Faithful Action Research Articles

On some planar Baumslag–Solitar actions

Let \mathrm{BS}(1,n)= \langle a,b : a b a^{-1}= b^{n}\rangle be the solvable Baumslag–Solitar group for n \geq 2 . We study representations of \mathrm{BS}(1, n) on the plane by orientation-preserving homeomorphisms, assuming that a acts as a linear map and b as a map with bounded displacement. We find that the possibilities for a faithful action depend greatly on the Jordan canonical form of the map h defined by the action of a . In case h is diagonalizable over \mathbb{R} , we shall give examples or prove rigidity theorems depending on the eigenvalues. We also show some rigidity in the cases where h is elliptic or parabolic. Then we give applications to the actions of \mathrm{BS}(1, n) by homeomorphisms of the torus.

Generic Stabilizers in Actions of Simple Algebraic Groups

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception, there is a dense open subset any point of which has stabilizer conjugate to a fixed subgroup, called the generic stabilizer. We provide tables listing generic stabilizers in the cases where they are non-trivial; in addition we decide whether or not there is a dense orbit, or a regular orbit for the action on the module.

Invariant Grassmannians and a K3 surface with an action of order 192*2

Given a complex vector space V of finite dimension, its Grassmannian variety parametrizes all subspaces of V of a given dimension. Similarly, if a finite group G acts on V, its invariant Grassmannian parametrizes all the G−invariant subspaces of V of a given dimension. Based on this fact, we develop an algorithm for finding equations of G−invariant projective varieties arising as an intersection of hypersurfaces of the same degree.We apply the algorithm to find equations describing a polarized K3 surface with a faithful action of T192⋊μ2 and some further symmetric K3 surfaces with a degree 8 polarization.

Bad Faith Actions of Professional Collectors and How to Fight Them

Bad Faith Actions of Professional Collectors and How to Fight Them

Freedom in an Age of Repression: The Role of Black Theology and Black-Produced Media in Forging Freedom

This paper will explore the role that black theology and black-produced films of 2016 play in creating a narrative that seeks freedom for African Americans in the United States during this age of brutality and mass incarceration. Starting with Alexander's The New Jim Crow and Duvernay's 13th, this paper illustrates how the media and the legal system have worked together to create a culture of criminality still imposed on black youth. Theologians Cone and Brown Douglas rely on the concepts of God's freedom, God's revolutionary love and faithful action to resist such a hostile culture, but two black-produced films of 2016 also rely on the concept of freedom in the face of criminality. Birth of a Nation not only to shows a positive portrayal of black men in the media, but Moonlight illustrates the complexity of growing up in communities that are repressed by this hostile culture.

Good Character, Good Deeds and Good Speech for Developing Multicultural Islamic Education: An Islamic Concept

This research is qualitative research that aims to develop an Islamic quality-of-life model for Islamic multicultural education. Research is conducted by referring to various sources of writing (literary research), and then formulating with deductive and inductive reasoning (thinking). The four criteria for a successful life (luck, win), namely faith, good deeds, correctness, and patience. These four criteria constitute a unified whole, and should not be broken down or reduced. The word 'sholih' means 'whole' (not broken apart) or 'complete', which is also usually translated as 'good'. Goodness due to wholeness and completeness. Wholeness and completeness in the concept of "Amal Sholih" include amal imaniah (faithful action), amal ilmiah (scientific action), amal karimah (noble action), amal rahmah (beloved action), amal barakah (better action), amal salamah (safe action), and amal kamilah (complete action). Faithful action is the action that must be based on faith, namely the six pillars of faith. Scientific action is an action that contains knowledge. Amal karimah is human deeds that show good deeds. Beloved action is the action that reflects rahmah (compassion, love), which arises from a clean conscience. Better action is a human action that provides benefits and added value (added goodness) to others and oneself. Safe action is the act of human beings who are safe and save themselves and others in this world and the hereafter. Complete action is the human action that fulfills 100% of the target.

Kähler–Einstein Fano threefolds of degree 22

We study the problem of existence of Kähler–Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 22 that admit a faithful action of the multiplicative group C ∗ \mathbb {C}^\ast . We prove that, with the possible exception of two explicitly described cases, all such smooth Fano threefolds are Kähler–Einstein.

