On the distribution of partial sums of irrational rotations

Periodica Mathematica Hungarica - For an irrational $$\alpha $$ , we investigate the sums $$\sum _{i=1}^n \left( \{i \alpha \} - \frac{1}{2} \right) $$ and $$\sum _{i=1}^n \left\{ \left( \{i \alpha...     

Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem

The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a (⌈D_s/2⌉+1)/(⌊log₂(D_s+1)⌋+1)-approximation algorithm for MVRST where D_s is the minimum diameter of spanning trees of G.     

有机材料(EDT-DSDTFVO)_2FeCl_4和(EDT-DSDTFVO)_2GaCl_4的磁电阻分析

有机材料(EDT-DSDTFVO)2FeCl4和(EDT-DSDTFVO)2GaCl4的输送实验结果,显示出这两类盐的电阻率对温度的依赖性以及压力效果十分相似,但是两种盐的磁电阻率却表现出很大的不同,FeCl4盐为负磁电阻,而GaCl4盐为正磁电阻。我们认为这种输送现象的差异性起源于π-d相互作用。我们用EDT-DSDTFVO表示ethylenedithiodiselenadithiafulvalenothioquinone-1,3-dithiole methide。     

Measurement of pole figures and orientation functions for Valonia cellulose

The x-ray pole-figure technique has been applied to the study of orientation in Valonia cellulose. It is found that the maximum of the orientation distribution of the (2 20) poles of crystallites in Valonia cell walls is precisely normal to the cell wall surface, and the pole population is denser in the longitudinal direction than in the transverse direction. The orientation is interpreted as a typical uniplanar-axial orientation after Heffelfinger and Burton's classification: a uniplanar orientation in (22 0), and two types of uniaxial orientation in the (220) and (400) planes based on the unit cell parameters for Valonia cellulose. The degree of biaxial orientation of the (22 0), (220), and (400) plane normals as well as three principal crystallographic axes are shown by Desper's equilateral triangle plots.     

Studies on isoindoline derivatives and related compounds. I Synthesis and reduction of 1,3-dicarboethoxymethyleneisoindoline

The reaction of iminoether III with benzyl cyanoacetate gave ethyl 1-(α-cyanocarbobenzyl-oxymethylene)isoindoline-3-acetate (V) in a 26% yield. Decarboxylation of ethyl 1-(α-cyanocarboxymethylene)isoindoline-3-acetate (VI), obtained by hydrogenolysis of V, gave a mixture of 1-carboethoxymethyleneisoindoline-3-acetonitrile (VII) as major component and 1-carboethoxymethylene-3-cyanomethyleneisoindoline (VIII) as minor component, which were reconvertible into each other. On the other hand, decarboxylation of VI was successfully carried out to give VII as a single product under a nitrogen atmosphere. Ethanolysis and autoxidation of VII gave crystalline diethyl 1,3-dicarboethoxymethyleneisoindoline (XIII). Catalytic hydrogenation of of XIII over platinum oxide gave diethyl isoindoline-cis-1,3-diacetate (XIV) in a yield of 92%. The uv spectra of these 1,3-disubstituted isoindoline derivatives are summarized in Table I.     

Irradiation of Phenolic Compounds with Ultraviolet Light Causes Release of Hydrated Electrons

Phenolic compounds are widely used for a number of purposes, including medical drugs, cosmetics, food additives, and supplementary foods, and are often exposed to the ultraviolet (UV) rays of the sun. We herein examined free radicals produced from phenolic compounds by UV irradiation using an electron paramagnetic resonance (ESR)-spin trapping technique with 5,5-dimethyl-1-pyrroline-N-oxide (DMPO). The ESR signals of DMPO adducts of the hydrogen radical (DMPO–H) and hydroxyl radical were detected following the UV irradiation of polyhydric phenols, such as hydroquinone, catechol, resorcinol, pyrogallol, and methyl gallate, in an aqueous solution. Radical adducts were not detected in monohydric phenols, such as phenol and methylparaben. The signal intensity of DMPO–H became stronger as the concentration of phenolic compounds increased. The signal intensity of DMPO–H decreased when the solution in which air was replaced with N₂O, a scavenger of hydrated electrons, was irradiated. However, sodium formate, a scavenger of the hydrogen radical, did not affect the signal intensity of DMPO–H. The signal intensity of DMPO–H became stronger as the pH of the solution increased. Semiquinone-type radicals increased following the UV irradiation of solutions of polyhydric phenols in the absence of DMPO. These results indicate that hydrated electrons are generated by the UV irradiation of polyhydric phenols, and that phenoxide ions are responsible for the production of hydrated electrons.     

Diels-alder reactions of substituted maleic anhydrides with 1-vinylcoclohexane: Stereospecific formation of a bicyclic intermediate useful for syntheses of clerodane diterpenes

The Diels-Alder reaction of 1-vinylcyclohexene with aconitic anhydride gives the adduct 5b which has the reversed stereochemistry of that predicted by Alder's endo rule. On the other hand, reactions with chloromethylmaleic anhydride and citraconic anhydride afford endo-adducts 23 and 24, respectively. Adduct 23 has the appropriate stereochemistry and functionality for the syntheses of clerodane and related diterpenes.