Partizan octal games: Partizan subtraction games

A subtraction gameS=(s ₁, ...,s _k)is a two-player game played with a pile of tokens where each player at his turn removes a number ofm of tokens providedmεS. The player first unable to move loses, his opponent wins. This impartial game becomes partizan if, instead of one setS, two finite setsS _L andS _R are given: Left removes tokens as specified byS _L, right according toS _R. We say thatS _L dominatesS _R if for all sufficiently large piles Left wins both as first and as second player. We exhibit a curious property of dominance and provide two subclasses of games in which a dominance relation prevails. We further prove that all partizan subtraction games areperiodic, and investigatepure periodicity.     

Search for direct photons from S-Au collisions at 200 GeV/nucleon

The CERES experiment has measured inclusive photon production in S-Au collisions of 200 GeV/nucleon at the CERN SPS. No evidence for direct emission of photons was found. For the kinematic region 2.1<y<2.65 and 0.4 GeV/c<p??<2.0 GeV/c the yield andp??-dependence of the observed photons are well reproduced by hadron decays. Furthermore, their production rate is found to be proportional to the charged particle density. The systematic errors comparing the measured and expected photon yield result in an upper limit of 14% for the emission of direct photons in central S-Au collisions. For a photon source with a yield depending quadratically on the charged particle density the limit can be reduced to 7%.     

Zusatz zu vorstehendem Aufsatz Herrn v. Neumanns

Ohne Zusammenfassung     

Theory of annihilation games—I

Place tokens on distinct vertices of an arbitrary finite digraph with n vertices which may contain cycles or loops. Each of two players alternately selects a token and moves it from its present position u to a neighboring vertex v along a directed edge which may be a loop. If v is occupied, and u ≠ v, both tokens get annihilated and phase out of the game. The player first unable to move is the loser, the other the winner. If there is no last move, the outcome is declared a draw. An O(n⁶) algorithm for computing the previous-player-winning, next-player-winning and draw positions of the game is given. Furthermore, an algorithm is given for computing a best strategy in O(n⁶) steps and winning—starting from a next-player-winning position—in O(n⁵) moves.     

The uniqueness of a family of steady vortex rings

Communicated by K. Kirchgässner     

Compound transfer and direct transfer reactions induced by 17O on 13C

The elastic scattering, inelastic scattering, single-neutron transfer reactions ¹³C(¹⁷O, ¹⁶O) ¹⁴C, ¹³C(¹⁷O, ¹⁸O)¹²C and ¹³C(¹⁷O, ¹⁸O_{2+, 1.98})¹²C, and seven other exit channels which involve ⁷Li, ⁹Be, ¹¹B and ¹⁵N have been measured for the system ¹⁷O+¹³C at 12.9 and 14 MeV c.m. It is shown that all reactions mentioned above have significant contributions from compound nuclear decay, following fusion of projectile and target.