Superspace gauge theories with central charges

The superspace constraints leading to off-shell formulations of extended supersymmetric Yang-Mills theories for N = 2 and 4 are generalised to N = 6 in the abelian case. This leads to an on-shell representation of linearized N = 6 supergravity.     

On positional games

Let {A_i} be a family of sets and let S = ∩_iA_i. By a positional game we shall mean a game played by two players on {A_i}. The players alternately pick elements of S and that player wins who fist has all the elements of one of the A_i. This paper deals with almost disjoint hypergraphs only, i.e., |A_i∪A_j| ? 1 if i ≠ j. Let $\text{M}{}^1\text{(n)}$ be the smallest integer for which there is an almost disjoint n-uniform hypergraph $\text{|T| = M}{}^1\text{(n)}$, so that the first player has a winning strategy. It is shown that $\text{lim}{}_{\mathrm{n}}\text{[M}{}^1\text{(n)]}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{= 4}$, which was conjectured by Erdös. The same method is applied to prove a conjecture of Hales and Jewett on r-dimensional tick-tack-toe if r is large enough. Finally we prove that for an arbitrary almost disjoint n-uniform hypergraph the second player has such a strategy that the first player unable to win in his mth move if m < (2 ? ?)ⁿ.     

Carbonylierung von bis(triphenylphosphin)-platin(II)- und -palladium(II)-komplexen in gegenwart von aminen und α-aminosäureestern

The crystal structure of (C₅H₅)₃Pr·CNC₆H₁₁ was determined from single-crystal X-ray diffraction data. The monoclinic unit cell of dimensions a = 8.298(3), b = 21.66(1), c = 11.943(4) Å, and β = 104.98(3)° contains four molecules in general positions of space group P2₁/c. Each molecule is composed of three C₅H₅ rings in a nearly exact trigonal array, η⁵-bonded to the Pr atom at a distance of 2.53 Å to the centroid of each ring, plus a single CNC₆H₁₁ adduct attached to the Pr atom along the trigonal axis at 2.65 Å. The presence of a CN triple bond in the isonitrile moiety and the nearly linear CNC configuration add credence to the previous proposal that there is a pure donor bond from the isonitrile carbon to the metal atom.