Non-Weyl Resonance Asymptotics for Quantum Graphs

We consider the resonances of a quantum graph $\mathcal G$ that consists of a compact part with one or more infinite leads attached to it. We discuss the leading term of the asymptotics of the number of resonances of $\mathcal G$ in a disc of a large radius. We call $\mathcal G$ a \emph{Weyl graph} if the coefficient in front of this leading term coincides with the volume of the compact part of $\mathcal G$. We give an explicit topological criterion for a graph to be Weyl. In the final section we analyze a particular example in some detail to explain how the transition from the Weyl to the non-Weyl case occurs.Comment: 29 pages, 2 figure

Excitation Spectra of Spin Models constructed from Quantized Affine Algebras of type Bn(1)B_n^{(1)}, Dn(1)D_n^{(1)}

The energy and momentum spectrum of the spin models constructed from the vector representation of the quantized affine algebras of type \B and \D are computed using the approach of Davies et al. \cite{DFJMN92}. The results are for the anti-ferromagnetic (massive) regime, and they agree with the mass spectrum found from the factorized S--matrix theory by Ogievetsky et al. \cite{ORW87}. The other new result is the explicit realization of the fusion construction for the quantized affine algebras of type \B and \D.}Comment: Plain TeX --- 178k including 3 eps files. 1. For correct cross-references, run twice (as with LaTeX). 2. The FIGURES for this paper are at the end of this file. They must split off and saved with names fig1.eps, fig2.eps, fig3.eps The standard macros package epsf.tex is also require

Discrete Nodal Domain Theorems

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem

The acrocallosal syndrome: A case report and literature survey

Acrocallosal syndrome (ACS) is a rare, genetically transmitted disorder characterized by facial deformities. These include a large forehead, large anterior fontanelle, broad nasal bridge with increased intercanthal distance, partial or complete agenesis of the corpus callosum, polysyndactyly, polydactyly, and mental retardation. Limited information concerning the dental development and treatment has been published. In addition to the classic facial deformities aforementioned, the other most commonly reported oral findings are: short philtrum/upper lip (30%); high-arched palate (30%); cleft lip/palate (20%); micro/retrognathia (13%); open mouth (15%); thin lips (11%); and 1 report of over-retained primary teeth. Seizure disorders are also a common finding due to the neuroanatomical deformities associated with this disorder. The purpose of this report was to describe the case of a 7-year-old male child with acrocallosal syndrome who presented with a cleft lip and palate, hydrocephalus, a seizure disorder, and delayed exfoliation of his primary dentition and was observed for 4 years. A review is conducted to present the pertinent medical literature concerning the oral findings associated with ACS. Dental management of this case and possible contributing factors of delayed exfoliation/permanent tooth eruption are also discussed

Robotic Surgery – A Personal View of the Past, Present and Future

Research into robotic surgery has been undertaken for over 25 years. In that period a small number of companies have been formed to exploit this research and have undertaken clinical trials on patients. However, far fewer clinical applications have been undertaken than would have been expected from the level of research activity. This paper puts forward a number of reasons for this, many of which are not to do with the technology but are a consequence of the clinical and business environments. Recommendations are provided that will hopefully increase the number of clinical systems being applied. Some predictions are made for the future which should increase the number of commercial systems and thus achieve patient benefits

The B(s)→D(s)lνB_{(s)} \to D_{(s)}l\nu Decay with Highly Improved Staggered Quarks and NRQCD

We report on progress of a lattice QCD calculation of the $B\to Dl\nu$ and $B_s\to D_s l\nu$ semileptonic form factors. We use a relativistic staggered action (HISQ) for light and charm quarks, and an improved non-relativistic (NRQCD) action for bottom, on the second generation MILC ensembles.Comment: Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory at Granada, Spain (18-24 June 2017