scholarly journals Linear extension sums as valuations on cones

2011 ◽  
Vol 35 (4) ◽  
pp. 573-610 ◽  
Author(s):  
Adrien Boussicault ◽  
Valentin Féray ◽  
Alain Lascoux ◽  
Victor Reiner
Keyword(s):  



2007 ◽  
Vol 07 (03) ◽  
pp. 389-401 ◽  
Author(s):  
L. B. RYASHKO

An exponential mean square stability for the invariant manifold [Formula: see text] of a nonlinear stochastic system is considered. The stability analysis is based on the [Formula: see text]-quadratic Lyapunov function technique. The local dynamics of the nonlinear system near manifold is described by the stochastic linear extension system. We propose a general notion of the projective stability (P-stability) and prove the following theorem. The smooth compact manifold [Formula: see text] is exponentially mean square stable if and only if the corresponding stochastic linear extension system is P-stable.



2001 ◽  
Vol 44 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Narutaka Ozawa

AbstractWe present an example of a $C^*$-subalgebra $A$ of $\mathbb{B}(H)$ and a bounded linear map from $A$ to $\mathbb{B}(K)$ which does not admit any bounded linear extension. This generalizes the result of Robertson and gives the answer to a problem raised by Pisier. Using the same idea, we compute the exactness constants of some Q-spaces. This solves a problem raised by Oikhberg. We also construct a Q-space which is not locally reflexive.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 46L07





Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1107
Author(s):  
Javier Cuesta

We study the relation between almost-symmetries and the geometry of Banach spaces. We show that any almost-linear extension of a transformation that preserves transition probabilities up to an additive error admits an approximation by a linear map, and the quality of the approximation depends on the type and cotype constants of the involved spaces.



2020 ◽  
Vol 811 ◽  
pp. 135970
Author(s):  
Fabio D'Ambrosio ◽  
Mudit Garg ◽  
Lavinia Heisenberg
Keyword(s):  


2020 ◽  
Vol 12 (2) ◽  
pp. 97-99
Author(s):  
Kimberly A. Sable ◽  
Eden Lake
Keyword(s):  




1867 ◽  
Vol 15 ◽  
pp. 356-356

These experiments are a continuation of those described in a paper read February 22, 1866, with some modifications in the apparatus employed which render the comparison between torsion and flexure more direct. The amount of torsion or flexure produced by subjecting a cylindrical rod to a uniform couple throughout its whole length, is measured by means of two mirrors clamped to the rod near its ends, in which, by the aid of two telescopes, the reflexions of a scale overhead are seen and the displace­ments read off. One end of the rod is fixed, and a couple (of torsion and flexure alternately) is applied to the other end. Three rods, of glass, brass, and steel, were experimented on, and the re­sults obtained were as follows—M, n , and k denoting the resistances (in kilogrammes per square millimetre) to linear extension, shearing, and cubical compression respectively, and σ denoting the ratio of lateral contraction to longitudinal extension:—



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