same epoch. Hard X-ray pulsations are detectable by BATSE for approximately 100 days surrounding the ROSAT observation (1992 Aug 28 - Dec 8). The total directly measured X-ray luminosity during the ROSAT observation is 1.0E38 (d/60 kpc)^2 ergs s-1. The pulse frequency increases rapidly during the outburst, with a peak spin-up rate of 1.2E-10 Hz s-1 and a total frequency change 1.8%. The pulsed percentage is 11.3% from 0.1-2.5 keV, increasing to at least 78% in the 20-70 keV band. These results establish RX J0117.6-7330 as a transient Be binary system.Comment: 17 pages, Latex, aasms, accepted for publication in ApJ Letter

Expected characteristics of the subclass of Supernova Gamma-ray Bursts (S-GRBs)

The spatial and temporal coincidence between the gamma-ray burst (GRB) 980425 and supernova (SN) 1998bw has prompted speculation that there exists a class of GRBs produced by SNe (``S-GRBs''). Robust arguments for the existence of a relativistic shock have been presented on the basis of radio observations. A physical model based on the radio observations lead us to propose the following characteristics of supernovae GRBs (S-GRBs): 1) prompt radio emission and implied brightness temperature near or below the inverse Compton limit, 2) high expansion velocity of the optical photosphere as derived from lines widths and energy release larger than usual, 3) no long-lived X-ray afterglow, and 4) a single pulse (SP) GRB profile. Radio studies of previous SNe show that only type Ib and Ic potentially satisfy the first condition. Accordingly we have investigated proposed associations of GRBs and SNe finding no convincing evidence (mainly to paucity of data) to confirm any single connection of a SN with a GRB. If there is a more constraining physical basis for the burst time-history of S-GRBs beyond that of the SP requirement, we suggest the 1% of light curves in the BATSE catalogue similar to that of GRB 980425 may constitute the subclass. Future optical follow-up of bursts with similar profiles should confirm if such GRBs originate from some fraction of SN type Ib/Ic.Comment: 11 pages of LaTeX with 1 figure. Submitted to the Astrophysical Journal Letter

Tangent bundle geometry induced by second order partial differential equations

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally