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.     

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.     

Michael addition reactions of acetoacetates and malonates with acrylates in water under strongly alkaline conditions

Michael addition reactions of acetoacetates and malonates with acrylates in a 5 M KOH aqueous solution without using any other catalysts are described. When they are either tert-butyl or benzyl esters, the reaction proceeded very rapidly to afford moderate to high yields of the corresponding bis-Michael adducts that are unexpectedly stable under these conditions.     

On the theory of coagulation and the coalescence of mercury droplets in aqueous solutions

Summary The potential ranges of polarization of a pair of dropping mercury electrodes, over which the two mercury droplets coalesced, were measured as functions of ionic concentrations for various electrolytes. In the case of simple inorganic electrolytes the condition of coalescence obtained was proved to be in quantitative agreement with theVerwey-Overbeek theory of coagulation of lyophobic sols, thus indicating that the interaction between sub-microscopic particles of hydrophobic sols is essentially the same as that between macroscopic mercury droplets. While, in the case of sodium citrate solutions two kinds of marked deviations from the theory were observed, which appeared to be due to the specific adsorption of citrate ions and to the formation of protective interfacial films.

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Zusammenfassung Die Potentialbereiche der Polariation eines Paares von Quecksilber-Tropfelektroden, über die die beiden Quecksilbertropfen koaleszieren, werden als Funktion der Ionenkonzentration verschiedener Elektrolyte gemessen. Im Fall einfacher anorganischer Elektrolyte wurde die erhaltene Bedingung der Koaleszenz mit der Theorie vonVerwey-Overbeek der Kaogulation lyophober Sole geprüft und in quantitativer übereinstimmung befunden. Das zeigt, da\ die Wechselwirkung zwischen submikroskopischen Partikeln hydrophober Sole im wesentlichen dieselbe ist wie zwischen den makroskopischen Quecksilbertröpfchen. Dagegen ergaben sich im Fall von Natriumzitratlösungen zwei Arten markanter Abweichungen von der Theorie. Diese scheinen spezifische Adsorption der Zitrationen und die Ausbildung von SchutzgrenzflÄchenfilmen zur Ursache zu haben.