Curvature and finite domination

Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.

     

Integral conditions on the asymptotic stability for the damped linear oscillator with small damping

The equation is considered under the assumption . It is proved that is sufficient for the asymptotic stability of , and is best possible here. This will be a consequence of a general result on the intermittent damping, which means that is controlled only on a sequence of non-overlapping intervals.

     

Local partial regularity theorems for suitable weak solutions of a class of degenerate systems

A partial regularity theorem is established for a particular class of weak solutions to the systemu/t– div(K(u)u)=(u)¦¦², div((u))=0 on a bounded domain inR ^N . Under our assumptions, (u) may exhibit exponential decay, and thus the system may be degenerate. Our proof is based upon a blow-up argument.This work was supported in part by NSF Grant DMS9424448.     

Analysis and simulation on the performance of a gyro-penitron amplifier

A cylindrical waveguide gyro-peniotron amplifier is analysed theoretically in this paper. By a ballistic method and directly using the energy conservation in the beam-wave system, a set of interaction equations for the cylindrical waveguide gyro-peniotron amplifier is derived. Computer simulation shows that under defined conditions an interaction efficiency of 47%, an output power of 240kW at a gain of 22. 5 dB and a 3 dB-instantaneous bandwidth of 1. 9% for a central frequency of 35GHz, TE₀₃ mode gyro-peniotron amplifier could be achieved. The influence of the operation parameters on the amplifier performance is also presented.     

Interfacial segregation in Ag-Au,Au-Pd,and Cu-Ni alloys: I. (100) surfaces

Atomistic simulations of segregation to (100) free surface in Ag–Au, Au–Pd, and Cu–Ni alloy systems have been performed for a wide range of temperatures and compositions within the solid solution region of these alloy phase diagrams. In addition to the surface segregation profiles, surface free energies, enthalpies, and entropies were determined. These simulations were performed within the framework of the free energy simulation method, in which an approximate free energy functional is minimized with respect to atomic coordinates and atomic site occupation. The effects of the relaxation with respect to either the atomic positions or the atomic concentrations are discussed. For all alloy bulk compositions (0.05 C 0.95) and temperatures (400 T(K) 1,100) examined, Ag, Au, and Cu segregates to the surface in the Ag–Au, Au–Pd, and Cu–Ni alloy systems, respectively. The present results are compared with several theories for segregation. The resultant segregation profiles in Au–Pd and Ag–Au alloys are shown to be in good agreement with an empirical segregation theory, while in Cu–Ni alloys the disagreement in Ni-rich alloys is substantial. The width of the segregation profile is limited to approximately three to four atomic planes. The surface thermodynamic properties depend sensitively on the magnitude of the surface segregation, and some of them are shown to vary linearly with the magnitude of the surface segregation.     

An Electrostatic Bond Energy Model for Enthalpies of Formation of Chloroalkanes in Gaseous States

An electrostatic bond energy model is formulated to fit the enthalpies of formation and dipole moments of the alkanes and chloroalkanes. In this model, the charge distributions are calculated by an electrostatic approach similar to the "MSE" method, and the enthalpy of formation of a molecule is the sum of the bond energy terms plus the electrostatic energy of the interactions between the charges on all atoms. All parameters of this model are obtained by parameterization. The calculated dipole moments for 13 chloroalkanes and enthalpies of formation for 19 alkanes and non-geminal chloroalkanes agree with the determined values very well. To calculate the enthalpies of formation of geminal chloroalkanes, a correction mainly attributed to the van der Waals interactions in the geminal substituted group, about 24 kJ/mol per pair of geminal chlorine atoms, is introduced.     

Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

The initial oxidation of magnesium: an in situ study with XPS,HERDA and ellipsometry

The initial oxidation of magnesium at oxygen partial pressures between 1.3 × 10^?8 and 1.3 × 10^?5 Pa and at temperatures ranging from 273 to 550 K has been investigated in situ with X‐ray photoelectron spectroscopy (XPS), ellipsometry and high resolution elastic recoil detection analysis (HERDA). Quantitative analysis of the XPS spectra showed a clear oxygen deficiency with respect to MgO for the initial oxide. HERDA measurements confirmed this relatively low oxygen content in the thin oxide layers formed. Ellipsometry measurements showed that the electronic structure of the initially formed oxide differs significantly from that of bulk MgO. The band gap values at room temperature for the oxide layers investigated are clearly smaller than the value for bulk MgO. Copyright © 2006 John Wiley & Sons, Ltd.     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.