Online Coloring of Bipartite Graphs with and without Advice

In the online version of the well-known graph coloring problem, the vertices appear one after the other together with the edges to the already known vertices and have to be irrevocably colored immediately after their appearance. We consider this problem on bipartite, i.e., two-colorable graphs. We prove that at least ?1.13746?log₂(n)?0.49887? colors are necessary for any deterministic online algorithm to be able to color any given bipartite graph on n vertices, thus improving on the previously known lower bound of ?log₂ n?+1 for sufficiently large n. Recently, the advice complexity was introduced as a method for a fine-grained analysis of the hardness of online problems. We apply this method to the online coloring problem and prove (almost) tight linear upper and lower bounds on the advice complexity of coloring a bipartite graph online optimally or using 3 colors. Moreover, we prove that \(O(\sqrt{n})\) advice bits are sufficient for coloring any bipartite graph on n vertices with at most ?log₂ n? colors.     

Behavioral Changes in Workers of the Leaf-Cutting Ant Atta sexdens rubropilosa Induced by Chemical Components of Eucalyptus maculata Leaves

The response of Atta sexdens rubropilosa Forel workers to essential oils, epicuticular wax and hexane, dichloromethane, ethyl acetate, and methanol extracts of Eucalyptus maculata was evaluated. Hexane extracts of E. maculata interfered with the recognition mechanism among workers. The main active compounds identified from this plant were the sesquiterpenes elemol and beta-eudesmol. These compounds may be responsible for the resistance of this species to ant attack.     

Blocking the Routes to Triviality with Depth Relevance

In Rogerson and Restall’s (J Philos Log 36, 2006, p. 435), the “class of implication formulas known to trivialize (NC)” (NC abbreviates “naïve comprehension”) is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.     

Synthesis of deuterated cyclopropene fatty esters structurally related to palmitic and myristic acids

To develop a synthesis of tritiated cyclopropene fatty acids (CPFA), compounds that should prove useful for affinity labeling of desaturases in insect pheromone biosynthetic studies, a series of novel, selectively deuterated CPFA analogues was prepared and characterized. In methyl [16-²H]12,13-methylene-12-hexadecenoate, the incorporation of deuterium was achieved by treatment of the corresponding ω-chloro derivative with sodium borodeuteride in dimethylsulfoxide at 70°C for 24 h (67% yield) following conventional procedures. Alkylation of the tetrahydropyranyl derivative of 13-tridecynol in the presence of lithium diisopropylamide in tetrahydrofuran at −20°C with 1-chloro-3-iodopropane in hexamethylphosphoramide, followed by Jones oxidation of the crude product, yielded 16-chloro-12-hexadecynoic acid (54%), which was esterified to the corresponding methyl ester by treatment with potassium carbonate and methyl iodide in dimethylformamide. Treatment of this acetylenic ester with ethyldiazoacetate in the presence of activated copper-bronze as catalyst followed by hydrolysis in KOH solution at room temperature yielded 16-chloro-12,13-(carboxymethylene)-12-hexadecenoic acid. This diacid was treated with excess oxalyl chloride to give the corresponding diacyl chloride, which was decarbonylated in a diethyl ether solution with zinc chloride, and the cyclopropenium ions thus formed were added at −40°C to a methanolic sodium hydroxide solution of sodium borohydride to give methyl 16-chloro-12,13-methylene-12-hexadecenoate. Analogous procedures were followed to prepare methyl [17-²H]10,11-methylene-10-hexadecenoate, methyl [17-²H]11,12-methylene-11-hexadecenoate and methyl [17-²H]12,13-methylene-12-hexadecenoate from the corresponding diacids using sodium borodeuteride in the reduction of the cyclopropenium ions. Alternatively, methyl [2,2,3,3-²H₄]hexadecynoate, prepared by reaction of methyl 2,11-hexadecadiynoate with magnesium in deuterated methanol at room temperature, was submitted to the above cyclopropenylation and reductive decarbonylation sequence to give methyl [2,2,3,3,17-²H₅]-11,12-methylene-11-hexadecenoate. In summary, complementary methods for the selective incorporation of one to five deuterium atoms into cyclopropene fatty acids, at different sites, in moderate to high yields have been developed. The methods should easily be applicable to the preparation of the corresponding tritiated analogues.     

