Degrees of Propositionality in Construals of Time Quantities1

The paper investigates the possible conceptual bases of differences between seemingly synonymous and easily definable temporal expressions. Looking at the usage patterns of nominal temporal phrases in reference corpora of English and Polish we attempt to relate these subtleties to the different granularity of the cognitive scales on which construals of time quantities in general are based. More specifically, we focus on a subset of nominal temporal expressions which adhere to the “number + time unit” pattern, matching what Haspelmath (1997: 26) describes as “culture-bound artificial time units”. Using the British National Corpus (BNC) and the National Corpus of Polish (NCP), we first analyse both the variation and the regularity found in naturally-occurring samples of Polish and English. Finally, we compare the patterns of use emerging from the two corpora and arrive at cross-linguistic generalisations about the conceptualisation of time quantities

Dirac Equation with External Potential and Initial Data on Cauchy Surfaces

With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindel\"of argument this evolution map is generalized to the Dirac evolution including the external potential. For the latter we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide another proof of the well-known existence and uniqueness of classical solutions and their causal structure

Ultraviolet Properties of the Spinless, One-Particle Yukawa Model

We consider the one-particle sector of the spinless Yukawa model, which describes the interaction of a nucleon with a real field of scalar massive bosons (neutral mesons). The nucleon as well as the mesons have relativistic dispersion relations. In this model we study the dependence of the nucleon mass shell on the ultraviolet cut-off $\Lambda$. For any finite ultraviolet cut-off the nucleon one-particle states are constructed in a bounded region of the energy-momentum space. We identify the dependence of the ground state energy on $\Lambda$ and the coupling constant. More importantly, we show that the model considered here becomes essentially trivial in the limit $\Lambda\to\infty$ regardless of any (nucleon) mass and self-energy renormalization. Our results hold in the small coupling regime.Comment: 30 pages, typos corrected, references extende

Recent progress in VSTOL technology

Progress in vertical and short takeoff and landing (V/STOL) aircraft technology, in particular, during the 1970 to 1980 period at Ames Research Center is discussed. Although only two kinds of V/STOL aircraft (the helicopter and the British direct lift Harrier) have achieved operational maturity, understanding of the technology has vastly improved during this 10 year period. To pursue an aggressive R and D program at a reasonable cost, it was decided to conduct extensive large scale testing in wind tunnel and flight simulation facilities, to develop low cost research aircraft using modified airframes or engines, and to involve other agencies and industry contractors in joint technical and funding arrangements. The STOL investigations include exploring STOL performance using the rotating cylinder flap concept, the augmentor wing, upon initiation of the Quiet Short Haul Research Aircraft program, the upper surface blown flap concept. The VTOL investigations were conducted using a tilt rotor aircraft, resulting in the XV-15 tilt rotor research aircraft. Direct jet lift is now being considered for application to future supersonic fighter aircraft