Strong Chromatic Index of Chordless Graphs

A strong edge coloring of a graph is an assignment of colors to the edges of the graph such that for every color, the set of edges that are given that color form an induced matching in the graph. The strong chromatic index of a graph G, denoted by , is the minimum number of colors needed in any strong edge coloring of G. A graph is said to be chordless if there is no cycle in the graph that has a chord. Faudree, Gyárfás, Schelp, and Tuza (The Strong Chromatic Index of Graphs, Ars Combin 29B (1990), 205–211) considered a particular subclass of chordless graphs, namely, the class of graphs in which all the cycle lengths are multiples of four, and asked whether the strong chromatic index of these graphs can be bounded by a linear function of the maximum degree. Chang and Narayanan (Strong Chromatic Index of 2‐degenerate Graphs, J Graph Theory, 73(2) (2013), 119–126) answered this question in the affirmative by proving that if G is a chordless graph with maximum degree Δ, then . We improve this result by showing that for every chordless graph G with maximum degree Δ, . This bound is tight up to an additive constant.     

Photocatalytic synthesis of urea from in situ generated ammonia and carbon dioxide

TiO(2) and Fe-titanate (different wt%) supported on zeolite were prepared by sol-gel and solid-state dispersion methods. The photocatalysts prepared were characterized by X-ray diffraction, scanning electron microscopy and ultraviolet (UV)-visible diffuse reflectance spectroscopy techniques. Photocatalytic reduction of nitrate in water and isopropanol/oxalic acid as hole scavengers are investigated in a batch reactor under UV illumination. The yield of urea increased notably when the catalysts were supported on zeolite. The Fe-titanate supported catalyst promotes the charge separation that contributes to an increase in selective formation of urea. The product formation is because of the high adsorption of in situ generated CO(2) and NH(3) over shape-selective property of the zeolite in the composite photocatalyst. The maximum yield of urea is found to be 18 ppm while 1% isopropanol containing solution over 10 wt% Fe-titanate/HZSM-5 photocatalyst was used.     

Mapping phosphorylation rate of fluoro-deoxy-glucose in rat brain by F chemical shift imaging

¹⁹F magnetic resonance spectroscopy (MRS) studies of 2-fluoro-2-deoxy-d-glucose (FDG) and 2-fluoro-2-deoxy-d-glucose-6-phosphate (FDG-6P) can be used for directly assessing total glucose metabolism in vivo. To date, ¹⁹F MRS measurements of FDG phosphorylation in the brain have either been achieved ex vivo from extracted tissue or in vivo by unusually long acquisition times. Electrophysiological and functional magnetic resonance imaging (fMRI) measurements indicate that FDG doses up to 500 mg/kg can be tolerated with minimal side effects on cerebral physiology and evoked fMRI-BOLD responses to forepaw stimulation. In halothane-anesthetized rats, we report localized in vivo detection and separation of FDG and FDG-6P MRS signals with ¹⁹F 2D chemical shift imaging (CSI) at 11.7 T. A metabolic model based on reversible transport between plasma and brain tissue, which included a non-saturable plasma to tissue component, was used to calculate spatial distribution of FDG and FDG-6P concentrations in rat brain. In addition, spatial distribution of rate constants and metabolic fluxes of FDG to FDG-6P conversion were estimated. Mapping the rate of FDG to FDG-6P conversion by ¹⁹F CSI provides an MR methodology that could impact other in vivo applications such as characterization of tumor pathophysiology.     

Effective operators and the truncation of shell model configuration space

An alternative derivation of the projection method for constructing effective operators in the truncated shell model space is presented. The results of explicit numerical calculations in three different nuclear regions are discussed. Non-hermiticity of the effective Hamiltonian and various hermitisation procedures are investigated in detail.     

Determination of Solifenacin Succinate in Pure and Pharmaceutical Dosage forms by Spectrophotometry

Journal of Analytical Chemistry - Four simple, precise and sensitive visible spectrophotometric methods were developed for the determination of solifenacin succinate in pure and pharmaceutical...     

Acyclic Edge Coloring of Triangle‐Free Planar Graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a′(G). It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a′(G) ? Δ + 2, where Δ = Δ(G) denotes the maximum degree of the graph. If every induced subgraph H of G satisfies the condition |E(H)| ? 2|V(H)|?1, we say that the graph G satisfies Property A. In this article, we prove that if G satisfies Property A, then a′(G) ? Δ + 3. Triangle‐free planar graphs satisfy Property A. We infer that a′(G) ? Δ + 3, if G is a triangle‐free planar graph. Another class of graph which satisfies Property A is 2‐fold graphs (union of two forests). © 2011 Wiley Periodicals, Inc. J Graph Theory     

Synthesis of some novel isatin-thiazole conjugates and their computational and biological studies

Structural Chemistry - The present work describes the synthesis of novel 3-[2-(5-phenyl-1,3-thiazol-2-yl)hydrazinyl]-1,3-dihydro-2H-indol-2-one derivatives 4(a-h) and the characterization of...     

Temperature dependence of 35Cl NQR in 2,6-dichloropyridine

Chlorine NQR in 2,6-dichloropyridine has been investigated in the temperature range 77 K to room temperature and a single resonance line has been observed throughout. Using this data, torsional frequencies of the molecule have been evaluated on the basis of both the Bayer theory and the modified Bayer theory incorporating Tatsuzaki correction.     

Photocatalytic reduction of CO2 over Cu-TiO2 /molecular sieve 5A composite

TiO(2) and different Cu wt% loaded TiO(2) (TC(0.5-5.0)), 10 wt% TC(2.0) supported on molecular sieve 5A (10 wt% TC(2.0)/MS) were prepared by impregnation and solid-state dispersion methods. The photocatalysts prepared were characterized using XRD, SEM, and UV-Vis DRS, TEM, XPS spectroscopy techniques. Photocatalytic reduction of CO(2) in water and alkaline solution are investigated in a batch reactor. The yield of oxalic acid increased notably when TC was supported on molecular sieve. The Cu-TiO(2) supported on molecular sieve catalyst promotes the charge separation that leads to an increase in the selective formation of oxalic acid in addition to methanol, acetic acid and traces of methane. The product formation is due to the high adsorption of CO(2), water and product shape selectivity of the composite photocatalyst. The maximum yield of oxalic acid was found to be 65.6 μg h(-1) g(-1) per cat using 0.2 N NaOH containing solution over 10 wt% TC(2.0)/MS photocatalyst. The difference in the photocatalytic activity is related to its physicochemical properties.     

Rainbow Connection Number and Radius

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) ≤  r(r + 2). We demonstrate that this bound is the best possible for rc(G) as a function of r, not just for bridgeless graphs, but also for graphs of any stronger connectivity. It may be noted that for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius (K _1,n for instance). We further show that for every bridgeless graph G with radius r and chordality (size of a largest induced cycle) k, rc(G) ≤  rk. Hitherto, the only reported upper bound on the rainbow connection number of bridgeless graphs is 4n/5 ? 1, where n is order of the graph (Caro et al. in Electron J Comb 15(1):Research paper 57, 13, 2008). It is known that computing rc(G) is NP-Hard (Chakraborty and fischer in J Comb Optim 1–18, 2009). Here, we present a (r + 3)-factor approximation algorithm which runs in O(nm) time and a (d + 3)-factor approximation algorithm which runs in O(dm) time to rainbow colour any connected graph G on n vertices, with m edges, diameter d and radius r.