The repetition threshold of episturmian sequences

The repetition threshold of a class $C$ of infinite $d$-ary sequences is the smallest real number $r$ such that in the class $C$ there exists a sequence that avoids $e$-powers for all $e> r$. This notion was introduced by Dejean in 1972 for the class of all sequences over a $d$-letter alphabet. Thanks to the effort of many authors over more than 30 years, the precise value of the repetition threshold in this class is known for every $d \in \mathbb N$. The repetition threshold for the class of Sturmian sequences was determined by Carpi and de Luca in 2000. Sturmian sequences may be equivalently defined in various ways, therefore there exist many generalizations to larger alphabets. Rampersad, Shallit and Vandome in 2020 initiated a study of the repetition threshold for the class of balanced sequences -- one of the possible generalizations of Sturmian sequences. Here, we focus on the class of $d$-ary episturmian sequences -- another generalization of Sturmian sequences introduced by Droubay, Justin and Pirillo in 2001. We show that the repetition threshold of this class is reached by the $d$-bonacci sequence and its value equals $2+\frac{1}{t-1}$, where $t>1$ is the unique positive root of the polynomial $x^d-x^{d-1}- \cdots -x-1$

Balancedness of Arnoux-Rauzy and Brun words

We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 letters

The International Space Station (ISS) Contest as STEM Educational Project

In the years 2015-2018, the Italian Ministry of Education, University and Research and the Italian Ministry of Defense proposed the joint initiative "Space for Your Future. The ISS: Innovatio, Scientia, Sapientia" in partnership with the Italian Space Agency. It was a competition addressed to secondary school students and aimed at developing innovative experiments to be conducted on the International Space Station, whose acronym (ISS) is the same of the Latin words "Innovatio, Scientia, Sapientia". Regardless of the odds of winning, "Space for Your Future" became a successful STEM educational project implemented in numerous schools. We illustrate how that Astronomy contest fostered a valid constructivist learning, a fruitful participatory science, and vast scientific research. We discuss, in particular, the activities of two teams of pupils from the Scientific High School "Giovanni Battista Grassi" in Latina (seat of the Planetarium "Livio Gratton") who participated within the thematic area No. 3 "Test the Sciences in Space". They all worked on chemical tests, suitable for the ISS microgravity, under the tutoring of Francesco Giuliano (Province Manager of the IYA 2009 and the IYC 2011 in Latina). The key reference is a talk given in the 104th annual congress of the Italian Physical Society at the University of Calabria (September 17-21, 2018) together with an invited lecture held in the 13th European Researchers' Night by Frascati Scienza (September 28, 2018).Comment: 28 pages, 11 figures, 9 table

Balance and Abelian complexity of the Tribonacci word

G. Rauzy showed that the Tribonacci minimal subshift generated by the morphism $\tau: 0\mapsto 01, 1\mapsto 02 and 2\mapsto 0$ is measure-theoretically conjugate to an exchange of three fractal domains on a compact set in $R^2$, each domain being translated by the same vector modulo a lattice. In this paper we study the Abelian complexity AC(n) of the Tribonacci word $t$ which is the unique fixed point of $\tau$. We show that $AC(n)\in {3,4,5,6,7}$ for each $n\geq 1$, and that each of these five values is assumed. Our proof relies on the fact that the Tribonacci word is 2-balanced, i.e., for all factors $U$ and $V$ of $t$ of equal length, and for every letter $a \in {0,1,2}$, the number of occurrences of $a$ in $U$ and the number of occurrences of $a$ in $V$ differ by at most 2. While this result is announced in several papers, to the best of our knowledge no proof of this fact has ever been published. We offer two very different proofs of the 2-balance property of $t$. The first uses the word combinatorial properties of the generating morphism, while the second exploits the spectral properties of the incidence matrix of $\tau$.Comment: 20 pages, 1 figure. This is an extended version of 0904.2872v

Social Media, Venue and the Right to a Fair Trial

Judicial failure to recognize social media\u27s influence on juror decision making has identifiable constitutional implications. The Sixth Amendment right to a fair trial demands that courts grant a defendant\u27s change of venue motion when media-generated pretrial publicity invades the unbiased sensibility of those who are asked to sit in judgment. Courts limit publicity suitable for granting a defendant\u27s motion to information culled from newspapers, radio, and television reports. Since about 2014, however, a handful of defendants have introduced social media posts to support their claims of unconstitutional bias in the community. Despite defendants\u27 introduction of negative social media in support of their claims, these same courts have yet to include social media in their evaluation of pretrial publicity bias. But social media is media, and as this article demonstrates, trial court judges faced with deciding change of venue motions have a constitutional obligation to include social media in their evaluations. The collective refusal to treat social media the same as biased television, radio, or print media, suggests an erroneous assumption on the part of lower courts that social media is somehow different. This article identifies three reasons as justification for dismissing social media: social media is too recent a medium to fully understand and analyze, social media is not a legitimate news source, and social media is opinion based. Application of pretrial social media publicity to long-standing Supreme Court change of venue doctrine, coupled with its exploration of scientific and social research on social media influence, debunk these lower court rationalizations. This article demonstrates that the reluctance of courts to consider social media evidence when deciding whether to grant a motion for a change of venue is a violation of any defendant\u27s Sixth Amendment right to a fair trial. On a larger scale, the article demands that courts embrace our new reality. Social media intersects with criminal justice, and our daily lives, in ways that demand judicial recognition

