In this paper, we construct a shift-splitting preconditioner for a class of block two-by-two linear systems. The proposed preconditioner is extracted from a stationary iterative method which is ...unconditionally convergent. Moreover, the eigenvalue distribution of the corresponding preconditioned matrix is studied. Numerical experiments are presented to show that our new preconditioner can be quite competitive when used to precondition Krylov subspace iterative methods such as GMRES.
We examined cultural differences in people’s lay theories of demeanor—how demeanor may be perceived as a straightforward and reliable reflection of reality (convergence theory) or as a deviating ...reflection of reality (divergence theory). Across different domains of competition, Euro-Canadians perceived greater competence in an opponent with a competent demeanor, whereas Chinese paradoxically perceived greater competence in an opponent with no signs of competence (Studies 1–4b). The results, unexplained by attributional styles (Study 1), likability (Study 3), or modesty (Study 3), suggest that Euro-Canadians endorse a stronger convergence theory than Chinese in their inferences of competence. Corroborated with qualitative data (Study 4a), such cultural differences were explained by the beliefs that demeanor can be a misleading reflection of reality, verified in college and community (Study 4b) samples. We discuss the implications for social perception, intergroup dynamics, and self-presentation in competitions.
In June 2020, the National Council of Teachers of Mathematics (NCTM) and the Association of Mathematics Teacher Educators (AMTE) released statements regarding racism, racial violence, and mathematics ...teaching. Pre-service elementary teachers (PSTs) in a mathematics content course wrote reactions to the organizations’ statements. After using an emergent coding process to code the reactions for major themes, the authors used a theory from communication studies called symbolic convergence theory to analyze how closely the PSTs’ understanding of the statements aligned with the vision espoused by the organizations in the statements. PSTs largely understood the need to make their classrooms safe and supportive spaces; however, they struggled to connect anti-racist ideals specifically to mathematics teaching. The authors discuss potential ways NCTM and AMTE can address this disconnect.
In the digital age, many corporations communicate with their publics via online channels. Among many channels, a corporation’s official Web site is often used for informing publics of its performance ...and other corporate-related information and for shaping a positive corporate image. This study quantitatively analyzed corporate Web sites, particularly the “About us” Web pages of Fortune 500 corporations based on symbolic convergence theory (SCT), which describes the formation of symbolic reality and the shared meaning of that symbolic reality among the public. A content analysis revealed that economic corporate management was the dominant rhetorical vision, and the fantasy, in the context of SCT, of being a superior company was emphasized by the 500 examined corporations. Such symbolic reality was constructed using corresponding structural tools of Web content, such as dramatis personae, plot line, and scene. In addition, the rhetorical vision and fantasy themes created by the Web sites turned out to be contingent on business classifications (retailer/distributor, manufacturers, and financial/informational/recreational services). Companies that pursued other types of fantasy themes (such as admirable, futuristic, and competent/stable) and rhetorical visions (such as socially responsible corporate management) were also identified. Some suggestions for corporate communicators are provided based on the results of this analysis.
The activities of the modern state are carried out taking into account the trends inherent in the global community. One of the driving forces behind these trends is the strengthening of economic ...integration due to the increasing role of finance in the world economy, the effects of globalisation, liberalisation, concentration and centralisation of financial capital, which have shaped the new shape of the modern economic system. The integration of the world economy requires the integration of law in accordance with generally recognised norms and principles at the international level. The international character of law is an external circumstance that determines the facts of legal regulation of the convergence of states and peoples, their economies, cultures and ideologies. Convergence leads to the convergence of different legal systems and economic models. These circumstances indicate the existence of a global phenomenon that can be described as the process of economic and legal convergence. The subject of the study is the patterns of convergence in the field of economics and law. The authors aim to study the genesis of the convergence theory, identify the main trends and prospects for the development of convergence in the current environment, and explain the patterns of convergence in the field of economics and law in the context of globalisation. The methodological basis of the research is the theory of economic and legal convergence, the theory of state regulation of the economy, the theory of socio-economic systems and economic growth developed in the works of domestic and foreign economists, lawyers and philosophers. The study of basic economic and legal institutions is carried out on the basis of the dialectical method, general scientific methods of abstraction, analysis, synthesis and systematic approach. The research of certain issues was carried out using special methods: historical, comparative, interpretation of law, logical and legal, as well as methods of specific economic research, etc. The authors analyse certain issues of economic and legal convergence in terms of their historical formation, relevance, efficiency and prospects for application. Results. Convergence in the field of economics and law is a process of interaction of relevant elements both within national systems and economic and legal systems of different states, characterised by convergence, an increase in the number of links between the elements of converging objects and a certain degree of consistency of the impact of these elements on social relations. On the basis of the study, the authors believe that the use of convergence processes in the field of economics and law at the global level should be carried out only in a harmonious manner, creating common balanced results based on a unifying model of coherent cooperation of the subjects of these processes.
This research lays emphasis on predominant corruption stories in popular Nigerian newspapers, by means of fantasy-theme analysis in reviewing issues that concern corruption within the Nigerian ...political sphere. Particularly, this analysis compares stories about Nigerian politicians who have been reported at various points in time by Nigerian newspapers as corrupt individuals, who in one way or the other were found guilty of syphoning funds and falsifying relevant information. Through a thorough examination of fantasy themes roles on these accounts and recognizing which parts of reality are significant, we conceive what the messages are able to achieve with regards to the creation of rhetorical visions within contexts of symbolic convergence theory. In this study, fantasy themes analysed disclose meanings regarding morality, personal decisions, and class privilege. This study also highlights how stories on corruption cases by political leaders could help in the establishment of proper, honourable societies that punish or reprimand certain corrupt behaviours via normative impact on audiences. Fundamentally, rhetorical visions derived in this paper suggest that decision to be corrupt or not, as a politician lies with the politician himself.
Inconsistent, unclear, and inaccurate messages can dissuade audiences from engaging in appropriate crisis response behaviors. Thus, message convergence is both a priority and a persistent challenge ...for crisis communicators. In 2013, the Porcine Epidemic Diarrhea virus (PEDv) caused substantial losses in the U.S. swine industry. This study examines interview responses by spokespersons from multiple swine agency experts and university extension agents through the lens of message convergence theory. Results extend previous research regarding what to communicate by revealing how to communicate effectively. Ultimately, this analysis explains how, when existing convergent messages are no longer accurate, practitioners must sometimes foster their own divergence to put forward a more accurate message (in this case, for effectively improving biosecurity).
Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time step ...everywhere with a crippling effect on any explicit time-marching method. In J. Diaz and M. J. Grote, SIAM J. Sd. Comput., 31 (2009), pp. 1985-2014 a leap-frog (LF)-based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time steps in the locally refined region and larger steps elsewhere. Here optimal convergence rates are rigorously proved for the fully discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.
Abstract
In practical engineering, many control problems usually can be transformed into solutions of the discrete algebraic Riccati equation (DARE), which has two matrix inverse operations formally. ...In this paper, first, by the relationship between properties of the matrix Schur complement and partitioned representation of inverse matrix, we change the DARE with twice inversions into an equivalent form with once inversion and propose a corresponding iterative algorithm. Next, for a special case of DARE, we deformed this DARE into a new equivalent one. For the equivalent form, we propose a new iterative algorithm in an inversion-free way. Furthermore, for these algorithms, we prove their monotone convergence and give the analysis of their errors. Last, comparing with some existing work on this topic, corresponding numerical examples are given to illustrate the superiority and effectiveness of our results.
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