Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations

Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H$_3^+=\{$p$^+,$p$^+,$p$^+,$e$^-,$e$^-\}$ molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result for this molecular ion with rovibrational results including non-adiabatic corrections.Comment: 29 pages, 3 figures, 4 table

USING A ROBUST LAYERED PARSER TO ANALYSE TECHNICAL MANUAL TEXT

This article describes an experiment an which a robust parser developed by the author was used to analyse a sample of sentences taken from a software instruction manual. The parser scans the text repeatedly analysing different constructs each time. The article describes the rationale behind the work, the parsing algorithm, the development of a grammar, the preparation of the evaluation materials and the method of evaluation. The results show that a good level of performance can be attained by tailoring the grammar to the domain.En este artículo se describe un experimento en el que se utilizó un analizador sintáctico robusto, desarrollado por el propio autor, para analizar una serie de oraciones extraídas de un manual de instrucciones de un programa informático. El analizador escanea el texto de forma repetida, generando cada vez estructuras sintácticas diferentes. A su vez, se detallan el algoritmo de análisis sintáctico, la implementación de la gramática. La preparación y selección de materiales y el método de evaluación. Los resultados apuntan a que el rendimiento del analizador puede optimizarse adaptando la gramática a los diversos dominios lingüísticos

Group Theoretical Properties and Band Structure of the Lame Hamiltonian

We study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits.Comment: 21 pages Revtex + 6 eps + 2 jpg figure

TOOLympics 2019: An Overview of Competitions in Formal Methods

Evaluation of scientific contributions can be done in many different ways. For the various research communities working on the verification of systems (software, hardware, or the underlying involved mechanisms), it is important to bring together the community and to compare the state of the art, in order to identify progress of and new challenges in the research area. Competitions are a suitable way to do that. The first verification competition was created in 1992 (SAT competition), shortly followed by the CASC competition in 1996. Since the year 2000, the number of dedicated verification competitions is steadily increasing. Many of these events now happen regularly, gathering researchers that would like to understand how well their research prototypes work in practice. Scientific results have to be reproducible, and powerful computers are becoming cheaper and cheaper, thus, these competitions are becoming an important means for advancing research in verification technology. TOOLympics 2019 is an event to celebrate the achievements of the various competitions, and to understand their commonalities and differences. This volume is dedicated to the presentation of the 16 competitions that joined TOOLympics as part of the celebration of the 25th anniversary of the TACAS conference

Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit

Emergent Chiral Symmetry: Parity and Time Reversal Doubles

There are numerous examples of approximately degenerate states of opposite parity in molecular physics. Theory indicates that these doubles can occur in molecules that are reflection-asymmetric. Such parity doubles occur in nuclear physics as well, among nuclei with odd A $\sim$ 219-229. We have also suggested elsewhere that such doubles occur in particle physics for baryons made up of `cbu' and `cbd' quarks. In this article, we discuss the theoretical foundations of these doubles in detail, demonstrating their emergence as a surprisingly subtle consequence of the Born-Oppenheimer approximation, and emphasizing their bundle-theoretic and topological underpinnings. Starting with certain ``low energy'' effective theories in which classical symmetries like parity and time reversal are anomalously broken on quantization, we show how these symmetries can be restored by judicious inclusion of ``high-energy'' degrees of freedom. This mechanism of restoring the symmetry naturally leads to the aforementioned doublet structure. A novel by-product of this mechanism is the emergence of an approximate symmetry (corresponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian. We also discuss the implications of this mechanism for Skyrmion physics, monopoles, anomalies and quantum gravity.Comment: 32 pages, latex. minor changes in presentation and reference

Pharmacokinetics, pharmacological and anti-tumour effects of the specific anti-oestrogen ICI 182780 in women with advanced breast cancer.

We have assessed the pharmacokinetics, pharmacological and anti-tumour effects of the specific steroidal anti-oestrogen ICI 182780 in 19 patients with advanced breast cancer resistant to tamoxifen. The agent was administered as a monthly depot intramuscular injection. Peak levels of ICI 182780 occurred a median of 8-9 days after dosing and then declined but were above the projected therapeutic threshold at day 28. Cmax during the first month was 10.5 ng/ml-1 and during the sixth month was 12.6 ng ml-1. The AUCs were 140.5 and 206.8 ng day ml-1 on the first and sixth month of dosing respectively, suggesting some drug accumulation. Luteinising hormone (LH) and follicle-stimulating hormone (FSH) levels rose after withdrawal of tamoxifen and then plateaued, suggesting no effect of ICI 182780 on the pituitary-hypothalamic axis. There were no significant changes in serum levels of prolactin, sex hormone-binding globulin (SHBG) or lipids. Side-effects were infrequent. Hot-flushes and sweats were not induced and there was no apparent effect of treatment upon the endometrium or vagina. Thirteen (69%) patients responded (seven had partial responses and six showed "no change' responses) to ICI 182780, after progression on tamoxifen, for a median duration of 25 months. Thus ICI 182780, given by monthly depot injection, and at the drug levels described, is an active second-line anti-oestrogen without apparent negative effects on the liver, brain or genital tract and warrants further evaluation in patients with advanced breast cancer

Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure