Geometric graph homomorphisms

A geometric graph is a simple graph drawn on points in the plane, in general position, with straightline edges. A geometric homomorphism from to is a vertex map that preserves adjacencies and crossings. This work proves some basic properties of geometric homomorphisms and defines the geochromatic number as the minimum n so that there is a geometric homomorphism from to a geometric n‐clique. The geochromatic number is related to both the chromatic number and to the minimum number of plane layers of . By providing an infinite family of bipartite geometric graphs, each of which is constructed of two plane layers, which take on all possible values of geochromatic number, we show that these relationships do not determine the geochromatic number. This article also gives necessary (but not sufficient) and sufficient (but not necessary) conditions for a geometric graph to have geochromatic number at most four. As a corollary, we get precise criteria for a bipartite geometric graph to have geochromatic number at most four. This article also gives criteria for a geometric graph to be homomorphic to certain geometric realizations of K_{2, 2} and K_{3, 3}. © 2011 Wiley Periodicals, Inc. J Graph Theory 69:97‐113, 2012     

Numerical Simulation of Mixing in a Micro-well Scale Bioreactor by Computational Fluid Dynamics

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Total synthesis of (+)-hatomarubigin B.

The first total synthesis of (+)-hatomarubigin 3 is described. The tetra-O-acetyl diborate promoted Diels-Alder reaction of 5-hydroxy-8-(2',3',4',6'-tetra-O-acetyl-beta-D-glucopyranosyloxy)-1,4-naphthoquinone 8 and (E, 1R*,5R*)-3-(2'-methoxyvinyl)cyclohex-2-enol (+/-)-7 gave a mixture of four cycloadducts from which (1S,3S,6S,6aR,12aR,12bS)-1,8-dihydroxy-6-dimethoxy-1-hydroxy-3-methyl-11-(2',3',4',6'-tetra-O-acetyl-beta-D-glucopyranosyloxy)-1,2,3,4,6,6a,12a,12b-octahydrobenz[a]anthracene-7,12-dione 12 was isolated in 51% yield. Selective methylation and acetylation of 12 gave (1S,3S,6S,6aR,12aR,12bS)-1-acetoxy-6,8-dimethoxy-3-methyl-11-(2,3,4,6-tetra-O-acetyl-alpha-D-glucopyranosyloxy)-1,2,3,4,6,6a,12a,12b-octahydrobenz[a]anthracene-7,12-dione 10a. Sequential aromatization, photooxidation and hydrolysis of the glucosyl unit gave (+)-3 (98% ee) in an 8% overall yield from 8.     

A 2.5-D dynamic model for a saturated porous medium. Part II: Boundary element method

The 3-D boundary integral equation is derived in terms of the reciprocal work theorem and used along with the 2.5-D Green’s function developed in Part I [Lu, J.F., Jeng, D.S., Williams, S., submitted for publication. A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function. Int. J. Solids Struct.] to develop the 2.5-D boundary integral equation for a saturated porous medium. The 2.5-D boundary integral equations for the wave scattering problem and the moving load problem are established. The Cauchy type singularity of the 2.5-D boundary integral equation is eliminated through introduction of an auxiliary problem and the treatment of the weakly singular kernel is also addressed. Discretisation of the 2.5-D boundary integral equation is achieved using boundary iso-parametric elements. The discrete wavenumber domain solution is obtained via the 2.5-D boundary element method, and the space domain solution is recovered using the inverse Fourier transform. To validate the new methodology, numerical results of this paper are compared with those obtained using an analytical approach; also, some numerical results and corresponding analysis are presented.     

A validated RP‐HPLC method for the evaluation of the influence of grapefruit juice on liver S9 activation of sacubitril

Grapefruit juice inhibits esterase enzyme. Therefore, a possible interaction with ester prodrugs should be taken into consideration. In this study, the influence of grapefruit juice on sacubitril (SAC) rat liver S9 activation by esterase enzyme was evaluated. An RP‐HPLC method was developed and validated for estimation of SAC in rat liver S9 fraction using a C₁₈ Cyano column as stationary phase and acetonitrile–sodium di‐hydrogen phosphate buffer (0.02 m , pH 4 adjusted by o‐phosphoric acid, 40:60, v/v), as mobile phase at a flow rate of 1 mL/min and UV detection at 254 nm. The method was successfully applied to an in vitro study in which SAC was incubated with rat liver S9 fraction prepared from rats that had previously ingested grapefruit juice for a week. The calculated SAC concentration after incubation was compared with that of SAC incubated with rat liver S9 fraction from the rat control group. The statistical significance between the results of test and control incubation sets was assessed. In conclusion, the current study demonstrated that grapefruit juice decreased SAC hydrolysis, hence delaying its activation to sacubitrilat (active form) in gut lumen. Based on this food–drug interaction, it may be required that grapefruit juice should be consumed with caution in patients receiving SAC.     

Evaluation of the shadowgraph method for the convective flow in a side-heated cavity

The shadowgraph method is used to visualize the convective flow in a water-filled square cavity, which is differentially heated and cooled from the opposing vertical sidewalls. Since in this system a quantitative recovery of the temperature field from the observed shadowgraph images is not possible, we apply a somewhat reverse procedure. The numerical solution of the cavity flow yields the field of the refractive index. By numerically integrating the path of light through this field, artificial shadowgraph images are constructed. This makes a comparison of the numerical and the experimental temperature fields possible and also leads to a clearer interpretation of the shadowgraph images and a better understanding of the way in which certain features are generated. The procedure is not restricted to the cavity flow, but can be applied whenever the field of the refractive index is available.     

Production of very massive Higgs bosons

We compare Higgs boson production mechanisms at multi-TeV hadronic colliders. In addition to the previously investigated processes gluon + gluon → H and $\text{q}\text{q}\text{→ V}{}^1\text{→}\text{VH}\text{(}\text{V}\text{=}\text{W, Z}\text{)}$, we consider Higgs boson formation by pairs of virtual W's or Z's, a process analogous to two-photon collisions in e⁺e^? scattering. The Higgs production process $\text{W}{}^1\text{W}{}^1\text{→}\text{H}$ is dominated by longitudinal W's and is the most important mechanism for M_H > 6 M_W, if the top quark mass is about 30 GeV.