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.     

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.     

Reaction of poly(vinyl alcohol) with tetravalent ceric ion

Poly(vinyl alcohol) (PVAI) was oxidized by ceric ion, Ce(IV), in aqueous HNO₃ medium at different temperatures and found to be degraded as a result of selective cleavage of the 1,2-glycol unit existing in PVAl. The rate of oxidation increased with increasing temperature. The aldehyde groups formed at the ends of the degraded polymer upon oxidation were relatively stable at 0°C. With rise of temperature, the aldehyde groups reacted either with excess of Ce(IV) to carboxylic acids or with hydroxyl groups of PVAl molecules to give acetal linkage. When the acetalization predominated over the oxidation to carboxyl group, gelation of the reaction mixture was observed. Based on these results, a plausible mechanism of oxidation of PVAl with Ce(IV) and the subsequent reactions is discussed.     

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.     

New catalytic cycle for couplings of aldehydes with organochromium reagents

[reaction: see text] A new catalytic cycle has been developed to effect all three subgroups of Cr-mediated couplings, i.e., (1) Ni/Cr-mediated alkenylation, alkynylation, and arylation, (2) Co/Cr-mediated 2-haloallylation, alkylation, and propargylation, and (3) Cr-mediated allylation. In the presence of chiral sulfonamide ligands, good asymmetric inductions can be achieved for some of the Ni/Cr-mediated alkenylation, Co/Cr-mediated 2-haloallylation and propargylation, and Cr-mediated allylation.     

Determination of optimal formulation for extrusion granulation by compression test of wet kneaded mass

The purpose of this study is to propose the application of a compression test to the determination of an optimal formulation for extrusion granulation. The electric current during extrusion was measured and the characteristics of the wet kneaded mass in the compression test were analyzed under various operating conditions, with different types of extruders and several formulations of kneaded mass. It was found that addition of a binder (HPC-L) to pharmaceutical powders lowered the load of a high-compressing type extruder, since the binder reduced the friction among the wet mass during extrusion. Also, the support stress was found to be proportional to the compression pressure without a binder, although an inflection point appeared on the support stress curve when a binder was present. This inflection point suggested large water retention of the wet kneaded mass, at which the medium of pressure was changed from a discontinuous solid powder to a continuous liquid, and large water retention contributed to the low friction of the wet mass. The friction of the wet kneaded mass and the aptitude of the formulation for extrusion were understood by using the compression test. The compression test is a very useful procedure at the first stage of a formulation study.     

Surprisingly efficient catalytic Cr-mediated coupling reactions

[reaction: see text] With use of 1 mol % of Cr catalyst 5, surprisingly efficient Cr-mediated couplings of aldehydes with various types of nucleophiles have been realized. The catalyst set of Cr catalyst 5 and Ni catalyst 4 is used for alkenylation, alkynylation, and arylation, whereas the catalyst set of Cr catalyst 5 and CoPc (cobalt phthalocyanine) is used for 2-haloallylation, alkylation, and propargylation. Only the Cr catalyst 5 is required for allylation. The reaction rates in DME and THF have been found significantly faster than that in MeCN.