Formalizing Mathematical Knowledge as a Biform Theory Graph: A Case Study

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory graph is a network of theories connected by meaning-preserving theory morphisms that map the formulas of one theory to the formulas of another theory. Theory graphs are in turn well suited for formalizing mathematical knowledge at the most convenient level of abstraction using the most convenient vocabulary. We are interested in the problem of whether a body of mathematical knowledge can be effectively formalized as a theory graph of biform theories. As a test case, we look at the graph of theories encoding natural number arithmetic. We used two different formalisms to do this, which we describe and compare. The first is realized in ${\rm CTT}_{\rm uqe}$, a version of Church's type theory with quotation and evaluation, and the second is realized in Agda, a dependently typed programming language.Comment: 43 pages; published without appendices in: H. Geuvers et al., eds, Intelligent Computer Mathematics (CICM 2017), Lecture Notes in Computer Science, Vol. 10383, pp. 9-24, Springer, 201

Radiation/convection coupling in rocket motor and plume analysis

A method for describing radiation/convection coupling to a flow field analysis was developed for rocket motors and plumes. The three commonly used propellant systems (H2/O2, RP-1/O2, and solid propellants) radiate primarily as: molecular emitters, non-scattering small particles (soot), and scattering larger particles (Al2O3), respectively. For the required solution, the divergence of the radiation heat flux was included in the energy equation, and the local, volume averaged intensity was determined by a solution to the radiative transfer equation. A rigorous solution to this problem is intractable, therefore, solution methods which use the ordinary and improved differential approximation were developed. This radiation model was being incorporated into the FDNS code, a Navier-Stokes flowfield solver for multiphase, turbulent combusting flows

Perceptions of strength training in dance

The aim of this study was to ascertain current perceptions of strength training in dance from the viewpoint of the professional dancer, dance teacher and student dancers across dance genres. A total of 168 responses (149=F, 19=M) to the modified Training Information Survey (TIS) were analysed for differences in perceptions of strength training between dance students, professional dancers and dance teachers. Some significant differences were found between professionals and teachers (p>0.05), and between students and teachers (p>0.001). In all instances, dance teachers were less likely to agree with; strength training is essential to my overall development as a dancer, Women should participate in strength training, men should participate in strength training, strength training should be part of every training programme regardless of dance style, strength training is beneficial to women and strength training increases bodyweight. It is evident that perceptions of strength training still vary across the dance sector and it is postulated that further education for dancers on the role strength training has to play on the development of a dancer would help to break down barriers to participation. From this investigation, it can also be concluded that the perception that dancers have a fear of muscle hypertrophy and a negative impact on aesthetics is no longer widely prevalent, although it still permeates throughout the dance sector

Theory of zone radiometry

A spectroscopic instrumentation system was developed which was used to measure temperature and concentration distributions in axisymmetric and two dimensional combusting flows. This measurement technique is known as zone radiometry

Self-Similar Force-Free Wind From an Accretion Disk

We consider a self-similar force-free wind flowing out of an infinitely thin disk located in the equatorial plane. On the disk plane, we assume that the magnetic stream function $P$ scales as $P\propto R^\nu$, where $R$ is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: $v_\phi = Mc$, where $M<1$ is a constant. For each choice of the parameters $\nu$ and $M$, we find an infinite number of solutions that are physically well-behaved and have fluid velocity $\leq c$ throughout the domain of interest. Among these solutions, we show via physical arguments and time-dependent numerical simulations that the minimum-torque solution, i.e., the solution with the smallest amount of toroidal field, is the one picked by a real system. For $\nu \geq 1$, the Lorentz factor of the outflow increases along a field line as \gamma \approx M(z/\Rfp)^{(2-\nu)/2} \approx R/R_{\rm A}, where \Rfp is the radius of the foot-point of the field line on the disk and R_{\rm A}=\Rfp/M is the cylindrical radius at which the field line crosses the Alfven surface or the light cylinder. For $\nu < 1$, the Lorentz factor follows the same scaling for z/\Rfp < M^{-1/(1-\nu)}, but at larger distances it grows more slowly: \gamma \approx (z/\Rfp)^{\nu/2}. For either regime of $\nu$, the dependence of $\gamma$ on $M$ shows that the rotation of the disk plays a strong role in jet acceleration. On the other hand, the poloidal shape of a field line is given by z/\Rfp \approx (R/\Rfp)^{2/(2-\nu)} and is independent of $M$. Thus rotation has neither a collimating nor a decollimating effect on field lines, suggesting that relativistic astrophysical jets are not collimated by the rotational winding up of the magnetic field.Comment: 21 pages, 15 figures, accepted to MNRA

Effects of systematic errors on the mixing ratios of trace gases obtained from occulation spectra

The influence of systematic errors in the parameters of the models describing the geometry and the atmosphere on the profiles of trace gases retrieved from simulated solar occultation spectra, collected at satellite altitudes, is investigated. Because of smearing effects and other uncertainties, it may be preferable to calibrate the spectra internally by measuring absorption lines of an atmospheric gas such as CO2 whose vertical distribution is assumed rather than to relay on externally supplied information

Conceptual design of a lunar base thermal control system

Space station and alternate thermal control technologies were evaluated for lunar base applications. The space station technologies consisted of single-phase, pumped water loops for sensible and latent heat removal from the cabin internal environment and two-phase ammonia loops for the transportation and rejection of these heat loads to the external environment. Alternate technologies were identified for those areas where space station technologies proved to be incompatible with the lunar environment. Areas were also identified where lunar resources could enhance the thermal control system. The internal acquisition subsystem essentially remained the same, while modifications were needed for the transport and rejection subsystems because of the extreme temperature variations on the lunar surface. The alternate technologies examined to accommodate the high daytime temperatures incorporated lunar surface insulating blankets, heat pump system, shading, and lunar soil. Other heat management techniques, such as louvers, were examined to prevent the radiators from freezing. The impact of the geographic location of the lunar base and the orientation of the radiators was also examined. A baseline design was generated that included weight, power, and volume estimates

Measurement of spray combustion processes

A free jet configuration was chosen for measuring noncombusting spray fields and hydrocarbon-air spray flames in an effort to develop computational models of the dynamic interaction between droplets and the gas phase and to verify and refine numerical models of the entire spray combustion process. The development of a spray combustion facility is described including techniques for laser measurements in spray combustion environments and methods for data acquisition, processing, displaying, and interpretation