Action Of Group Research Articles

Low-Carbon Transformation of Chinese Steel Enterprises Under the Dual Carbon Goals: Taking Baowu Group as An Example

The profound changes in the environment have led to increasing global concerns about the negative impacts of carbon emissions. Against the backdrop of the environmental crisis, the concept of “dual carbon” emerged in China, aiming to achieve carbon peaking and carbon neutrality and mitigate the adverse effects of climate change. The establishment of these goals in 2020 marked a significant milestone in global efforts towards a more sustainable future. The paper initially delves into a comprehensive macro and micro analysis, reviewing significant policy measures introduced since the "dual carbon" goals were established in 2020. It pays particular attention to documents that have had a profound impact on the steel industry, emphasizing the urgency of low-carbon transformation among steel enterprises. Amidst the challenges posed by the macroeconomic environment and within the framework of the "dual carbon" policy, the paper takes Baowu Group, China's leading steel enterprise, as the focal point of this analysis. The paper meticulously scrutinizes seven specific measures implemented by Baowu Group in its journey towards low-carbon transformation, adopting a multifaceted perspective. It provides a comprehensive assessment of the effectiveness of Baowu Group's transformation from diverse perspectives, highlighting the successful outcomes of both Chinese government policies and corporate efforts. In conclusion, the paper presents tailored policy recommendations and transformation strategies tailored specifically for the steel industry.

Lie 2-groups from loop group extensions

We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies several constructions previously given in the literature. More generally, we construct strict 2-group extensions for a Lie group from a central extension of its based loop group, under the assumption that this central extension is disjoint commutative. We show in particular that this condition is automatic in the case that the Lie group is semisimple and simply connected.

Optimal System for non-linear Burger equation ut = uxx + uux.

The paper discusses the optimal system for a nonlinear Burger equation whose coefficients are dependent on first order spatial derivatives. The main purpose for the project is to determine the optimal system for the operators accepted by the equation. We construct the principal Lie algebra, calculate transformations for the generators which provide one-parameter group of transformations for the operator using Lie equations. We construct optimal systems for the equation where the method requires a simplification of a vector to a general form for each of the transformations of the generators. These are finally used to determine invariant solutions for some operators.

QUASI-HEREDITARY SKEW GROUP ALGEBRAS

Abstract Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and on the corresponding skew group algebra. Assuming a natural compatibility condition on the partial order, we show that the skew group algebra is quasi-hereditary if and only if the original algebra is. Moreover, we show that in this setting an exact Borel subalgebra of the original algebra which is invariant as a set under the group action gives rise to an exact Borel subalgebra of the skew group algebra and that under this construction, properties such as normality and regularity of the exact Borel subalgebra are preserved.

Listening to regulators about the challenges in regulating emerging disruptive technologies

PurposeThis study aims to investigate the regulatory challenges of emerging disruptive Information and Communication Technologies (ICT) in Brazil and the strategies regulators use to address them.Design/methodology/approachIt is an empirical qualitative research on Brazil’s three administrative levels, focusing on the legislative houses’ specialised Science and Technology Committees. It combines archival analysis of public meeting records with elite interviews of parliamentarians and technocrats who participated in Public Hearings in 2019, which results in this paper analysed through the Theory of Communicative Action with a critical stance.FindingsThe research reveals that regulatory challenges gain new dimensions by involving discussions about emerging ICT. Factors such as time constraints, rapid technological evolution and widespread adoption compound these challenges, straining the preference for the incremental pace of regulation and the traditional model of specialised regulatory agencies. The research captures some regulators’ values, underlying concerns and perceived necessities for surmounting these challenges. It also outlines the preferred process for ICT regulation, revealing parliamentary assistants and executive intermediate-level specialists as gateways for interest groups’ action.Social implicationsThe study's findings highlight the crucial role of specific actors as gateways to the covert action of interest groups, particularly Big Tech firms. This contribution is significant as it empowers civil society and academia to monitor and mitigate the risk of regulatory capture, thereby promoting a more transparent and equitable regulatory environment.Originality/valueThis research is original in directly engaging with the key figures (lawmakers, legislative assistants and specialised bureaucrats) involved in the critical and timely issue of regulating emerging disruptive technologies.

Equivariant birational geometry of linear actions

In this paper, we study linear actions of finite groups in small dimensions, up to equivariant birationality.