РОЛЬ УПОЛНОМОЧЕННОГО ОРГАНА В ВЫЯВЛЕНИИ И ПРЕДОТВРАЩЕНИИ ПОСЛЕДСТВИЙ НЕДОБРОСОВЕСТНЫХ ДЕЙСТВИЙ СУБЪЕКТОВ ОТНОШЕНИЙ НЕСОСТОЯТЕЛЬНОСТИ

The Federal Tax Service of Russia, within the framework of performing the functions of an authorized body in cases of bankruptcy of legal entities, is vested with certain powers to protect the interests of the Russian Federation as a creditor. High requirements for high-quality support of bankruptcy procedures increase the attention of the scientific community to the problem of improving the activities of the authorized body to identify and prevent the consequences of dishonest actions of insolvency entities. The purpose of the study is to summarize the experience of the authorized body in identifying dishonest actions of the debtor and its controlling persons, preventing their consequences in the framework of a bankruptcy case, as well as developing methodological recommendations for improving the preparation of a package of evidence confirming the grounds for bringing the persons controlling the debtor to subsidiary liability. Based on the results of the analysis of arbitration practice, typical dishonest actions of the beneficiaries of the debtor's bankruptcy were identified and systematized (withdrawal of the debtor's assets, encumbrance of the debtor's obligations with artificial accounts payable of affiliated persons, implementation of various schemes (transactions) aimed at evading payment of accounts payable, etc.), methods of preventing body of the consequences of bad faith actions of the subjects of insolvency relations, as well as a methodological approach to justifying the holding of the controlling debtor of persons to subsidiary liability for bad faith actions against the debtor and independent creditors. The role of the authorized body in accompanying bankruptcy procedures is much broader than ensuring the interests of the state as a creditor, therefore, the implementation of the proposed methodological approach to the economic justification of the reasons (grounds) for bringing the persons controlling the debtor to subsidiary liability, which includes several successive stages, will improve the standards of proof in cases of bankruptcy, reduce errors of justice and, ultimately, improve the effectiveness and efficiency of the institution of bankruptcy.

Anosov diffeomorphisms on infra‐nilmanifolds associated to graphs

AbstractAnosov diffeomorphisms on closed Riemannian manifolds are a type of dynamical systems exhibiting uniform hyperbolic behavior. Therefore, their properties are intensively studied, including which spaces allow such a diffeomorphism. It is conjectured that any closed manifold admitting an Anosov diffeomorphism is homeomorphic to an infra‐nilmanifold, that is, a compact quotient of a 1‐connected nilpotent Lie group by a discrete group of isometries. This conjecture motivates the problem of describing which infra‐nilmanifolds admit an Anosov diffeomorphism. So far, most research was focused on the restricted class of nilmanifolds, which are quotients of 1‐connected nilpotent Lie groups by uniform lattices. For example, Dani and Mainkar studied this question for the nilmanifolds associated to graphs, which form the natural generalization of nilmanifolds modeled on free nilpotent Lie groups. This paper further generalizes their work to the full class of infra‐nilmanifolds associated to graphs, leading to a necessary and sufficient condition depending only on the induced action of the holonomy group on the defining graph. As an application, we construct families of infra‐nilmanifolds with cyclic holonomy groups admitting an Anosov diffeomorphism, starting from faithful actions of the holonomy group on simple graphs.

Increasing Youth Political Engagement with Efficacy Not Obligation: Evidence from a Workshop-Based Experiment in Zambia.

In many places around the world, young voters participate in politics at low rates. What factors might increase youth political participation? We investigate one possibility: exposure to a religious message that emphasizes the possibility of change through faithful action. We argue that this message, which is common in religious groups that attract large numbers of youth around the world, addresses several barriers to political participation by young voting-age adults. Working in collaboration with the major religious coalitions in Zambia, we randomly assigned young adults (18–35 years old) into civic engagement workshops. Identical informational material, based on pre-existing, non-partisan curricula, was presented in each workshop. Workshops then concluded with one of two randomly assigned, pre-recorded Christian motivational messages based on existing religious programming in Zambia. In some workshops, the concluding message emphasized a Christian obligation to work towards the greater good. In other workshops, the message emphasized the power of faith to make change in the world. We found that the power of faith message moved workshop participants to be more willing to participate in protest, to disavow political violence, and to criticize other people who choose not to participate, relative to pre-workshop measures and to an information-only condition. By contrast, the message focused on an obligation to the greater good did not change political participation, resulting in lower willingness to participate in politics than the power of faith message. We discuss implications for youth political participation and the study of religion and politics.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11109-022-09794-2.

