A note on the illumination of convex bodies

LetKE ^d be a convex body and letl _r(K) denote the minimum number ofr-dimensional affine subspaces ofE ^d lying outsideK with which it is possible to illuminateK, where 0rd–1. We give a new proof of the theorem thatl _r(K)(d+1)/(r+1) with equality for smoothK.The work was supported by Hung. Nat. Found. for Sci . Research No. 326-0213 and 326-0113.     

Reaction-diffusion model for combustion with fuel consumption: II. Robin boundary conditions

A model, derived in a previous paper, for the reaction betweena gaseous oxidant and a solid porous fuel is analysed furtherfor general Robin boundary conditions. Numerical solutions areobtained and the effects of varying the dimensionless parameters,particularly the Frank-Kamenetskii parameter and the Lewisnumber L, are discussed in detail and compared with resultsobtained previously when Dirichlet boundary conditions are applied.Analytic solutions are obtained for the small-time developmentand for large values of . This latter solution shows the existenceof a propagating reaction-diffusion burning wave, and has featureswhich are qualitatively different to those derived earlier.     

Matching the Kerr solution on the surface of a rotating perfect fluid

We investigate the possible shapes of the surface of a rigidly rotating perfect fluid on which is matched the Kerr metric, using the Boyer (1965) surface condition. The solution, given in Figures 1 to 5, depends on three parameters, = qK, q = a/m, - (a/gwc), wherem denotes the mass of the source, a its angular momentum per unit mass, the angular velocity of rotation, andK is an integration constant appearing in Boyer's surface condition. When < 1, as in Figures 1 to 3, there are, for givenq and, two possible surfaces, of which the smaller one touches the ring-singularity at = a, z = 0. When > 1, as in Figures 4 and 5, there is only one possible surface of kidney-shaped tori, which also touch the ring singularity. In the case of a differentially rotating perfect fluid, we find a variety of possible strictly spheroidal surfaces, depending on the choice of an arbitrary integration function() of the angular velocity . If we choose() so that, at each point on the surface, is single-valued, then the resulting distribution exhibits an equatorial acceleration, similar to what is observed on the surface of the sun. This angular velocity distribution turns out to be identical with Thorne's (1971) angular velocity of cumulative dragging.     

Synthesis of polypyromellitimidoamides from dihydrazides of aromatic and aliphatic acids and pyromellitic dianhydride

Polyamido acids have been synthesized from pyromellitic dianhydride and dihydrazides of terephthalic, isophthalic, sebacic, and adipic acids. The polyamido acids obtained have been cyclized at 220° C, and it has been shown by IR spectroscopy that the polymers contain five-membered imide rings.     

Technetium-99m-diethyl-IDA instant kit: Labelling kinetics and biological properties

A formulation of stannous-diethyl-IDA freeze-dried kit, containing 50 mg diethyl-IDA and 0.4 mg hydrated stannous chloride, to be labelled with technetium has been developed for hepatobiliary scintigraphy. Gel chromatography column scanning technique has been applied for determination of technetium fractions in the preapration. The optimal pH value of the preparation with a high hepatobiliary specificity was found between 5.5 to 6.0. Effect of ligand to metal ratio on the stability of the prepared Sn-diethyl-IDA solution prior mixing with technetium has been investigated. The reaction conditions (initial pH) between the ligand and stannous ion affects the percent hydrolysis of the labelled compund, i.e. the formation rate of the complex. The organ distribution data of^99mTc-diethyl-IDA in mice for 60 minutes post injection were satisfactory. The radiopharmaceutical exhibits rapid blood clearance, great hepatic clearance and very short hepatocyte transit time. Uptake of the radiopharmaceutical in various organs of mouse at 5 minute post injection showed that the greater part of the injected radioactivity has distributed between liver and intestine. However, about 12% and 60% of the injected dose has been found in liver and intestine respectively. The renal uptake of the HB agent in mice is relatively low and decreases with time to become about 0.3% at 60 minutes post injection. Blood clearance data of the radiopharmaceutical kit in rabbits showed that the HB agent is-rapidly cleared, since the initial decrease was very fast with a half-time of 1.5 minutes.     

Discrimination ofn=2→2 UV transitions of he-like ions in a recoil light source

Neon and argon recoil ions were produced by collisions with 5.9 MeV/amu uranium projectiles andΔn=0 ultraviolet transitions from the metastable 1s2p ³ P _0,2 levels of the target ions were measured in delay to the pulsed projectile beam.