A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

AbstractIn this research, we explore a finite horizon optimal stabilization and tracking control scheme for the dynamical model of a 6‐DOF Autonomous Underwater Vehicle (AUV). Dynamical equations of the AUV are represented in a Lie group () framework, encompassing both translational and rotational motions. Utilizing a left Lie group action on , we define error function for velocities via a right transport map to effectively address optimal trajectory tracking. The optimal control objective is formulated as a trade‐off problem, aiming to minimize both errors and control effort simultaneously. Left action on yields the left trivialized Hamiltonian function from which the concomitant state and costate dynamical equations are derived using Pontryagin's Minimum Principle (PMP). Consequently, the resulting two‐point boundary value problem is solved to obtain optimal trajectories. We demonstrate the optimality of the resulting solution obtained from the derived control law. For ensuring boundedness in the presence of small disturbances, this study incorporates the effects of internal parametric uncertainties associated with added mass and inertia components, along with the influence of external disturbances induced by ocean currents. Through simulation validations, we confirm the alignment of our results with the theoretical developments, demonstrating that the proposed control law effectively mitigates both parametric uncertainties and ocean current disturbances.

Some aspects of formation labor behavior during the period of martial status

Problem setting. Modern political, economic, and social demands of society pose tasks to the state that require urgent solutions and are of urgent importance for all spheres of life. Therefore, a significant number of studies are focused on solving theoretical and practical issues of legal regulation of social relations during the war and in the conditions of martial law on the territory of Ukraine. Solving issues of the possibility and specifics of citizens’ realization of the right to work are of great importance. Since, during the period of martial law, the norms of labor legislation are not applied in the part of relations regulated by the Law of Ukraine “On the Organization of Labor Relations in the Conditions of Martial Law” (hereinafter the Law). According to the Final Provisions, it is valid for the period of martial law in Ukraine, introduced in accordance with the Law of Ukraine “On the Legal Regime of Martial Law”, and becomes invalid from the moment of termination and cancellation of martial law. During the period of martial law, its norms have an overriding force over the norms of the Code of Labor Laws of Ukraine. The provisions of this Law significantly narrow the rights of workers compared to peacetime. Therefore, the relevance of the toolkit of labor law as a regulator of social relations in the field of labor relations and ways of realizing the right to work by citizens under martial law is increasing. Analysis of recent researches and publications. Analysis of recent research and publications. Such scientists as: T. Gerasimov, T. Glynska, V. Lytvynenko, O. Lukyanchikov, D. Novikov, A. Shvets and others were engaged in the study of the theoretical and practical essence of the chosen topic. In addition, the following scientists paid attention to the legal regulation of labor relations under martial law in Ukraine in their works: V. Andriiv, M. Lukashevich, M. Doronina, N. Yesinov, L. Nikolayeva, D. Shvets, and others. Purpose of research is to investigate labor behavior, which is a complex of individual and group actions and deeds that determine the direction and intensity of a person’s performance of their labor function and factors that negatively affect labor behavior. And also consider the legislation of Ukraine, which concerns the regulation of labor relations during the period of martial law and analyze the changes that took place in the field of labor relations after the declaration of martial law in the state and how they affected the labor behavior of the employee. Article’s main body. A special role in solving this issue is played by the principles, methods and ways of motivating work, which act as a leading organizational and economic tool for managing the work behavior of employees. In this regard, solving both theoretical and practical problems of labor behavior management through the use of new socioeconomic methods of labor motivation, which would make it possible to increase the interest of workers to work productively and effectively in various spheres of the economy, becomes important. Modern labor relations increasingly single out the employee’s behavior as an important characteristic of his labor potential, the quality of which depends on the effectiveness of the team’s work and the survival of the enterprise, institution or organization in an unpredictable economic environment. Therefore, the study of labor behavior as a form of employee activity and the determination of the main factors influencing it is quite relevant in this period of time. Conclusions and prospects for the development. Formation of labor behavior of employees is an actual and complex process that requires a systematic approach. According to the results of the research, it was established that the essence of labor motivation is to develop such a system of incentives that would satisfy all the needs of the employee in the best way and would interest him in achieving better results of his activity. This will help increase labor productivity, increase the income and profits of enterprises, as a result of which the material situation of employees will improve, which is the key to successful motivation to work.

Actions on classifiable C*‐algebras without equivariant property (SI)

AbstractWe exhibit examples of actions of countable discrete groups on both simple and non‐simple nuclear stably finite C*‐algebras that are tracially amenable but not amenable. We furthermore obtain that, under the additional assumption of strict comparison, amenability is equivalent to tracial amenability plus the equivariant analogue of Matui–Sato's property (SI). By virtue of this equivalence, our construction yields the first known examples of actions on classifiable C*‐algebras that do not have equivariant a over show that such actions can be chosen to absorb the trivial action on the universal UHF algebra, thus proving that equivariant ‐stability does not in general imply equivariant property (SI).

