NLOphoric Triphenylamine Derived Donor‐π‐Acceptor‐π‐Donor Based Colorants: Synthesis,Spectroscopic, Density Functional Theory and Z‐scan Studies

Three Donor‐π‐Acceptor‐π‐Donor type styryl dyes ( 5a‐c ) with different secondary donors are synthesized and characterized to study their nonlinear and linear optical properties. The structure–property relationships of the dyes are described in the light of systematic photophysical and theoretical investigations. The photophysical characteristics of 5a‐c are influenced by the polarity of the medium, with an appreciable bathochromic shift in emission ( 5b = 81 nm) and large Stoke shifts ( 5b = 104–173 nm) in polar solvents. 5a‐c showed intramolecular charge transfer characteristics recognized with the help of emission solvatochromism, solvent polarity graphs, natural bond orbital analysis and HOMO–LUMO energy difference. The optimized geometry and frontier molecular orbitals reveal that the electron donation takes place from secondary donors and not from a fixed donor (triphenylamine) which is more twisted. The nonlinear optical properties obtained using solvent induced spectral shift and computational methods are found within the limiting values. Z‐scan results reveal saturable kind of behavior for 5a , 5b and 5c , whereas 5a and 5b show reverse saturable kind of behavior in acetone and ethanol and hence give optical limiting values. The two‐photon absorption cross section described by two‐level approximation is highest for 5b (251–300 GM).     

Hyperelliptic Curves Describing Coulomb Phase of N = 2 Supersymmetric Theories with Classical Gauge Groups SU(3) and SO(6)

Breaking N = 2 SU(3) and N =2 SO(6) supersymmetric Yang–Mills theoriesto corresponding N = 1 theories by suitable tree-levelsuperpotentials, thehyperelliptic curves describing the Coulomb phase of these theories have beenobtained and it has been shown that the mass gap in the N = 1confining phaseof these theories vanishes when N = 1 parameters are properlytuned to approachthe highest critical points.     

Confocality in image fiber bundle based microscope: A theoretical analysis

In confocal microscopes employing image fiber bundle, a focused beam is scanned sequentially over each fibers to build up the image. The effect of neighboring fibers around the illumination fiber on the confocality achieved is studied using Gaussian theory. It is shown that with proper packing of the fibers in the image fiber bundle, multiple fibers can be illuminated simultaneously without affecting the confocality. This will reduce the scanning time considerably without affecting the image resolution.     

Maximal Induced Matchings in Triangle‐Free Graphs

An induced matching in a graph is a set of edges whose endpoints induce a 1‐regular subgraph. It is known that every n‐vertex graph has at most  maximal induced matchings, and this bound is the best possible. We prove that every n‐vertex triangle‐free graph has at most  maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K_{3, 3}. Our result implies that all maximal induced matchings in an n‐vertex triangle‐free graph can be listed in time , yielding the fastest known algorithm for finding a maximum induced matching in a triangle‐free graph.     

Computational Design,Synthesis, and Pharmacological Evaluation of Naproxen-Guaiacol Chimera for Gastro-Sparing Anti-Inflammatory Response by Selective COX2 Inhibition

The 4-allyl guaiacol is a natural phenolic molecule that has been widely studied for its antioxidant capacity against reactive-oxygen-species-mediated cellular damage. Therefore, we hypothesized that concomitant use of an antioxidant and NSAID may decrease the risk of gastrointestinal toxicity and make the therapy safer. To address the gastrointestinal toxicity of conventional NSAIDs, a new S-naproxen-4-allyl guaiacol chimera (MAS-1696) was computationally developed, chemically synthesized, and tested for anti-inflammatory effectiveness and gastrointestinal safety. The inhibitory potency of MAS-1696 tested against cyclooxygenase-2 (COX2), 15-lipoxygenase-2 (15-LOX2), and lipoxygenase-5 (5-LOX) in vitro revealed a stronger inhibition of COX2. Furthermore, the MAS-1696 chimera increased the COX selectivity index by 23% as compared to the parent compound naproxen, implying higher efficacy and gastric safety. In vivo data showed that MAS-1696 was less likely to cause gastrointestinal harm than naproxen while also exerting anti-inflammatory and analgesic effects equivalent to or superior to naproxen. In conclusion, MAS-1696 is orally active, bio-labile, and crystalline, making it a medication that may be administered orally.     

A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) 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). Let Δ=Δ(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K_n,n. Alon, McDiarmid and Reed observed that a^′(K_p−1,p−1)=p for every prime p. In this paper we prove that a^′(K_p,p)≤p+2=Δ+2 when p is prime. Basavaraju, Chandran and Kummini proved that a^′(K_n,n)≥n+2=Δ+2 when n is odd, which combined with our result implies that a^′(K_p,p)=p+2=Δ+2 when p is an odd prime. Moreover we show that if we remove any edge from K_p,p, the resulting graph is acyclically Δ+1=p+1-edge-colorable.     

The oxidation of carbohydrazide by the 12-tungstocobaltate(III) ion in acidic medium: Kinetics and mechanism

The redox reaction between the 12-tungstocobaltate(III) ion and carbohydrazide is first order with respect to both the oxidant and the substrate. The observed pseudo first-order rate constant, k_obs, is retarded by increasing the concentrations of H⁺ and alkali metal ion (Li⁺, Na⁺ and K⁺). There is a linear correlation between the k_obs and the concentrations of carbohydrazide and H⁺ ion, but the plots of k_obs against the concentrations of the alkali metal ions is non-linear. However, the same data is applicable to the Davies equation for the effect of the ionic strength on the k_obs.     

Dipolar correlations and the dielectric permittivity of water

The static dielectric properties of liquid and solid water are investigated within linear response theory in the context of ab initio molecular dynamics. Using maximally localized Wannier functions to treat the macroscopic polarization we formulate a first-principles, parameter-free, generalization of Kirkwood's phenomenological theory. Our calculated static permittivity is in good agreement with experiment. Two effects of the hydrogen bonds, i.e., a significant increase of the average local moment and a local alignment of the molecular dipoles, contribute in almost equal measure to the unusually large dielectric constant of water.     

Water-walking devices

We report recent efforts in the design and construction of water-walking machines inspired by insects and spiders. The fundamental physical constraints on the size, proportion and dynamics of natural water-walkers are enumerated and used as design criteria for analogous mechanical devices. We report devices capable of rowing along the surface, leaping off the surface and climbing menisci by deforming the free surface. The most critical design constraint is that the devices be lightweight and non-wetting. Microscale manufacturing techniques and new man-made materials such as hydrophobic coatings and thermally actuated wires are implemented. Using high-speed cinematography and flow visualization, we compare the functionality and dynamics of our devices with those of their natural counterparts. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.