Home About us Contact
|
Home About us Contact | ||
|
|
||
Numbers Greater (number + greater)
Selected AbstractsColoring H-free hypergraphsRANDOM STRUCTURES AND ALGORITHMS, Issue 1 2010Tom Bohman Abstract Fix r , 2 and a collection of r -uniform hypergraphs . What is the minimum number of edges in an -free r -uniform hypergraph with chromatic number greater than k? We investigate this question for various . Our results include the following: An (r,l)-system is an r -uniform hypergraph with every two edges sharing at most l vertices. For k sufficiently large, there is an (r,l)-system with chromatic number greater than k and number of edges at most c(kr,1 log k)l/(l,1), where This improves on the previous best bounds of Kostochka et al. (Random Structures Algorithms 19 (2001), 87,98). The upper bound is sharp apart from the constant c as shown in (Random Structures Algorithms 19 (2001) 87,98). The minimum number of edges in an r -uniform hypergraph with independent neighborhoods and chromatic number greater than k is of order kr+1/(r,1) log O(1)k as k , ,. This generalizes (aside from logarithmic factors) a result of Gimbel and Thomassen (Discrete Mathematics 219 (2000), 275,277) for triangle-free graphs. Let T be an r -uniform hypertree of t edges. Then every T -free r -uniform hypergraph has chromatic number at most 2(r , 1)(t , 1) + 1. This generalizes the well-known fact that every T -free graph has chromatic number at most t. Several open problems and conjectures are also posed. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source] Review: Biological methylation of less-studied elementsAPPLIED ORGANOMETALLIC CHEMISTRY, Issue 12 2002John S. Thayer Abstract Biological methylation is an enzymatic process in which a methyl group is transferred from one atom to another. For elements having atomic number greater than 11, biological methylation has been most extensively studied for three elements: arsenic, mercury and sulfur. However, many other elements also undergo biological methylation but have received less attention. Recent work on these less-studied elements and new applications of biological methylation to environmental remediation, along with a description of these reactions in terms of bonding models, is the focus of this review. Copyright © 2002 John Wiley & Sons, Ltd. [source] Evaluation of Lipid Oxidation and Oxidative Products as Affected by Pork Meat Cut, Packaging Method, and Storage Time during Frozen Storage (,10 °C)JOURNAL OF FOOD SCIENCE, Issue 2 2007S.Y. Park ABSTRACT:, Lipid oxidation and oxidative volatiles as affected by pork meat cut and packaging method during frozen storage at ,10 °C were evaluated. Pork belly cut had higher thiobarbituric acid reactive substance (TBARS) and pH values than did the loin, whereas the loin had higher free fatty acid (FFA) values than that of the belly cut. Peroxide values increased with increased storage time, but were not affected by pork meat cut and packaging method. Volatiles with carbon numbers less than 10 in the belly cut were higher than those in the loin cut, whereas those with carbon numbers greater than 10 in the loin cut were higher than those in belly cut. Most volatiles were decreased with increased storage time, except for propane. Both 4-pentenal and 4-methyl-2-hexanone in the belly cut showed a positive correlation with FFA, whereas 2,4-dimethyl-1-heptene and 9-octadecenal in the loin cut were positively correlated with TBARS and FFA, respectively, even though the values were not high enough to predict the degree of lipid oxidation. [source] Existence of a critical carbon number in the aging of a wax-oil gelAICHE JOURNAL, Issue 9 2001Probjot Singh A fundamental study was carried out to understand the aging (or hardening) of the wax-oil gels formed in the subsea pipelines during the flow of crude oil from offshore wells to shore. The aging process is a counterdiffusion phenomenon where there exists a critical carbon number (CCN), and wax molecules with carbon numbers greater than the CCN diffuse into the gel matrices and vice versa. Using a careful analysis of carbon number distributions of gel deposits, collected from a cold finger after various deposition time intervals, the CCN for the wax-oil system was obtained. A mathematical model, based on a modified version of UNIQUAC model, was developed to predict the CCN for wax-oil systems. The size of the interaction units for n-alkanes in the solid-phase UNIQUAC model was found to be a strong function of the mean carbon number in the solid phase. [source] Soret Diffusion and Non-Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler NumbersTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2007Laurence A. Belfiore Abstract The adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion-thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non-ideal pseudo-binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion-controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300-400 K and thermal diffusion enhances the flux of "smaller" reactants toward the centre of the catalyst. For "large-molecule reactants" that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off-diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two-body interactions for Lennard-Jones molecules in the virial equation of state. On prédit l'augmentation de la température adiabatique dans les pastilles catalytiques à partir d'une version modifiée de l'équation de Prater. Les relations réciproques d'Onsager pour le transfert de chaleur et de matière couplé sont violées dans une analyse de la diffusion thermique dans les catalyseurs macroporeux avec réaction chimique exothermique lorsque la conduction de Dufour (p.ex., l'effet de thermo-diffusion) est négligée. Dans cet article, on analyse la conduction de Dufour pour des mélanges de gaz pseudo-binaires idéaux et non idéaux qui simulent la production de méthanol à partir d'oxyde de carbone et d'hydrogène. Dans le régime à diffusion contrôlée à grand nombre de Damköhler entre les pastilles pour lesquels les collisions entre les molécules fournit la résistance dominante au transfert de matière à l'intérieur des pores catalytiques, les températures dans le noyau catalytique pourraient être bien plus grandes que les prédictions basées sur l'équation de Prater originale lorsque le nombre de Prater excède 0,30. Le flux moléculaire de l'énergie thermique inclut la loi de Fourier, le flux interdiffusionnel, et la conduction de Dufour. Le flux massique diffusionnel inclut la loi de Fick et l'effet Soret. Toutes les propriétés physicochimiques du mélange de gaz réactif montre une dépendance thermique. Il n'y a essentiellement pas de différence entre les prédictions des températures maximales entre les pastilles qui incluent ou négligent la conduction de Dufour idéale quand les températures de surface catalytiques externes sont comprises entre 300 et 400 K; la diffusion thermique améliore le flux des réactifs «plus petits» vers le centre du catalyseur. Pour les «réactifs composés de grandes molécules» qui participent aux réactions exothermiques, la diffusion thermique s'oppose à la loi de Fick et la conduction de Dufour à la loi de Fourier. Dans ces conditions, il est démontré que les températures de noyau sont surestimées en négligeant les deux mécanismes de couplage hors-diagonales (c.à-d. la diffusion de Soret et la conduction de Dufour). Des nombres de Prater plus grands que l'unité et des pressions de gaz élevées peu réalistes sont nécessaires pour distinguer les températures maximales entre les pastilles entre les simulations de gaz idéales et réelles, en considérant pour ces dernières les interactions à deux corps pour les molécules de Lennard-Jones dans l'équation d'état du viriel. [source] | ||||||||||