The nonexistence of expansive polycyclic group actions on some Peano continua

The nonexistence of expansive polycyclic group actions on some Peano continua

Quasi-invariant states

In this paper, we develop the theory of quasi-invariant (respectively, strongly quasi-invariant) states under the action of a group [Formula: see text] of normal ∗-automorphisms of a ∗-algebra (or von Neumann algebra) [Formula: see text]. We prove that these states are naturally associated to left-[Formula: see text]-[Formula: see text]-cocycles. If [Formula: see text] is compact, the structure of strongly [Formula: see text]-quasi-invariant states is determined. For any [Formula: see text]-strongly quasi-invariant state [Formula: see text], we construct a unitary representation associated to the triple [Formula: see text]. We prove, under some conditions, that any quantum Markov chain with commuting, invertible and Hermitian conditional density amplitudes on a countable tensor product of type I factors is strongly quasi-invariant with respect to the natural action of the group [Formula: see text] of local permutations and we give the explicit form of the associated cocycle. This provides a family of nontrivial examples of strongly quasi-invariant states for locally compact groups obtained as inductive limit of an increasing sequence of compact groups.

Index theorem for homogeneous spaces of Lie groups

We study index theory for homogeneous spaces associated to an almost connected Lie group in terms of the topological and analytic aspects. For the topological aspect, we obtain a topological formula as a result of the Riemann–Roch formula for proper cocompact actions of the Lie group, inspired by the work of Paradan and Vergne. For the analytic aspect, we apply heat kernel methods to obtain a local index formula representing the higher indices of equivariant elliptic operators with respect to a proper, cocompact action of the Lie group.

Equivariant prime ideals for infinite dimensional supergroups

Let A A be a commutative algebra equipped with an action of a group G G . The so-called G G -primes of A A are the equivariant analogs of prime ideals, and of central importance in equivariant commutative algebra. When G G is an infinite dimensional group, these ideals can be very subtle: for instance, distinct G G -primes can have the same radical. In previous work, the second author showed that if G = G L ∞ G=\mathbf {GL}_{\infty } and A A is a polynomial representation, then these pathologies disappear when G G is replaced with the supergroup G L ∞ | ∞ \mathbf {GL}_{\infty |\infty } and A A with a corresponding algebra; this leads to a geometric description of G G -primes of A A . In the present paper, we construct an abstract framework around this result, and apply the framework to prove analogous results for other (super)groups. We give some applications to the isomeric determinantal ideals (commonly known as “queer determinantal ideals”).

Isotropy group on some topological transformation group structures

This paper explores the topological properties of irresolute topological groups, their quotient maps, and the role of topology in normal subgroups. It provides a detailed analysis\linebreak using examples and counterexamples. The study focuses on the essential features of irresolute topological groups and their quotient groups, for understanding the topological aspects of isotropy groups. For a trans\-for\-ma\-tion group $(\mathsf{H}, \mathsf{Y}, \psi)$ and a point $y \in \mathsf{Y},$ the set \centerline{$\mathsf{H}_{y} = \{h \in \mathsf{H} \colon hy = y\}$} \noi consisting of elements of $\mathsf{H}$ that fix $y$, is called the isotropy group at $y$. The paper highlights the distinct topological characteristics of isotropy groups in transformation group structure. It demonstrates that if $(\mathsf{H}, \mathsf{Y}, \psi)$ is an Irr$^{*}$-topological transformation group, then $( \mathsf{H}/ \mathop{Ker} \psi, \mathsf{Y}, \overline{\psi})$ forms an effective Irr$^{*}$-topological transformation group. By investigating both irresolute topological groups and isotropy groups, the study provides a clear understanding of their topological features. This research improves our understanding of these groups by offering clear examples and counterexamples, leading to a thorough conclusion about their different topological features.

Jacobian varieties with group algebra decomposition not affordable by Prym varieties

The action of a finite group G on a compact Riemann surface X naturally induces another action of G on its Jacobian variety J(X). In many cases, each component of the group algebra decomposition of J(X) is isogenous to a Prym varieties of an intermediate covering of the Galois covering πG:X→X/G; in such a case, we say that the group algebra decomposition is affordable by Prym varieties. In this article, we present an infinite family of groups that act on Riemann surfaces in a manner that the group algebra decomposition of J(X) is not affordable by Prym varieties; namely, affine groups Aff(Fq) with some exceptions: q=2, q=9, q a Fermat prime, q=2n with 2n−1 a Mersenne prime and some particular cases when X/G has genus 0 or 1. In each one of this exceptional cases, we give the group algebra decomposition of J(X) by Prym varieties.

On the Construction of Congruences over Generalized Fuzzy G-Acts

Group action is defined to support Cayley’s claim that every group is isomorphic to a suitable subgroup of a symmetric group. Group actions have a wide range of applications, including the analysis of symmetries of geometric objects and algorithms and cryptographic systems. In 1965, Zadeh introduced the concept of fuzzy sets and provided a mathematical formulation for various concepts in this area. Since then, the concept of fuzziness has been integrated into several branches of mathematics to address the uncertainties of real-life scenarios. This article introduces the concept of group action in a fuzzy environment, termed fuzzy G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-subacts. The study provide the concept of fuzzy G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-orbits and fuzzy G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-stabilizers and clearly outlines fuzzy permutation representations of G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document} and fuzzy G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-morphisms. The research findings significantly contributes to the understanding of fuzzy G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-congruences and fuzzy quotient G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-subacts with the help of fuzzy G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document}-partitions. This approach not only refines the underlying theories but also opens up new possibilities for practical implementation. Thus, the study demonstrates how the more complex fuzzy theory can expand and enrich the mathematical structures of abstract algebra, making them highly applicable.