Diffusional kinetics of metalliding zinc into solid copper

The process of incorporation of zinc into a copper cathode has been experimentally studied in a molten salt system at 381±2° C and at various current densities. The process is shown to be kinetically controlled by the diffusion of Zn into the solid matrix. A galvanostatic pulse titration technique has been used to determine the chemical diffusion coefficient at various alloy compositions, and an exponential relationship has been found between the diffusivity and the third power of the zinc concentration in the alloy. This relationship was then used in the diffusion equation within the solid matrix and a numerical integration was performed. Very good agreement was found between the calculated and experimental data for Zn interfacial concentration versus time. The same calculation procedure was used to determine zinc concentration profiles in the alloys.Nomenclature c _A concentration of the diffusing metal (mol cm^–3) - D _AB chemical diffusion coefficient of A into B (cm² s^–1) - E cell e.m.f. (mV) - F Faraday number - i current density (A cm^–2) - t time (s) - V _M alloy molar volume (cm³ mol^–1) - x linear dimension in the diffusion direction (cm) - X zinc mass fraction in the alloy - z ionic valence of Zn - stoichiometric ratio Zn/Cu     

Morphology and thermomechanical properties of recycled PET–organoclay nanocomposites

Recycled PET/organoclay nanocomposites were prepared by melt intercalation process with several amounts (1, 3, and 5 wt %) of clay modified with quaternary ammonium salt (DELLITE 67G) dispersed in a recycled poly(ethylene terephthalate) (rPET) matrix. The resultant mechanical properties (modulus and yield strength) of the nanocomposites were found to be different from those of rPET. Wide angle X‐ray scattering (WAXS) and Transmission Electron Microscopy (TEM) measurements have shown that although complete exfoliation was not achieved, delaminated clay platelets could be observed. Thermal analysis did not show significant changes in the thermal properties from those of recycled PET. Mechanical testing showed that nanocomposite properties were superior to the recycled PET in terms of strength and elasticity modulus. This improvement was attributed to nanoscale effects and strong interaction between the rPET matrix and the clay interface, as revealed by WAXS and TEM. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1839–1844, 2007     

Effect of olive paste kneading process time on the overall quality of virgin olive oil

The influence of the olive paste malaxation time on the composition and the industrial output of oil was investigated. To this purpose, three Italian olive varieties (Leccino, Dritta, Caroleo) were processed with a centrifugal system for six malaxation periods (0, 15, 30, 45, 60 and 75 min). The concentrations of the majority of the oil constituents changed during the malaxation. However, these changes were not significant for all of them: the contents of β‐carotene, the major xanthophylls, chlorophylls a and b, pheophytins a and b in the oils increased progressively with increasing malaxing times, whereas the contents of simple and hydrolysable phenols (secoiridoid derivatives), o‐diphenols and total phenols decreased. A significant increase in total volatiles and green volatiles of the lipoxygenase cascade (C₆ aldehydes, C₆ alcohols, C₅ alcohols and C₅ carbonyls) was detected. An opposite trend was observed for the green C₆ esters. As a result, the global analytical quality, flavour, aroma and shelf‐life of the oils were negatively affected. The oil yield increased substantially up to 45 min of paste malaxation times. Beyond 60 min, the yields tended to decrease.     

Classification of vegetable oils by high-resolution <Superscript>13</Superscript>C NMR spectroscopy using chromatographically obtained oil fractions

¹³C NMR spectra of oil fractions obtained chromatographically from 109 vegetable oils were obtained and analyzed to evaluate the potential use of those fractions in the classification of vegetable oils and to compare the results with the NMR analysis of complete oils. The oils included the following: virgin olive oils from different cultivars and regions of Europe and north Africa; “lampante” olive, refined olive, refined olive pomace, hazelnut, rapeseed, high-oleic sunflower, corn, grapeseed, soybean, and sunflower oils; and mixtures of virgin olive oils from different geographical origins. Oils were divided into two sets of samples. The training set (98 samples) was employed to select the variables that resulted in significant discrimination among the different oil classes. By using stepwise discriminant analysis, more than 98% of correct validated assignments were obtained; these results were confirmed when applied to the test set (11 blind samples). Results suggest that the use of oil fractions considerably increases the discriminating power of NMR in the analysis of vegetable oils.