scholarly journals Stability for Representations of Hecke Algebras of Type A

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 32
Author(s):  
Kun Wang ◽  
Shanshan Qi ◽  
Haitao Ma ◽  
Zhujun Zheng

In this paper, we introduce the concept of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence of the representations of Hecke algebras is representation stable.

2021 ◽  
Author(s):  
Saika Iwamatsu ◽  
Yasunori Nihei ◽  
Kazuhiro Iijima ◽  
Tomoki Ikoma ◽  
Tomoki Komori

Abstract In this study, a series of dedicated water tank tests were conducted in wind and waves to investigate the stability performance and turning motion of Floating Offshore Wind Turbine (FOWT) equipped with two vertical axis wind turbines (VAWT). The FOWT targeted in this study is called Multi-connection VAWT, which is a new type of FOWT moored by Single-Point-Mooring (SPM) system. We designed and manufactured two types of semi-submersible floating bodies. One is a type in which VAWTs are mounted in two places of a right-angled isosceles triangle (Type-A) on a single floater, and the other is two independent units equipped with VAWTs on two separate floaters centered on a moored body. This is a type in which two semi-submersible floating bodies are lined up in a straight line (Type-B). The experimental conditions were determined by scaling down to 1/100 using Froude’s scaling law based on a wind thrust load of 320 kN (rated wind speed of 12 m/s) assuming an actual machine. In the free yawing test in waves, Type-A turned downwards, while Type-B was barely affected by the waves. Furthermore, in the free yawing test in wind, both Type-A and Type-B turned leeward and stabilized at a final point where the wind load was balanced.


1996 ◽  
Vol 109 (12) ◽  
pp. 2875-2884 ◽  
Author(s):  
L. Johannes ◽  
F. Doussau ◽  
A. Clabecq ◽  
J.P. Henry ◽  
F. Darchen ◽  
...  

Rab3 is a monomeric GTP-binding protein associated with secretory vesicles which has been implicated in the control of regulated exocytosis. We have exploited Rab3 mutant proteins to investigate the function of Rab3 in the process of neurotransmitter release from Aplysia neurons. A GTPase-deficient Rab3 mutant protein was found to inhibit acetylcholine release suggesting that GTP hydrolysis by Rab3 is rate-limiting in the exocytosis process. This effect was abolished by a mutation in the effector domain, and required the association of Rab3 with membranes. In order to determine the step at which Rab3 interferes with the secretory process, tetanus and botulinum type A neurotoxins were applied to Aplysia neurons pre-injected with the GTPase-deficient Rab3 mutant protein. These neurotoxins are Zn(2+)-dependent proteases that cleave VAMP/synaptobrevin and SNAP-25, two proteins which can form a ternary complex (termed the SNARE complex) with syntaxin and have been implicated in the docking of synaptic vesicles at the plasma membrane. The onset of toxin-induced inhibition of neurotransmitter release was strongly delayed in these cells, indicating that the mutant Rab3 protein led to the accumulation of a toxin-insensitive component of release. Since tetanus and botulinum type A neurotoxins cannot attack their targets, VAMP/synaptobrevin and SNAP-25, when the latter are engaged in the SNARE complex, we propose that Rab3 modulates the activity of the fusion machinery by controlling the formation or the stability of the SNARE complex.


2003 ◽  
Vol 12 (07) ◽  
pp. 899-904 ◽  
Author(s):  
MEINOLF GECK ◽  
NICOLAS JACON

We give a new simple proof for the weights of Ocneanu's trace on Iwahori–Hecke algebras of type A. This trace is used in the construction of the HOMFLYPT-polynomial of knots and links (which includes the famous Jones polynomial as a special case). Our main tool is Starkey's rule concerning the character tables of Iwahori–Hecke algebras of type A.


2017 ◽  
Vol 39 (3) ◽  
pp. 583-596
Author(s):  
Yasushi GOMI
Keyword(s):  
Type A ◽  

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