Nature Of Action Research Articles

A new meteorological pressure index to support a sustainable nuclear energy programme

Today, the evaluation of a site for innovative nuclear installations represents a fundamental step in supporting the implementation of a sustainable nuclear power program. One major concern is the potential for radioactive releases and their effects on the biosphere, particularly on human health. To address this issue, a new Meteorological Pressure Index (MPI) has been developed to identify sites with resilience capacity in terms of transport phenomena correlated to natural wind actions on a regional scale. The MPI utilizes a fuzzy approach that combines data on 3D wind speed, direction, and frequency, providing maps that are useful in the site selection process. The application of MPI in the Sicily region of Italy has allowed to identify bordering areas that that are more affected by efficient air mass transport mechanisms. Consistency analyses have been conducted among MPI maps, observed wind distributions using wind rose charts, and stagnation S and recirculation R factors. The results confirm the MPI's ability to aggregate meteorological data on a regional level, making it a suitable tool when compared to disaggregated data that may not always provide a comprehensive viewpoint.

Sea Level Rise Impacts in Coastal Areas and Possible Mitigation Engineering Approaches

Coastal areas are subjected to both natural and man-made actions, leading to a deterioration of coastal structures. Climate change has had a heavy impact on these areas in recent years. An important consequence of these actions is sea level rise. This phenomenon is the most important cause of coastal erosion, a serious problem with ecological, economic, and human health consequences. The countermeasures to contrast this phenomenon and the degradation of the entire coastal system, are represented by engineering interventions. These basically consist of approaches for adaptation to sea level rise, namely protection, retreat, and accommodation. Variations and site adaptation of these actions can involve procedures of no intervention; advancement; protection; retreat; accommodation; and ecosystem-based adaptation. While these procedures have provided coastal benefits and protection, in the long run, they may cause further coastal disruption and further aggravate the situation. Such interventions, therefore, require an accurate assessment of the advantages and disadvantages. However, it is certainly necessary to proceed with actions aimed at mitigating climate change, respecting the rules in a sustainable way.

Domain knowledge-guided adversarial adaptive fusion of hybrid breast ultrasound data

Contrast-enhanced ultrasound (CEUS), which provides more detailed microvascular information about the tumor, is always taken by radiologists in clinic diagnosis along with B-mode ultrasound (B-mode US). However, automatically analyzing breast CEUS is challenging due to the difference between the CEUS video and the natural video, e.g., sports or action videos, where the CEUS video has no positional displacements. Additionally, most existing methods rarely use the Time Intensity Curve (TIC) information of CEUS and non-imaging clinical (NIC) data. To address these issues, we propose a novel breast cancer diagnosis framework that learns the complementarity and correlation across hybrid modal data, including CEUS, B-mode US, and NIC data, by an adversarial adaptive fusion method. Furthermore, to fully exploit the CEUS information, the proposed method, inspired by the clinical processing of radiologists, first extracts the TIC parameters of CEUS. Then, we select a clip from CEUS using a frame screening strategy and finally get spatio-temporal features from these clips through a critical frame attention network. To our knowledge, this is the first AI system to use TIC parameters, NIC data, and ultrasound imaging in diagnoses. We have validated our method on a dataset collected from 554 patients. The experimental results demonstrate the excellent performance of the proposed method. The result shows that our method can achieve an accuracy of 87.73%, which is higher than that of uni-modal approaches by nearly 5%.

Идея опосредования Л.С. Выготского: семиотические и образовательные проекции

<p>The work is aimed at discussing and clarifying the understanding of L.S. Vygotsky's idea of mediation in relation to educational processes and the semiotic perspective of their research. The provisions interpreting the concept of "sign" as a mediating mechanism of cultural and historical development of a person, the growing up of a child, the development of his mental processes, language thinking are presented. The history of the formation of semiotic concepts, their isomorphism to the ideas of L.S. Vygotsky is considered: the development of a sign, including verbal, allows you to move from natural actions into a conditional, virtual space, with a wide repertoire of not only mimesis, but also symbolic actions. The idea of the mediating mechanism of speech reflection as the basis of functional literacy is being developed. Speech reflection and diary activity are considered as the realization of the idea of mediation in language teaching. The semiotic interpretation of L.S. Vygotsky's mediation theory is presented, educational projections of its implementation in teaching the native language are shown. From the point of view of epistemological searches, a comparison of the ideas of Vygotsky and Levi-Strauss is undertaken. L.S. Understanding model Vygotsky, which underlies modern ideas about meaning and speech affirmation, is indicated by the metaphor of translation: it is the translation of alienated external meanings into the mental language of internal speech and the transformation of meaning into meaning, and then - the "internalization" of meaning, that is, the translation of the meanings that have arisen into external speech and the formation of a new, enriched meaning. It is shown that L.S. Vygotsky's semiotic merit also consists in the fact that the scientist understood the linguistic sign as an intermediary sign and brought it into the space of culture, thereby opening the cultural and historical horizon of interpretation of semiotic phenomena.</p>

