scholarly journals $(3/2)$ -dimensional measure of singular sets of some Kleinian groups

1972 ◽  
Vol 24 (3) ◽  
pp. 448-464 ◽  
Author(s):  
Tohru AKAZA
Keyword(s):  
Kleinian Groups ◽  
Dimensional Measure ◽  
Singular Sets

scholarly journals Singular Sets of Some Kleinian Groups (II)

1967 ◽  
Vol 29 ◽  
pp. 145-162 ◽  
Author(s):  
Tohru Akaza
Keyword(s):  
Kleinian Groups ◽  
Singular Set ◽  
Fundamental Domains ◽  
Dimensional Measure ◽  
Singular Sets ◽  
Discontinuous Groups ◽  
Positive Capacity ◽  
Automorphic Functions

In the theory of automorphic functions it is important to investigate the properties of the singular sets of the properly discontinuous groups. But we seem to know nothing about the size or structure of the singular sets of Kleinian groups except the results due to Myrberg and Akaza [1], which state that the singular set has positive capacity and there exist Kleinian groups whose singular sets have positive 1-dimensional measure. In our recent paper [2], we proved the existence of Kleinian groups with fundamental domains bounded by five circles whose singular sets have positive 1-dimensional measure and presented the problem whether there exist or not such groups in the case of four circles. The purpose of this paper is to solve this problem. Here we note that, by Schottky’s condition [4], the 1-dimensional measure of the singular set is always zero in the case of three circles.

scholarly journals Singular Sets of Some Kleinian Groups

1966 ◽  
Vol 26 ◽  
pp. 127-143 ◽  
Author(s):  
Tohru Akaza
Keyword(s):  
Kleinian Groups ◽  
Schottky Groups ◽  
Dimensional Measure ◽  
Singular Sets

In our paper Cl] we showed that there exist Schottky groups whose singular sets have positive 1-dimensional measure. Since the example was very complicated, it is natural to seek for simpler examples. Further the problem how about the singular sets of more general groups occurs.

scholarly journals Singular sets of some infinitely generated Kleinian groups

1975 ◽  
Vol 26 (4) ◽  
pp. 485-497
Author(s):  
Tohru Akaza ◽  
Eiichi Sakai
Keyword(s):  
Kleinian Groups ◽  
Singular Sets

Development and validation of a multi-dimensional measure of sport thoughts

2003 ◽  
Author(s):  
The Yannis Zervas ◽  
Nektarios A. Stavrou ◽  
Maria Psychountaki
Keyword(s):  
Dimensional Measure ◽  
Development And Validation

scholarly journals Local Regularity for the Harmonic Map and Yang–Mills Heat Flows

2021 ◽  
Author(s):  
Ahmad Afuni
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Map ◽  
Local Regularity ◽  
Yang Mills ◽  
Heat Flows ◽  
Singular Sets ◽  
Regularity Results ◽  
Local Monotonicity ◽  
Partial Differ ◽  
Singular Time

AbstractWe establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4, respectively, obtaining criteria for the smooth local extensibility of these flows. As a corollary, we obtain new characterisations of singularity formation and use this to obtain a local estimate on the Hausdorff measure of the singular sets of these flows at the first singular time. Finally, we show that smooth blow-ups at rapidly forming singularities of these flows are necessarily nontrivial and admit a positive lower bound on their heat ball energies. These results crucially depend on some local monotonicity formulæ for these flows recently established by Ecker (Calc Var Partial Differ Equ 23(1):67–81, 2005) and the Afuni (Calc Var 555(1):1–14, 2016; Adv Calc Var 12(2):135–156, 2019).

Beyond Bounded Rationality: CEO Reflective Capacity and Firm Sustainability Performance

2021 ◽  
pp. 1-38
Author(s):  
Yingya Jia ◽  
Anne S. Tsui ◽  
Xiaoyu Yu
Keyword(s):  
Decision Making ◽  
Bounded Rationality ◽  
Three Dimensional ◽  
Strategic Decision ◽  
Future Research ◽  
Sustainability Performance ◽  
Business Executives ◽  
Dimensional Measure ◽  
Reflective Capacity ◽  
Mediating Mechanisms

ABSTRACT Optimal or rational decision making is not possible due to informational constraints and limits in computation capability of humans (March & Simon, 1958; March, 1978). This bounded rationality serves as a filtering process in decision making among business executives (Hambrick & Mason, 1984). In this study, we propose the concept of CEO reflective capacity as a behavior-oriented cognitive capability that may overcome to some extent the pervasive limitation of bounded rationality in executive decision-making. Following Hinkin's (1998) method and two executive samples, we developed and validated a three-dimensional measure of CEO reflective capacity. Based on two-wave surveys of CEOs and their executive-subordinates in 213 Chinese small-medium sized firms, we tested and confirmed three hypotheses on how CEO reflective capacity is related to a firm's sustainability performance (including economic, societal, and environmental dimensions) through the mediating mechanisms of strategic decision comprehensiveness and CEO behavioral complexity. We discuss the contribution of this study to the literature on the upper echelons and information processing perspectives. We also identify the implications for future research on strategic leadership and managerial cognition in complex and dynamic contexts.

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