On Degenerations of Projective Varieties to Complexity-One T-Varieties

Abstract Let $R$ be a positively graded finitely generated $\textbf {k}$-domain with Krull dimension $d+1$. We show that there is a homogeneous valuation ${\mathfrak {v}}: R \setminus \{0\} \to {\mathbb {Z}}^d$ of rank $d$ such that the associated graded $\operatorname {gr}_{\mathfrak {v}}(R)$ is finitely generated. This then implies that any polarized $d$-dimensional projective variety $X$ has a flat deformation over ${\mathbb {A}}^1$, with reduced and irreducible fibers, to a polarized projective complexity-one $T$-variety (i.e., a variety with a faithful action of a $(d-1)$-dimensional torus $T$). As an application we conclude that any $d$-dimensional complex smooth projective variety $X$ equipped with an integral Kähler form has a proper $(d-1)$-dimensional Hamiltonian torus action on an open dense subset that extends continuously to all of $X$.

Arithmeticity of the monodromy of the Wiman–Edge pencil

The Wiman–Edge pencil is the universal family of projective, genus 6, complex-algebraic curves endowed with a faithful action of the icosahedral group. The goal of this paper is to prove that its monodromy group is commensurable with a Hilbert modular group; in particular is arithmetic. We then give a modular interpretation of this, as well as a uniformization of its base.

Triple transitivity and non‐free actions in dimension one

The transitivity degree of a group G $G$ is the supremum of all integers k $k$ such that G $G$ admits a faithful k $k$ -transitive action. Few obstructions are known to impose an upper bound on the transitivity degree for infinite groups. The results of this article provide two new classes of groups whose transitivity degree can be computed, as a corollary of a classification of all 3-transitive actions of these groups. More precisely, suppose that G $G$ is a subgroup of the homeomorphism group of the circle Homeo ( S 1 ) $\operatorname{Homeo}(\mathbb {S}^1)$ or the automorphism group of a tree Aut ( T ) $\operatorname{Aut}(\mathcal {T})$ . Under natural assumptions on the stabilizers of the action of G $G$ on S 1 $\mathbb {S}^1$ or ∂ τ $\partial\tau$ , we use the dynamics of this action to show that every faithful action of G $G$ on a set that is at least 3-transitive must be conjugate to the action of G $G$ on one of its orbits in S 1 $\mathbb {S}^1$ or ∂ T $\partial \mathcal {T}$ .

POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS

We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on a central simple division algebra, and we construct such a division algebra. This is in contrast to earlier work of Etingof and Walton, in which it was shown that most pointed Hopf algebras do not admit faithful actions on fields. We consider all bosonizations of Nichols algebras of finite Cartan type, small quantum groups, generalized Taft algebras with non-nilpotent skew primitive generators, and an example of non-Cartan type.

Infinitely many Lagrangian fillings

We prove that all maximal-tb positive Legendrian torus links $(n,m)$ in the standard contact $3$-sphere, except for $(2,m)$, $(3,3)$, $(3,4)$ and $(3,5)$, admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances that induce faithful actions of the modular group $\mathrm{PSL}(2,\mathbb{Z})$ and the mapping class group $M_{0,4}$ into the coordinate rings of algebraic varieties associated to Legendrian links. In particular, our results imply that there exist Lagrangian concordance monoids with subgroups of exponential-growth, and yield Stein surfaces homotopic to a $2$-sphere with infinitely many distinct exact Lagrangian surfaces of higher-genus. We also show that there exist infinitely many satellite and hyperbolic knots with Legendrian representatives admitting infinitely many exact Lagrangian fillings.