USING CRITICAL INFRASTRUCTURE AS A STRATEGIC RESOURCE FOR IMPROVING THE COMPETITIVENESS OF THE STATE

This article explores the theoretical and practical aspects of protecting critical infrastructure as a strategic resource for improving the competitiveness of the state. In the article, the concept of critical infrastructure is defined and justified as a strategic resource for improving the competitiveness of the state. Also, a number of threats are identified that can affect the functioning of objects of critical infrastructure and cause instability at different levels, including national security, which significantly affects the competitiveness of the state. One of the directions for ensuring effective protection of critical infrastructure is to develop a policy of “efficiency” – to optimize the distribution and application of state security resources for localizing potential sources of threat and enhancing the competitiveness of the state. The approach to formulating content of the concept of “threat” in the context of competitiveness of the state is analyzed and improved. The focus is on identifying critical objects on national, regional and local levels of infrastructure as a strategic resource for improving the competitiveness of the state. The methodology for attributing objects of national infrastructure to the field of critical infrastructure in accordance with their importance functions and services that they perform is described. A list of vitally important functions and services provided by representatives that require protection is presented, as well as representatives that are objects of critical infrastructure in the context of national security and competitiveness of the state. The content of relevant normative-legal acts that provided grounds for specifying a list of threats to critical infrastructure and confirming its inclusion in strategic resources for ensuring national security and enhancing competitiveness of the state is analyzed. Based on a critical analysis, it is generalized that there are three main categories of threats to critical infrastructure: natural origin, technological nature and malicious actions. It is proposed to supplement this list with combined threats that can cause “synergy effect” destabilization of critical infrastructure, reducing competitiveness of the state.

A syntactic analysis of a complex motor action: the octopus arm ‘slap’

The analysis of a natural motor action is always difficult, especially when different motor programs are combined within the same interaction with the environment. We analyzed the behavior of an octopus, Abdopus sp., filmed in tidal pools in Okinawa, Japan, which used the kinematic primitives of rotation and translation of its hydrostatic arms, and combined these kinematic behaviors serially and in parallel to ‘slap’ at fish in the wild. In total, 19 slaps were analyzed. The kinematics of arm movement were measured in both external and animal-centered reference frames, while the octopus was slapping at the fish. By combining these primitives, the octopus is able to maintain flexibility while controlling only a few degrees of freedom, a concept we term ‘flexible rigidity’. This slapping action supports Flash and Hochner’s embodied organization view of motor behavior, as well as their idea that motor primitives can combine syntactically to form a complex action. The octopus’s ability to use sensory feedback from the position of a moving fish target, along with the feed-forward motor primitives, allows for the building of complex actions at dynamic equilibrium with the environment. Over all, these findings lead to a more realistic view of how a complex behavior allows an animal to coordinate with its environment.

Global concerns related to water biology and security: The need for language and policies that safeguard living resources versus those that dilute scientific knowledge

