scholarly journals RELATIONS Vs FUNCTIONS

2020 ◽  
pp. 35-39
Keyword(s):  
Cartesian Product ◽  
Clear Picture ◽  
Product Domain ◽  
The Given ◽  
Ordered Pairs

This paper aims to understand the concepts of relations and functions as well with the inclusive of ordered pairs ,Cartesian product ,domain ,codomain ,range of a function. This paper also focusing on some of the special types of functions and also facilitates better idea on when a relation can be a function. This article also provides clear picture on what magic involved in the given relation to identify whether a function using graphing functions.

scholarly journals A study of a system of operator inclusions via a fixed point approach and applications to functional-differential inclusions

2016 ◽  
Vol 32 (3) ◽  
pp. 349-361 ◽  
Author(s):  
ADRIAN PETRUSEL ◽  
◽  
GABRIELA PETRUSEL ◽  
JEN-CHIH YAO ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Metric Spaces ◽  
Mixed Boundary ◽  
Cartesian Product ◽  
Qualitative Properties ◽  
Initial Value ◽  
Functional Differential ◽  
The Given ◽  
Functional Differential Inclusions

In this paper, some existence results for a system of operator inclusions are presented. Qualitative properties of the solution set are also discussed. The method is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. The approach is new even for the case of the metric spaces. As an application, an existence result for a mixed boundary and initial value problem for a system of second order differential inclusions is given.

scholarly journals N-harmonic extensions of weighted integrable distributions

2006 ◽  
Vol 4 (3) ◽  
pp. 305-327 ◽  
Author(s):  
Josefina Alvarez ◽  
Martha Guzmán-Partida ◽  
Salvador Pérez-Esteva
Keyword(s):  
Natural Product ◽  
Half Plane ◽  
Poisson Kernel ◽  
Weighted Space ◽  
Cartesian Product ◽  
Tempered Distributions ◽  
Product Domain ◽  
Upper Half Plane ◽  
Optimal Space

We obtainn-harmonic extensions to the Cartesian product ofncopies of the upper half-plane, of distributions in the weighted spacew12?wn2DL1', which is known to be the optimal space of tempered distributions that areS'-convolvable with a natural product domain version of the Poisson kernel.

XXV.—Properties of I-extensions of Anti-commutative Algebras

1961 ◽  
Vol 65 (4) ◽  
pp. 345-357
Author(s):  
E. W. Wallace
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Commutative Algebra ◽  
Characteristic Zero ◽  
Cartesian Product ◽  
Paper Properties ◽  
Commutative Algebras ◽  
The Given

SYNOPSISS. T. Tsou and A. G. Walker have defined the I-extension of a given Lie algebra as a certain Lie algebra on the Cartesian product of the given algebra and one of its ideals (Tsou 1955). I-extensions have been studied also in connection with metrisable Lie groups and metrisable Lie algebras. The definition can be applied immediately to any anti-commutative algebra, and in this paper properties of such I-extensions are established. A list of all proper I-extensions of dimension not greater than four over a field of characteristic zero is also given together with a set of characters.

scholarly journals Some properties of the containing spaces and saturated classes of spaces

2003 ◽  
Vol 4 (2) ◽  
pp. 487 ◽  
Author(s):  
S.D. Iliadis
Keyword(s):  
Open Subset ◽  
Closed Subset ◽  
Dense Subset ◽  
Simple Condition ◽  
Specific Subset ◽  
Universal Element ◽  
The Given ◽  
Ordered Pairs

