scholarly journals Tilings Generated by Ito-Sadahiro and Balanced (-ß)-numeration Systems

10.14311/1255 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
P. Ambrož
Keyword(s):  
Numeration System ◽  
Numeration Systems ◽  
Definition Of ◽  
Pisot Unit

Let β > 1 be a cubic Pisot unit. We study forms of Thurston tilings arising from the classical β-numeration system and from the (−β)-numeration system for both the Ito-Sadahiro and balanced definition of the (−β)-transformation.

scholarly journals A DECISION PROBLEM FOR ULTIMATELY PERIODIC SETS IN NONSTANDARD NUMERATION SYSTEMS

2009 ◽  
Vol 19 (06) ◽  
pp. 809-839 ◽  
Author(s):  
JASON BELL ◽  
EMILIE CHARLIER ◽  
AVIEZRI S. FRAENKEL ◽  
MICHEL RIGO
Keyword(s):  
Finite Automaton ◽  
Regular Language ◽  
Decision Problem ◽  
Decision Procedure ◽  
Fibonacci Sequence ◽  
Finite Union ◽  
Numeration System ◽  
Periodic Sets ◽  
Numeration Systems ◽  
The One

Consider a nonstandard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure for this problem, under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language.

scholarly journals Integer Semigroups Associated with Dumont-Thomas Numeration Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Víctor F. Sirvent
Keyword(s):  
Identity Element ◽  
Finitely Generated ◽  
Numeration System ◽  
Primitive Substitution ◽  
Binary Operations ◽  
Numeration Systems ◽  
Positive Integers

Given a primitive substitution, we define different binary operations on infinite subsets of the nonnegative integers. These binary operations are defined with the help of the Dumont-Thomas numeration system; that is, a numeration system associated with the substitution. We give conditions for these semigroups to have an identity element. We show that they are not finitely generated. These semigroups define actions on the set of positive integers. We describe the orbits of these actions. We also estimate the density of these sets as subsets of the positive integers.

Math Roots: Understanding Aztec and Mayan Numeration Systems

2006 ◽  
Vol 12 (1) ◽  
pp. 55-62
Author(s):  
Angela L.E. Walmsley
Keyword(s):  
Current System ◽  
Numeration System ◽  
Numeration Systems

Numbers have been recorded in a variety of ways throughout time. For example, the Babylonians used marks pressed in clay; the Egyptians used papyrus and ink brushes to create tally marks; and the Maya introduced a symbol for zero (Billstein, Libeskind, and Lott 2001). All these ancient peoples used numerals, or written symbols, to express what they meant mathematically. They created their own numeration system, which is a collection of uniform symbols and properties to express numbers systematically. The Hindu- Arabic system is one such numeration method; however, understanding others can reveal to students that our current system finds its roots in what has come before.

scholarly journals Multidimensional Numbers and Semantic Numeration Systems:Theoretical Foundation and Application

2019 ◽  
Vol 16 (2) ◽  
Author(s):  
Alexander Ju. Chunikhin
Keyword(s):  
Image Compression ◽  
Number System ◽  
Abstract Entity ◽  
Two Dimensional ◽  
Numeration System ◽  
New Class ◽  
Abstract Entities ◽  
Numeration Systems ◽  
Theoretical Foundations

In this article, we present a new class of numeration systems, namely Semantic Numeration Systems. The methodological background and theoretical foundations of such systems are considered. The concepts of abstract entity, entanglement and valence of abstract entities, and the topology of the numeration system are introduced. The proposed classification of semantic numeration systems allows to choose the numeration system depending on the problem being solved. Examples of the use of a two-dimensional number system for image compression problems and computation of a two-dimensional convolution are given.

Inventing a numeration system

1973 ◽  
Vol 20 (7) ◽  
pp. 550-553
Author(s):  
Karl J. Smith
Keyword(s):  
Numeration System ◽  
Numeration Systems

Many of the current textbooks discuss and develop historical numeration systems, as well as numeration systems with bases other than ten. To allow the class to invent their own numeration system could be a worthwhile activity. This paper shows how this might be done.

scholarly journals Addition and multiplication of beta-expansions in generalized Tribonacci base

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Petr Ambrož ◽  
Zuzana Masáková ◽  
Edita Pelantová
Keyword(s):  
Real Root ◽  
Fractional Part ◽  
Arithmetic Operations ◽  
Numeration System ◽  
The Real ◽  
Infinite Words ◽  
Combinatorial Properties ◽  
Greedy Expansion ◽  
International Audience ◽  
Numeration Systems

International audience We study properties of β-numeration systems, where β > 1 is the real root of the polynomial x3 - mx2 - x - 1, m ∈ ℕ, m ≥ 1. We consider arithmetic operations on the set of β-integers, i.e., on the set of numbers whose greedy expansion in base β has no fractional part. We show that the number of fractional digits arising under addition of β-integers is at most 5 for m ≥ 3 and 6 for m = 2, whereas under multiplication it is at most 6 for all m ≥ 2. We thus generalize the results known for Tribonacci numeration system, i.e., for m = 1. We summarize the combinatorial properties of infinite words naturally defined by β-integers. We point out the differences between the structure of β-integers in cases m = 1 and m ≥ 2.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

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.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

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.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

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