Applied topology: recent progress for computer science, fuzzy mathematics and economics.

Theoretical Foundations of the Automatic Production and Processing of Technical Reports

Journal of Technical Writing and Communication ◽

10.2190/yjdv-5wm8-jpta-kdbg ◽

1979 ◽

Vol 9 (3) ◽

pp. 239-269 ◽

Cited By ~ 2

Author(s):

Robert De Beaugrande

Keyword(s):

Artificial Intelligence ◽

Computer Science ◽

Computer System ◽

Recent Progress ◽

Automatic Production ◽

Reading And Writing ◽

Artificial Intelligence Research ◽

Theoretical Foundations

The following treatise surveys the issues and approaches for designing a computer system capable of reading, understanding, and writing technical reports. Recent progress in computer science and artificial intelligence research is used to specify the nature of the modules in the system. The processing of a sample text is observed during the phases of reading and writing a report on the origin of sunspots. The author advances some proposals for correlating syntax and semantics of English from a procedural standpoint. The discussion is illustrated with structural diagrams.

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An extension problem of a connectedness preserving map between Khalimsky spaces

Filomat ◽

10.2298/fil1601015h ◽

2016 ◽

Vol 30 (1) ◽

pp. 15-28 ◽

Cited By ~ 1

Author(s):

Sang-Eon Han

Keyword(s):

Computer Science ◽

Mathematical Morphology ◽

Digital Images ◽

Digital Topology ◽

Extension Problem ◽

Topological Spaces ◽

Digital Geometry ◽

Applied Topology ◽

Continuous Map ◽

Connected Sets

The goal of the present paper is to study an extension problem of a connected preserving (for short, CP-) map between Khalimsky (K-for brevity, if there is no ambiguity) spaces. As a generalization of a K-continuous map, for K-topological spaces the recent paper [13] develops a function sending connected sets to connected ones (for brevity, an A-map: see Definition 3.1 in the present paper). Since this map plays an important role in applied topology including digital topology, digital geometry and mathematical morphology, the present paper studies an extension problem of a CP-map in terms of both an A-retract and an A-isomorphism (see Example 5.2). Since K-topological spaces have been often used for studying digital images, this extension problem can contribute to a certain areas of computer science and mathematical morphology.

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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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