Bounds on vertex colorings with restrictions on the union of color classes

A proper coloring of a graph is a labeled partition of its vertices into parts which are independent sets. In this paper, given a positive integer j and a family ? of connected graphs, we consider proper colorings in which we require that the union of any j color classes induces a subgraph which has no copy of any member of ?. This generalizes some well‐known types of proper colorings like acyclic colorings (where j = 2 and ?is the collection of all even cycles) and star colorings (where j = 2 and ?consists of just a path on 4 vertices), etc. For this type of coloring, we obtain an upper bound of O(d^{(k ? 1)/(k ? j)}) on the minimum number of colors sufficient to obtain such a coloring. Here, d refers to the maximum degree of the graph and k is the size of the smallest member of ?. For the case of j = 2, we also obtain lower bounds on the minimum number of colors needed in the worst case. As a corollary, we obtain bounds on the minimum number of colors sufficient to obtain proper colorings in which the union of any j color classes is a graph of bounded treewidth. In particular, using O(d^8/7) colors, one can obtain a proper coloring of the vertices of a graph so that the union of any two color classes has treewidth at most 2. We also show that this bound is tight within a multiplicative factor of O((logd)^1/7). We also consider generalizations where we require simultaneously for several pairs (j_i, ?_i) (i = 1, …, l) that the union of any j_i color classes has no copy of any member of ?_i and obtain upper bounds on the corresponding chromatic numbers. © 2011 Wiley Periodicals, Inc. J Graph Theory 66: 213–234, 2011     

Ambient pressure drying: a successful approach for the preparation of silica and silica based mixed oxide aerogels

Silica aerogels have received much attention in recent years as it has got a wide range of properties like high surface area, low density, high porosity, low dielectric constant, low thermal conductivity. Recently to make aerogels for commercial application ambient pressure drying has been preferred and also a cheap precursor like sodium silicate has been employed as the starting material instead of the alkoxides. In this review, attention will be given to the synthesis adopted for the preparation of silica and silica based mixed oxide/composite aerogels through ambient pressure drying. The properties of the prepared aerogels are also discussed in detail.     

Radical chemistry of glucosamine naphthalene acetic acid and naphthalene acetic acid: a pulse radiolysis study

Free radical‐induced oxidation reactions of glucosamine naphthalene acetic acid (GNaa) and naphthalene acetic acid (Naa) have been studied using pulse radiolysis. GNaa was synthesized by covalently attaching Naa on glucosamine. Hydroxyl adduct (from the reaction of hydroxyl radicals (^●OH) at the naphthalene ring) was identified as the major transient intermediate (suggesting that the ^●OH reaction is on the naphthalene ring) and is characterized by its absorption maxima of 340 and 400 nm. Both GNaa and Naa undergo similar reaction pattern. The bimolecular rate constants determined for the reactions are 4.8 × 10⁹ and 8.9 × 10⁹ dm³ mol^?1 s^?1 for GNaa and Naa respectively. The mechanism of reaction of ^●OH with GNaa was further confirmed using steady‐state method. Radical cation of GNaa was detected as an intermediate during the reaction of sulfate radical (SO₄^●?) with GNaa (k₂ = 4.52 × 10⁹ dm³ mol^?1 s^?1). This radical cation transforms to a ^●OH adduct at higher pH. The radical cation of GNaa is comparatively long lived, and a cyclic transition state by neighboring group participation accounts for its stability. The oxy radical anion (O^●?) reacts with GNaa (k₂ = 1.12 × 10⁹ dm³ mol^?1 s^?1) mainly by one‐electron transfer mechanism. The reduction potential values of Naa and GNaa were determined using cyclic voltammetric technique, and these are 1.39 V versus NHE for Naa and 1.60 V versus NHE for GNaa. Copyright © 2014 John Wiley & Sons, Ltd.     

Parity Proofs of the Bell-Kochen-Specker Theorem Based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.     