Increasingly, scientists and non-scientists, especially employees of government agencies, tend to use weak or equivocal language when making statements related to science policy and governmental regulation. We use recent publications to provide examples of vague language versus examples of strong language when authors write about regulating anthropogenic pressures on natural resources. Lifeless language is common in agency reports, policy documents, and even scientific papers published by academics. Such language limits success in regulating anthropogenic pressures on natural resources. This challenge must be recognized and countered as a driver of the condition of water and associated resources. We also list sources of vague wording, provide global examples of how ambiguous language and political influences have contributed to water resource degradation, discuss the recent history of science censorship, and offer possible solutions for more direct scientific discourse. We found that: (1) equivocal language was especially common in concluding statements and not only by government employees; (2) authors discussed confusing language concerns in an agency publication; and (3) agency employees sometimes used active, strong language. Key drivers of weak language include: (1) holding on to old paradigms and resisting new knowledge; (2) scientific uncertainty; (3) institutional manuscript review policies; (4) employment and funding insecurity; and (5) avoiding the appearance of advocacy. Examples associated with euphemistic language included climate change, flow and physical habitat alteration, dams, agriculture, mining, forestry, and fisheries, as well as resistance towards monitoring, assessing, and reporting ecological conditions. Suggestions for mitigating equivocal language involve employment protections and greater focus on scientific ethics. We conclude that natural resource scientists should resist calls to employ imprecise language. Instead, they should be strong advocates for prescriptive and protective natural resource actions—based on their science—to halt and reverse the systemic degradation of those resources.

ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds

We study the moduli space of SU(4) invariant BPS conditions in supersymmetric gauge theory on non-commutative C4 by means of an ADHM-like quiver construction and we classify the invariant solutions under the natural toric action in terms of solid partitions. In the orbifold case C4/G, G being a finite subgroup of SU(4), the classification is given in terms of coloured solid partitions. The statistical weight for their counting is defined through the associated equivariant cohomological gauge theory. We explicitly compute several terms of the partition function expansion in the instanton counting parameter on C4 and C2×(C2/Z2), which conjecturally provides the corresponding orbifold Donaldson-Thomas invariants.

Deformations of 𝔞𝔣𝔣(n|1)-module of weighted densities on ℝ1|n, n ≥ 2

Over the [Formula: see text]-dimensional real superspace, [Formula: see text], we study non-trivial deformations of the natural action of the affine Lie superalgebra [Formula: see text] on the direct sum of the superspaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action and we prove that any formal deformation is equivalent to its infinitesimal part. This work is the simplest generalization of a result by Basdouri and Omri [Cohomology and deformation of [Formula: see text] acting on differential operators, Int. J. Geom. Methods Mod. Phys. 15 (2018) 1850072].

Topical issues of criminal offenses against sexual freedom and sexual inviolability of the person

Purpose. The aim of the work is to study topical problems of criminal offenses against sexual freedom and sexual inviolability of a person; to outline positive changes and shortcomings of innovations; to formulate offers for the improvement of existing criminal-law norms in this area. Methodology. The methodology includes a comprehensive analysis and generalization of available scientific-theoretical, legislative material and the formulation of relevant conclusions. During the research, the following methods of scientific knowledge were used: comparative-legal, logical-grammatical, systemic-structural, modeling ones. Results. In the research process, it was recognized that the current criminal legislation of Ukraine lacks a unified approach to the definition of the criminal offenses against sexual freedom and sexual immunity of a person. It became especially noticeable after the changes made to the Criminal Code of Ukraine in recent years, as a result of which the traditional approach to the concept of rape was changed, the list of actions of sexual nature with a young person and coercion to enter into sexual intercourse (sexual abuse) a minor was expanded, responsibility for sexual violence and child molestation was established. In this regard, there was a necessity for a more detailed analysis of legislative initiatives regarding the formation of a perfect model of criminal-law norms in Chapter IV of the Special Part of the Criminal Code of Ukraine with the aim of effective countering the commission of criminal offenses against the sexual freedom and sexual inviolability of a person. Scientific novelty. In the process of research, a number of both progressive and not entirely successful provisions in the current criminal legislation regarding actions related to violations of sexual freedom and sexual inviolability of a person have been identified; they can be taken into account in the future for legislative initiatives regarding criminal liability for criminal offenses in this sphere. Practical significance. The results of the research could be used in law-making activities in the further improvement of national criminal legislation regarding criminal offenses against sexual freedom and sexual immunity of a person, as well as in the educational process during the teaching and learning of the academic disciplines “Topical issues of criminal law and process” and “Criminal law of Ukraine. A special part”.

Quantitative inverse theorem for Gowers uniformity norms and in

AbstractWe prove quantitative bounds for the inverse theorem for Gowers uniformity norms $\mathsf {U}^5$ and $\mathsf {U}^6$ in $\mathbb {F}_2^n$ . The proof starts from an earlier partial result of Gowers and the author which reduces the inverse problem to a study of algebraic properties of certain multilinear forms. The bulk of the work in this paper is a study of the relationship between the natural actions of $\operatorname {Sym}_4$ and $\operatorname {Sym}_5$ on the space of multilinear forms and the partition rank, using an algebraic version of regularity method. Along the way, we give a positive answer to a conjecture of Tidor about approximately symmetric multilinear forms in five variables, which is known to be false in the case of four variables. Finally, we discuss the possible generalization of the argument for $\mathsf {U}^k$ norms.