НЕЗАВИСИМОСТЬ И ДОБРОСОВЕСТНОСТЬ СУДА И СУДЕЙ В ЦИФРОВУЮ ЭПОХУ: ИНТЕГРАЦИОННЫЙ ОПЫТ

Introduction: the article is devoted to the problems of judicial independence and standards of judicial conduct. Purpose: to analyze the independence of judges tracing its procedural and judicial development through the example of the activities of the Court of the EAEU, as well as in the light of the emergence of new virtual forms of influence on judges and their independence. Methods: general scientific methods of analysis, synthesis, generalization, comparative legal method, cultural-historical approach. Results: the EAEU has already established international integration management bodies; however, violation of procedural regulations (or their absence) generates unacceptable dishonesty in the implementation of norms. A conflict that slows down the integration can arise not only directly in the economic turnover but can also be artificially created by a bad faith influence on the court from the public, for example, in a digital environment. This happens in case of violation of standards of international service such as competence, objectivity, conflict of interest, and good faith. Pressure to change a judicial act is a particularly dangerous form of violation of these standards. Conclusions: it is necessary to improve the procedural formalization of the activities of the EAEU bodies: the methods of voting on economic issues in supranational bodies should be changed, as well as the structure of the Court of the EAEU. Changes are also required in the mechanism of execution of the Court’s judgments. Publicity as well as stricter mechanisms for appointing judges, including those of an international court, can serve as a serious antidote to bad faith actions in a virtual environment.

Fiduciary accountability shattered

Abstract The law of fiduciary accountability has for some time been harried by the misinformed assertions and suppositions of various judges and writers. The numerous misconceptions increased the risk that the conventional understanding of the jurisdiction would collapse. That has now happened. The Supreme Court unconsciously (or consciously) rejected its own jurisprudence to reshape the conventional regulation into an extensive judicial power to assess the merits of the good faith actions of fiduciaries.

Equivariant splitting of the Hodge\u2013de Rham exact sequence

Let X be an algebraic curve with a faithful action of a finite group G over a field k. We show that if the Hodge–de Rham short exact sequence of X splits G-equivariantly then the action of G on X is weakly ramified. In particular, this generalizes the result of Köck and Tait for hyperelliptic curves. We discuss also converse statements and tie this problem to lifting coverings of curves to the ring of Witt vectors of length 2.

The Evolution of Liability Measures Applied in Bankruptcy to Creditors’ Property Rights Violators in Russia

One of the tasks the modern law in the field of insolvency of legal entities pursues is to ensure the maximum balance of the rules governing the measures of liability applied to managers, participants and other entities controlling the debtor. In this regard, the author applies historical and comparative method of studying the measures of responsibility applied during the development of domestic legal regulation of insolvency and the critical assessment method that forms the basis for the analysis of the current Russian legislation. The paper carries out a retrospective analysis of the form and degree of fault as an element of the offense that traditionally acted as one of the criteria for choosing the type of insolvency, as well as for imposing the measures of responsibility. A comparative analysis of the norms of the Russian bankrupt legislation in historical retrospect allowed raising problematic issues of the current legislation and making proposals aimed at their resolution. Currently, the rules of the current domestic insolvency legislation provide an equal amount of responsibility for both bad faith (intentional) and unreasonable (careless) actions of entities controlling the debtor. The normative consolidation of measures of responsibility dependent on the form of fault, namely, the separate qualification of intentional and careless offenses, will secure coherent application of the principle of justice. Modern Russian law contains the concepts of “insolvency” and “bankruptcy”, which in some cases creates legal uncertainty. Therefore, it is proposed to delineate these concepts by law, eliminate the term “objective bankruptcy” from the application, and shift its semantic burden to the concept of “insolvency”. Thereby, a separate category of insolvency will be included in the current legislation.

Protection of Parties In The Consumer To Consumer Business Model Using Social Commerce In Indonesia

This study aims to examine the extent of protection of parties in the consumer to consumer business model using social commerce in Indonesia. This study uses normative study methods accompanied by statute approach and comparative approach. Based on the study the authors showed that the application of the C2C business model using social commerce has a very large risk of bad faith actions. This is based on two main factors. First, there is still a lack of pre-emptive action taken by the platform provider (in this case Instagram) in verifying the identity and data of information related to businesses. Thus indicates that the platform is merely a provider of communication containers without any protection to consumers. Second, there is still a lack of small and medium-sized businesses that understand the importance of e-contracts in establishing alliance relationships with consumers. There are some suggestions recommended by the author, such as the identity of business actors, domicile, and track record of business actors that must be clearly listed through the certification of business actors increasing the knowledge of businesses related to the use of payment media that is friendly and accessible to consumers. Keyword s : C2C, S ocial c ommerce, e - c ommerce DOI: 10.7176/JLPG/107-11 Publication date: March 31 st 2021