Acyclic edge coloring of 2‐degenerate 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). A graph is called 2‐degenerate if any of its induced subgraph has a vertex of degree at most 2. The class of 2‐degenerate graphs properly contains series–parallel graphs, outerplanar graphs, non ? regular subcubic graphs, planar graphs of girth at least 6 and circle graphs of girth at least 5 as subclasses. 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. We prove the conjecture for 2‐degenerate graphs. In fact we prove a stronger bound: we prove that if G is a 2‐degenerate graph with maximum degree Δ, then a′(G)?Δ + 1. © 2010 Wiley Periodicals, Inc. J Graph Theory 69: 1–27, 2012     

A nonlinear stability analysis for rotating magnetized ferrofluid heated from below saturating a porous medium

A nonlinear (energy) stability analysis is performed for a rotating magnetized ferrofluid layer heated from below saturating a porous medium, in the stress-free boundary case. By introducing a generalized energy functional, a rigorous nonlinear stability result for a thermoconvective rotating magnetized ferrofluid is derived. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body force. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M ₃, medium permeability, D _a , and rotation, , on subcritical instability region has also been analyzed. It is shown that with the increase of magnetic parameter, M ₃, and Darcy number, D _a , the subcritical instability region between the two theories decreases quickly while with the increase of Taylor number, , the subcritical region expands. We also demonstrate coupling between the buoyancy and magnetic forces in the presence of rotation in nonlinear energy stability analysis as well as in linear instability analysis.      

Quantification of Flavonoids,Phenols and Antioxidant Potential from Dropped Citrus reticulata Blanco Fruits Influenced by Drying Techniques

Physiologically dropped immature Citrus reticulata Blanco fruits are regarded as waste and discarded in the citrus orchard but are a good source of bioactive compounds including flavonoids, antioxidants and total phenols. A study was undertaken to identify and quantify these bioactive compounds and to investigate the influence of different drying techniques, namely freeze drying and hot air oven drying, on flavonoids namely flavanone glycosides, antioxidant potential and total phenol content in immature dropped fruits of Citrus reticulata Blanco. Flavonoids were quantified in high-performance liquid chromatography (HPLC). The antioxidant activity were investigated with three assays azino-bis [3-ethylbenzthiazoline-6-sulfonic acid]) (ABTS), 2,2-diphenyl-1-picrylhydrazyl radical (DPPH), Ferric Reducing Ability of Plasma (FRAP) and total phenol content was determined. Freeze dried samples of 12 and 14 mm size retained maximum hesperidin flavonoid content (27.03% and 27.20%) as compared to the hot air dried samples (17.99%) and retained higher phenolic content ranged from 50.54–54.19 mg GAEL⁻¹. The antioxidant activity in freeze dried fruits was from 12.21–13.55 mM L⁻¹ Trolox and 15.27–16.72 mM L⁻¹ Trolox with ABTS, DPPH assay and FRAP values ranging from 7.31–9.07 mM L⁻¹ Trolox. Significant positive correlation was found between the flavonoid hesperidin with antioxidant assays and total phenolic content (TPC). The results showed that waste citrus fruits can act as potential source of bioflavonoids, especially hesperidin, and antioxidants for pharmaceutical as well as nutraceutical industry.     

Unexpected ambidoselectivity in crossed-aldol reactions of α-oxy aldehyde trichlorosilyl enolates

The ambido-, stereo- and enantioselectivity of the phosphoramide-promoted aldol reactions of α-oxy aldehyde trichlorosilyl enolates with benzaldehyde has been investigated. Analysis of the products from α-tert-butyldimethylsilyloxy α-deuterioacetaldehyde trichlorosilyl enolate confirmed that this 1,2-bis-silyloxyethene derivative reacted as a tert-butyldimethylsilyl enolate rather than trichlorosilyl enolate in the aldol reaction with very high ambidoselectivity. The phosphoramide-coordinated trichlorosilyl group acted as an organizing center for the aldol reaction. From the aldol process, excellent anti-diastereoselectivity could be achieved. The enantioselectivity remained moderate to low for both anti- and syn-diastereomer with a wide range of phosphoramide catalysts. α-Triisopropylsilyloxy, phenoxy and benzyloxy acetaldehyde trichlorosilyl enolates also reacted in a similar fashion with benzaldehyde to give aldol products with varying degrees of selectivities.     