Vulnerability of Affordable Housing to Global Warming in South Africa: Case Study of a Masonry House in Johannesburg

Global warming is expected to lead to longer and more intense heatwaves, which will have negative environmental and socioeconomic impacts around the world. South Africa is projected to experience significant warming, with surface temperatures possibly increasing by up to 3 °C by mid-century. This warming trend has implications for architecture, as the demand for cooling in buildings could rise dramatically. However, socioeconomic conditions in developing countries may limit the use of air conditioning to mitigate indoor overheating. In South Africa, research has shown that government provided low-cost housing structures are thermally inefficient, with temperatures occasionally exceeding outdoor levels. Residents often rely on natural ventilation and personal actions to cope with heat. However, the effects of climate change may render these strategies insufficient if energy poverty and housing improvement are not addressed. This study aims to examine the impact of global warming on a high mass, naturally ventilated, affordable housing structure in Johannesburg, South Africa. Measured operative temperature data from a long-term experimental study, alongside adaptive temperature limits to evaluate overheating, highlight the vulnerability of indoor spaces without adequate insulation and/or thermal mass. The results underscore concerns about the performance of low-cost and affordable housing in warmer future climates in the South African interior.

Learning ensembles of process-based models for high accurately evaluating the one-hundred-year carbon sink potential of China’s forest ecosystem

China’s forests play a vital role in the global carbon cycle through the absorption of atmospheric CO2 to mitigate climate change caused by the increase of anthropogenic CO2. It is essential to evaluate the carbon sink potential (CSP) of China’s forest ecosystem. Combining NDVI, field-investigated, and vegetation and soil carbon density data modeled by process-based models, we developed the state-of-the-art learning ensembles model of process-based models (the multi-model random forest ensemble (MMRFE) model) to evaluate the carbon stocks of China’s forest ecosystem in historical (1982–2021) and future (2022–2081, without NDVI-driven data) periods. Meanwhile, we proposed a new carbon sink index (CSindex) to scientifically and accurately evaluate carbon sink status and identify carbon sink intensity zones, reducing the probability of random misjudgments as a carbon sink. The new MMRFE models showed good simulation results in simulating forest vegetation and soil carbon density in China (significant positive correlation with the observed values, r = 0.94, P < 0.001). The modeled results show that a cumulative increase of 1.33 Pg C in historical carbon stocks of forest ecosystem is equivalent to 48.62 Bt CO2, which is approximately 52.03% of the cumulative increased CO2 emissions in China from 1959 to 2018. In the next 60 years, China’s forest ecosystem will absorb annually 1.69 (RCP45 scenario) to 1.85 (RCP85 scenario) Bt CO2. Compared with the carbon stock in the historical period, the cumulative absorption of CO2 by China’s forest ecosystem in 2032–2036, 2062–2066, and 2077–2081 are approximately 11.25–39.68, 110.66–121.49 and 101.31–111.11 Bt CO2, respectively. In historical and future periods, the medium and strong carbon sink intensity regions identified by the historical CSindex covered 65% of the total forest area, cumulative absorbing approximately 31.60 and 65.83–72.22 Bt CO2, respectively. In the future, China’s forest ecosystem has a large CSP with a non-continuous increasing trend. However, the CSP should not be underestimated. Notably, the medium carbon sink intensity region should be the priority for natural carbon sequestration action. This study not only provides an important methodological basis for accurately estimating the future CSP of forest ecosystem but also provides important decision support for future forest ecosystem carbon sequestration action.

