A new matrix method based on rigid elements and its application to plane problems

A new matrix is proposed here which is based on rigid elements. The efficiency and usefulness of this method has been demonstrated for plane problems. The purpose of this paper is to formulate the method and to indicate its validity.     

An improved process of separation of R- and S-timolol

Diastereomeric timolol tartrates 4 are obtained in a one-pot synthesis from the racemic base 2 and optically active O,O-diacetyl- or O,O-dibenzoyltartaric anhydrides 3 , as only one of the diastereomers precipitates from acetone solution. Acidic hydrolysis as the corresponding 4 leads to timolol in high yield and optical purity.     

Alternating copolymerization of carbon dioxide and epoxide by manganese porphyrin: The first example of polycarbonate synthesis from 1-atm carbon dioxide

The first successful example of the formation of polycarbonate from 1-atm carbon dioxide and epoxide was demonstrated by the alternating copolymerization of carbon dioxide and epoxide with manganese porphyrin as a catalyst. The copolymerization of carbon dioxide and cyclohexene oxide with (porphinato)manganese acetate proceeded under the 1-atm pressure of carbon dioxide to give a copolymer with an alternating sequence. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3549–3555, 2003     

Estimates for Hyperbolic Equations of Space Dimension 3

We discuss the problem of boundedness fromL^p(Rⁿ) toL^p′(Rⁿ) (1/p+1/p′=1, 1?p?2) of operators of the typeM=F⁻¹e^i?(ξ)a(ξ) F, which is related to the study of hyperbolic equations with constant coefficients. The boundedness is dependent on a geometrical property ofΣ=?⁻¹(1), and its dependence has been exactly determined in the casesn=2, 1?p?2 andn?3,p=1, 2 (M. Sugimoto,Math. Z.215(1994), 519–531;222(1996), 521–531). This paper is devoted to the unsolved case 1<p<2, and a strange phenomenon is exhibited in the simplest casen=3.     

Side‐chain crystallization behavior of graft copolymers consisting of an amorphous main chain and crystalline side chains. II. Poly(n‐hexyl methacrylate)‐graft‐poly(ethylene glycol)

The phase behavior and crystallization of graft copolymers consisting of poly(n‐hexyl methacrylate) (PHMA) as an amorphous main chain and poly(ethylene glycol) (PEG) as crystallizable side chains (HMAx with 15 ≤ x ≤ 73, where x represents the weight percentage of PEG) were investigated. Small‐angle X‐ray scattering profiles measured above the melting temperature of PEG suggested that a microdomain structure with segregated PHMA and PEG domains was formed in HMA40 and HMA46. This phase behavior was qualitatively described by a calculated phase diagram based on the mean‐field theory. Because of the segregation of PEG into microdomains, the crystallization temperature of the PEG side chains in HMAx was higher than that in poly(methyl acrylate)‐graft‐poly(ethylene glycol) having a similar value of x, which was considered to be in a disordered state above the melting temperature. In HMAx with x ≤ 40, PEG crystallization was strongly restricted, probably because the PEG microdomains were isolated in the PHMA matrix. As a result, the growth of PEG spherulite was not observed because the PEG crystallization occurred after vitrification of the PHMA segregated domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 129–137, 2007     

Electrical conducting and magnetic properties of (ethylenedithiotetrathiafulvalenothioquinone-1,3-diselenolemethide)2.FeBr4 (GaBr4) crystals with two different interlayer arrangements of donor molecules

