Markov semigroups, monoids, and groups

A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown to be equivalent. Various interesting examples are presented, including an example of a non-Markov monoid that nevertheless admits a regular language of unique representatives over any generating set. It is shown that all finitely generated commutative semigroups are strongly Markov, but that finitely generated subsemigroups of virtually abelian or polycyclic groups need not be. Potential connections with word-hyperbolic semigroups are investigated. A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finite-index subsemigroups and extensions. Several questions are posed.Comment: 40 pages; 3 figure

Context-free rewriting systems and word-hyperbolic structures with uniqueness

This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan & Gilman by exhibiting an example of a word-hyperbolic monoid that does not admit a word-hyperbolic structure with uniqueness (that is, in which the language of representatives maps bijectively onto the monoid)

The Relationship between Control over a Deal and Cognitive-Based Trust in an International Business Partnership

Background and purpose: Trust is embedded into the national culture. It is a tool that helps create strategic partÂnerships and facilitates deals that carry certain risks. Cultural differences and norms can affect business relations, but more often focus is on the obvious differences. Although trust in a business partner may be due to non-obvious differences, for example, which part of the deal the partner wants to control himself and which part of the deal he wants to give to the partner to control. If the difference between the real and desired levels of the partner's control over the deal is large, then is trust possible, especially in intercultural business relations? Objective: One aim of our study is to find out whether trust may be considered as moderator of control in a business deal. In other words, if the level of trust in a business partner is higher, are the partners more open to sharing their control over the deal with each other? The other aim is to identify the links between these indicators (trust and conÂtrol) in business partnerships of partners from different cultures. Design/Methodology/Approach: The study investigated the answers of 103 Slovenian and 124 Russian business partners. The Organizational Trust Inventory (OTI) and the 5-items questionnaire on control over deal were used to collect data. Descriptive and inferential statistics were used to process the data collected. Results: The probability that the business partner will not fulfil their obligations in the deal negatively relates to the level of trust. The difference between degree of desired control and degree of control negatively relates to the level of trust. Conclusion: As our results showed, trust cannot be considered as a strong moderator of control between partners. In response to greater trust, the respondents only agree to increase their partner's control, but are not willing to reÂduce their own. Moreover, this finding is stronger in the group of Russian partners than in the Slovenian ones. © 2020 Sciendo. All rights reserved

A characterization of those automata that structurally generate finite groups

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper

Влияние экологических факторов на развитие рыбного хозяйства Украины

Аквакультура становится одной из наиболее перспективных отраслей сельского хазяйства. При рациональном использовании водных ресурсов можно обеспечить потребителей качественной, безопасной и полезной продукцией широкого ассортимента. Современное использование водных ресурсов для ведения аквакультуры базируется на принципе обязательного сохранения их естественного воспроизводства

Identities of the kauffman monoid K4 and of the Jones Monoid J4

Kauffman monoids Kn and Jones monoids Jn, n=2,3,…, are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids K3 and K4 satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in K4. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid J4. © Springer Nature Switzerland AG 2020.M. V. Volkov—Supported by Ural Mathematical Center under agreement No. 075-02-2020-1537/1 with the Ministry of Science and Higher Education of the Russian Federation

ПОРІВНЯЛЬНА ЕФЕКТИВНІСТЬ АД’ЮВАНТНОЇ ТЕРАПІЇ В КОМБІНОВАНОМУ ЛІКУВАННІ ПОВЕРХНЕВОГО РАКУ СЕЧОВОГО МІХУРА Та-Т2а СТАДІЙ ПІСЛЯ ВІДКРИТИХ І ТРАНСУРЕТРАЛЬНИХ РЕЗЕКЦІЙ

The results of using various regimens of an adjuvant chemoradiation effect in a combined treatment of urinary bladder cancerfolloving open and transurethral resections are presented. The most effective is the regimen which includes a method of endolymphatic polychemotherapy, enabling to achieve a 5-year survival in 94.6±5.26 % of the cases and the average duration of life 4.92±0.03 years.Представлены результаты использования различных режимов адъювантного химиолучевого воздействия в комбинированном лечении рака мочевого пузыря после открытых и трансуретральных резекций. Наиболее эффективной является схема, включающая способ эндолимфатической полихимиотерапии, позволяющая достичь 5-летней выживаемости в 94,6±5,26% случаев и средней продолжительности жизни 4,92±0,03 года.Наведені результати використання різноманітних режимів ад’ювантного хіміопроменевого впливу в комбінованому лікуванні раку сечового міхура після відкритих і трансуретральних резекцій. Найбільш ефективною є схема, яка включає спосіб ендолімфатичної поліхіміотерапії, що дозволяє досягнути 5-річного виживання у 94,6±5,26% випадків та середньої тривалості життя 4,92±0,03 років

Minimally invasive methods in treatment of pilonidal disease (review of the literature)

The objective was to compare the most common methods of minimally invasive treatment of pilonidal disease and to evaluate their effectiveness according to the literature. Minimally invasive methods of treatment could be successfully used in patients with a small spread of pilonidal disease. Improving the effectiveness of treatment of this category of patients was directly related to the strict selection of patients