Cluster sets and corona theorems

Author(s):  
Stephen Scheinberg
Keyword(s):  

1979 ◽  
Vol 5 (2) ◽  
pp. 303
Author(s):  
Layek
Keyword(s):  


1977 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
Layek ◽  
Mukhopadhyay
Keyword(s):  


Author(s):  
Thiago R. Alves ◽  
Daniel Carando


2013 ◽  
Vol 39 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Gavin L. Moir ◽  
Bruce W. Graham ◽  
Shala E. Davis ◽  
John J. Guers ◽  
Chad A. Witmer

Abstract The purpose of the present study was to investigate the effects of different configurations of repetitions within a set of deadlifts on the mechanical variables of concentric force, concentric time under tension, impulse, work, power, and fatigue. Eleven resistance trained men (age: 21.9 ± 1.0 years; deadlift 1 repetition maximum: 183.2 ± 38.3 kg) performed four repetitions of the deadlift exercise with a load equivalent to 90% of 1 repetition maximum under three different set configurations: Traditional (continuous repetitions); Doubles cluster (repetitions 1 and 2, and 3 and 4 performed continuously with a 30 s rest inserted between repetitions 2 and 3); Singles cluster (30 s rest provided between repetitions). The order of the sessions was counterbalanced across the subjects and the mechanical variables were calculated during each repetition from the synchronized signals recorded from force platforms and a motion analysis system. Relative to the Traditional set, the insertion of rest periods in the cluster set configurations resulted in greater time under tension (p < 0.001) and therefore, greater impulse (p < 0.001) during the repetitions. Reductions in power were observed during the cluster sets compared to the Traditional set (p = 0.001). The Doubles cluster set resulted in greater fatigue scores for power compared to the Traditional set (p = 0.04). The influence of cluster sets on mechanical variables appears to be mediated by the mechanical characteristics of the exercise (i.e. stretch-shortening cycle) and the competing physiological mechanisms of fatigue and potentiation.



2006 ◽  
Vol 25 (2) ◽  
pp. 211-219 ◽  
Author(s):  
L. Bernal-Gonzalez ◽  
A. Bonilla ◽  
M.C. Calderon-Moreno ◽  
J.A. Prado-Bassas


2021 ◽  
Author(s):  
Ciaran M Fairman ◽  
Otis L Owens ◽  
Kristina L Kendall ◽  
James Steele ◽  
C Latella ◽  
...  

Abstract Background: Symptom burden remains a critical concern for individuals with non-small cell lung cancer (NSCLC) following the completion of treatment. The most common symptom clusters, dyspnea (shortness of breath) and fatigue,can contribute to physical decline, reductions in quality of life, and a higher risk of comorbidities and mortality. Dyspnea is a primary limiter of exercise capacity in individuals with lung cancer, resulting in exercise avoidance and an accelerated physical decline. As such, designing resistance training with cluster sets to mitigate symptoms of dyspnea and fatigue may result in improved exercise tolerance. Thus, maintainingthe exercise stimulus via cluster sets, combined with improved tolerance of the exercise, could result in maintenance of physical function and quality of life. The purpose of this study is to investigate the feasibility and preliminary efficacy of a hybrid-delivery home-based cluster-set resistance training program in individuals with NSCLC. Methods: Individuals with NSCLC (n=15), within 12-months of completion of treatment will be recruited to participate in this single arm feasibility trial. Participants will complete 8-weeks of home-based resistance training designed to minimizedyspnea and fatigue. The hybrid-delivery of the program will include supervised sessions in the participants’ home, and virtual supervision via video conferencing. The primary outcome of feasibility will be quantifiedby recruitment rates, retention, acceptability, and intervention fidelity. Exploratory outcomes (dyspnea, fatigue, quality of life, physical function, and body composition) will be assessed pre- and post- intervention. Discussion: This study will provide important data on the feasibility of delivering this intervention and inform procedures for a future randomized controlled trial. Trial Registration: Record not yet public



1983 ◽  
Vol 115 (3) ◽  
pp. 155-161
Author(s):  
Jan Jastrzębski
Keyword(s):  


2018 ◽  
Vol 61 (2) ◽  
pp. 282-288
Author(s):  
Paul M. Gauthier

AbstractFor an analytic curve γ (a, b) → ℂ, the set of values approached by γ(t), as t ↘ a and as t ↗ b can be any two continua of ℂ ⋃ {∞}.



1978 ◽  
Vol 70 ◽  
pp. 1-6 ◽  
Author(s):  
Shigeo Segawa

Consider a single-valued meromorphic function w = f(p) defined on an open Riemann surface R with an ideal boundary β. In [1], Collingwood and Cartwright introduced the global cluster set for a function meromorphic on the unit disk. Generalizing the definition of global cluster sets to our present setting, we define the global cluster set for w = f(p) as follows;A value w in the extended complex plane is called a cluster value at β if there exists a sequence in R converging to β such that



Author(s):  
Brian S. Thomson
Keyword(s):  


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