A methodology for assessing the pressures on transboundary groundwater quantity and quality – experiences from the Dinaric karst

A relatively novel and abridged methodology for assessing the quantity and quality status of groundwater bodies has been applied in the Dinaric karst of SE Europe. Validation of pressure on quantity is based on groundwater budgeting and the correlation of available groundwater reserves and projected water demands, while pressure on quality is estimated by GIS-created maps: vulnerability – hazard – risk. The results obtained from the studied groundwater bodies indicate mostly low pressure on water quantity, but increased risk from diffuse and point pollution sources. The application of methods is possible in many transboundary and inner aquifer systems even in geologically complex environments where there is insufficient monitoring dataon the groundwater regime.</p

The Origine and Evolution of Coastal and Submarine Springs in Bakar Bay

Članek obravnava obalne in podmorske izvire v Bakarskem zalivu. Največ izvirov je ob severovzhodni obali zaliva, kjer je najnižji del kontakta med kraškim vodonosnikom in flišem, ki predstavlja hidrogeološko bariero. Študijsko območje obsega obalo med Črnim in Žminjco, kjer voda izteka koncentrirano v nizu kraških izvirov in difuzno na večih območjih. Ob dvigu morske gladine ob koncu pleistocena so nekateri obalni izviri prešli pod gladino, pojavili pa so se tudi novi, višji izviri. Veliko podmorskih izvirov ni poznanih, vendar na njihov obstoj kaže študija vodne bilance. Zaradi velikega hidravličnega gradienta veliko podmorskih izvirov deluje kot vrulje. Mešanje morske in sladke vode v hidravlično nestabilnem območju je vzrok, da je voda iz teh izvirov po večini brakična.The paper presents coastal and submarine springs in Bakar Bay. The northeastern coast of Bakar Bay is abound in springs, since there is the lowest placed contact between large karst aquifer and flysch lithogenetic complex which forms hydrogeological barrier. Studied area is situated between Črno and Žminjca locations, where water flows out in series of concentrated coastal and submarine springs as well as on the places of a diffuse outflow. A rapid raise of sea-level from the end of the Pleistocene changed the hydrogeological conditions so that coastal springs were submerged and new ones, at higher levels appeared. Some of submerged springs continued to throw out water, that is, they started to function as submarine springs (vrulja) due to a strong inflow from the background and high pressures. Some of them were not registered, although according to water balance analyses of wider area, widespread evidences of groundwater outflow could be expected. Their position reflects geological fabric of the area. Groundwaters have intensive flowing gradient. Their flowing out in hydraulically unstable zone have facilitated mixing of sea- water and fresh-water and as a result spring-water is usually brackish

Episturmian words: a survey

In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. We also consider lexicographical properties of episturmian words, as well as their connection to the balance property, and related notions such as finite episturmian words, Arnoux-Rauzy sequences, and "episkew words" that generalize the skew words of Morse and Hedlund.Comment: 36 pages; major revision: improvements + new material + more reference

Impact of floods on the quality of life of Croatian and Serbian citizens : half a century after

Poplave su na teritorijama Republike Hrvatske i Republike Srbije relativno česta pojava. Pre pola stoleća, tačnije 1964. godine dogodile su se velike poplave na teritoriji tadašnje SR Hrvatske, kada se izlila reka Sava i naredne godine u SR Srbiji, kada su se izlili Dunav i Tisa. Prošle godine (2014. godine), dogodile su se poplave u Hrvatskoj i Srbiji, kada je nekoliko desetina građana izgubilo svoje živote. Autori će pokušati u radu da kvantitativnom analizom utvrde nivo kvaliteta života građana ovih dveju država u razmaku od 50 godina i uticaj poplava na kvalitet života građana, nivo nastale štete, gubitak života i druge varijable koje su od značaja za utvrđivanje odnosa kvaliteta života i kvantiteta nastale štete. Kvalitet života biće prikazan pomoću kvantitativnih pokazatelja, kao što je npr. BND per capita.Floods on the territories of Croatia and Serbia are relatively common. Half a century ago, more precisely in 1964, there was massive fl ooding on the territory of the former Socialist Republic of Croatia, when the Sava River spilled and the next year in SR Serbia, when the rivers Danube and Tisa spilled. Last year (2014) there were floods in Croatia and Serbia, where several dozen people lost their lives. This paper will try by quantitative analysis to determine the level of the quality of life of the citizens of these two countries in the span of 50 years and the impact of fl oods on the quality of life of the citizens, the level of the damage, loss of lives and other variables that are important for determining the relationship of quality of life and quantity of the resulting damage. The quality of life will be shown by quantitative indicators, such as e.g. GNP per capita