The Sheffer functions of 3-valued logic

1954 ◽  
Vol 19 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Norman M. Martin
Keyword(s):  
Present Author ◽  
Binary Function ◽  
Truth Values ◽  
Co Substitution ◽  
Substitution Property ◽  
Class A ◽  
Substitution Law ◽  
Sheffer Function

In previous papers, Post, Webb, Götlind and the present author have described some Sheffer functions (in Swift's terminology, “independent binary generators”) in m-valued logic. Professor J. Dean Swift has recently isolated the symmetric Sheffer functions of 3-valued logic. In the present paper, we will prove some properties of Sheffer functions in m-valued logic and isolate all of the Sheffer functions of 3-valued logic.Before we proceed we will define some terms which we will find convenient. A set of functions in m-valued logic is functionally complete, if the set of the functions which can be defined explicitly from the functions of the set is exactly the set of all functions of m-valued logic. A function is functionally complete, if its unit set is functionally complete. A Sheffer function is a two-place functionally complete function. If i and j are truth values (1 i, j ≤ m), we will say i ~ j (D), if D is a decomposition of the truth values 1, …, m into 2 or more disjoint non-empty classes and i and j are elements of the same class. A binary function f(p, q) satisfies the substitution law for a decomposition D, if for any truth values h, i, j, k, whenever h ~ j (D) and i~k(D), then f(h, i) ~ f(j, k) (D). The function f(p,q) satisfies the co-substitution law for D, if for any truth values h, i, j, k, whenever f(h, i) ~ f(j, k) (D), then h ~ j (D) or i ~ k (D). We will say f(p, q) has the proper substitution property, if there is a decomposition of the truth values into less than m classes for which it satisfies the substitution law.

Further results on infinite valued predicate logic

1964 ◽  
Vol 29 (2) ◽  
pp. 69-78 ◽  
Author(s):  
L. P. Belluce
Keyword(s):  
Real Number ◽  
Present Author ◽  
Closed Interval ◽  
Abelian Groups ◽  
Predicate Logic ◽  
Real Numbers ◽  
The Real ◽  
Truth Values ◽  
Recursively Enumerable ◽  
Weakened Form

In a previous paper [1] Chang and the present author presented a system of infinite valued predicate logic, the truth values being the closed interval [0, 1] of real numbers. That paper was the result of an investigation attempting to establish the completeness of the system using the real number 1 as the sole designated value. In fact, we fell short of our mark and proved a weakened form of completeness utilizing positive segments, [0, a], of linearly ordered abelian groups as admissible truth values. A result of Scarpellini [8], however, showing that the set of well-formed formulas of infinite valued logic valid (with respect to the sole designated real number 1) is not recursively enumerable indicates the above mentioned result is the best possible.

Quantitative parallel EELS spectrum imaging developed as a new tool in AEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1202-1203
Author(s):  
Gianluigi Botton ◽  
Gilles L'espérance
Keyword(s):  
Statistical Analysis ◽  
Spatial Resolution ◽  
Personal Computer ◽  
Systematic Study ◽  
Present Author ◽  
Chemical Elements ◽  
Detection Limits ◽  
Research Groups ◽  
Quantitative Performance ◽  
Spectrum Imaging

As interest for parallel EELS spectrum imaging grows in laboratories equipped with commercial spectrometers, different approaches were used in recent years by a few research groups in the development of the technique of spectrum imaging as reported in the literature. Either by controlling, with a personal computer both the microsope and the spectrometer or using more powerful workstations interfaced to conventional multichannel analysers with commercially available programs to control the microscope and the spectrometer, spectrum images can now be obtained. Work on the limits of the technique, in terms of the quantitative performance was reported, however, by the present author where a systematic study of artifacts detection limits, statistical errors as a function of desired spatial resolution and range of chemical elements to be studied in a map was carried out The aim of the present paper is to show an application of quantitative parallel EELS spectrum imaging where statistical analysis is performed at each pixel and interpretation is carried out using criteria established from the statistical analysis and variations in composition are analyzed with the help of information retreived from t/γ maps so that artifacts are avoided.

The observation of nano-voids in Au thin films

1987 ◽  
Vol 45 ◽  
pp. 366-367
Author(s):  
William Krakow
Keyword(s):  
Thin Films ◽  
Melting Point ◽  
Present Author ◽  
Stacking Faults ◽  
Damage Threshold ◽  
Ionic Species ◽  
Rare Gases ◽  
Chain Defects ◽  
Vacancy Chains ◽  
Au Thin Films

It has long been known that defects such as stacking faults and voids can be quenched from various alloyed metals heated to near their melting point. Today it is common practice to irradiate samples with various ionic species of rare gases which also form voids containing solidified phases of the same atomic species, e.g. ref. 3. Equivalently, electron irradiation has been used to produce damage events, e.g. ref. 4. Generally all of the above mentioned studies have relied on diffraction contrast to observe the defects produced down to a dimension of perhaps 10 to 20Å. Also all these studies have used ions or electrons which exceeded the damage threshold for knockon events. In the case of higher resolution studies the present author has identified vacancy and interstitial type chain defects in ion irradiated Si and was able to identify both di-interstitial and di-vacancy chains running through the foil.

