Master integrals for massless three-loop form factors: One-loop and two-loop insertions

The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop integrals. Of these, six have the form of a bubble insertion inside a one-loop or two-loop vertex integral. We compute all master integrals with these insertion topologies.     

Functorial methods in the theory of group representations I

We introduce a candidate for the group algebra of a Hausdorff group which plays the same role as the group algebra of a finite group. It allows to define a natural bijection betweenk-continuous representations of the group in a Hilbert space and continuous representations of the group algebra. Such bijections are known, but to our knowledge only for locally compact groups. We can establish such a bijection for more general groups, namely Hausdorff groups, because we replace integration techniques by functorial methods, i.e., by using a duality functor which lives in certain categories of topological Banach balls (resp., unit balls of Saks spaces).This paper was written while the authors were supported by the Swiss National Science Foundation under grant 21-33644.92.     

New Interfaces for Coupling TLC with TOF SIMS

JPC – Journal of Planar Chromatography – Modern TLC - Two interfaces have been tested for coupling thin-layer chromatography (TLC) with time-of-flight secondary-ion mass spectrometry...     

Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

CuAl2Cl8. Darstellung und Kristallstruktur

CuAl₂Cl₈. Preparation and Crystal Structure. Crystals of CuAl₂Cl₈ have been prepared. Their remission spectrum agrees with that of gaseous CuAl₂Cl₈. The crystal structure (P2₁/c;a = 6.614, b = 7.376, c = 12.319 Å; β = 94.11°) shows a molecular lattice with Cu in square planar coordination, which is completed to a stretched octahedron (as in solid CuCl₂) by two Cl atoms from neighbour molecules. Al has tetrahedral coordination.     

Ungewöhnliche Bildung und Struktur eines O‐Sulfinato‐Zinkkomplexes

Unusual Formation and Structure of a O‐Sulfinato Zinc Complex Whereas the reaction between hydrotris[(N‐xylyl)‐thioimidazolyl]borato‐zinc perchlorate ([ L· Zn‐OClO₃]) and ethanethiolate under an inert atmosphere leads to the thiolate complex [ L· Zn‐SC₂H₅], the same reaction in air produces the sulfinato complex [ L· Zn‐O‐S(O)‐C₂H₅] ( 1 ). 1 is the first fully characterized sulfinato‐zinc complex. Its structure determination has confirmed the unusual coordination of the sulfinato ligand via one of its oxygen atoms.