Neue Aromadendran-Derivate aus Tolu-Balsam

New Aromadendrane Derivatives from Tolu Balsam Five new aromadendrane derivatives were isolated from tolu balsam by HPLC and their structures elucidated by NMR spectroscopy.     

Non-standard gauge-boson self-interactions within a gauge invariant model

We examine dimension-six extensions of the standard electroweak Lagrangian which are invariant under localSU(2) _L ×U(1) _Y -transformations. The dimensionfour trilinear and quadrilinear effective interactions of the vector bosons with one another are found to coincide with the vector boson interactions previously derived from globalSU(2) weak isospin symmetry broken by electromagnetism. Supplementing the model by a well-known dimension-six single-parameter quadrupole interaction leads to the most general vector boson self-couplings that can be obtained by addition of dimension-six terms to the standard Lagrangian. We examine in some detail anotherSU(2) _L ×U(1) _Y -symmetric interaction which containsW ₃ B mixing and modifies both vector boson self-couplings and fermionic interactions. Independently of being strongly constrained by the LEP 1 data, the addition of this interaction to the above-mentioned non-standard ones does not change the form of the trilinear and quadrilinear non-standard self-couplings of the vector bosons. Therefore, while being interesting in itself with respect to LEP 1 physics, this term is irrelevant with respect to the phenomenology of the vector-boson self-interactions.     

Weighted domination in triangle-free graphs

A weighted graph (G,w) is a graph G together with a positive weight-function on its vertex set w : V(G)→R^>0. The weighted domination number γ_w(G) of (G,w) is the minimum weight w(D)=∑_vDw(v) of a set DV(G) such that every vertex xV(D)−D has a neighbor in D. If ∑_vV(G)w(v)=|V(G)|, then we speak of a normed weighted graph. Recently, we proved that

for normed weighted bipartite graphs (G,w) of order n such that neither G nor the complement has isolated vertices. In this paper we will extend these Nordhaus–Gaddum-type results to triangle-free graphs.