scholarly journals On Cohomological Equations for Suspension Flows over Vershik Automorphisms

2016 ◽  
Vol 16 (2) ◽  
pp. 381-391 ◽  
Author(s):  
Dmitry Zubov
Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 338
Author(s):  
Rosário D. Laureano

It is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically oriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural notion of symmetry for cocycles. It is discussed the fundamental relationship between the existence of solutions of cohomological equations and the behavior of the cocycles along periodic orbits. The generalization of this theorem to a class of suspension flows is also discussed and proved. This generalization allows giving a different proof of the Livschitz Theorem for flows based on the construction of Markov systems for hyperbolic flows.


1992 ◽  
Vol 68 (05) ◽  
pp. 589-594 ◽  
Author(s):  
Alon Margalit ◽  
Avinoam A Livne

SummaryHuman platelets exposed to hypotonicity undergo regulatory volume decrease (RVD), controlled by a potent, yet labile, lipoxygenase product (LP). LP is synthesized and excreted during RVD affecting selectively K+ permeability. LP is assayed by its capacity to reconstitute RVD when lipoxygenase is blocked. Centrifugation for preparing washed platelets (1,550 × g, 10 min) is sufficient to express LP activity, with declining potency in repeated centrifugations, indicating that it is not readily replenish-able. When platelet suspension flows in a vinyl tubing (1 mm i.d.), at physiological velocity, controlled at 90–254 cm/s, LP formation increases as a function of velocity but declines as result of increasing the tubing length. Stirring the platelets in an aggregometer cuvette for 30 s, yields no LP unless the stirring is intermittent. No associated platelet lysis or aggregation are observed following the mechanical stress applications. These results demonstrate that although mechanical stresses result in LP production, the mode of its application plays a major role. These results may indicate that LP is synthesized under pathological conditions and could be of relevance to platelets behavior related to arterial stenosis.


2021 ◽  
Vol 31 (3) ◽  
pp. 033129
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko
Keyword(s):  

2021 ◽  
pp. 1-13
Author(s):  
Erwan Lanneau ◽  
Stefano Marmi ◽  
Alexandra Skripchenko

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
Henk Bruin

AbstractWe show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the billiard flow, including Stable Limits if the parameter of the Torricelli trumpet is chosen in (1, 2).


Author(s):  
Vladimir Shelukhin ◽  
Vladimir Neverov

Abstract We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of L. D. Landau and I. M. Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a 10 tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Fick's law for the particle mass concentration flux vector.


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