ON THE BURNSIDE SEMIGROUPS xn = xn+m

1996 ◽  
Vol 06 (02) ◽  
pp. 179-227 ◽  
Author(s):  
ALAIR PEREIRA DO LAGO
Keyword(s):  
Word Problem ◽  
Maximal Subgroups ◽  
Substantial Part ◽  
Minimal Generator ◽  
Rewriting System ◽  
The Stability ◽  
Elementary Concept ◽  
Congruence Classes

In this paper we prove that the congruence classes of A* associated to the Burnside semigroup with |A| generators defined by the equation xn=xn+m, for n≥4 and m≥1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m=1 and n≥2. De Luca and Varricchio solved the problem for n≥5 in 90. A little later, McCammond extended the problem for m≥1 and solved it independently in the cases n≥6 and m≥1. Our work, which is based on the techniques developed by de Luca and Varricchio, extends both these results. We effectively construct a minimal generator Σ of our congruence. We introduce an elementary concept, namely the stability of productions, which allows to eliminate all hypothesis related to the values of n and m. A substantial part of our proof consists of showing that all productions in Σ are stable, for n≥4 and m≥1. We also show that Σ is a Church-Rosser rewriting system, thus solving the word problem, and show that the semigroup is finite [Formula: see text]-above. We prove that the frame of the ℛ-classes of the semigroup is a tree. We characterize and calculate the ℛ-classes, ℋ-classes and the [Formula: see text]-classes of the semigroup, regular or not, and prove that its maximal subgroups are cyclic of order m whenever all productions of Σ are stable. Recently Guba extended the cases in which the conjecture holds to n≥3 and m≥1. Using his work we obtain the stability of the productions of Σ for n=3 and m≥1 too and, hence, all properties about the semigroup structure hold in this case.

REWRITING SYSTEMS IN ALTERNATING KNOT GROUPS

2006 ◽  
Vol 16 (04) ◽  
pp. 749-769 ◽  
Author(s):  
FABIENNE CHOURAQUI
Keyword(s):  
Word Problem ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Regular Position

Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the augmented Dehn presentation of the knot group of a tame, prime, alternating knot in regular position, with a common projection has a finite and complete rewriting system. This provides an algorithm for solving the word problem with this presentation and we find an algorithm for solving the word problem with the Dehn presentation also.

COMPLETE REWRITING SYSTEMS FOR CODIFIED SUBMONOIDS

2005 ◽  
Vol 15 (02) ◽  
pp. 207-216
Author(s):  
ANTÓNIO MALHEIRO
Keyword(s):  
The Other ◽  
Maximal Subgroups ◽  
Rewriting Systems ◽  
Group Of Units ◽  
Rewriting System ◽  
Other Hand

Given a complete rewriting system R on X and a subset X0 of X+ satisfying certain conditions, we present a complete rewriting system for the submonoid of M(X;R) generated by X0. The obtained result will be applied to the group of units of a monoid satisfying H1 = D1. On the other hand we prove that all maximal subgroups of a monoid defined by a special rewriting system are isomorphic.

scholarly journals Religiosity and Mental Health: A Contribution to Understanding the Heterogeneity of Research Findings

2020 ◽  
Vol 17 (2) ◽  
pp. 494 ◽  
Author(s):  
Klara Malinakova ◽  
Peter Tavel ◽  
Zdenek Meier ◽  
Jitse P. van Dijk ◽  
Sijmen A. Reijneveld
Keyword(s):  
Mental Health ◽  
Mental Health Problems ◽  
Religious Affiliation ◽  
Substantial Part ◽  
Religious Attitudes ◽  
Conversion Experience ◽  
Research Findings ◽  
Nationally Representative ◽  
Religiosity And Spirituality ◽  
The Stability

