Some recent progress on functional inequalities and applications

FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025700000194 ◽

2000 ◽

Vol 03 (02) ◽

pp. 263-295 ◽

Cited By ~ 40

Author(s):

FENG-YU WANG

Keyword(s):

Riemannian Manifolds ◽

Recent Progress ◽

Spectral Gap ◽

Jump Processes ◽

Sobolev Type ◽

Functional Inequalities ◽

Sobolev Constant

This paper gives a reasonably self-contained account for some recent progress on functional inequalities, semigroup properties and spectrum estimates. Two sorts of functional inequalities are considered, they are actually equivalent and are general forms of Sobolev type inequalities. Semigroup properties, spectrum estimates and concentration of measures are described using these inequalities. Some criteria of functional inequalities and estimates of the spectral gap and the log-Sobolev constant are presented for diffusions on Riemannian manifolds and jump processes. Most yet unpublished results are reproved.

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Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100069387 ◽

1970 ◽

Vol 28 ◽

pp. 478-479

Author(s):

Teruo Someya ◽

Jinzo Kobayashi

Keyword(s):

Surface Layer ◽

Electric Fields ◽

Quantitative Study ◽

Recent Progress ◽

Ferroelectric Domain ◽

Resolving Power ◽

Surface Pattern ◽

Crystal Surfaces ◽

One Dimensional ◽

Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

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The Nature of Oxide Surfaces: Topographic and Electronic Structure

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100150666 ◽

1993 ◽

Vol 51 ◽

pp. 966-967

Author(s):

Dawn A. Bonnell ◽

Yong Liang

Keyword(s):

Transition Metal Oxides ◽

Electronic Structures ◽

Recent Progress ◽

Spatial Localization ◽

Level Of Detail ◽

Scanning Tunneling ◽

Oxide Surfaces ◽

Tunneling Microscopy ◽

Considerable Effort ◽

Complete Understanding

Recent progress in the application of scanning tunneling microscopy (STM) and tunneling spectroscopy (STS) to oxide surfaces has allowed issues of image formation mechanism and spatial resolution limitations to be addressed. As the STM analyses of oxide surfaces continues, it is becoming clear that the geometric and electronic structures of these surfaces are intrinsically complex. Since STM requires conductivity, the oxides in question are transition metal oxides that accommodate aliovalent dopants or nonstoichiometry to produce mobile carriers. To date, considerable effort has been directed toward probing the structures and reactivities of ZnO polar and nonpolar surfaces, TiO2 (110) and (001) surfaces and the SrTiO3 (001) surface, with a view towards integrating these results with the vast amount of previous surface analysis (LEED and photoemission) to build a more complete understanding of these surfaces. However, the spatial localization of the STM/STS provides a level of detail that leads to conclusions somewhat different from those made earlier.

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