scholarly journals Methods of Numeration of Discrete Sequences

2021 ◽  
pp. 63-67
Author(s):  
N.A. Gupal
Keyword(s):  
Complete List ◽  
Natural Numbers ◽  
Famous Theorem ◽  
Code Number ◽  
Fundamental Part ◽  
Effective Operation ◽  
Discrete Sequences

Introduction. Numeration, or code, discrete sequences act fundamental part in the theory of recognition and estimation. By the code get codes or indexes of the programs and calculated functions. It is set that the universal programs are that programs which will realize all other programs. This one of basic results in the theory of estimation. On the basis of numeration of discrete sequences of Godel proved a famous theorem about incompleteness of arithmetic. Purpose of the article. To develop synonymous numerations by the natural numbers of eventual discrete sequences programs and calculable functions mutually. Results. On the basis of numerations of eventual discrete sequences numerations are built for four commands of machine with unlimited registers (MUR) in the natural numbers of type of 4u, 4u +1, 4u+2, 4u+3 accordingly. Every program consists of complete list of commands. On the basis of bijection for four commands of MUR certainly mutually synonymous numerations for all programs of MUR. Thus, on the basis of the set program it is possible effectively to find its code number, and vice versa, on the basis of the set number it is possible effectively to find the program. Conclusions. Synonymous numerations by the natural numbers of complete discrete sequences are developed mutually, programs for MUR and calculable functions. Leaning against numeration of the programs it is set in the theory of calculable functions, that the universal programs are, that programs which will realize all other programs. By application of the calculated functions and s-m-n theorem are got to operation on the calculated functions: combination ?x and ?y, giving work ?x?y, operation of conversion of functions, effective operation of recursion. Thus, the index of function ?x?y is on the indexes of x and y [2]. Keywords: numeration, Godel code number, diagonal method.

The Problem of Mathematical Objects

2020 ◽  
pp. 213-224
Author(s):  
Bob Hale
Keyword(s):  
Natural Numbers ◽  
Real Numbers ◽  
Mathematical Objects ◽  
Epistemological Foundation ◽  
Fundamental Part ◽  
Object Based

If fundamental mathematical theories such as arithmetic and analysis are taken at face value, any attempt to provide an epistemological foundation—roughly, an account which explains how we can know standard mathematical theories to be true, or at least justifiably believe them—must confront the problem of mathematical objects—the problem of explaining how a belief in the existence of an infinity of natural numbers, an uncountable infinity of real numbers, etc., is to be justified. One small but fundamental part of the problem is discussed: whether we can be justified in believing that there is a denumerable infinity of natural numbers, or, more generally, an infinity of objects of any kind. The chapter considers two broad approaches to this problem—what are called object-based and property-based approaches.

Stick number of tangles

2017 ◽  
Vol 26 (13) ◽  
pp. 1750094
Author(s):  
Youngsik Huh ◽  
Jung Hoon Lee ◽  
Kouki Taniyama
Keyword(s):  
Disjoint Union ◽  
Unit Interval ◽  
Complete List ◽  
Natural Numbers ◽  
Line Segments ◽  
Text String ◽  
Nonincreasing Sequence

An [Formula: see text]-string tangle is a pair [Formula: see text] such that [Formula: see text] is a disjoint union of properly embedded [Formula: see text] arcs in a topological [Formula: see text]-ball [Formula: see text]. And an [Formula: see text]-string tangle is said to be trivial (or rational)[Formula: see text], if it is homeomorphic to [Formula: see text] as a pair, where [Formula: see text] is a 2-disk, [Formula: see text] is the unit interval and each [Formula: see text] is a point in the interior of [Formula: see text]. A stick tangle is a tangle each of whose arcs consists of finitely many line segments, called sticks. For an [Formula: see text]-string stick tangle its stick-order is defined to be a nonincreasing sequence [Formula: see text] of natural numbers such that, under an ordering of the arcs of the tangle, each [Formula: see text] denotes the number of sticks constituting the [Formula: see text]th arc of the tangle. And a stick-order [Formula: see text] is said to be trivial, if every stick tangle of the order [Formula: see text] is trivial. In this paper, restricting the [Formula: see text]-ball [Formula: see text] to be the standard 3-ball, we give the complete list of trivial stick-orders.

