Transient binary nucleation from ethanol-hexanol vapour

We study condensation of ethanol-hexanol vapour by numerical solution of kinetic equations. The number of droplets formed in unit volume is computed within self-consistent classical model. It is shown that formation of ethanol-rich droplets prevails at the initial stage of nucleation process, but in the stationary state formation of droplets near the saddle point (on cluster formation energy surface) plays the dominant role. Presented at the 6th Joint Seminar “Development of Materials Science in Research and Education”, Karlštejn, Czech Republic, 17–19 September 1996. This work was supported by Grant No. A1010615 of the Grant Agency of the Academy of Sciences of the Czech Republic.     

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     

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.     

H2S·HOH or H2O·HSH, which is more stable in the water-hydrogen sulfide complex?

High-level ab initio calculations are carried out to study the relative stability of the two hydrogen bonded structures of water-hydrogen sulfide complex, one with water as the proton donor (A) and the other with hydrogen sulfide as the proton donor (B). The results show that structure A is considerably more stable than B at the correlated level, which is in contrast with previous results obtained from Hartree-Fock calculations.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Faddeev-Noble Versus Sasakawa-Sawada Equations for the Nuclear Three-Body Coulomb Problem

We compare the efficiency of two Faddeev-type approaches for the nuclear three-body Coulomb problem. The first one is a modification of Noble’s approach, the second one is due to Sasakawa and Sawada. In an integral-equation formulation both of these methods rely on the same Green’s operators and driving terms. The differences lie in the treatment of the long-range Coulomb potentials. Numerical examples show that the modified Faddeev-Noble approach provides for faster convergence.