Some undecidable determined games

Computing machines using algorithms play games and even learn to play games. However, the inherent finiteness properties of algorithms impose limitations on the game playing abilities of machines. M. Rabin illustrated this limitation in 1957 by constructing a two-person win-lose game with decidable rules but no computable winning strategies. Rabin's game was of the type where two players take turns choosing integers to satisfy some decidable but very complicated winning condition. In the present paper we obtain similar theorems of this type but the winning conditions are extremely simple relations (polynomial equations). Specific examples are given.     

Angular distributions in proton-nucleus interactions in emulsion at 800 GeV

Data on angular distributions of heavily ionizing and shower particles in incoherent protonnucleus collisions in emulsion at 800 GeV are reported and discussed in details. Dependence of angular distributions on the mass number of a target nucleus and on the multiplicity of charged particles is investigated. The data presented are systematically compared with results of emulsion experiments at lower energies and with predictions of the Lund Monte Carlo model FRITIOF.     

Regular orientable imbeddings of complete graphs

This paper classifies the regular imbeddings of the complete graphs K_n in orientable surfaces. Biggs showed that these exist if and only if n is a prime power p^e, his examples being Cayley maps based on the finite field F = GF(n). We show that these are the only examples, and that there are $\text{φ(n ? 1)}\text{e}$ isomorphism classes of such maps (where φ is Euler's function), each corresponding to a conjugacy class of primitive elements of F, or equivalently to an irreducible factor of the cyclotomic polynomial Φ_{n ? 1}(z) over GF(p). We show that these maps are all equivalent under Wilson's map-operations H_i, and we determined for which n they are reflexible or self-dual.     

Ignition temperatures of carbon samples containing metal oxide catalysts by a DTA method

The variation of the ignition temperature of a carbon black impregnated with various amounts of manganese oxide and uranium oxide has been measured by a DTA method. The technique allows a rapid assessment to be made of sample reactivity and only small amounts (approximately 5 mg) are required. Correlation of sample reactivity by ignition temperature measurement and isothermal weight-loss data is shown.