Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces

We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space.     

Linear polystyrene-stabilized PdO nanoparticle-catalyzed Mizoroki-Heck reactions in water

Linear polystyrene-stabilized PdO nanoparticles (PS-PdONPs) were prepared by thermal decomposition of Pd(OAc)(2) in the presence of polystyrene. X-ray diffraction (XRD) and transmission electron microscopy (TEM) indicated the production of PdO nanoparticles. The loading of palladium was determined by inductively coupled plasma-atomic emission spectroscopy (ICP-AES). PS-PdONPs exhibited high catalytic activity for Mizoroki-Heck reactions under air in water and could be recycled without loss of activity.     

Lamellar structural changes in miscible crystalline polymer blends during melting and crystallization processes,as studied by real‐time small‐angle X‐ray scattering measurements

Real‐time small‐angle X‐ray scattering (SAXS) measurement using synchrotron radiation was applied to study the lamellar structural changes in miscible crystalline polymer blends of poly(1,4‐butylene succinate) (PBSU) and poly(vinylidene fluoride) (PVDF) during melting and crystallization processes. The lamella of PBSU is either included in the interlamellar region of PVDF (interlamellar inclusion structure), or rejected from the interlamellar region of PVDF (interlamellar exclusion structure). The two lamellar structures coexists in the melt‐quenched samples of the PBSU/PVDF = 30/70 blend. Only the interlamellar exclusion structure exists in the drawn films of the PBSU/PVDF = 30/70 blend. The real‐time SAXS results show that the interlamellar exclusion structure in these samples is irreversibly transformed into the interlamellar inclusion structure by heating the sample above the melting temperature of PBSU and that the PBSU chains are crystallized between the lamellae of PVDF during the cooling process. The factors controlling the lamellar structural changes are possibly a balance of the miscibility and the chain exclusion by tie‐molecules and/or the chain diffusion under confinement by the lamellae of PVDF with higher melting temperature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1959–1969, 2007     

Pressure-induced phase transitions of lanthanide monoarsenides LaAs and LuAs with a NaCl-type structure

By use of synchrotron radiation the powder X-ray diffraction of lanthanide monoarsenides LaAs and LuAs with a NaCl-type structure has been studied up to 60 GPa at room temperature. First-order phase transitions with the crystallographic change were found at around 20 GPa for LaAs, and 57 GPa for LuAs. The high-pressure form of LaAs is a tetragonal structure and can be viewed as a distorted CsCl-type structure. The atoms in the tetragonal structure are located at La: 0, 0, 0; As: 1/2, 1/2, 1/2. The space group is P4/mmm. The structural change to the tetragonal structure occurs with the volume collapse of about 10%. The structure of these high-pressure phases of LuAs is unknown. The volume vs. pressure curves for LaAs and LuAs are fitted by a Birch equation of state. The bulk moduli of both arsenides are 92±6 GPa for LaAs and 85±3 GPa for LuAs. The high-pressure structural behavior of LaX (X=P, As and Sb) and LnAs (Ln=lanthanide) with the NaCl-type structure is discussed.     

Isothermal cis-trans isomerization behavior of polyacetylene films

Isothermal cis-trans isomerization behavior was studied by differential scanning calorimetry for conventional Shirakawa polyacetylene (S-PA) film and highly stretchable polyacetylene (hs-x) films synthesized using catalysts aged at high temperature. The rate of isomerization is slower for S-PA than for hs-x. Kinetic results of isomerization are analyzed by a stretched exponential function with exponent n (0 < n < 1), which is different from the previously assumed single exponential function. An activation energy of 31 kcal/mol was obtained for all the samples. © 1995 John Wiley & Sons, Inc.     

Grain boundary relaxation phenomena in block and graft copolymers

Summary The grain boundary relaxation phenomena, which have been found in the mechanical relaxation of the cast films of a series ofgraft copolymers ofpoly(methyl acrylate) with styrene, are examined again, in order to understand its relaxation mechanism, by using some particular series of heterogeneous systems of two components having different interaction between the two phases and, subsequently, different grain boundary structure; i. e., two series of poly(vinyl acetate) filled with two types of carbon blacks having relatively high and low surface activities, respectively, a series ofmechanical mixtures ofpoly(vinyl acetate) with polystyrene, and a series of styrene-isoprene-styrene tri-block copolymers.The grain boundary relaxation phenomena are again detected for the series of the tri-block copolymers but definitely not for the series of the mechanical mixtures, suggesting that the grain boundary relaxation phenomena must arise not from the heterogeneous structures themselves but from characteristic arrangements of molecular chains at the boundary of the two phases. That is, there must be a considerably strong interaction between the two phases, and there exists an intermediate phase in which the polymer segments of soft component are rigidified while the other polymer segments of hard component are softened. In other words, there must be a cooperative motions of chain segments of the two components to produce a mechanical relaxation under a certain environmental condition, such as temperature and time scale of observation.

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Zusammenfassung Die Korngrenzenrelaxationsphänomene, die in der mechanischen Relaxation einer Serie von aus Graft-Copolymeren von Polymethylacrylat mit Styrol gefunden wurden, wurden erneut geprüft, um den Relaxations-mechanismus zu verstehen, unter Verwendung einer besonderen Serie von heterogenen Systemen zweier Komponenten, die verschiedene Wechselwirkungen zwischen den zwie Phasen besitzen und deshalb verschiedene Korgrenzenstrukturen. Das heißt, wir verwendeten zwei Serien von Polyvinylacetaten, gefüllt mit zwei Rußtypen von vergleichsweise hoher und niedriger Oberflächenaktivität, eine Serie von mechanischen Mischungen aus Polyvinylacetat mit Polystyrol und eine Serie von Styrol-Isopren-Dreiblockcopolymeren. Die Korngrenzenrelaxationsphänomene, wurden für die Serie der Dreiblockcopolymeren wiederum festgestellt, aber definitiv nicht für die Serie der mechanischen Mischungen. Das läßt vermuten, daß Korngrenzenrelaxation nicht von heterogenen Strukturen selbst, sondern von charakteristischen Anordnungen der molekularen Kette an der Grenze von zwei Phasen herrührt. Das heißt, es muß eine beträchtlich strenge Wechselwirkung zwischen den zwei Phasen bestehen, und es muß eine Zwischenphase existieren, in welcher die Polymersegmente der weichen Komponente versteift werden, während die anderen Polymersegmente der harten Komponente erweicht werden. Mit anderen Worten, es müssen cooperative Bewegungen von Kettensegmenten der zwei Komponenten vorhanden sein, um eine mechannische Relaxation unter gewissen Umgebungsbedingungenzuerzeugen, Umgebungsbedingungen wie Temperatur und Zeitskala der Beobachtungen.

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With 6 figures and 13 tables

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Presented at the 20th Annual Symposium on Rheology, Japan, Fukui, Oct. 18, 1972.     

Nonexponential proton relaxation in (NH4)2 HPO4

Nonexponential relaxation of protons in (NH₄)₂HPO₄ was found from 420 K to 110 K and was interpreted by the three-bath model below 167 K; inter-NH₄ group dipolar coupling above 167 K, and was attributed to non-equivalent NH₄ groups in a molecule.     

Effect of hydrostatic pressure on the Raman spectrum of anatase (TiO2)

Raman spectra of anatase have been investigated under pressures up to 60 kbar and at room temperature. A pressure-induced phase transition is observed at pressures above 25.6 kbar. The 197 cm^-1 mode (at 1 atm.) of six Raman active modes exhibits anomalous pressure dependence in which the frequency decreases with increasing pressure. This mode may be significant in the phase transition. The remaining modes show usual behavior.