Reaction of hydroxyl radicals with S-nitrosothiols: Formation of thiyl radical (RS?) as the intermediate

The decomposition studies of S-nitrosothiols (RSNO) are important due to their potential role in vivo in connection with the storage and transport of nitric oxide (^•NO) within the body. Reactions of hydroxyl radicals (^•OH) with a number of RSNOs (S-nitroso derivatives of N-acetyl-dl-penicillamine, l-cysteinemethylester, N-acetylcysteamine, and dl-penicillamine) in aqueous medium at neutral and acidic pH have been reported in the present study. Radiation chemical technique (steady state and pulse radiolysis) has been utilized for the determination of the reaction rate constants, the end product analyses, and the transient intermediate species. The rate constants for the reaction of ^•OH with the selected RSNOs were determined using a competition kinetic method with 2′-deoxy-d-ribose as the competitor. All the rate constants were found to be of the order of diffusion controlled (10¹⁰ M⁻¹ s⁻¹). The degradation yield of RSNOs was found to be quantitative (i.e., G(–RSNO) ≈ G(^•OH)) at neutral and acidic pH. The major products of decomposition were the respective disulfide (RSSR) and nitrite (NO₂ ⁻). A good material balance is also obtained between the degradation yield and the formation of the products (i.e., G(–RSNO) ≈ G(RSSR) + G(NO₂ ⁻)). The major transient intermediate was the thiyl radical (RS^•). Its intermediacy was confirmed by making use of the electron transfer reaction of 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonate) (ABTS²⁻) to RS^•, which results in the formation of ABTS^•− having a transient absorption spectrum with λ_max at 410 nm. Based on these results, a generalized reaction mechanism is deduced for the reaction of ^•OH with RSNO.     

Physicochemical properties of {1-methyl piperazine (1) + water (2)} system at T = (298.15 to 343.15) K and atmospheric pressure

Densities (ρ) and viscosities (η) of aqueous 1-methylpiperazine (1-MPZ) solutions are reported at T = (298.15 to 343.15) K. Refractive indices (n_D) are reported at T = (293.15 to 333.15) K, and surface tensions (γ) are reported at T = (298.15 to 333.15) K. Derived excess properties, except excess viscosities (Δη), are found to be negative over the entire composition range. The addition of 1-MPZ reduces drastically the surface tension of water. The temperature dependence of surface tensions is explained in terms of surface entropy (S^S) and enthalpy (H^S). The measured and derived properties are used to probe the microscopic liquid structure of the bulk and surface of the aqueous amine solutions.     

Effects of CO2 dilution on partially premixed CH4-air flames in swirl and bluff body stabilized combustor

The effect of CO₂ dilution on the flame characteristics and pollutant emission of a partially premixed CH₄-air flame in a confined bluff body and swirl influenced flowfield is investigated using optical and laser diagnostic methods. The non-premixed burner produced a converging-diverging flowfield at the burner exit and a lifted flame is produced at all test cases, with an upstream movement of the flame with decreasing global equivalence ratios (?_g). Based on variations in ?_g, two flame stabilization modes – bluff body influenced and swirl stabilized – with a transition mode in-between is observed for the cases with (flame FB) and without dilution (flame FM). The characteristics of the heat release zone are influenced by dilution, with the FB flames being longer and also less intense when compared to FM flames. Pollutant measurement at 30 mm downstream from the combustor exit highlighted the ultra-low NO_x capability of the IIST-GS2 burner. CO₂ dilution leads to a reduction in NO_x emission due to both thermal and chemical effects. For ?_g ≥ 0.7 extreme low levels of CO and unburned hydrocarbons (UHC) are observed for both cases. For ?_g ≤ 0.6 the dramatic increase of both CO and UHC maybe due to the lower flame temperatures and shorter flame zone residence times, respectively.     

Cs2PtI6 Halide Perovskite is Stable to Air,Moisture, and Extreme pH: Application to Photoelectrochemical Solar Water Oxidation

Halide perovskites show incredible photovoltaic power conversion efficiency coupled with several hundreds of hours of device stability. However, their stability is poor in aqueous electrolyte media. Reported here is a vacancy ordered halide perovskite, Cs₂PtI₆, which shows extraordinary stability under ambient conditions (1 year), in aqueous media of extreme acidic (pH 1), basic (pH 13), and under electrochemical reduction conditions. It was employed as an electrocatalyst and photoanode for hydrogen production and water oxidation, respectively. The catalyst remains intact for at least 100 cycles of electrochemical cycling and six hours of hydrogen production at pH 1. Cs₂PtI₆ was employed as a photoanode for PEC water oxidation, and the material displayed a photocurrent of 0.8 mA cm^?2 at 1.23 V (vs. RHE) under simulated AM1.5G sunlight. Using constant voltage measurement, Cs₂PtI₆ exhibited over 12 hours of PEC stability without loss of performance.     

Synthesis of Quinoline Analogs: Search for Antimalarial Agents

Summary. Novel synthesis routes for the promising antimalarial agents 4(3-hydroxypyrrolidin-1-yl) and 4(3-hydroxypiperidine-1-yl)-2,8-bis(trifluoromethyl)quinoline have been developed.