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41.
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 相似文献
42.
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.
相似文献
43.
Dinesh Kumar Milind S. Ladaniya Manju Gurjar Sunil Kumar Sachin Mendke 《Molecules (Basel, Switzerland)》2021,26(14)
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. 相似文献
44.
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. 相似文献
45.
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. 相似文献
46.
Photoisomerization dynamics of 3,3'-diethyloxadicarbocyanine iodide (DODCI) has been examined in a series of 1-alkyl-3-methylimidazolium (alkyl = methyl, ethyl, propyl, butyl, and hexyl) bis(trifluoromethylsulfonyl)imides by measuring its fluorescence lifetimes and quantum yields. This study has essentially been undertaken to find out whether the process of photoisomerization of DODCI in ionic liquids is different compared to that observed in conventional solvents such as alcohols. Activation energy of the reaction has been attained with the aid of isoviscosity plots and was found to be 22 ± 3 kJ mol(-1), which is a factor of two higher compared to that obtained in alcohols. The significantly higher activation energy obtained in bis(trifluoromethylsulfonyl)imides compared to alcohols is probably due to the highly ordered nature of the ionic liquids, which hinders the twisting process. Kramers theory has been applied to understand the reduced isomerization rate constants in terms of solvent friction. As in case of alcohols, the isomerization data could not be explained by the Kramers model. However, a power law relation, which is a phenomenological functional form, could mimic the observed trend. 相似文献
47.
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). 相似文献
48.
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. 相似文献
49.
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 下载免费PDF全文
Swapnil G. Yerande Sunil D. More Mayur Bhandari Kiran M. Newase Kareem Khoury Kan Wang Alexander Dömling 《Journal of heterocyclic chemistry》2014,51(Z1):E358-E363
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. 相似文献
50.
Swapnil R. Sarda Jagpal D. Kale Sunil K. Wasmatkar Vijay S. Kadam Pravin G. Ingole Wamanrao N. Jadhav Rajendra P. Pawar 《Molecular diversity》2009,13(4):545-549
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. 相似文献