Restricted set addition: The exceptional case of the Erd?s-Heilbronn conjecture

Let A≠B be nonempty subsets of the group of integers modulo a prime p. If p?|A|+|B|−2, then at least |A|+|B|−2 different residue classes can be represented as a+b, where a∈A, b∈B and a≠b. This result complements the solution of a problem of Erd?s and Heilbronn obtained by Alon, Nathanson, and Ruzsa.     

Heterogeneous crystal nucleation: the effect of lattice mismatch

A simple dynamical density functional theory is used to investigate freezing of an undercooled liquid in the presence of a crystalline substrate. We find that the adsorption of the crystalline phase on the substrate, the contact angle, and the height of the nucleation barrier are nonmonotonic functions of the lattice constant of the substrate. We show that the free-growth-limited model of particle-induced freezing by Greer et al. [Acta Mater. 48, 2823 (2000)] is valid for larger nanoparticles and a small anisotropy of the interface free energy. Faceting due to the small size of the foreign particle or a high anisotropy decouples free growth from the critical size of homogeneous nuclei.     

Investigation of the regeneration of the passive surface oxide layer of TiAl6V4 alloy printed by WAAM technology using different electrochemical test methods

The kinetics of oxide layer formation on surface of Ti6Al4V alloy samples is a very important property especially if their application as medical implants is planned. Damaged protective surface layer usually heals in ambient condition however; during the self-healing process toxic species can get into the surrounding living tissue. In our experiment the kinetics of the healing process proceeding at 3D printed alloy surface has been studied using electrochemical methods, among them scanning electrochemical microscopy. More than 40 min. time period was found long enough for total healing.     

Novel 2-phosphabicyclo[2.2.2]oct-5-ene derivatives and their use in phosphinylations

The [4 + 2] cycloaddition of the double-bond isomers ( A and B ) of dihydrophosphinine oxide 1 afforded novel phosphabicyclo[2.2.2]oct-5-ene derivates ( 2–4 ), formation of which was justified by PM3 semiempirical calculations. The compounds of dimer type ( 2–4 ) were utilized in the UV light-mediated fragmentation-related phosphinylation of nucleophiles, especially in that of alcohols. To explore the role of structural modifications on the fragmentation ability, disulfide 5 , phosphabicyclooctane 7 obtained by the hydrogenation of 2 , and the adduct of dihydrophosphinine oxide 1 with benzoquinone ( 7 ) were also synthesized and tested in fragmentation. © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:97–106, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10221     

P-Substituted 3-phosphabicyclo [3.1.0] hexane 3-oxides from diastereoselective substitution at phosphorus

Preparation of P-amino-3-phosphabicyclo[3.1.0]-hexane 3-oxides either by addition of dichlorocarbene to the double bond of 1-amino-2,5-dihydro-1H-phosphole 1-oxides or by substitution of the P-chloro derivative of the bicyclic system was accomplished. Two different diastereomers are obtained by the two approaches; their ¹³C NMR spectra were interpreted on the basis of the P-ethoxy isomers, whose structures were confirmed by X-ray analysis. The P-hydroxy adduct was also prepared, and it was found that intermolecular O H … O hydrogen bonding connects the molecules together in the solid phase. This effect eliminates the possibility of diastereoisomerism, as was also observed in the case of P-hydroxy tetrahydrophosphinine oxides. Thermolysis of the P-hydroxy adduct is a better way to synthesize 1-hydroxy-1,2-dihydrophosphinine oxides than by hydrolysis of the phosphinic chlorides.     

Formation of aryl dialkylphosphinates from dialkylphosphinous chlorides and arylmagnesium bromides under oxidative conditions

The reaction of dialkylphosphinous chlorides ( 1 ) with arylmagnesium bromides carried out in the air atmosphere was found to afford aryl‐dialkylphosphine oxides ( 2 ) and aryl dialkylphosphinates ( 3 ) in a comparable quantity. Formation of the latter product ( 3 ) is the first example that an aryl‐dialkylphosphine, formed as an intermediate, is autooxidized to the corresponding phosphinate. © 2001 John Wiley & Sons, Inc. Heteroatom Chem 12:38–41, 2001