Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Structure of enantiopure and racemic alanine adlayers on Cu(1 1 0)

Plane wave density functional theory has been employed to analyze the structure of alanine adlayers on the Cu(1 1 0) surface. Alanine forms (3 × 2) adlayers on Cu(1 1 0) that are closely related to the structures of glycine on the same surface. There is essentially no energy difference between the most stable racemic and enantiopure alanine adlayers. This observation implies that adsorption of racemic alanine on Cu(1 1 0) will result in a pseudoracemate adlayer.     

Preparation and properties of homogeneous V2O5-SiO2 xerogel composite based on interpenetrating polymer network

In this paper, we report the conducting and electrochemical properties of a homogeneous V₂O₅-SiO₂ xerogel composite obtained from the simultaneous polymerization in both inorganic components (Si-O and V-O based polymers) forming an interpenetrating polymer network, where a mutual “solubility” due to cross-links and entanglements was observed. The presence of V₂O₅ inside the silica matrix has a strong effect on electrical conductivity; measurements showed room temperature conductivity almost 1000 times higher than what is found in the literature. In addition, the electrochemical behavior is quite similar to that found in V₂O₅ xerogel. Moreover, the effects of thermal treatment on the conducting and electrochemical properties were investigated. It was found that both properties were improved with no significant effect on V₂O₅ xerogel layered structure.     

Effect of genesis on the properties and hydrogen reducibility of NiO-ZnO mixed oxides

The physico-chemical properties and reactivity tested by hydrogen reduction have been studied for two series of NiO-ZnO mixed oxides of various composition. The solid nickel oxide or zinc oxide in interaction with the solution of nitrate of the second component were used as the precursors in each series. The differences in some physico-chemical parameters of the samples in both series were correlated with their reduction behaviour, followed both in iso- and non-isothermal regime. Moreower, the influence of various factors modifying the reactivity of mixed oxides was also investigated and the results were compared with those obtained from earlier studied analogous systems of quite different origin.This revised version was published online in November 2005 with corrections to the Cover Date.     

Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].     

Ultrathin Fe film on Cu(0 0 1): Exchange splitting of image states from first principles

The theoretical investigation of the image states in front of an ultrathin iron film grown on copper has been performed by means of the embedding method and a recently developed procedure for the inclusion of the image potential tail in a first principle calculation. From the electronic response to an applied electric field, the image plane position has been evaluated. This also allows one to obtain useful information about the spin dependent screening properties of the system. Exchange splitting, effective mass, and lifetime of such surface states result in good agreement with recently performed two-photon photoemission experiments [see A.B. Schmidt, M. Pickel, M. Wiemhöfer, M. Donath, M. Weinelt, Phys. Rev. Lett. 95 (2005) 107402].     

Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.