Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi-Witten string in the light-cone gauge are reviewed.     

Time-resolved synchrotron X-ray study of crystalline phase transition in poly(aryl ether ketone ketone) containing alternated terephthalic/isophthalic moieties

Unique crystallization and melting behavior in poly(aryl ether ketone ketone) containing alternated terephthalic and isophthalic moieties were studied by time-resolved synchrotron x-ray methods. Recently, this material has been shown to exhibit three polymorphs (forms I, II, and III). In this work, we further investigated their distinctive thermal properties and found that form I is the dominating and the most thermally stable phase while form II is favored by fast nucleation conditions and is the least stable phase. On the other hand, form III represents a minor intermediate phase that usually coexists with form I and can be transferred from form II and to form I. Structural and morphological changes in form I have been followed by simultaneous wide-angle x-ray diffraction (WAXD)/small-angle x-ray scattering (SAXS) measurements during cold- or melt-crystallization and subsequent melting. In all cases, a larger dimensional change was found in the crystallographic a-axis than the b-axis during heating and cooling. This may be due to the greater lateral stress variation with respect to temperature along the a direction of the primary lamellae which is induced by either the formation of secondary lamellae or the preferential chain-folding direction in poly(aryl ether ketone ketone)s. During the phase transitions of form II ← III in the cold-crystallized specimen and form III ← I in the melt-crystallized samples, lamellar variables (long period, lamellar thickness, and invariant) obtained from SAXS remain almost constant. This indicates that the density distribution in the long spacing is independent of the melting in form II or III. For melt-crystallization, the corresponding changes in unit-cell dimensions and lamellar morphology during the annealing-induced low endotherm are most consistent with the argument that these changes are due to the melting of thin lamellar population. © 1995 John Wiley & Sons, Inc.     

Parasupersymmetric quantum mechanics of arbitrary order withN parasupercharges

Parasupersymmetric quantum mechanics is generalized to the case of an arbitrary number of parasuperchanrgesN and the order of paraquantizationp. We show that parasuperpotentials can be explicitly expressed via a single arbitrary function. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1291–1294, September, 1996.     

Decomposability of matrix polynomials with coefficients possessing quasi-simple structure

The decomposability of matrix polynomials with commuting coefficients of quasi-simple structure into regular factors and the solvability of the corresponding matrix polynomial one-sided equations are investigated.Translated from Ukrainskii Matematicheskie Zhurnal, Vol. 44, No. 12, pp. 1716–1718, December, 1992.     

Selective saturation and inversion of multiple resonances in high-resolution solid-state 13C experiments using slow spinning CP/MAS and tailored DANTE pulse sequences.

Taking advantage of the long 13C T1 values generally encountered in solids, selective saturation and inversion of more than one resonance in 13C CP/MAS experiments can be achieved by sequentially applying several DANTE pulse sequences centered at different transmitter frequency offsets. A new selective saturation pulse sequence is introduced composed of a series of 90 degrees DANTE sequences separated by interrupted decoupling periods during which the selected resonance is destroyed. Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described. The determination of the aromaticity of coal using a relatively slow MAS rate is also described.     

Infrared Spectroscopic Analysis of Chrysene and 1.2-Benzanthracence in Wax films

Chrysene and 1.2-benzanthracene are successfully doped in a solid wax film and their vibrational spectra in gooo--400cm^-1 are discussed. The harmonic frequencies and relative intensities of both the molecules observed in the film are compared with theoretical values calculated by the density functional theory （DFT） model as well as with the previous experimental data. The effects on spectra due to change of matrix and some additional bands observed in the wax film are also reported. Excellent agreement in the spectral positions and strengths between the experiments and DFT values are found.     

Observation of spontaneous pattern with six-fold symmetry in disk-shaped ZnO complex microstructures

Using a simple vapor phase transport technique, we have fabricated unique complex disk-shaped ZnO microstructures comprising a small disk coaxially grown on a large one and observed spatially perfect six-fold symmetric patterns. The observed results can be explained based on the spontaneous nanoindentation (NI) effect under the geometric constraints and the explanation can be extended to fathom the growth mechanism of other highly symmetrical ZnO nanostructures. Our results indicate that NI not only can elucidate the mechanical properties of surfaces and thin films but also is an effective approach to fabricate ordered nanostructures with high precision on the location of the building blocks. PACS 81.16.Rf; 81.07.-b; 81.05.Dz