Most studies report positive associations between religiosity and spirituality and aspects of mental health, while a small proportion report mixed or fully negative associations. The aim of this study was to assess the associations of religiosity measured more specifically, with mental health in a secular environment, using a nationally representative sample of Czech adults (n = 1795). We measured religious affiliation, conversion experience, non-religious attitudes and the stability of these attitudes, mental health problems, and anxiety levels. Compared to stable non-religious respondents, unstable non-religious and converted respondents who perceived God as distant were more likely to experience anxiety in close relationships, and had higher risks of worse mental health. Our findings support the idea that the heterogeneity of findings in associations between religiosity/spirituality and mental health could be due to measurement problems and variation in the degree of secularity. A shift towards religiosity could be expected to be seen in a substantial part of non-religious respondents in problematic times.

scholarly journals Translation Theory between Theorization and Theoricization

2021 ◽  
pp. 47-81
Author(s):  
Dr. Hasan Ghazala ◽  
Keyword(s):  
Comparative Study ◽  
Substantial Part ◽  
Translation Theory ◽  
Body Of Knowledge ◽  
The World ◽  
The Stability ◽  
Definition Of ◽  
Key Terms ◽  
Considerable Damage

There has been an accumulation of a huge stuff of theorization about translation enveloping and cramming translation theory and threatening its existence by demeaning and probably blasting its bases, thus leading to the chaos in translation theory. Yet, a substantial part of this theorization is mere destructive theoricization that has caused considerable damage to translation theory. In translation, it aims at creating ambivalent situations and conflicting hypotheses in translation theory, tools and tactics, casting doubts on some basic topics of translation theory, including claims like untranslatability of culture, translation prescriptivism vs. descriptivism, equivalence as a chimera, breaking translation norms, regularities and boundaries, demoralising the SL text and putting it in the service of the TL culture and suspecting the definition of key terms in the field on the top of which is the term "translation. That would jeopardize the stability and credibility of translation theory as a whole, and may render it inoperative. This is indeed the most serious challenge for the substance of contemporary translation theory. The present paper is a comparative study drawn between the facts of genuine constructive theorization and damaging destructive theoricization that aims at suffocating any attempt to set out an institutionalized body of knowledge of guidelines and principles of a solid translation theory, and develop it in a systematic and on-the-ground way to tackle any new issue or problem of translation in application. The study virtually ends up with a decisive conclusive result that, despite few shortcomings, a rigorous, practice-based translation theory does exist the world over.

THE SOLUTION TO THE WORD PROBLEM FOR THE RELATIVELY FREE SEMIGROUPS SATISFYING Ta = Ta+b WITH a ≥ 6

1991 ◽  
Vol 01 (01) ◽  
pp. 1-32 ◽  
Author(s):  
J. McCAMMOND
Keyword(s):  
Word Problem ◽  
Maximal Subgroups ◽  
Finite State Automaton ◽  
Cyclic Groups ◽  
Finite State ◽  
Free Semigroups ◽  
Positive Integers

In this article the word problem for certain Burnside semigroups is shown to be decidable. For each word W ∈ A* a nondeterministic, finite-state automaton is constructed. This automaton accepts a word iff it is equivalent to W under the relations Ta = Ta+b, where a and b are fixed positive integers and T is an arbitrary word in A*. The method decides the word problem for those cases where a ≥ 6. The maximal subgroups are shown to be cyclic groups of order b.

The dynamics of organic production in the Rockall Channel area

1986 ◽  
Vol 88 ◽  
pp. 207-220
Author(s):  
B. Zeitzschel
Keyword(s):  
Spring Bloom ◽  
Standing Stock ◽  
Euphotic Zone ◽  
Organic Production ◽  
Substantial Part ◽  
Cell Aggregates ◽  
Nutrient Depletion ◽  
New Production ◽  
Faecal Pellets ◽  
The Stability