Mapping the Environmental Vulnerability of a Lagoon Using Fuzzy Logic and the AHP Method

Environmental vulnerability refers to the susceptibility of a region to damage when it is subjected to natural or anthropogenic actions. The assessment of environmental vulnerability in lakes is an important tool to assist managers in planning and intervening for sustainable production and environmental preservation. The combination of geotechnologies, fuzzy logic and the analytic hierarchy process (AHP) has been applied by professionals and researchers to improve the work and research conducted in various areas and environments. In this context, the objective of this work was to map the environmental vulnerability of a lake and its surroundings through fuzzy logic and the AHP method. The study area comprises the Juparanã Lagoon Drainage Surface (JLDS), Espírito Santo state, Brazil. A survey of the physical characteristics of the watershed (drainage surface) that feeds the Juparanã Lagoon was carried out and also of the land use of this surface. To achieve the proposed objectives, the following methodological steps were implemented: (a) delimitation of watersheds, (b) spatialization of Permanent Preservation Areas (APP) based on the Brazilian Forestry Code (Law nº 12,651/2012), (c) application of logic fuzzy and AHP to spatialize the environmental vulnerability and (d) application of an evaluation of environmental vulnerability to the Preservation Areas (APP). Environmental vulnerability was modeled using Euclidean distance analysis, fuzzy logic and the AHP method, as proposed by Saaty (1977). For the development of this work, geotechnologies were used, with special emphasis on the use of the free software QGIS. The analysis revealed that 31.20%, 32.86% and 20.93% of the JLDS have very high, high and medium vulnerability, respectively. The evaluation of the environmental vulnerability of the APP showed that there is protection in the APP of the JLDS at rates of 47.35%, 34.05% and 14.5% for very high, high and medium vulnerability classes, respectively. The difficulties encountered were related to the lack of studies in the area of environmental vulnerability with a particular focus on lagoons. Here, for the first time, we perform a photointerpretation of the surroundings of Juparanã Lagoon. An important improvement measure would be the application of a temporal analysis to assess the dynamics of environmental vulnerability over time, considering socioeconomic, climatic and environmental changes. This would provide a more complete understanding of the distribution of environmental vulnerability in the study area. The methodology can be adapted to consider different scales of analysis, from local to regional, national and global scales, to assess environmental vulnerability at various scopes and levels of complexity. It can also be adapted to include local communities and governments.

Real Power Loss Reduction by Maine Coon and Perognathinae Based Optimization Algorithm

This paper proposes Maine Coon and Perognathinae based optimization (MPO) algorithm for solving the power loss lessening problem. Usual behaviour between Maine Coon and Perognathinae is imitated to formulate the MPO algorithm. In the proposed MPO, the crusade of Maine Coon towards Perognathinae as well as the spurt of Perognathinae in the direction of anchorages is replicated. Proposed MPO is population-based procedure which is premeditated by imitating the natural actions of a Maine Coon assaults on Perognathinae and absconding of Perognathinae to the anchorage. The exploration agents in the projected MPO algorithm are alienated into two clusters of Maine Coon’s and Perognathinae that examine the problem exploration space with arbitrary activities. The projected MPO algorithm apprises population associates in two segments. In the principal segment, the crusade of Maine Coon’s in the direction of Perognathinae is modelled, and in the subsequent segment, the absconding behaviour of Perognathinae to anchorages to protect its life is designed. From a scientific fact of opinion, every associate of the populace is a recommended solution to the problem. In detail, an associate of the population postulates standards for the problem parameters rendering to its location in the exploration space. Proposed MPO algorithm is appraised in IEEE 30 bus system and IEEE 14, 30, 57, 118, 300 bus test systems without considering the voltage constancy index. True power loss lessening, voltage divergence curtailing, and voltage constancy index augmentation has been attained

Consolation Gestures as Non-Verbal Markers of Stress when Discussing an Acute Social Issue

The article is devoted to the issue of identifying non-verbal stress markers in oral discourse on an acute social topic. The relevance of the research is due to: 1) the growing interest of linguists in the study of linguistic manifestations of emotions and the identification of markers of various psycho-emotional states with the subsequent possibility of developing algorithms for their automatic detection; 2) the severity of the problem of stress in modern society. The novelty of the study is predetermined by the fact that it is focused on a specific type of communicative behavior (discussion of an acute social issue) studied from the perspective of multimodal linguistics postulating an inextricable link between understanding and generating messages in natural language and body actions. The goal of the paper is to identify and describe non-verbal stress markers that we call consolation gestures, allowing us to identify this psychoemotional state in the course of spontaneous oral communication. The research material is represented by 4 hours of structured interview video recordings with 11 French and 11 Russian respondents (average age – 21) on the topic of radical body positivity. The leading research method is multimodal analysis, implemented using multi-layer markup in the ELAN program. In the process of marking, the following types of layers were used: gestures, eye movements, facial expressions, verbal component, intonation. The statistical analysis of frequency and distribution of annotations have revealed the following consolation gestures: 1) stroking different parts of the body; 2) scratching different parts of the body, 3) interacting with other objects, 4) facial markers. Consolation gestures are regarded by us as a kind of body-oriented repetitive behavior disorders, which allows us to differentiate them from gestures that are hesitation/silence fillers. Thus, the following constitutive features are determined: 1) repetition of the action, 2) focus on the body, 3) features conditioned by a sense of tension or anxiety rather than by preoccupation with appearance, 4) a subsequent sense of relief and emotional discharge. The prospect of further research is seen in the expansion of experimental material through interviews with representatives of other linguocultures, followed by interpreting the results in the cross-cultural perspective.