Effective operations in a general setting

1964 ◽  
Vol 29 (4) ◽  
pp. 163-178 ◽  
Author(s):  
A. H. Lachlan
Keyword(s):  
General Setting ◽  
Natural Numbers ◽  
Recursive Functions ◽  
Effective Operation ◽  
Positive Results

There are essentially two ‘positive’ results concerning the extension of effective operations to partial recursive functionals. The first proved by Myhill and Shepherdson in [9] states that any effective operation whose domain is the set of all partial recursive (p.r.) functions is potentially p.r. The second proved originally by Kreisel, Lacombe, and Shoenfield in [5] states: Let F be an effective operation mapping a set of recursive functions into the natural numbers; if has a recursively dense base, then F is potentially p.r. The main objective of this paper is to present these two theorems in a general setting.

scholarly journals A simple model for a weak system of arithmetic

1974 ◽  
Vol 11 (3) ◽  
pp. 321-323
Author(s):  
D.W. Barnes ◽  
G.P. Monro
Keyword(s):  
Simple Model ◽  
Complete List ◽  
Natural Numbers ◽  
Successor Function ◽  
First Order ◽  
Nonstandard Model ◽  
Infinite Elements

The natural, first order version of Peano's axioms (the theory T with 0, the successor function and an induction schema) is shown to possess the following nonstandard model: the natural numbers together with a collection of ‘infinite’ elements isomorphic to the integers. In fact, a complete list of the models of this theory is obtained by showing that T is equivalent to the apparently weaker theory with the induction axiom replaced by axioms stating that there are no finite cycles under the successor function and that 0 is the only non-successor.

A Walk through Various Data Hiding Techniques

2017 ◽  
Vol 7 (8) ◽  
pp. 52
Author(s):  
Manoj Kumar ◽  
Rohit Tanwar
Keyword(s):  
Data Hiding ◽  
Data Framework ◽  
Web Information ◽  
Fundamental Part ◽  
Secure Information ◽  
Numerous Data ◽  
Security Information ◽  
Security Procedures

In the computerized age as a result of the broad utilization of web, information covering up in advanced symbolism assumes a fundamental part to guarantee copyright assurance and power from pernicious assaults. Today the exponential development in web clients request secure information correspondence, for that it is required to send the information as encoded or shrouded shape. Numerous data framework security procedures are accessible.Information transmission needs security. Information covering up can be accomplished through numerous techniques. Distinctive information concealing procedures are talked about in this paper which incorporates watermarking, steganography, fingerprinting, cryptography and advanced mark.

Thinking About Rural Development.—By Arther T. Mosher. New York: Agricultural Development Council, Inc., 1976. xii+pp.350.

1978 ◽  
Vol 17 (3) ◽  
pp. 382-383
Author(s):  
Javed Iqbal
Keyword(s):  
New York ◽  
Rural Development ◽  
Agricultural Development ◽  
Complete List ◽  
Basic Defect ◽  
Considerable Length ◽  
Selection Of

This book is essentially a selection of the articles written by Arther T. Mosher during his long career as a rural development expert. Also appended at the end is a complete list of writings by him. The Agricultural Development Council has chosen to publish this book to honour the author, who was its President during 1967-1973, The publication of this book is welcome in the context of the recent rediscovery of rural development as a principal plank of need-oriented develop¬ment strategies. A basic defect of writing on rural development has been excessive resort to stereotype rehtoric, over-enthusiasm and a certain pedanticism. Fortunately, Mosher's orientation is practical, not doctrinaire. Although the book is titled "Thinking About Rural Development", the author keeps on bring¬ing together the thinking and practice into their validly interactive perspectives. Not surprisingly so, for the author has himself worked in the field as a rural development practitioner for a considerable length of time.

Diatoms in waterbodies and watercourses of Privolzhskaya Hills (Penza Region)

2008 ◽  
Vol 42 ◽  
pp. 24-35
Author(s):  
M. S. Kulikovskiy
Keyword(s):  
Species Composition ◽  
Complete List ◽  
Russian Plain ◽  
Taxonomic Analysis

Species composition of diatoms from different waterbodies and watercourses Privolzhskaya Hills (Penza Region, Russian Plain, Russia) is studied. The complete list of revealed species of centric and pinnate diatoms (299 taxa) and a brief taxonomic analysis are given. The name Sellaphora bacilloides is validated.

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