A k-L(2, 1)-labelling of a graph G is a mapping f : V (G) → {0, 1, 2, . . . , k} such that |f(u)− f(v)| ≥ 2 if uv ∈ E(G) and f(u) 6= f(v) if u, v are distance two apart. The smallest positive integer k such that G admits a k-L(2, 1)-labelling is called the λ-number of G. In this paper we study this quantity for cubic Cayley graphs (other than the prism graphs) on dihedral groups, which are call...

This work is a sequel of [6]. In algebraic geometry, when discussing the compactification of the moduli space of complex manifoldX with ample canonical bundle KX , it is necessary to consider holomorphic degeneration family π : X → B, where Xt = π (t) are smooth except for t = 0, such that the canonical bundle of Xt for t 6= 0 and the dualizing sheaf of X0 are ample. We will call such degenerat...

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a U (1) × U (1) group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, t...

We classify orbifolds obtained by taking the quotient of a three torus by Abelian extensions of Z/n×Z/n automorphisms, where each torus has a multiplicative Z/n action (n ∈ {3, 4, 6}). This ’completes’ the classification of orbifolds of the above type initiated by Donagi and Faraggi ([4]) and, Donagi and Wendland ([5]).

Critical values of Wilson lines and general background fields for toroidal compactifications of heterotic string theories are constructed systematically using Dynkin diagrams. This work is part of a Ph.D. thesis in preparation at the science faculty of the university of Münster.

The doubly circular relations of the major and minor keys based on all twelve pitchclasses can be depicted in toroidal models. We demonstrate a convergence of derivations from the different bases of conventional harmonic theory and recent experiments in music psychology. We present a formalization of the music-theoretical derivation from Gottfried Weber’s 1817 chart of tone-centers by using a t...

It is well known that if n is even, the addition table for the integersmodulo n (whichwe denote by Bn) possesses no transversals.We show that ifn is odd, then the number of transversals in Bn is at least exponential in n. Equivalently, for odd n, the number of diagonally cyclic latin squares of order n, the number of completemappings or orthomorphisms of the cyclic group of order n, the number ...

Toroidal or cylindrical holographic gratings may be aplanetic at one wavelength in the XUV. Imaging of expanding plasmas may then be used for optical diagnostics of hot plasmas.

Using mostly elementary considerations, we find out who wins the game of Domineering on all rectangular boards of width 2, 3, 5, and 7. We obtain bounds on other boards as well, and prove the existence of polynomial-time strategies for playing on all boards of width 2, 3, 4, 5, 7, 9, and 11. We also comment briefly on toroidal and cylindrical boards.