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.     

Reactivity of α-acylated β-enamino ketones and esters: Synthesis of pyrazoles

The reactivity of the enamino compounds 4-amino-3-phenylamino(thio)carbonyl-3-penten-2-one 1 and 2 and ethyl 3-amino-2-phenylamino(thio)carbonyl-2-butyrate 7 and 8 was studied using the reaction with hydrazine hydrate and hydrazine hydrochloride to evaluate the 1,3 electrophilic center of the compounds by the formation of the pyrazole rings. The pyrazoles 3, 4, 5, 9, 11 and 13 were obtained depending on the reaction conditions employed.     

The reconstruction of maximal planar graphs II. Reconstruction

In the first paper [3], the author, together with Fiorini, has shown that maximal planar graphs are recognizable from their decks of vertex-deleted subraphs. The aim of this paper is to show that such graphs are reconstructible.     

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.     

Analysis of ALD-processed thin films by ion-beam techniques

This review introduces the possibilities of ion-beam techniques for the analysis of thin films and thin-film structures processed by atomic layer deposition (ALD). The characteristic features of ALD are also presented. The analytical techniques discussed include RBS, NRA and ERDA with its variants, viz. the TOF-ERDA and HI-ERDA. The thin film examples are taken from flat-panel display technology (TFEL structures) and the semiconductor industry (high-k insulators).Dedicated to the memory of Wilhelm Fresenius     

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.     

Origin of the failure of classical nucleation theory: incorrect description of the smallest clusters

We carry out molecular Monte Carlo simulations of clusters in an imperfect vapor. We show that down to very small cluster sizes, classical nucleation theory built on the liquid drop model can be used very accurately to describe the work required to add a monomer to the cluster. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range. We calculate factors needed to correct the cluster formation work given by the liquid drop model. The corrected work of formation results in nucleation rates in good agreement with recent nucleation experiments on argon and water.