Important Compounds in the Cocaine Class: A Synthesis Overview

1991 ◽  
Author(s):  
F.I. Carroll ◽  
◽  
Anita H. Lewin
Keyword(s):  
Class A

Parameters of bed occupancy of intensive care units in Hungary

2011 ◽  
Vol 152 (24) ◽  
pp. 946-950 ◽  
Author(s):  
Miklós Gresz
Keyword(s):  
Health Care ◽  
Intensive Care Unit ◽  
Intensive Care ◽  
Health Insurance ◽  
Intensive Care Units ◽  
Emergency Care ◽  
Present Author ◽  
Bed Occupancy ◽  
National Network ◽  
Bed Capacity

According to the Semmelweis Plan for Saving Health Care, ”the capacity of the national network of intensive care units in Hungary is one but not the only bottleneck of emergency care at present”. Author shows on the basis of data reported to the health insurance that not on a single calendar day more than 75% of beds in intensive care units were occupied. There were about 15 to 20 thousand sick days which could be considered unnecessary because patients occupying these beds were discharged to their homes directly from the intensive care unit. The data indicate that on the whole bed capacity is not low, only in some institutions insufficient. Thus, in order to improve emergency care in Hungary, the rearrangement of existing beds, rather than an increase of bed capacity is needed. Orv. Hetil., 2011, 152, 946–950.

DISTRIBUIÇÃO DA EVAPORAÇÃO EM ESTUFA PLÁSTICA NA PRIMAVERA

Irriga ◽  
2001 ◽  
Vol 6 (3) ◽  
pp. 120-127
Author(s):  
Reginaldo Ferreira Santos ◽  
Antonio Evaldo Klar
Keyword(s):  
Spatial Variability ◽  
Pan Evaporation ◽  
Spring Season ◽  
Class A ◽  
Agricultural Sciences ◽  
E Mail ◽  
Center Area ◽  
Class A Pan

DISTRIBUIÇÃO DA EVAPORAÇÃO EM ESTUFA PLÁSTICA NA PRIMAVERA  Reginaldo Ferreira SantosCentro de Ciências Exatas e Tecnológica da UNIOESTE- CP 711CEP 858114-110, Cascavel, PR - Fone: 0XX45 2203155.  E-mail: [email protected] Evaldo KlarDepartamento de Engenharia Rural - Faculdade de Ciências Agronômica- UNESP - CEP 18603-970 - Botucatu, SP. CP: 237.  E-mail:  [email protected]  1  RESUMO O presente trabalho teve como objetivo avaliar a distribuição da evaporação no interior de uma estufa plástica, com uma cultura de pimentão, através da variabilidade espacial e comparar a evaporação dos microevaporímetros com os valores do Tanque classe "A". O experimento foi conduzido no Campus da Universidade Estadual Paulista - FCA/UNESP, no período de primavera, em estufa plástica de polietileno de baixa densidade (PEBD). Na distribuição da evaporação em estufa com orientação norte/sul, verificou-se que as maiores evaporações ocorreram nas extremidades sul e norte tendente ao lado oeste. Já as menores evaporações localizaram-se no centro. No período de primavera, a evaporação média nos microevaporímetros superestimou em 55% a evaporação determinada no Tanque classe "A". UNITERMOS: evaporação, geoestatística, estufa.  SANTOS, R.F, KLAR, A.E.  EVAPORATION DISTRIBUTION INSIDE A PLASTIC TUNNEL IN THE SPRING SEASON  2  ABSTRACT                 The main aim of this study was to verify the evaporation distribution inside a plastic tunnel, with pepper crop, oriented to north/south, through spatial variability and to compare Class A Pan evaporation to punctual evaporations of 40 equidistant microevaporimeters placed from 50cm the soil. The study was carried out at the College of Agricultural Sciences/UNESP, Botucatu – SP in the spring season.  The highest evaporation occurred next to north and to south sides of the tunnel, with tendency to west. Consequently, the lowest evaporations occurred at the center area. The microevaporimeter evaporations were 55% higher than those obtained from Class A Pan. KEYWORDS: evaporation distribution, microevaporimeter.

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