The molecular approach to heterogeneous nucleation

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.     

Proof of Harary's conjecture on the reconstruction of trees

We prove that a tree with at least three cutvertices is reconstructible from its cutvertex- deleted subgraphs. This answers in the affirmative a question raised by Professor Harary at the Seventh British Combinatorial Conference in 1979.     

Atomic layer deposition of PbZrO3 thin films

In this paper, we report on the preparation of lead zirconate films for the first time using atomic layer deposition in an attempt to investigate some of the film properties and also to evaluate possible use of the precursor combination to prepare more complex lead titanate zirconate. In the depositions tetraphenyl lead (Ph₄Pb) was used as the lead and zirconium 2,2,6,6-tetramethyl-3,5-heptadionato (Zr(thd)₄) as the zirconium precursor, while ozone was used as the oxygen source. Film growth, stoichiometry and quality were studied using different pulsing ratios at deposition temperatures of 275 and 300 °C. According to X-ray diffraction, the crystalline perovskite phase was observed when films deposited on SrTiO₃(1 0 0) were annealed at 600 °C. Surface roughness was reduced for lead deficient films as well as in annealed samples.     

A double arity hierarchy theorem for transitive closure logic

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k–1)-ary fragment of partial fixed point logic by all (2k–1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, we show that an extension is possible when we close this logic under congruence.Supported by a grant from the University of Helsinki. This research was initiated while he was a Junior Researcher at the Academy of FinlandThis article was processed by the author using the LATEX style filepljourlm from Springer-Verlag.     

An NMR-Based Approach to the Measurement of High Log K HL Values at Low Ionic Strength. 31P NMR Study of 1,2-Diaminoethane-N,N,N′,N′-tetra(methylenephosphonic Acid) Protonation Equilibrium at pH > 12

A sequential NMR based approach is proposed for measurements of high log K values at low ionic strength. [³¹P] NMR technique is used to determine the protonation constants of 1,2-diaminoethane-N,N,N,N-tetra(methylenephosphonic acid) (EDTPH, H₈L) at 25°C in 0.1 mol-dm^–3 KNO₃ and at 37°C in 0.15 mol-dm^–3 NaCl at pH 11–14. For equilibrium L + H HL log K are found to be 13.3 (0.1) and 12.9 (0.1), respectively.     

Synthesis of Amphiphilic Amino Alcohols

An efficient and general approach for the synthesis of amphiphilic 1,2-amino alcohols is reported. The use of N-benzyl protecting groups is essential for obtaining good yields when opening a long-chain terminal epoxide with an amine.     

Experimental study of the multiple scattering effect on the flow velocity profiles measured in Intralipid phantoms by DOCT

Time domain Doppler Optical Coherence Tomography (DOCT) technique was applied to measure flow velocity profiles in highly scattering media. We analyzed the distortions of the measured velocity profiles of the 1% Intralipid solution flow embedded into the scattering medium at different embedding depths. For this purpose a tissue phantom consisting of a plain glass capillary (inner diameter 0.3 mm) embedded into a slab of Intralipid solution mimicking human skin was designed. The measured flow velocity profiles and behavior of distortions caused by multiple scattering are shown.     

Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes

We prove an Itô–Tanaka formula and existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by Föllmer and as pathwise generalized Lebesgue–Stieltjes integrals introduced by Zähle. As an application, we illustrate the importance of the Itô–Tanaka formula for pricing and hedging of financial derivatives.