Two donor molecules newly synthesized, dimethylthio- and ethylenedithio-tetrathiafulvalenothioquinone-1,3-diselenolemethides (1 and 2), were used to prepare their charge-transfer (CT) salts with a magnetic FeBr(4)(-) counteranion. For 1, a low electrical conducting 1:1 salt (1.FeBr(4)) was obtained, in which molecules of 1 are tightly dimerized in a one-dimensional (1D) stacking column. On the other hand, 2 gave a 2:1 salt (2(2).FeBr(4)) as two different kinds of plate crystals (I and II). Both I and II possess similar stacking structures of molecules of 2 in each 1D column with a half-cut pipelike structure along the c axis. However, for I, the stacking columns are aligned in the same direction along the a and b axes, while for II they are in the same direction along the a axis, but in the reverse direction along the b axis, resulting in the difference in the relative arrangement of molecules of 2 and FeBr(4)(-) ions between the two crystals. The room-temperature electrical conductivities of the single crystals of I and II were 13.6 and 12.7 S cm(-)(1), respectively. The electrical conducting behavior in I was metallic above 170 K but changed to be semiconducting with a very small activation energy of 7.0 meV in the temperature range 4-170 K. In contrast, II showed the semiconducting behavior in the whole temperature range 77-285 K. The corresponding nonmagnetic GaBr(4)(-) salts with almost the same crystal structure as I and II showed definitively different electrical conducting properties in the metal to semiconductor transition temperature in I as well as in the magnitude of activation energy in the semiconducting region of I and II. The interaction between the d spins of FeBr(4)(-) ions was weak and antiferromagnetic in both I and II, but the magnitude of the spin interaction was unexpectedly larger compared with that in the FeBr(4)(-) salt of the corresponding sulfur derivative of 2 with closer contact between the neighboring FeBr(4)(-) ions. These electrical conducting and magnetic results suggest a significant interaction between the conducting pi electrons and the d spins of FeBr(4)(-) ions located near the columns or layers.     

Effect of titanium dioxide on photostability of solid-state mequitazine

TiO(2) has been widely used in pharmaceutical products, and it also has been used as a photocatalyst. In this study, the influence of photocatalytic activity on the stability of solid-state mequitazine, an H(1)-blocker, was investigated. The photo-degradation of mequitazine with TiO(2) occurred under irradiation with both light sources. The degree of degradation of mequitazine with anatase was higher than that of rutile. The degradation was significantly enhanced with increasing relative humidity. The relationship between the apparent degradation rate constant and water vapor pressure could be clearly described by a simple power law. The major photo-degradation products of mequitazine, resulting from photocatalytic activity of TiO(2), were mequitazine-S-oxide and mequitazine-sulphone. A remarkable degradation of mequitadine occurred with addition of TiO(2), and its photocatalytic activity was controlled by water vapor pressure. The photo-degradation of mequitazine with TiO(2) is a different process from mequitazine without TiO(2), because mequitazine-S-oxide and mequitazine-sulphone are not formed with normal photo-degradation of mequitazine.     

Measurement of acid-catalyzed isomerization of unsaturated aldehyde-2,4-dinitrophenylhydrazone derivatives by high-performance liquid chromatography analysis

Aldehyde-2,4-dinitrophenylhydrazones exist as (E)- and (Z)-geometrical isomers, and adventitious isomerization during sample preparation can cause analytical errors. Purified alkenal-2,4-dinitrophenylhydrazone derivatives comprise only the (E)-isomer. However, partial isomerization to the (Z)-isomer occurs upon addition of acid to attain an equilibrium isomer ratio. The UV-visible spectral properties of the isomers differ; the (Z)-isomer exhibiting a 6-10 nm lower absorption maximum compared to the (E)-isomer. Alkenal-2,4-dinitrophenylhydrazones having a CC double bond at the 2- or 3-position of the alkenal exhibited similar absorption maxima with an equilibrium isomer ratio (0.035) that was much lower than those of other alkenals. The CC double bond at the 3-position migrates to a position of conjugation with the CN double bond during hydrazone synthesis to form a stabilized molecular structure. Alkenal-2,4-dinitrophenylhydrazones having a double bond at the 4-position or greater exhibited a similar absorption maxima equilibrium isomer ratio (0.14) to alkanal-2,4-dinitrophenylhydrazones. The quantitative analysis of carbonyl compounds in air or water using DNPH is usually conducted in the presence of an acid catalyst. Consequently, the solution of the direct extract prepared for HPLC or GC analysis contains both (E)- and (Z)-isomers.