A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times.     

Ar-Broadening of isotropic Raman lines in the ν2 band of acetylene

Using a high resolution Raman spectrometer, we have measured Ar-broadening coefficients in the ν₂Q branch of C₂H₂ for 22 lines at 295 K, 20 lines at 174 K, and 16 lines at 134 K. These lines with J values ranging from 1 to 23 are located in the spectral range 1970.9-1974.3 cm⁻¹. The collisional widths are obtained by fitting each spectral line with a Rautian profile. The resulting broadening coefficients are compared with theoretical values arising from close coupling and coupled states calculations. A satisfactory agreement is obtained at room as well as at low temperatures, especially for odd J lines. By comparing broadening coefficients at 295, 174, and 134 K from a simple power law, the temperature dependence of these broadenings has been determined both experimentally, and theoretically.     

Rotational spectra, conformational structures, and dipole moments of thiodiglycol by jet-cooled FTMW and ab initio calculations

The rotational spectra of three low-energy conformers of thiodiglycol (TDG) (HOCH₂CH₂SCH₂CH₂OH) have been measured in a molecular beam using a pulsed-nozzle Fourier-transform microwave spectrometer. To determine the likely conformational structures with ab initio approach, conformational structures of 2-(ethylthio)ethanol (HOEES) (CH₃CH₂SCH₂CH₂OH) were used as starting points together with the consideration of possible intramolecular hydrogen bonding in TDG. Three lower-energy conformers have been found for TDG at the MP2=Full/6311G** level and ab initio results agree nicely with experimentally determined rotational constants. In addition, Stark measurements were performed for two of the three conformers for dipole moment determinations, adding to our confidence of the conformational structure matches between experimental observations and ab initio calculations. Of the three lower-energy conformers, one displays a compact folded-like structure with strong hydrogen bonding between the two hydroxyl groups and the central sulfide atom. Two other conformers have relatively open chain-like structures with hydrogen bonding between each of the hydroxyl groups to the central sulfur atom, of which one has pure b-type dipole moment according to the ab initio results.     

FTIR measurements of CO2 line positions and intensities at high temperature in the 3700-3750 cm spectral region

Positions and intensities for 453 spectral lines in 12 rovibrational bands of ¹²C¹⁶O₂ have been determined between 3700 and 3750 cm⁻¹. At three temperatures (294, 500, and 698 K) eight spectra have been recorded at a pressure around 5 mbar and for an absorption path of about 190 cm⁻¹ using a Bomen DA3 Fourier transform spectrometer (4 × 10⁻³ cm⁻¹ resolution). Some of the measured positions and intensities can be compared with recent experimental results that validate the experimental set-up and the data analysis procedure. The results are also compared with the values listed in the HITRAN 2000 database. If the agreement is generally good, discrepancies are observed for three hot bands.     

Zero Tension Kardar-Parisi-Zhang Equation in (d + 1)–Dimensions

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension d + 1-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height's PDF of zero tension KPZ equation shows lack of positivity after a finite time t _c . The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale t _c and the singularity time scale t _c.v→0 of the KPZ equation with an infinitesimal surface tension is investigated.     

Linearized Stability of Charged Thin-Shell Wormholes

The linearized stability of charged thin shell wormholes under spherically symmetric perturbations is analyzed. It is shown that the presence of a large value of charge provides stabilization to the system, in the sense that the constraints onto the equation of state are less severe than for non-charged wormholes.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

Optical limiters and diffraction elements based on a COANP-fullerene system: Nonlinear optical properties and quantum-chemical simulation

The results of optical study and quantum-chemical simulation of a conjugated organic system, 2-cyclooctylamino-5-nitropyridine (COANP)-fullerene, performed to determine its potential for application as a limiter of visible and near-IR laser radiation and as a material for diffraction elements in systems for reversible recording of optical information, are presented. Complexation between a COANP molecule and fullerene is considered as one of the main mechanisms responsible for the corresponding properties of this system. For the first time, nonlinear optical characteristics of COANP-C₆₀ and COANP-C₇₀ systems are comparatively studied and the intermolecular interaction between a COANP molecule and fullerene is analyzed on the quantum-chemical level.     

Symmetry of internal dynamics of the tetrahydrofuran molecule

A noninvariant geometrical group characterizing the internal dynamics of the tetrahydrofuran molecule C₄H₈O with allowance for the clearly pronounced pseudorotation effect is constructed. On this basis, some qualitative features of the energy spectrum of the molecule following from the analysis of high-resolution spectroscopic data are explained.