scholarly journals Affine Maps That Induce Polyhedral Complex Isomorphisms

2000 ◽  
Vol 24 (1) ◽  
pp. 49-60 ◽  
Author(s):  
A. Dress ◽  
K. T. Huber ◽  
V. Moulton
Keyword(s):  
Polyhedral Complex ◽  
Affine Maps

scholarly journals Tropical ideals do not realise all Bergman fans

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Jan Draisma ◽  
Felipe Rincón
Keyword(s):  
Tropical Geometry ◽  
Tensor Products ◽  
Tropical Variety ◽  
Polyhedral Complex ◽  
Direct Sum ◽  
Weight One ◽  
Polyhedral Complexes

AbstractEvery tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.

scholarly journals Ergodic affine maps of locally compact groups

1985 ◽  
Vol 37 (3) ◽  
pp. 363-372 ◽  
Author(s):  
Masahito DATEYAMA ◽  
Tatsuro KASUGA
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Affine Maps

The quasi-affine maps and fractals

1997 ◽  
Vol 2 (1) ◽  
pp. 9-12
Author(s):  
Lunhai Long ◽  
Gang Chen
Keyword(s):  
Affine Maps

scholarly journals Equivalence betweenp-cyclic quasimonotonicity andp-cyclic monotonicity of affine maps

Optimization ◽  
2014 ◽  
Vol 64 (7) ◽  
pp. 1487-1497
Author(s):  
Eladio Ocaña ◽  
John Cotrina ◽  
Orestes Bueno
Keyword(s):  
Affine Maps ◽  
Cyclic Monotonicity

scholarly journals Amoeba-Shaped Polyhedral Complex of an Algebraic Hypersurface

2018 ◽  
Vol 29 (2) ◽  
pp. 1356-1368 ◽  
Author(s):  
Mounir Nisse ◽  
Timur Sadykov
Keyword(s):  
Polyhedral Complex ◽  
Algebraic Hypersurface

An L 2 convergence theorem for random affine mappings

1995 ◽  
Vol 32 (01) ◽  
pp. 183-192 ◽  
Author(s):  
Robert M. Burton ◽  
Uwe Rösler
Keyword(s):  
Hilbert Space ◽  
Lyapunov Exponent ◽  
Bilinear Form ◽  
Convergence Theorem ◽  
Convergence In Distribution ◽  
Wasserstein Metric ◽  
Affine Mappings ◽  
Affine Maps ◽  
Second Moments ◽  
Contraction Condition

We consider the composition of random i.i.d. affine maps of a Hilbert space to itself. We show convergence of thenth composition of these maps in the Wasserstein metric via a contraction argument. The contraction condition involves the operator norm of the expectation of a bilinear form. This is contrasted with the usual contraction condition of a negative Lyapunov exponent. Our condition is stronger and easier to check. In addition, our condition allows us to conclude convergence of second moments as well as convergence in distribution.

Sign in / Sign up

Export Citation Format

Share Document