SynopsisFor the onset of the phytoplankton spring bloom in temperate waters, the irradiance, the concentration of accumulated nutrients and the stability of the water column are of great importance. The “new” production in spring is produced mainly by chain forming diatoms.The dissipation of the spring bloom is due to nutrient depletion in the stabilised surface layer, loss of cells by sinking and grazing by herbivorous zooplankton. After the nutrient concentration is lowered, the rate of production will depend primarily on the rate of replenishment of nutrients. In open ocean environments we find “regenerated production” which is due to exudated and excreted nutrient salts e.g. ammonium. The dominating group of phytoplankters are small flagellates. It is argued that a substantial part of the phytoplankton standing stock in spring is lost from the euphotic zone due to direct sinking of cells or accelerated sinking of cell-aggregates. It is postulated that faecal pellets of micro- and mesozooplankton are retained and recycled in the mixed layer, whereas macrozooplankton faecal strings transport a considerable amount of organic matter to the benthal.

scholarly journals IDENTITIES IN THE ALGEBRA OF PARTIAL MAPS

2006 ◽  
Vol 16 (06) ◽  
pp. 1131-1159 ◽  
Author(s):  
MARCEL JACKSON ◽  
TIM STOKES
Keyword(s):  
Word Problem ◽  
Equational Theory ◽  
Term Rewriting ◽  
Deductive System ◽  
Natural Order ◽  
Term Rewriting System ◽  
Rewriting System ◽  
Clifford Semigroups

We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

FINITE IDEMPOTENT INVERSE MONOID PRESENTATIONS

2011 ◽  
Vol 21 (07) ◽  
pp. 1111-1133 ◽  
Author(s):  
PEDRO V. SILVA
Keyword(s):  
Word Problem ◽  
Elementary Solution ◽  
Maximal Subgroups ◽  
Inverse Monoid ◽  
Inverse Monoids ◽  
Unexpected Consequence ◽  
Insight Into

Several decidability problems for finite idempotent presentations of inverse monoids are solved, giving also insight into their structure. Besides providing a new elementary solution for the problem, solutions are obtained for the following problems: computing the maximal subgroups, being combinatorial, being semisimple, being fundamental, having infinite [Formula: see text]-classes. The word problem for the least fundamental quotient is also solved, with an unexpected consequence.

scholarly journals A solution of the word problem for braid groups via the complex reflection group G12

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 461-467
Author(s):  
Ahmet Cevik ◽  
Amer Albargi
Keyword(s):  
Word Problem ◽  
Braid Group ◽  
Decision Problem ◽  
Normal Forms ◽  
Reflection Group ◽  
Braid Groups ◽  
Complex Reflection ◽  
Complex Reflection Group ◽  
Main Target ◽  
Congruence Classes

It is known that if there exists a Gr?bner-Shirshov basis for a group G, then we say that one of the decision problem, namely the word problem, is solvable for G as well. Therefore, as the main target of this paper, we will present a (non-commutative) Gr?bner-Shirshov basis for the braid group associated with the congruence classes of complex reflection group G12 which will give us normal forms of the elements of G12 and so will obtain a new algorithm to solve the word problem over it.

scholarly journals THE IMPACT OF ECONOMIC SITUATION IN THE COUNTRIES RECEIVING MIGRANTS ON REMITTANCES FLOWS

2020 ◽  
pp. 49-55
Author(s):  
Andrej Přívara
Keyword(s):  
Household Income ◽  
Opposite Effect ◽  
Consumption Patterns ◽  
The Other ◽  
Substantial Part ◽  
Host Countries ◽  
Economic Issues ◽  
Money Transfers ◽  
The Stability ◽  
The Impact

The studies on remittances focus mainly on their effects on the stability of households’ incomes and/or consumption patterns. The purpose of the current paper is to highlight that the volatility of remittances can have the opposite effect. We believe that the conjuncture of the countries that receive migrants also determines their money transfers and their changes are then transmitted to the economy of the migrants’ country of origin, thus increasing the instability in the latter. We believe that the volatility of remittances is higher under specific conditions, namely, when they represent a substantial part of household income and when migrants are highly concentrated in one or several countries only. Otherwise, even if one of the recipient countries is experiencing temporary economic issues, flows will be less affected since the other host countries may not be affected by such a downturn in their economy. Diversification of the diaspora is therefore crucial for the stability of remittances since the more is the number of host countries, the less likely is a sudden decline in remittances in the event of a recession in one of those countries.

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