THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

On CCE graphs of doubly partial orders

Let D be a digraph. The competition-common enemy graph (CCE graph) of D has the same set of vertices as D and an edge between vertices u and v if and only if there are vertices w and x in D such that (w,u), (w,v), (u,x), and (v,x) are arcs of D. We call a graph a CCE graph if it is the CCE graph of some digraph. In this paper, we show that if the CCE graph of a doubly partial order does not contain C₄ as an induced subgraph, it is an interval graph. We also show that any interval graph together with enough isolated vertices is the CCE graph of some doubly partial order.     

Depigmenting activity and low cytotoxicity of alkoxy benzoates or alkoxy cinnamte in cultured melanocytes

To obtain effective and safe topical depigmenting agents, we synthesized hydroxybenzoates, alkoxybenzoates, and 3,4,5-trimethoxycinnamate containing a thymol moiety and screened then for high-level inhibitory activity against melanin synthesis in cultured melanocytes. Eight compounds were tested for their depigmenting effect and cytotoxicity using a murine melanocyte cell line. We found that 3,4,5-trialkoxybenzoates and 3,4,5-trimethoxycinnamate, synthesized by conjugating 3,4,5-trialkoxybenzoic acids and 3,4,5-trimethoxycinnmic acid with thymol, showed a potent depigmenting effect and low cytotoxicity. Compound 4h, 5-methyl-2-(methylethyl)phenyl (2E)-3-(3,4,5-trimethoxyphenyl)prop-2-enoate, showed the most potent depigmenting effect (IC50=10 microM) with low cytotoxicity (IC50=200 microM).     

Total synthesis and absolute stereochemistry of (9R,10S)-epoxyheptadecan-4,6-diyn-3-one, a diacylglycerol acyltransferase inhibitor from Panax ginseng

Asymmetric synthesis of four possible stereoisomers of (9,10)-epoxyheptadecan-4,6-diyn-3-one was accomplished, and the absolute configuration of the naturally occurring (9R,10S)-epoxyheptadecan-4,6-diyn-3-one (1) was elucidated.     

Liquid fluidized bed starter culture ofTrichoderma reesei for cellulase production

A starter culture ofTrichoderma reesei (Rut-C30) prepared in a liquid fluidized bed reactor (LFBR) gave better growth and greater cellulase production in submerged fermentation than a conventional shake flask inoculum. The LFBR starter was prepared by first coatingT. reesei spores to 0.25 mm size corncob (1.0x10⁸g^-1) in a medium containing 1.0% corncob, 0.5 gL^-1 xylose and 0.1 gL^-1 lactose in a balanced salt solution, then fluidizing the particles in the LFBR for 36 h to allow germination of the spores, and covering the particles with an approx 30 μm thick biofilm. This biofilm that developed in constant adherence to the lignocellulosic carrier, apparently became well adapted to grow rapidly on insoluble cellulose substrates (Solca Floc), and had the enzymes of the cellulase complex induced for increased cellulase production. The LFBR starter used in a stirred tank reactor (STR) gave 15 gL^-1 biomass production and 6.5 IU mL^-1 overall cellulase activity with a volumetric productivity of 64 IU L^-1h^-1 in a 5 d fermentation, compared with a 7 d shake flask inoculum that gave 11 gL^-1 biomass and 3.2 IU mL^-1 cellulase activity, with a volumetric productivity of 31IU L^-1h^-1. The LFBR starter culture retained its viability in dry storage for 6–9 mo.