An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.     

Some characterisations of supported algebras

We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L₀ and R₀ which consist respectively of the predecessors of the projective modules, and of the successors of the injective modules.     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

关于不含k-C-圈的n阶r-一致超图的若干结果

主要讨论了不含k-C-圈的n阶r-一致超图,对不同的k,分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件.     

Measurement of surface topography by RGB Shadow-Moiré with direct phase demodulation

In this paper we present the application of a direct demodulation method for the measurement of surface topography by means of Shadow-Moiré. In our set-up, we use three LEDs (with green, red and blue peak wavelengths) to illuminate the grating. Due to the different position of these light sources, a polychromatic Shadow-Moiré fringe pattern is produced, which can be described as the superposition of three monochromatic (red, green and blue) fringe patterns. Taking the image of this polychromatic fringe pattern with a RGB CCD camera, we get a monochromatic fringe pattern stored at each RGB channel of the CCD. The direct demodulation algorithm employed uses these fringe patterns to calculate the wrapped phase map. After unwrapping the phase map using a standard multi-grid technique, we implemented an automatic procedure to detect the area of interest of the phase map by removing low modulation zones and to calculate the absolute value of the phase. In this way it is possible to determine the topography of a surface with a single RGB snapshot maintaining a simple experimental set-up, which is an important feature, especially for the study of dynamic phenomena such as deformations. We present the experimental results obtained after measuring different objects with both smooth and rough surface textures.     

The electrochemical reduction of perezone in the presence of benzoic acid in acetonitrile

An electrochemical study using transient techniques of a quinone-type natural product, perezone, has been performed in acetonitrile and in the presence of benzoic acid. Using linear sweep voltametry and single potential step chronoamperometry, it was possible to establish that the reduction mechanism of perezone involves a monoelectronic charge-transfer step, followed by a protonation step and homogeneous charge transfer due to disproportionation of the protonated intermediate. The mechanism for the homogeneous charge-transfer step was found to be of the type DISP1 (disproportionation order one) from the results of double potential step chronoamperometry experiments. The occurrence of the DISP1 mechanism was provoked by the mildly acidic medium used in this study.