<p>Subjects of this paper are: (a) containing spaces constructed in [2] for an indexed collection S of subsets, (b) classes consisting of ordered pairs (Q,X), where Q is a subset of a space X, which are called classes of subsets, and (c) the notion of universality in such classes.</p> <p>We show that if T is a containing space constructed for an indexed collection S of spaces and for every X ϵ S, Q<sup>X</sup> is a subset of X, then the corresponding containing space TI<sub>Q</sub> constructed for the indexed collection Q ={Q<sup>X</sup> : X ϵ S} of spaces, under a simple condition, can be considered as a specific subset of T. We prove some “commutative” properties of these specific subsets.</p> <p>For classes of subsets we introduce the notion of a (properly) universal element and define the notion of a (complete) saturated class of subsets. Such a class is “saturated” by (properly) universal elements. We prove that the intersection of (complete) saturated classes of subsets is also a (complete) saturated class.</p> <p>We consider the following classes of subsets: (a) IP(Cl), (b) IP(Op), and (c) IP(n.dense) consisting of all pairs (Q;X) such that: (a) Q is a closed subset of X, (b) Q is an open subset of X, and (c) Q is a never dense subset of X, respectively. We prove that the classes IP(Cl) and IP(Op) are complete saturated and the class IP(n.dense) is saturated. Saturated classes of subsets are convenient to use for the construction of new saturated classes by the given ones.</p>

Study 3-2: An Exploration of Transitivities Formulated from a Set of Piagetian-Derived Operations and Their Implications in Traversing Learning Hierarchies

1973 ◽  
Vol 4 (2) ◽  
pp. 121-125
Author(s):  
Layne V. Hopkins
Keyword(s):  
Systematic Procedure ◽  
Instructional Objectives ◽  
Modes Of Representation ◽  
The Matrix ◽  
The One ◽  
The Given ◽  
Ordered Pairs

In the Paradigms studies by Klein (1970) and Farris (1970), selected relationships among the three modes of representation (enactive, iconic, and symbolic) were carefully examined. These researchers conceptualized instructional objectives as ordered pairs, where the first element represented the mode of representation of the given component of an objective and the second element represented the mode of representation of the required performance of the objective. Further, they used an ordered-pair matrix that consisted of nine cells so that a systematic procedure could be established for investigating selected relationships among the cells of the matrix. This study, in conjunction with the one conducted by Sawada (1971), investigated selected relationships within cells of this modes-of-representation matrix.

Personal Problem Solving of Partners in Divorce Proceedings

2015 ◽  
Vol 36 (1) ◽  
pp. 82-103 ◽  
Author(s):  
Tereza Soukupova ◽  
Petr Goldmann
Keyword(s):  
Gender Differences ◽  
Problem Solving ◽  
Thematic Apperception Test ◽  
Scoring Systems ◽  
Personal Control ◽  
Personality Characteristics ◽  
Personal Problem ◽  
Thematic Apperception ◽  
And Gender ◽  
The Given

Abstract. The Thematic Apperception Test is one of the most frequently administered apperceptive techniques. Formal scoring systems are helpful in evaluating story responses. TAT stories, made by 20 males and 20 females in the situation of legal divorce proceedings, were coded for detection and comparison of their personal problem solving ability. The evaluating instrument utilized was the Personal Problem Solving System-Revised (PPSS-R) as developed by G. F. Ronan. The results indicate that in relation to card 1, men more often than women saw the cause of the problem as removable. With card 6GF, women were more motivated to resolve the given problem than were men, women had a higher personal control and their stories contained more optimism compared to men’s stories. In relation to card 6BM women, more often than men, used emotions generated from the problem to orient themselves within the problem. With card 13MF, the men’s level of stress was less compared to that of the women, and men were more able to plan within the context of problem-solving. Significant differences in the examined groups were found in those cards which depicted significant gender and parental potentials. The TAT can be used to help identify personality characteristics and gender differences.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

Coordinating Medical Literature with Patient Care

1977 ◽  
Vol 16 (04) ◽  
pp. 234-240 ◽  
Author(s):  
Joann Gustafson ◽  
J. Nelson ◽  
Ann Buller
Keyword(s):  
Health Care ◽  
Medical Staff ◽  
Medical Information ◽  
Medical Literature ◽  
Medical Information System ◽  
Staff Members ◽  
Information Displays ◽  
Medical Displays ◽  
Computerized Medical Information ◽  
The Given