Synthesis of dihydropyrazolo[3′,4′:3,4]pyrrolo[1,2-a]indoles and spiro-[3H-indole-3,3′-[Δ-1,2,4]-triazolin]-2-ones via intra and intermolecular 1,3-dipolar cycloadditions

A new class of dihydropyrazolo[3′,4′:3,4]pyrrolo[1,2-a]indoles and spiro[3H-indole-3,3′-[Δ²-1,2,4]-triazoline]-2-ones were synthesised via intra and intermolecular 1,3-dipolar cycloaddition reactions in good yields.     

Determination of organic acid impurities in lactic acid obtained by fermentation of sugarcane juice

Lactic acid produced by fermentation process mostly contains a number of aliphatic carboxylic acids as impurities. In this work, carboxylic acid impurities in lactic acid samples from a number of sources were determined at ppm levels. A simple HPLC method was developed that utilized a new generation polar embedded reverse phase, 20mM phosphate buffer at pH 2.20 (±0.05) and UV detection at 210 nm. The method enabled quantitative analysis of the above acids in lactic acid matrix. The experimental conditions for column temperature, mobile phase pH and flow rate were optimized. A detailed validation of the method was performed for linearity, precision, accuracy, selectivity, limit of detection (LOD), limit of quantitation (LOQ), ruggedness and repeatability and reproducibility (R&R).     

Upper rim appended hybrid calixarenes via click chemistry

We report the application of "click" chemistry for the synthesis of hybrid calixarenes appended on the upper rim with carbohydrate and N,C-protected alpha-amino acids. The chemoselective N- or C-deprotection of the alpha-amino acids and their subsequent transformation into dipeptides is described. The first example of a chemo-enzymatic synthesis on upper rim derived calix[4]arenes using trans-sialidase affords sialylated lactose calix[4]arenes. Our innovative chemo-enzymatic process paves the way for further applications.     

A Facile Diversity‐Oriented Multicomponent One‐Pot Synthesis of 3‐Amino‐6,7‐dihydrobenzo[c]thiophen‐4(5H)‐one Derivatives from α‐Oxo‐N,S‐ketene Acetal

A convenient one‐pot multicomponent method for the preparation of 3‐amino‐6,7‐dihydrobenzo[c]thiophen‐4(5H)‐one derivative has been developed. Reaction of 1,3‐cyclohexanedione and phenyl isothiocynate gave α‐oxo‐N,S‐ketene acetal that were reacted in situ with 2‐chloromethylquniazoline‐4‐one derivatives, in the presence of sodium hydride to afford the target compound in reasonable overall yields.     

An efficient synthesis of pyrazole chalcones under solvent free conditions at room temperature

An easy,safe,solvent free and effective method for the synthesis of pyrazole-substituted chalcones has been achieved by grinding pyrazole aldehydes and acetophenones in the presence of activated barium hydroxide(C-200) in high yield within short span of time.All reactions were carried out just by grinding the two reactants in the presence of activated barium hydroxide(C-200). Results are also compared with sodium hydroxide and potassium hydroxide.     

An efficient protocol for the synthesis of 2-amino-4,6-diphenylpyridine-3-carbonitrile using ionic liquid ethylammonium nitrate

Chalcones on condensation with malononitrile and ammonium acetate in the presence of ionic liquid ethylammonium nitrate affords the corresponding 2-amino-4, 6-diphenylpyridine-3-carbonitrile in excellent yield. The ionic liquid is recycled and reused several times.