Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003     

On global integrability of BMO functions on general domains

Extending results of Staples and Smith-Stegenga, we characterize measurable subsets of a given domainD ⊃R ⁿ on which BMO(D) functions areL ^p integrable or exponentially integrable. In particular, we characterize uniform domains by the integrability of BMO functions. We also remark on the boundedness of domains satisfying a certain integrability condition for the quasihyperbolic metric.     

Mass spectrometric analysis of low molecular mass polyesters by laser desorption/ionization on porous silicon

A low molecular mass polyester was analyzed by desorption/ionization on porous silicon (DIOS) mass spectrometry. The results were compared with those of matrix-assisted laser desorption ionization (MALDI) mass spectrometry using matrixes of alpha-cyano-4-hydroxycinnamic acid (CHCA) and 10,15,20-tetrakis(pentafluorophenyl)porphyrin (F20TPP). The CHCA matrix was not suitable for characterization of low molecular mass components of the polyester because the matrix-related ions interfered with the component ions. On the other hand, the F20TPP matrix showed no interference because no matrix-related ions appeared below m/z 822. However, the solvent selection for determining optimal conditions of sample preparation was limited, because F20TPP does not dissolve readily in any of the available organic solvents. In the DIOS spectra, the polymer ions were observed at high sensitivity without a contaminating ion. No matrix is needed for DIOS spectra of low molecular mass polyesters, facilitating sample preparation and selectivity of a precursor ion in post-source decay measurements.     

Reaction of indium ate complexes with allylic compounds. Controlling SN2/SN2′ selectivity by solvents

Vinyl and methylindium ate complexes (indates) were prepared and both the tendency of immigration and regioselectivity toward cinnamyl bromide were investigated. The vinyl group was more preferably transferred than the Me group, giving a regioisomeric mixture of S_N2 and S_N2′ products. The ratio of S_N2/S_N2′ selectivity can be controlled by solvents; in the presence of polar solvents, such as N-butylpyrrolidone (NBP) and THF, the S_N2′ product was mainly obtained, whereas the S_N2 product was selectively prepared in solutions containing hexane. The vinylindium compound, generated by the reaction of allylic-type diindium reagents with imine, was also converted to the corresponding vinyl indate, which was allowed to react with allyl chloride to give a three-component coupling product.     

Non-destructive determination of spontaneously fissioning nuclides by neutron coincidence counting using multichannel time spectroscopy

A non-destructive method for determining the amount of actinoids has been developed. The method is based on thermal neutron coincidence counting and employs a selective detection of neutrons resulting from the spontaneous fission of actinoids. The detection system is described in detail and the measurement results of²⁴⁴Cm as an example are presented. The results show that the measured fission rate of²⁴⁴Cm is consistent with the fission rate calculated from ENDF/B-V data and that the amount of²⁴⁴Cm can be determined within about 5% accuracy even in the presence of a large amount of actinoids, for example, up to 2.6·10⁶, 3.6·10⁴, or 1.6·10³ times in the mass ratio of²³⁹Pu,²⁴¹Am, or²⁴⁰Pu to²⁴⁴Cm, respectively.     

Phase-transfer catalytic activity of soluble polystyrenes containing crown ether moieties and hydroxyl groups adjacent to the macrorings

Soluble polystyrenes with crown ether structures and hydroxyl groups adjacent to the macrorings were prepared by the reaction of epoxide-containing polystyrenes with monoaza-15-crown-5 or monoaza-18-crown-6. Rate of formation of the polymer-bound alkali cation-crown alkoxide ion pair from the soluble polystyrenes and aqueous NaOH or KOH depended on the loading of crown ether and hydroxyl units and on the size of the macroring. The elimination of HCl from less reactive 2-chloroethylbenzene with aqueous NaOH or KOH in the presence of the soluble polystyrene catalysts under two-phase conditions was limited mainly by the intrinsic reaction rate. The elimination of HBr from more reactive 2-bromoethylbenzene in the presence of the less (11%) ring-substituted polymer catalyst with 18-crown unit was limited by the alkoxide formation rate. © 1994 John Wiley & Sons, Inc.     

Molecular Recognition of Nucleic Acid Bases in Water by Hydrogen Bonding of Poly(vinyldiaminotriazine)

Poly(2-vinyl-4,6-diamino-1,3,5-triazine) efficiently binds nucleic acid bases and nucleosides in water by using complementary hydrogen bonding. The binding activity decreases in the order: U, T > A C, G. The corresponding monomer shows virtually no activity, indicating a predominant role of polymer effect for the molecular recognition in water.     

Surprising 1,7-cyclization of vinyl carbonyl ylides generated from reaction of indanetrione with vinyl diazo compounds

Reactions of tricarbonyl compounds with vinyl diazo compounds 2 were carried out. Reaction of 1,2,3-indanetrione with 2a,b,c gave the spiroindan-1,3-dione-2,2′-benzodihydrooxepin 7a,b,c, but not normal products oxirane and dihydrofuran derivatives expected from intermediate vinyl carbonyl ylides 4. Formation of 7 requires isomerization of vinyl carbonyl ylides 4 bearing a (Z)-cyanostyryl group to unstable (E)-form 5 and subsequent cyclization to oxepin 6 followed by a 1,5-hydrogen shift. However, reaction of 2 with six-membered cyclic tricarbonyl compounds 1,2,3-trioxo-2,3-dihydrophenalene 11 and dimethylalloxane 13 gave the dioxole 12 and the dihydrofuran 14, respectively, typical products expected from vinyl carbonyl ylides.     

Formation and stabilization model of the 42-mer Abeta radical: implications for the long-lasting oxidative stress in Alzheimer's disease

Amyloid fibrils mainly consist of 40-mer and 42-mer peptides (Abeta40, Abeta42). Abeta42 is believed to play a crucial role in the pathogenesis of Alzheimer's disease because its aggregative ability and neurotoxicity are considerably greater than those of Abeta40. The neurotoxicity of Abeta peptides involving the generation of free radicals is closely related to the S-oxidized radical cation of Met-35. However, the cation's origin and mechanism of stabilization remain unclear. Recently, structural models of fibrillar Abeta42 and Abeta40 based on systematic proline replacement have been proposed by our group [Morimoto, A.; et al. J. Biol. Chem. 2004, 279, 52781] and Wetzel's group [Williams, A. D.; et al. J. Mol. Biol. 2004, 335, 833], respectively. A major difference between these models is that our model of Abeta42 has a C-terminal beta-sheet region. Our biophysical study on Abeta42 using electron spin resonance (ESR) suggests that the S-oxidized radical cation of Met-35 could be generated by the reduction of the tyrosyl radical at Tyr-10 through a turn structure at positions 22 and 23, and stabilized by a C-terminal carboxylate anion through an intramolecular beta-sheet at positions 35-37 and 40-42 to form a C-terminal core that would lead to aggregation. A time-course analysis of the generation of radicals using ESR suggests that stabilization of the radicals by aggregation might be a main reason for the long-lasting oxidative stress of Abeta42. In contrast, the S-oxidized radical cation of Abeta40 is too short-lived to induce potent neurotoxicity because no such stabilization of radicals occurs in Abeta40.