Assessing Sustainable Development of Deep Aquifers

AbstractDeep groundwater aquifers are exploited for a variety of purposes. In general, impermeable rock layers protect these aquifers from anthropogenic influences. As such, they are a last resort for groundwater in a pre-industrial state, and a crucial resource in cases of emergency, such as floods contaminating shallow groundwater. The EU Water Framework Directive (WFD) provides the regulatory framework to protect its quality and quantity. Recent monitoring of the hydrochemical state of Upper Jurassic wells in Bavaria and Austria has shown fluctuations that were connected to new exploitation activities and might indicate an unsustainable development of the aquifer. We propose a new workflow in accordance with the WFD which uses clustering algorithms to assess these fluctuations. Our data consists of 5 to 42 hydrochemical analyses per well with yearly sampling intervals spanning up to 30 years. From the cluster analysis we derived thresholds for two corridors: Natural Range Corridor (NC) and Action Corridor (AC). While the NC represents a well-specific natural variation range, the AC hints towards unsustainable development and should trigger a detailed (re)assessment. To show the potential of the new method, the workflow was applied to two wells with different geological characteristics. Distinct fluctuation events were clearly recognized and can be used in the context of an early warning system, such that malign hydrochemical variations can be detected before they become legally problematic to well operators. Our workflow thus provides a novel, robust, and reproducible method to assess the grade of sustainability at which a well is exploited and ensures a good status of a unique and important resource.

Radial rapid decay does not imply rapid decay

We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $\Gamma := \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with coefficients in $\mathbb{F}_q$, endowed with the length function coming from a natural action of $\Gamma$ on a product of two trees, to show that is has the radial rapid decay (RRD) property and doesn't have the rapid decay (RD) property. The criterion also applies to irreducible lattices in semisimple Lie groups with finite center endowed with a length function defined with the help of a Finsler metric. These examples answer a question asked by Chatterji and moreover show that, unlike the RD property, the RRD property isn't inherited by open subgroups.

Coincidences of division fields

Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let $\rho_E\colon {\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\to {\rm GL}(2,\widehat{ \mathbb{Z} })$ be the adelic representation associated to the natural action of Galois on the torsion points of $E(\overline{\mathbb{Q}})$. By a theorem of Serre, the image of $\rho_{E}$ is open, but the image is always of index at least $2$ in ${\rm GL}(2,\widehat{\mathbb{Z}})$ due to a certain quadratic entanglement amongst division fields. In this paper, we study other types of abelian entanglements. More concretely, we classify the elliptic curves $E/\mathbb{Q}$, and primes $p$ and $q$ such that $\mathbb{Q}(E[p])\cap \mathbb{Q}(\zeta_{q^k})$ is non-trivial, and determine the degree of the coincidence. As a consequence, we classify all elliptic curves $E/\mathbb{Q}$ and integers $m,n$ such that the $m$-th and $n$-th division fields coincide, i.e., when $\mathbb{Q}(E[n])=\mathbb{Q}(E[m])$, when the division field is abelian.

Limit sets of cyclic quaternionic Kleinian groups

In this paper, we consider the natural action of $$\textrm{SL}(3, \mathbb {H})$$ on the quaternionic projective space $$ {\mathbb {P}}_{\mathbb {H}}^2$$ . Under this action, we investigate limit sets for cyclic subgroups of $$\textrm{SL}(3, \mathbb {H})$$ . We compute two types of limit sets, which were introduced by Kulkarni and Conze-Guivarc’h, respectively.