scholarly journals Definition of Flat Poset and Existence Theorems for Recursive Call

2014 ◽  
Vol 22 (1) ◽  
pp. 1-10
Author(s):  
Kazuhisa Ishida ◽  
Yasunari Shidama ◽  
Adam Grabowski

Summary This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this we extensively use technical Mizar functors like BaseFunc or RecFunc. The remaining part builds the background for information engineering approach for lists, namely recursive call for posets [21].We formalized some facts from Chapter 8 of this book as an introduction to the next two sections where we concentrate on binary product of posets rather than on a more general case.

1995 ◽  
Vol 4 (1) ◽  
pp. 5-15 ◽  
Author(s):  
S. Ford ◽  
G. Aouad ◽  
J. Kirkham ◽  
P. Brandon ◽  
F. Brown ◽  
...  

2010 ◽  
Vol 18 (1) ◽  
pp. 47-51 ◽  
Author(s):  
Kazuhisa Ishida ◽  
Yasunari Shidama

Fixpoint Theorem for Continuous Functions on Chain-Complete PosetsThis text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].


Author(s):  
Robin Sibson

We define an unbased H-space to be a pair (A, m) where A is a space andis a map such that the maps La: x → m(a, x), Ra: x → m(x, a) are homotopy equivalences for all a ∈ A. This is the same as James's definition of an H'-space in (3); we follow his notation as far as possible. (A, m) is homotopy-associative if the maps m(m × 1) and m(l × m) are homotopic. A left (right) a-inverse (a ∈ A) is a map w: A → A such that the composition m(w × 1) d (w(1 × w) d) is homotopic to ka, the constant map to a. d denotes the diagonal map a → (a, a).


2011 ◽  
Vol 271-273 ◽  
pp. 1326-1329
Author(s):  
Chen Chen Liu ◽  
Zheng You Wang ◽  
Jin Sha

According to the ambiguous definition of Information Engineering Specialty (IES) and its weakened characteristics in Shijiazhuang Tiedao University, the research determined the specialty’s orientation based on the educational goal, and reformed correspondent curriculum system by constructing several course groups. In this paper, as an example, we select and focus upon the development of signal and information processing course group, which is the most important operational part to guarantee our educational objective of IES, namely thick foundation, broad range, strong ability and high quality. Along with amendment of theoretic contents in teaching, we also proposed an experiment instruction modal to strength students’ practical ability in information engineering. In the end, a new curriculum framework was built. Through specific result, the proposed curriculum reform method is proved to improve our cultivation quality and the students’ professional competence.


Author(s):  
Helena A. Frijns ◽  
Oliver Schürer

In the present work, we provide a short literature review of three different ways of approaching the topics of context and context-awareness and relate these to developments in Human-Robot Interaction (HRI) and social robotics. We distinguish an engineering approach to context-awareness, the study of social context in human-centred design, and a view of context as a cognitive component in interaction. We propose a revised definition of context to capture these three views and discuss implications.


1993 ◽  
Vol 11 (5) ◽  
pp. 384-397 ◽  
Author(s):  
G. F. Aouad ◽  
J. A. Kirkhami * ◽  
P. S. Brandon ◽  
F. E. Brown ◽  
G. S. Cooper ◽  
...  

Author(s):  
V.E. Belousov ◽  
◽  
D.V. Dorofeev ◽  
E.N. Zenkova

In this work the task is formulated and the method of reconfiguration of systems of organizational management on the basis of synthesis of the functional structure having an impact on an appearance of all system considerably defining an order of its functioning, integrating in a whole of means of technical and mathematical, program and information support is offered. The research objective consists in need of increase in effective management of organizational systems on the basis of complex development, implementation and application of funds of automated management of its elements. Expert systems on the basis of declarative programming languages are applied to synthesis of similar structures. Research methods. As the tool for definition of the knowledge base about the field of restructuring of structure of management calculation of expressions and language of a predicate logic, that is a logic theory of first order is used. Then, the problem of reconfiguration of hierarchical structure of management system can be presented doubly. First, as a problem of definition of the changes of the known rational hierarchical structure providing minimum loss from the arisen functional failures. Secondly, as a problem of creation of new rational structure which provides optimum use of the resources used in the course of achievement of definite purposes in the changing conditions. Results. As a result of a research, on the basis of de Morgan's law the factors influencing a system status of organizational management in general are defined. The necessary structure of solvable tasks of all hierarchical structure is defined by extent of influence of different factors on characteristics of structure of management. Conclusion. Work of the received expert system consists in consecutive execution or failure to follow rules and transition from one status to another. In case of an impasse the expert system gives the report in the form of requirements of alternative change of these or those rules (factors). New rules are remembered. Thus, the system of knowledge is increased.


1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.


1975 ◽  
Vol 26 ◽  
pp. 21-26

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.


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