Well-solvable special cases of the TSP : a survey

The Traveling Salesman Problem belongs to the most important and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently. We survey these special cases with emphasis on results obtained during the decade 1985-1995. This survey complements an earlier survey from 1985 compiled by Gilmore, Lawler and Shmoys. Keywords: Traveling Salesman Problem, Combinatorial optimization, Polynomial time algorithm, Computational complexity

In-medium operator product expansion for heavy-light-quark pseudoscalar mesons

The operator product expansion (OPE) for heavy-light-quark pseudoscalar mesons (D-mesons and B-mesons) in medium is determined, both for a moving meson with respect to the surrounding medium as well as for a meson at rest. First of all, the OPE is given in terms of normal-ordered operators up to mass dimension 5, and the mass of the heavy-quark and the mass of the light-quark are kept finite. The Wilson coefficients of such an expansion are infrared (IR) divergent in the limit of a vanishing light-quark mass. A consistent separation of scales necessitates an OPE in terms of non-normal-ordered operators, which implies operator mixing, where the IR-divergences are absorbed into the operators. It is shown that the Wilson coefficients of such an expansion are IR-stable, and the limit of a vanishing light-quark mass is perfomed. Details of the major steps for the calculation of the Wilson coefficients are presented. By a comparison with previous results obtained by other theoretical groups we have found serious disagreements.Comment: 51 pages, 3 figure

Photon production at c.m. energies of 200 and 900 GeV

We present data on photon production in non single-diffractive p {Mathematical expression}-collisions at c.m. energies of 200 and 900 GeV. Besides the general properties of photon production, i.e. pseudorapidity distribution and average multiplicity, we also investigate photon-charged two-particle pseudorapidity and multiplicity correlations. We find for the average number of photons in non single-diffractive p {Mathematical expression}-collisions 22.2±1.4±2.0 at 200 GeV and 41.4±2.1±3.5 at 900 GeV, where the first error is statistical and the second systematic. The analysis of photon-charged particle multiplicity correlations reveals strong positive correlations between the average number of photons and the number of simultaneously produced charged particles, as expected from FNAL and ISR studies and from our result at 546 GeV. We obtain for the correlation slope 0.95±0.08±0.11 at 200 GeV and 1.09±0.09±0.13 at 900 GeV (first error is statistical and the second systematic). The investigation of photon-charged two-particle pseudorapidity correlations shows that these correlations are of short range and compatible with the observed charged two-particle pseudorapidity correlations. These correlations and the results for the average number of photons as a function of the produced number of charged particles favour the conclusion that photon sources other than π0 s contribute significantly to the observed photon yield in non single-diffractive p {Mathematical expression}-collisions. For example, if all photons are assumed to come from π0 s and η mesons, a η/π0 ratio of about 20% is inferred. © 1989 Springer-Verlag.0SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Fluid systems in foreland fold-and-thrust belts : on overview from the Southern Pyrennees

The analysis of three different regions of the South- Pyrenean fold-and-thrust belt reveals that during the Tertiary compression the hydrological system was compartmentalised in time and space. During the early-middle Eocene, when the thrust front affected marine soft-sediments in the Ainsa basin, the thrust fault zones were dominated by formation fluids derived from Eocene marine waters trapped in the underlying Eocene marls, although influences of meteoric waters were also present. During the middle-late Eocene, when the thrust front emplaced marine rocks over continental redbeds in the eastern Catalan basin (L'Escala thrust), the thrust fault zones were dominated by meteoric fluids. These fluids flowed preferentially along these faults, draining laterally the meteoric fluids and acting as barriers hindering their flowing towards more external parts of the belt. During the Oligocene, the most external part of the fold-and-thrust belt in the eastern Catalan basin developed on top of a salt detachment horizon. The thrust front affected continental materials of late Eocene-Oligocene age. At this moment, the thrusts were conduits for meteoric fluids arriving from the surface and also for evolved meteoric fluids migrating over short distance upwards after being in contact with the underlying evaporitic beds. Most of the fractures show a similar sequence of microfractures. Microfractures of stage 1 formed when the sediment was poorly lithified. Microfractures of stage 2 represent the main episode of vein formation which developed when a progressive induration of the host sediment occurred. During microfracture stage 3, formed in an extensional regime, the host sediment was more indurated. The repetition of this sequence of microfractures in different fracture generations of the same outcrop indicates that the sediment induration was restricted to the vicinity of the vein. Away from the veins, the sediment remained poorly lithified during the entire deformation cycle. Calcite cement within the host rock precipitated later than the syn-compressive veins, when the sediment was more indurated. Elemental geochemistry and stable isotopes of the calcite veins indicates that early generation of microfractures is infilled by local fluids (either marine or meteoric), whereas external fluids (meteoric or evolved meteoric) infilled the main compressive stage of microfractures. The hot temperature of these fluids (157°C to 183°C in the Atiart-Arro example) indicates their circulation through deep parts of the thrust belt. The progressive increase of the 87Sr/86Sr ratio through time is due to the progressive uplift, exposure and erosion of the internal Pyrenean Axial Zone