The inductive Alperin–McKay condition for 2-blocks with cyclic defect groups

We verify the inductive Alperin–McKay condition introduced by the second author, for 2-blocks of the covering groups of finite simple non-abelian groups with cyclic defect groups.     

Statistics of velocity gradients in turbulence at moderate reynolds numbers

A direct numerical simulation of the Navier-Stokes equation is performed in order to investigate the small scale structure of turbulence at moderately large microscale Reynolds numbers 40–140, using the spectral method with 340³ modes starting from a high-symmetric flow. It is shown that the small scale motion is statistically isotropic. The probability density distribution of the velocity is Gaussian, while those of the velocity gradients and the vorticity are not Gaussian but have long exponential tails. The moments of the velocity gradients are expressed in terms of the gamma function, and the ratio of the moments of the velocity gradients of successive orders increases linearly with the order. A comparison is made with a laboratory experiment.     

Color speckle

Speckle is a random distribution of a radiant power density or an irradiance on the observation plane (retina of observers in the laser display) due to the interference of randomly phase-modulated wavefronts. Since a color is synthesized by the superposition of red-green-blue (RGB) primary-color lasers in laser displays, if the speckle patterns of RGB lasers are uncorrelated with each other, then the fluctuation in radiant power density results in a change in color received by the observer. We name this random distribution of color “color speckle”. The distribution of color on the xy chromaticity diagram is investigated for speckle patterns of various speckle contrasts. We demonstrate a numerical simulation of color speckle. Then, we derive the theoretical expressions of the variance and covariance of the distribution of xy chromaticity under the assumption of low speckle contrast.     

Nonuniform intensity distribution of the scattered light by moving diffuser across projection lens pupil and its influence in speckle reduction

The measurement of the nonuniform intensity distribution of scattered light by a moving diffuser using an integrating sphere, which lowers the effective numerical aperture of the projection lens and affects the lowest speckle contrast, is reported. A comparison of the effective numerical apertures realized by several diffusers revealed that JIS #600 or #800 diffusers are most appropriate for efficient speckle reduction     

A Two-Step Synthesis Of (±)-Blastmycinolactol Using Acylurea

A convenient synthesis of natural (±)-blastmycino-lactol from the aldol addition reaction of n-pentanoylurea and (±)-2-benzyloxypropionaldehyde is described.     

Thermal Degradation and Flame Resistivity of Tetrabrominated Epoxy Resin

The thermal degradation mechanism of tetrabrominated epoxy resin was investigated in order to explain its flame retardant mechanism. From the results obtained it was concluded that the flame retardant mechanisms are 1) a lowering of temperature through degradation and 2) the formation of hydrogen bromide and its role in catalysis in the condensation reaction of the resin.

These mechanisms were investigated by the pyrolysis behavior of the resin by gas chromatography, thermal gravimetric analysis, and differential thermal analysis studies.     

Synthesis and Characterization of Novel Methacrylic Copolymers: Determination of Monomer Reactivity Ratios

A new methacrylic monomer, 4‐nitro‐3‐methylphenyl methacrylate (NMPM) was prepared by reacting 4‐nitro‐3‐methyl phenol dissolved in methyl ethyl ketone (MEK) in the presence of triethylamine as a catalyst. Copolymerization of NMPM with methyl methacrylate (MMA) has been carried out in methyl ethyl ketone (MEK) by free radical solution polymerization at 70±1°C utilizing benzoyl peroxide (BPO) as initiator. Poly (NMPM‐co‐MMA) copolymers were characterized by FT‐IR, ¹H‐NMR and ¹³C‐NMR spectroscopy. The molecular weights (M_w and M_n) and polydispersity indices (M_w/M_n) of the polymers were determined using a gel permeation chromatograph. The glass transition temperatures (T_g) of the copolymers were determined by a differential scanning calorimeter, showing that T_g increases with MMA content in the copolymer. Thermogravimetric analysis of the polymers, performed under nitrogen, shows that the stability of the copolymer increases with an increase in NMPM content. The solubility of the polymers was tested in various polar and non‐polar solvents. Copolymer compositions were determined by ¹H‐NMR spectroscopy by comparing the integral peak heights of well separated aromatic and aliphatic proton peaks. The monomer reactivity ratios were determined by the Fineman‐Ross (r₁ =7.090:r₂=0.854), Kelen‐Tudos (r₁=7.693: r₂=0.852) and extended Kelen‐Tudos methods (r₁=7.550: r₂= 0.856).     

Straightforward synthesis of fucoxanthin short-chain derivatives via modified-Julia olefination

Fucoxanthin is an essential pigment for the light-harvesting of aquatic algae. It exhibits high energy transfer efficiencies to Chl a (>80%) as well as peridinin (>95%). In order to verify the generality and specificity of the noticeable observation on the ICT excited energy state character, which was found in the study of peridinin, we achieved the straightforward synthesis of a series of fucoxanthin short-chain derivatives via the modified-Julia olefination with the aldehyde half segment possessing a β,γ-epoxyketone function. The established method was successfully applied to the synthesis of the epoxy olefin derivative as an allene modified fucoxanthin analogue.