scholarly journals Return Words and Recurrence Function of a Class of Infinite Words

10.14311/920 ◽  
2007 ◽  
Vol 47 (2-3) ◽  
Author(s):  
L’. Balková
Keyword(s):  

Many combinatorial and arithmetical properties have been studied for infinite words ub associated with ß-integers. Here, new results describing return words and recurrence function for a special case of ub will be presented. The methods used here can be applied to more general infinite words, but the description then becomes rather technical. 

2014 ◽  
Vol 35 (6) ◽  
pp. 1767-1782
Author(s):  
JAMES D. CURRIE ◽  
NARAD RAMPERSAD ◽  
KALLE SAARI

Let $A$ be a finite alphabet and $f:~A^{\ast }\rightarrow A^{\ast }$ be a morphism with an iterative fixed point $f^{{\it\omega}}({\it\alpha})$, where ${\it\alpha}\in A$. Consider the subshift $({\mathcal{X}},T)$, where ${\mathcal{X}}$ is the shift orbit closure of $f^{{\it\omega}}({\it\alpha})$ and $T:~{\mathcal{X}}\rightarrow {\mathcal{X}}$ is the shift map. Let $S$ be a finite alphabet that is in bijective correspondence via a mapping $c$ with the set of non-empty suffixes of the images $f(a)$ for $a\in A$. Let ${\mathcal{S}}\subset S^{\mathbb{N}}$ be the set of infinite words $\mathbf{s}=(s_{n})_{n\geq 0}$ such that ${\it\pi}(\mathbf{s}):=c(s_{0})f(c(s_{1}))f^{2}(c(s_{2}))\cdots \in {\mathcal{X}}$. We show that if $f$ is primitive, $f^{{\it\omega}}({\it\alpha})$ is aperiodic, and $f(A)$ is a suffix code, then there exists a mapping $H:~{\mathcal{S}}\rightarrow {\mathcal{S}}$ such that $({\mathcal{S}},H)$ is a topological dynamical system and ${\it\pi}:~({\mathcal{S}},H)\rightarrow ({\mathcal{X}},T)$ is a conjugacy; we call $({\mathcal{S}},H)$ the suffix conjugate of $({\mathcal{X}},T)$. In the special case where $f$ is the Fibonacci or Thue–Morse morphism, we show that the subshift $({\mathcal{S}},T)$ is sofic, that is, the language of ${\mathcal{S}}$ is regular.


2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.


Author(s):  
Dr. G. Kaemof

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.


2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.


2019 ◽  
Vol 3 (4) ◽  
pp. 209-222
Author(s):  
Philipp K. Görs ◽  
Henning Hummert ◽  
Anne Traum ◽  
Friedemann W. Nerdinger

Digitalization is a megatrend, but there is relatively little knowledge about its consequences for service work in general and specifically in knowledge-intensive business services (KIBS). We studied the impact of digitalization on psychological consequences for employees in tax consultancies as a special case of KIBS. We compare two tax consulting jobs with very different job demands, those of tax consultants (TCs) and assistant tax consultants (ATCs). The results show that the extent of digitalization at the workplace level for ATCs correlates significantly positively with their job satisfaction. For TCs, the same variable correlates positively with their work engagement. These positive effects of digitalization are mediated in the case of ATCs by the impact on important job characteristics. In the case of TCs, which already have very good working conditions, the impact is mediated by the positive effect on self-efficacy. Theoretical and practical consequences of these results are discussed.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zofia Wysokińska ◽  
Tomasz Czajkowski ◽  
Katarzyna Grabowska

AbstractNonwovens are one of the most versatile textile materials and have become increasingly popular in almost all sectors of the economy due to their low manufacturing costs and unique properties. In the next few years, the world market of nonwovens is predicted to grow by 7%–8% annually (International Nonwovens & Disposables Association [INDA], European Disposables and Nonwovens Association [EDANA], and Markets and Markets). This article aims to analyze the most recent trends in the global export and import of nonwovens, to present two case studies of Polish companies that produce them, and to present one special case study of the market of nonwoven geotextiles in China and India, which are the Asian transition economies among the BRICS countries (Brazil, Russia, India, China, and South Africa).


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