Minimal compact group actions on C∗-algebras with simple fixed point algebras

The notion of quasi-product actions of a compact group on a C[Formula: see text]-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm’s characterization of non-type I C[Formula: see text]-algebras. We show that a faithful minimal action of a second countable compact group on a separable C[Formula: see text]-algebra is quasi-product whenever its fixed point algebra is simple. This was previously known only for compact abelian groups and for profinite groups. Our proof relies on a subfactor technique applied to finite index inclusions of simple C[Formula: see text]-algebras in the purely infinite case, and also uses ergodic actions of compact groups in the general case. As an application, we show that if moreover the fixed point algebra is a Kirchberg algebra, such an action is always isometrically shift-absorbing, and hence is classifiable by the equivariant KK-theory due to a recent result of Gabe-Szabó.

The renewed tin-weighting treatment as sustainable and durable flame-retardant approach for protein silk fabric

The facile development of a sustainable and durable flame-retardant approach for protein silk is of interest. Inspired by silk tin-weighting technology, this study developed a novel and sustainable in-situ deposition strategy based on biomass phytic acid to impart durable flame-retardant performance to silk fabrics. The chemical structure of insoluble chelating precipitation, and the surface morphology, thermal stability, combustion behavior, flame-retardant capacity, laundering resistance, and flame-retardant mode of action of the tin-weighting silk samples, were explored. The Sn-, P-, Si-containing insoluble chelating precipitation formed within the fiber interior and combined with silk fibers through electrostatic attraction and metal salt chelation. As a result, the tin-weighting silk displayed excellent self-extinguishing capacity, with the damaged length reduced to 9.2 cm and the LOI increased to 31.6 %; it also achieved self-extinguishing after 30 washing cycles, demonstrating high flame-retardant efficacy and laundering resistance. Moreover, the tin-weighting silk also showed the obvious suppression in smoke and heat generation by 55.6 % and 35.7 %, respectively. The synergistic charring action of phosphate groups, tin metal salts, and silicates was beneficial for enhancing the fire safety of silk. The tin-weighting treatment also displayed a minor impact on mechanical performance of silk fabrics.

Centralizers of Hamiltonian finite cyclic group actions on rational ruled surfaces

Let M = ( M , ω ) M=(M,\omega ) be either S 2 × S 2 S^2 \times S^2 or C P 2 # C P 2 ¯ \mathbb {C}P^2\# \overline {\mathbb {C}P^2} endowed with any symplectic form ω \omega . Suppose a finite cyclic group Z n \mathbb {Z}_n is acting effectively on ( M , ω ) (M,\omega ) through Hamiltonian diffeomorphisms, that is, there is an injective homomorphism Z n ↪ H a m ( M , ω ) \mathbb {Z}_n\hookrightarrow Ham(M,\omega ) . In this paper, we investigate the homotopy type of the group S y m p Z n ( M , ω ) Symp^{\mathbb {Z}_n}(M,\omega ) of equivariant symplectomorphisms. We prove that for some infinite families of Z n \mathbb {Z}_n actions satisfying certain inequalities involving the order n n and the symplectic cohomology class [ ω ] [\omega ] , the actions extend to either one or two toric actions, and accordingly, that the centralizers are homotopically equivalent to either a finite dimensional Lie group, or to the homotopy pushout of two tori along a circle. Our results rely on J J -holomorphic techniques, on Delzant’s classification of toric actions, on Karshon’s classification of Hamiltonian circle actions on 4 4 -manifolds, and on the Chen-Wilczyński classification of smooth Z n \mathbb {Z}_n -actions on Hirzebruch surfaces.

Differentials of the basis in Clifford Geometric Algebra

In this paper we discuss the dynamic effects of the varying frames. The differential of frame or basis vectors is always equivalent to a linear transformation of the frame, and the linear transformation is not the same in different contexts. In differential geometry, the linear transformation is the connection operator. While in quantum mechanics, the operator algebra corresponds to the differentials of matrices. Corresponding to the variation of the metric, the variation of the frame contains a unusual fourth-order tensor. We also derive the Lie differential of the frame corresponding to the Lorentz transformation group. The definition of differential of the frame is different, so the corresponding linear transformation is also different. In this paper, the unified point of view to deal with the variation of frame or basis vectors will bring great convenience to the research and application of Clifford algebras.