scholarly journals Strong connectedness of the invertibles in a finite subdiagonal algebra

2000 ◽  
Vol 128 (10) ◽  
pp. 2967-2973
Author(s):  
Michael Marsalli ◽  
Graeme West
Keyword(s):  
Strong Connectedness ◽  
Subdiagonal Algebra

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

Grown Local: Community Attachment and Market Entries in the Franconian Beer Industry

2017 ◽  
Vol 39 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Margarita Cruz ◽  
Nikolaus Beck ◽  
Filippo Carlo Wezel
Keyword(s):  
Empirical Analysis ◽  
Local Community ◽  
New Ventures ◽  
Community Attachment ◽  
Residential Stability ◽  
Beer Industry ◽  
Unfavorable Effect ◽  
Strong Connectedness ◽  
Positive Effect

Geographic communities are often thought to support new ventures, particularly when newcomers are able to replicate incumbents’ characteristics. This paper elaborates on the conditions under which geographic communities may hinder the action of newcomers. Particular attention is dedicated to the case in which incumbents’ identities build on community traditions and rely on strong connectedness with community inhabitants, as these factors are difficult for newcomers to replicate. We explore this question within the context of market entries in the Franconian microbrewery industry. The results of our empirical analysis confirm that geographic communities exert an unfavorable effect on the entry of new organizations when incumbents are deeply attached to the community. Conversely, when incumbents relate poorly to the community, residential stability within the community displays a positive effect on founding.

scholarly journals Hilbert transform associated with finite maximal subdiagonal algebras

1998 ◽  
Vol 65 (3) ◽  
pp. 388-404 ◽  
Author(s):  
Narcisse Randrianantoanina
Keyword(s):  
Hilbert Transform ◽  
Von Neumann Algebra ◽  
Weak Type ◽  
Function Algebra ◽  
Measurable Operator ◽  
Von Neumann ◽  
Continuous Map ◽  
Subdiagonal Algebra ◽  
Algebra Theory ◽  
The Hilbert Transform

AbstractLet ℳ be a von Neumann algebra with a faithful normal trace τ, and let H∞ be a finite, maximal. subdiagonal algebra of ℳ. We prove that the Hilbert transform associated with H∞ is a linear continuous map from L1 (ℳ, τ) into L1.∞ (ℳ, τ). This provides a non-commutative version of a classical theorem of Kolmogorov on weak type boundedness of the Hilbert transform. We also show that if a positive measurable operator b is such that b log+b ∈ L1 (ℳ, τ) then its conjugate b, relative to H∞ belongs to L1 (ℳ, τ). These results generalize classical facts from function algebra theory to a non-commutative setting.

scholarly journals Beyond Topological Persistence: Starting from Networks

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3079
Author(s):  
Mattia G. Bergomi ◽  
Massimo Ferri ◽  
Pietro Vertechi ◽  
Lorenzo Zuffi
Keyword(s):  
Persistent Homology ◽  
Data Types ◽  
Full Generality ◽  
Simple Graphs ◽  
Topological Persistence ◽  
Strong Connectedness ◽  
Recent Extension

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and digraphs. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness—clique communities, k-vertex, and k-edge connectedness—directly on simple graphs and strong connectedness in digraphs.

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