The contribution of a special library project to a computerized problem-oriented medical information system (PROMIS) is discussed. Medical information displays developed by the PROMIS medical staff are accessible to the health care provider via touch screen cathode terminals. Under PROMIS, members of the library project developed two information services, one concerned with the initial building of the medical displays and the other with the updating of this information. Information from 88 medical journals is disseminated to physicians involved in the building of the medical displays. Articles meeting predetermined selection criteria are abstracted and the abstracts are made available by direct selective dissemination or via a problem-oriented abstract file. The updating service involves comparing the information contained in the selected articles with the computerized medical displays on the given topic. Discrepancies are brought to the attention of PROMIS medical staff members who evaluate the information and make appropriate changes in the displays. Thus a feedback loop is maintained which assures the completeness, accuracy, and currency of the computerized medical information. The development of this library project and its interface with the computerized health care system thus attempts to deal with the problems in the generation, validation, dissemination, and application of medical literature.

Identification and Transformation of Terminal Morphemes in Medical English

1969 ◽  
Vol 8 (02) ◽  
pp. 84-90 ◽  
Author(s):  
A. W. Pratt ◽  
M. Pacak
Keyword(s):  
Word Form ◽  
Subsequent Transformation ◽  
Part Of Speech ◽  
Morphological Segmentation ◽  
Medical English ◽  
Nominal Form ◽  
Admissible Path ◽  
Near Future ◽  
The Given ◽  
Admissible Sequences

The system for the identification and subsequent transformation of terminal morphemes in medical English is a part of the information system for processing pathology data which was developed at the National Institutes of Health.The recognition and transformation of terminal morphemes is restricted to classes of adjectivals including the -ING and -ED forms, nominals and homographic adjective/noun forms.The adjective-to-noun and noun-to-noun transforms consist basically of a set of substitutions of adjectival and certain nominal suffixes by a set of suffixes which indicate the corresponding nominal form(s).The adjectival/nominal suffix has a polymorphosyntactic transformational function if it has the property of being transformed into more than one nominalizing suffix (e.g., the adjectival suffix -IC can be substituted by a set of nominalizing suffixes -Ø, -A, -E, -Y, -IS, -IA, -ICS): the adjectival suffix has a monomorphosyntactic transformational property if there is only one admissible transform (e.g., -CIC → -X).The morphological segmentation and the subsequent transformations are based on the following principles:a. The word form is segmented according to the principle of »double consonant cut,« i.e., terminal characters following the last set of double consonants are analyzed and treated as a potential suffix. For practical purposes only such terminal suffixes of a maximum length of four have been analyzed.b. The principle that the largest segment of a word form common to both adjective and noun or to both noun stems is retained as a word base for transformational operations, and the non-identical segment is considered to be a »suffix.«The backward right-to-left character search is initiated by the identification of the terminal grapheme of the given word form and is extended to certain admissible sequences of immediately preceding graphemes.The nodes which represent fixed sequences of graphemes are labeled according to their recognition and/or transformation properties.The tree nodes are divided into two groups:a. productive or activatedb. non-productive or non-activatedThe productive (activated) nodes are sequences of sets of graphemes which possess certain properties, such as the indication about part-of-speech class membership, the transformation properties, or both. The non-productive (non-activated) nodes have the function of connectors, i.e., they specify the admissible path to the productive nodes.The computer program for the identification and transformation of the terminal morphemes is open-ended and is already operational. It will be extended to other sub-fields of medicine in the near future.

The Role and Place of Budget Procedure in the System

2003 ◽  
pp. 42-49 ◽  
Author(s):  
E. Bushmin
Keyword(s):  
Budget Process ◽  
Public Expenditures ◽  
Principal Role ◽  
Process Trends ◽  
The Given ◽  
Rules Of The Game

The article is devoted to the analysis of improving budget process trends. The author offers the concept of "financial technologism". Its usage should promote an essential improvement of the budget process. The given concept is based on the fact that the regulation of budget procedure is the process of determination of "rules of the game", and the order of interaction of different institutions within the framework of the budget process, and the trends and volumes of expenses are the strategy of institutions. The procedure within the budget process plays a principal role as compared with the trends and volumes of public expenditures.

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