New geometry-inspired relaxations and algorithms for the metric Steiner tree problem

Determining the integrality gap of the bidirected cut relaxation for the metric Steiner tree problem, and exploiting it algorithmically, is a long-standing open problem. We use geometry to define an LP whose dual is equivalent to this relaxation. This opens up the possibility of using the primal-dual schema in a geometric setting for designing an algorithm for this problem. Using this approach, we obtain a 4/3 factor algorithm and integrality gap bound for the case of quasi-bipartite graphs; the previous best integrality gap upper bound being 3/2 (Rajagopalan and Vazirani in On the bidirected cut relaxation for the metric Steiner tree problem, 1999). We also obtain a factor \({\sqrt{2}}\) strongly polynomial algorithm for this class of graphs. A key difficulty experienced by researchers in working with the bidirected cut relaxation was that any reasonable dual growth procedure produces extremely unwieldy dual solutions. A new algorithmic idea helps finesse this difficulty—that of reducing the cost of certain edges and constructing the dual in this altered instance—and this idea can be extracted into a new technique for running the primal-dual schema in the setting of approximation algorithms.     

Transport coefficients of quark-gluon plasma

Transport coefficients of quark-gluon plasma are discussed in the framework of relativistic kinetic theory with the relaxation time approximation of Boltzmann transport equation. The expressions for the coefficients of shear and volume viscosities and heat conductivity are derived assuming quark-gluon plasma to be a non-reactive mixture of quarks, anti-quarks and gluons. A lowest order in deviations from local thermal equilibrium and in plasma phase, lowest order in coupling constant are assumed. Entropy production due to irreversible processes is discussed.     

On the problem of uniqueness under pressure loading

Zusammenfassung Die Bedingung für das Auftreten einer Verzweigung bei einem beliebigen festen Körper wird allgemein für den Fall diskutiert, dass Teile der Oberfläche unter einer druckartigen Belastung stehen. Besondere Beachtung wird der Frage der Eindeutigkeit bei konventionellen plastischen Körpern geschenkt und mit Beispielen illustriert. Die Formel mit dem Tangentenmodul für das Beulen einer langen dünnwandigen Zylinderschale unter sehr flüssigem Druck wird verbessert.     

Ferromagnetic resonance studies in some polycrystalline magnesium nickel ferrites

Ferromagnetic resonance measurements were carried out on various compositions of magnesium nickel ferrites prepared by various heat treatments. Corrections were applied for polycrystalline and size effects for calculating the g factor and linewidth. The variation of these parameters has been explained on the basis of the cation distribution in these compounds as obtained from magnetization data assuming a collinear model of spin distribution.     

Asymptotic behaviour of high Gaussian minima

We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the extent to which the high level is exceeded, the conditional shape of the process above the high level, and the location of the minimum of the process given that the sample path is above a high level.     

Integrality gap of the hypergraphic relaxation of Steiner trees: A short proof of a 1.55 upper bound

Recently, Byrka, Grandoni, Rothvoß and Sanità gave a 1.39 approximation for the Steiner tree problem, using a hypergraph-based linear programming relaxation. They also upper-bounded its integrality gap by 1.55. We describe a shorter proof of the same integrality gap bound, by applying some of their techniques to a randomized loss-contracting algorithm.     

Structural Investigation of the Hormone Melatonin and Its Alkali and Alkaline Earth Metal Complexes in the Gas Phase

Gas phase infrared dissociation spectra of the radical cation, deprotonated and protonated forms of the hormone melatonin, and its complexes with alkali (Li⁺, Na⁺, and K⁺) and alkaline earth metal ions (Mg²⁺, Ca²⁺, and Sr²⁺) are measured in the spectral range 800–1800 cm^?1. Minimum energy geometries calculated at the B3LYP/LACVP++** level are used to assign structural motifs to absorption bands in the experimental spectra. The melatonin anion is deprotonated at the indole-N. The indole-C linking the amide chain is the most favored protonation site. Comparisons between the experimental and calculated spectra for alkali and alkaline earth metal ion complexes reveal that the metal ions interact similarly with the amide and methoxy oxygen atoms. The amide I band undergoes a red shift with increasing charge density of the metal ion and the amide II band shows a concomitant blue shift. Another binding motif in which the metal ions interact with the amide-O and the π-electron cloud of the aromatic group is identified but is higher in energy by at least 18 kJ/mol. Melatonin is deprotonated at the amide-N with Mg²⁺ and the metal ion coordinates to the amide-N and an indole-C or the methoxy-O. These results provide information about the intrinsic binding of metal ions to melatonin and combined with future studies on solvated melatonin-metal ion complexes may help elucidate the solvent effects on metal ion binding in solution and the biochemistry of melatonin. These results also serve as benchmarks for future theoretical studies on melatonin-metal ion interactions.

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An expedient, regioselective synthesis of novel 2-alkylamino- and 2-alkylthiothiazolo[5,4-e]- and -[4,5-g]indazoles and their anticancer potential

Several novel 2-alkylamino- and 2-alkylthiothiazolo[5,4-e]- and -[4,5-g]indazoles and their 6-alkyl and 8-alkyl derivatives have been synthesised in high overall yields starting from 5-nitro and 6-nitroindazoles in a three-step route involving the regioselective cyclisation of thioureidoindazoles and indazolyl dithiocarbamates as the key steps. Some assorted thiazoloindazoles have been screened for anticancer properties, which demonstrated the anticancer potential of at least one product, justifying its further follow-up.     

Ortho‐Trialkylstannyl Arylphosphanes by C–P and C–Sn Bond Formation in Arynes

A novel and efficient approach to ortho‐trialkylstannyl arylphosphanes by the reaction of arynes generated in situ with stannylated phosphanes (R₃Sn? PR₂) is described. Concurrent C? P and C? Sn bond formation occurs with high yields, and stannylated products are easily transformed into valuable ortho‐substituted arylphosphanes. The reaction features high efficiency, good regioselectivity, and excellent practicality.