Approximation Algorithms for Steiner and Directed Multicuts

In this paper we consider theSteiner multicutproblem. This is a generalization of the minimum multicut problem where instead of separating nodepairs, the goal is to find a minimum weight set of edges that separates all givensetsof nodes. A set is considered separated if it is not contained in a single connected component. We show anO(log³(kt)) approximation algorithm for the Steiner multicut problem, wherekis the number of sets andtis the maximum cardinality of a set. This improves theO(t log k) bound that easily follows from the previously known multicut results. We also consider an extension of multicuts to directed case, namely the problem of finding a minimum-weight set of edges whose removal ensures that none of the strongly connected components includes one of the prespecifiedknode pairs. In this paper we describe anO(log² k) approximation algorithm for this directed multicut problem. Ifk ? n, this represents an improvement over theO(log n log log n) approximation algorithm that is implied by the technique of Seymour.     

Absolute configuration of crotsparine,crotsparinine and sparsiflorine

Absolute configurations of crotsparine, crotsparinine and sparsiflorine have been determined.     

Adler-Bardeen theorem in path integral formulation

The higher order contributions to Jacobian in Fujikawa’s path integral framework is considered and the form of anomaly equation in higher orders is established. An argument for the Adler-Bardeen theorem in this formulation is given.     

A novel synthesis of 1-aryl tetrazoles promoted by employing the synergy of the combined use of DMSO and an ionic liquid as the solvent system at ambient temperature

The synergy of the combined use of DMSO and an ionic liquid viz. (bbim)⁺Br⁻ has brought about a mild, convenient, efficient, and rapid protocol for the synthesis of 1-substituted-1H-1,2,3,4-tetrazoles via the condensation of amines, triethyl orthoformate, and sodium azide at ambient temperature in excellent isolated yields (85-90%). The inherent Bronsted acidity of ionic liquid and high polarity of both IL and DMSO resulted in a significant enhancement in the reaction rate.     

A new multi-objective genetic algorithm applied to hot-rolling process

A new genetic algorithms based multi-objective optimization algorithm (NMGA) has been developed during study. It works on a neighborhood concept in the functional space, utilizes the ideas on weak dominance and ranking and uses its own procedures for population sizing. The algorithm was successfully tested with some standard test functions, and when applied to a real-life data of the hot-rolling campaign of an integrated steel plant, it outperformed another recently developed multi-objective evolutionary algorithm.     

Comparison of hydrophobicity studies of silica aerogels using contact angle measurements with water drop method and adsorbed water content measurements made by Karl Fischer’s titration method

Hydrophobic silica aerogels possesses potential applications as insulating materials for refrigerators, furnaces and thermos flasks. In such applications, aerogel materials may get exposed for longer time to atmosphere and the adsorbed water content from surroundings may deteriorate its properties. Therefore, hydrophobicity of the arogels becomes crucial parameter and needs to be evaluated critically. In the present works, silica alcogels were prepared using the mixture of tetramethoxysilane and methyltrimethoxysilane (MTMS) as precursor chemicals for silica. The concentration of MTMS, which is used as hydrophobic reagent, in the said mixture of silicon alkoxide was varied between 0 and 100% in steps of 25%. After gelation, the alcogels were dried supercritically by solvent extraction method. Resulted aerogels were exposed to relative humidity of 90% for a period of one month which were then characterized to assess hydrophobicity by the contact angle using water drop method and adsorbed water content measurements by Karl Fischer’s Titration method. Observed contact angle and water content measurements were compared and the results are reported in the present research paper.     

Water-soluble aminocalix[4]arene receptors with hydrophobic and hydrophilic mouths

We report the new water-soluble aminocalix[4]arene hosts 1 and 2 with deep hydrophobic cavity facilitating hydrophobic mouth and hydrophilic mouth, respectively. The ¹H NMR titrations revealed that host 1 shows high selectivity for neutral guests 9 and 10, with log K of 4.2 and 4.6, respectively. The host 2 shows log K of 4.9 for binding with guest 15. Moreover, the binding ability of the host 2 for guest 14 is stronger by a factor of 1000 than that of the host 1.     

Circular logic: nonribosomal peptide-like macrocyclization with a ribosomal peptide catalyst

A protease from ribosomal peptide biosynthesis macrocyclizes diverse substrates, including those resembling nonribosomal peptide and hybrid polyketide-peptide products. The proposed mechanism is analogous to thioesterase-catalyzed chemistry, but the substrates are amide bonds rather than thioesters.     

Thermodynamic Investigation of Molecular Interactions in 1,3-Dioxolane or 1,4-Dioxane+Benzene or Toluene+Formamide or +<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-Dimethylformamide Ternary Mixtures at 308.15 K and Atmospheric Pressure

Excess molar volumes, V^E₁₂₃V^{\mathrm{E}}_{123} of 1,3-dioxolane or 1,4-dioxane (1) + benzene or toluene (2) + formamide or + N,N-dimethylformamide (3) ternary mixtures at 308.15 K and at atmospheric pressure have been determined dilatometrically over the entire composition range. The excess molar volumes data of these ternary systems were fitted to the Redlich–Kister equation. The data have been analyzed in terms of Graph theory (model) to understand the nature and strength of molecular interactions existing in these mixtures. It has been observed that V^E₁₂₃V^{\mathrm{E}}_{123} values predicted by Graph theory compare well with their corresponding experimental values.