Algorithms for clique-independent sets on subclasses of circular-arc graphs

A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a -free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n²). These algorithms suppose that an HCA model of the graph is given.     

Niobian iron oxides as heterogeneous Fenton catalysts for environmental remediation

Heterogeneous Fenton or Fenton-like reagents consist of a mixture of an iron-containing solid matrix and a liquid medium with H₂O₂. The Fenton system is based on the reaction between Fe^2?+? and H₂O₂ to produce highly reactive intermediate hydroxyl radicals (^???OH), which are able to oxidize organic contaminants, whereas the Fenton-like reaction is based on the reaction between Fe^3?+? and H₂O₂. These heterogeneous systems offer several advantages over their homogeneous counterparts, such as no sludge formation, operation at near-neutral pH and the possibility of recycling the iron promoter. Some doping transition cations in the iron oxide structure are believed to enhance the catalytic efficiency for the oxidation of organic substrates in water. In this work, goethites synthesized in presence of niobium served as precursors for the preparation of magnetites (niobian magnetites) via chemical reduction with hydrogen at 400°C. These materials were used as Fenton-like catalysts. Both groups of (Nb, Fe)-oxide samples were characterized by ⁵⁷Fe Mössbauer spectroscopy at 298 K. The results show that increasing niobium contents raise the catalytic potential for decomposition of methylene blue, which was, in this work, used as a model molecule for organic substrates in water.     

Raman spectra of a pseudo‐oxocarbon anion in ionic liquids

Raman and electronic spectra of the [3,5‐bis(dicyanomethylene)cyclopentane‐1,2,4‐trionate] dianion, the croconate violet (CV), are reported in solutions of ionic liquids based on imidazolium cations. Different normal modes of the CV anion, ν (CO), ν (CO) + ν (CC) + ν (CCN), and ν(C≡N), were used as probes of solvation characteristics of ionic liquids, and were compared with spectra of CV in common solvents. The spectra of CV in ionic liquids are similar to those in dichloromethane solution, but distinct from those in protic solvents such as ethanol or water. The UV–vis spectra of CV in ionic liquids strongly suggest π–π interactions between the CV anion and the imidazolium cation. Copyright © 2009 John Wiley & Sons, Ltd.     

Raman spectra of acetonitrile in imidazolium ionic liquids

Raman spectra of dilute solutions of acetonitrile in ionic liquids reveal the characteristic features of ionic liquids' polarity. This is accomplished by investigating the Raman bandshape of the ν (CN) band, corresponding to the CN stretching mode of CH₃CN, which is a very sensitive probe of the local environment. The amphiphilic nature of the CH₃CN molecule allows us to observe the effect of electron pair acceptor and electron pair donor characteristics on ionic liquids. It has been found that the overall polarity of nine different ionic liquids based on 1‐alkyl‐3‐methylimidazolium cations is more dependent on the anion than cation. The observed wavenumber shift of the ν (CN) band of CH₃CN in ionic liquids containing alkylsulfate anions agrees with the significant different values previously measured for the dielectric constant of these ionic liquids. The conclusions obtained from the analysis of the ν (CN) band were corroborated by the analysis of the symmetric ν₁ (CD₃ ) stretching mode of deuterated acetonitrile in different ionic liquids. Copyright © 2010 John Wiley & Sons, Ltd.     

A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce \({\mathcal O}(1)\) evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.     

Long cycles and paths in distance graphs

For n∈N and D⊆N, the distance graph has vertex set {0,1,…,n−1} and edge set {ij∣0≤i,j≤n−1,|j−i|∈D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs.A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of a Hamiltonian cycle are all equivalent. Our main result suitably extends this equivalence to distance graphs. We prove that for a finite set D of order at least 2, there is a constant c_D such that the greatest common divisor of the integers in D is 1 if and only if for every n, has a component of order at least n−c_D if and only if for every n≥c_D+3, has a cycle of order at least n−c_D. Furthermore, we discuss some consequences and variants of this result.     

Chiral boron enolate aldol additions to chiral aldehydes

We have examined the double-diastereodifferentiating aldol addition reactions of chiral enolborinate 1a with chiral aldehydes leading to the corresponding aldol adducts with excellent levels of 1,5-anti diastereoselection.     

Optical Diagnosis for Thyroid and Parathyroid Tissues—A Review

Abstract

This article presents an overview of optical methodologies to aid the diagnosis and differentiation of thyroid and parathyroid tissues. In particular, we review the several techniques and associated methodologies that allow in vivo and ex vivo optical characterization of thyroid and parathyroid tissues. Emphasis is placed on the research potential of these techniques and whether intrinsic characteristics can provide useful contrast for the diagnosis of human thyroid and parathyroid malignant lesions.     

Stationary solutions for generalized boussinesq models

We study the existence, regularity and conditioas for uniqueness of solutions of a generalized Boussinesq model for thermally driven convection. The model allows temperature dependent viscosity and thermal conductivity.