Exploiting planarity in separation routines for the symmetric traveling salesman problem

At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut. The success of branch-and-cut is due in large part to the availability of effective separation procedures; that is, routines for identifying violated linear constraints.

For two particular classes of constraints, known as comb and domino-parity constraints, it has been shown that separation becomes easier when the underlying graph is planar. We continue this line of research by showing how to exploit planarity in the separation of three other classes of constraints: subtour elimination, 2-matching and simple domino-parity constraints.     

Submillimeter-wave and far-infrared spectroscopy of high-J transitions of the ground and ν2 = 1 states of ammonia

Complete and reliable knowledge of the ammonia spectrum is needed to enable the analysis and interpretation of astrophysical and planetary observations. Ammonia has been observed in the interstellar medium up to J=18 and more highly excited transitions are expected to appear in hot exoplanets and brown dwarfs. As a result, there is considerable interest in observing and assigning the high J (rovibrational) spectrum. In this work, numerous spectroscopic techniques were employed to study its high J transitions in the ground and ν(2)=1 states. Measurements were carried out using a frequency multiplied submillimeter spectrometer at Jet Propulsion Laboratory (JPL), a tunable far-infrared spectrometer at University of Toyama, and a high-resolution Bruker IFS 125 Fourier transform spectrometer (FTS) at Synchrotron SOLEIL. Highly excited ammonia was created with a radiofrequency discharge and a dc discharge, which allowed assignments of transitions with J up to 35. One hundred and seventy seven ground state and ν(2)=1 inversion transitions were observed with microwave accuracy in the 0.3-4.7 THz region. Of these, 125 were observed for the first time, including 26 ΔK=3 transitions. Over 2000 far-infrared transitions were assigned to the ground state and ν(2)=1 inversion bands as well as the ν(2) fundamental band. Of these, 1912 were assigned using the FTS data for the first time, including 222 ΔK=3 transitions. The accuracy of these measurements has been estimated to be 0.0003-0.0006?cm(-1). A reduced root mean square error of 0.9 was obtained for a global fit of the ground and ν(2)=1 states, which includes the lines assigned in this work and all previously available microwave, terahertz, far-infrared, and mid-infrared data. The new measurements and predictions reported here will support the analyses of astronomical observations by high-resolution spectroscopy telescopes such as Herschel, SOFIA, and ALMA. The comprehensive experimental rovibrational energy levels reported here will permit further refinement of the potential energy surface to improve ammonia ab initio calculations and facilitate assignment of new high-resolution spectra of hot ammonia.     

Precision mass measurements of neutron halo nuclei using the TITAN Penning trap

Precise atomic mass determinations play a key role in various fields of physics, including nuclear physics, testing of fundamental symmetries and constants and atomic physics. Recently, the TITAN Penning trap measured the masses of several neutron halos. These exotic systems have an extended, diluted, matter distribution that can be modelled by considering a nuclear core surrounded by a halo formed by one or more of loosely bound neutrons. Combined with laser spectroscopy measurements of isotopic shifts precise masses can be used to obtain reliable charge radii and two-neutron-seperation energies for these halo nuclei. It is shown that these results can be used as stringent tests of nuclear models and potentials providing an important metric for our understanding of the interactions in all nuclei.     

Collinear laser spectroscopy with reverse-extracted bunched beams at TRIUMF

Collinear laser spectroscopy with reverse-extracted cooled bunched beams was performed at TRIUMF with radioactive ion beams. Surface-ionized ^78,78mRb ions were injected into TITAN??s cooler-buncher, and reverse-extracted to the laser beam line. There they were neutralised and excited with a counter-propagating laser beam. The fluorescence signal from the D ₂ line was recorded with a photomultiplier tube. The cooler provided typically 50 ion bunches per second, with each bunch containing approximately 10⁵ ions, temporally distributed with a 1.6 ??s width. A hardware gate was set on the signal, suppressing the background by four orders of magnitude.     

On Spectral Hypergraph Theory of the Adjacency Tensor

We study both H and E/Z-eigenvalues of the adjacency tensor of a uniform multi-hypergraph and give conditions for which the largest positive H or Z-eigenvalue corresponds to a strictly positive eigenvector. We also investigate when the E-spectrum of the adjacency tensor is symmetric.     

Improving the energies of approximate wave functions using the concepts of density functional theory

A simple method, derived from DFT, for improving the energy of a trial density is modified for the case of atoms. It is assumed that errors in the interelectronic repulsion are the only significant ones. The errors in the energies of single‐ζ Slater orbitals for the atoms from He to Ne are reduced an average factor of 21. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Measurements of NH3 in the ν2 = 1 state by a solid-state, photomixing, THz spectrometer, and a simultaneous analysis of the microwave, terahertz, and infrared transitions between the ground and ν2 inversion-rotation levels

In this paper, we report 30 THz measurements of ammonia in its excited, ν₂ = 1, inversion state. These measurements include transition frequencies and pressure shifts (where significant enough to be observed). Included in the data are two forbidden and three ro-inversion transitions, as well as 18 transitions never directly measured before. The measurements were made with an all-solid-state, diode-laser, difference-frequency spectrometer. Using an innovative laser-frequency locking scheme, this spectrometer provided accurately determined and continuously tuned THz-frequencies without requiring accurate knowledge of the absolute laser frequencies. The details of the spectrometer’s frequency calibration is discussed. A global analysis of NH₃ based on the available ground state, ν₂ = 1 state, and ν₂-band transitions was carried out, and the resulting set of recommended molecular effective-Hamiltonian parameters for ammonia is presented. In addition, calculated center frequencies and intensities for all possible transitions up to J = 20 between rotation, inversion, and vibration levels in the ground and ν₂ = 1 states are included as supplementary material.     

On the Fermi functionsI −(n+1/2)

We point out that an integral representation is possible for the Fermi functionsI _?3/2,I _?5/2,I _?7/2,I _?9/2, andI _?11/2 that arise in the extended Thomas-Fermi theory of hot, non-relativistic fermion systems. These functions can thus be computed by straightforward numerical integration, thereby avoiding problems previously encountered.