Rare K-Decays as Crucial Tests for Unified Models with Gauged Baryon Number:

In the grand-unified models based on SU(15) and SU(16) in which the quarks and leptons are un-unified at the intermediate stages, we show that ${\rm BR}\; (K_L \to \mu e) \leq 10^{-14}$ and ${\rm BR}\; (K^+ \to \pi^+\mu e) \leq 10^{-14}$ despite the presence of leptoquark gauge bosons. Thus, the observation of these processes in the ongoing or upcoming experiments will rule out the models.Comment: (7 pages, LATEX, including figures drawn by LATEX) DOE-ER40200-304 CPP-5

Regularity of operators on essential extensions of the compacts

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of compacts by unital or abelian C^*-algebras, semiregularity leads to regularity. Two examples coming from quantum groups are discussed.Comment: LaTeX2e, 13 pages, no figures, to appear in the Proceedings of the AM

Minimum multicuts and Steiner forests for Okamura-Seymour graphs

We study the problem of finding minimum multicuts for an undirected planar graph, where all the terminal vertices are on the boundary of the outer face. This is known as an Okamura-Seymour instance. We show that for such an instance, the minimum multicut problem can be reduced to the minimum-cost Steiner forest problem on a suitably defined dual graph. The minimum-cost Steiner forest problem has a 2-approximation algorithm. Hence, the minimum multicut problem has a 2-approximation algorithm for an Okamura-Seymour instance.Comment: 6 pages, 1 figur

Canonical decomposition of operators associated with the symmetrized polydisc

A tuple of commuting operators $(S_1,\dots,S_{n-1},P)$ for which the closed symmetrized polydisc $\Gamma_n$ is a spectral set is called a $\Gamma_n$-contraction. We show that every $\Gamma_n$-contraction admits a decomposition into a $\Gamma_n$-unitary and a completely non-unitary $\Gamma_n$-contraction. This decomposition is an analogue to the canonical decomposition of a contraction into a unitary and a completely non-unitary contraction. We also find new characterizations for the set $\Gamma_n$ and $\Gamma_n$-contractions.Comment: Complex Analysis and Operator Theory, Published online on August 28, 2017. arXiv admin note: text overlap with arXiv:1610.0093