scholarly journals An invariant property of balls in arrangements of hyperplanes

1993 ◽  
Vol 10 (4) ◽  
pp. 421-425 ◽  
Author(s):  
Boris Aronov ◽  
Daniel Q. Naiman ◽  
János Pach ◽  
Micha Sharir
Keyword(s):  
Invariant Property ◽  
Arrangements Of Hyperplanes

An isotopically invariant property of automorphic Moufang loops

2019 ◽  
Vol 58 (4) ◽  
pp. 458-466
Author(s):  
A. N. Grishkov ◽  
M. N. Rasskazova ◽  
L. L. Sabinina
Keyword(s):  
Invariant Property ◽  
Moufang Loops

scholarly journals Pointwise multiple averages for sublinear functions

2018 ◽  
Vol 40 (6) ◽  
pp. 1594-1618
Author(s):  
SEBASTIÁN DONOSO ◽  
ANDREAS KOUTSOGIANNIS ◽  
WENBO SUN
Keyword(s):  
Large Class ◽  
Explicit Formula ◽  
Pointwise Convergence ◽  
Limit Function ◽  
Invariant Property ◽  
Ergodic Averages ◽  
Order Zero ◽  
Good For ◽  
Sublinear Functions ◽  
Uniquely Ergodic

For any measure-preserving system $(X,{\mathcal{B}},\unicode[STIX]{x1D707},T_{1},\ldots ,T_{d})$ with no commutativity assumptions on the transformations $T_{i},$$1\leq i\leq d,$ we study the pointwise convergence of multiple ergodic averages with iterates of different growth coming from a large class of sublinear functions. This class properly contains important subclasses of Hardy field functions of order zero and of Fejér functions, i.e., tempered functions of order zero. We show that the convergence of the single average, via an invariant property, implies the convergence of the multiple one. We also provide examples of sublinear functions which are, in general, bad for convergence on arbitrary systems, but good for uniquely ergodic systems. The case where the fastest function is linear is addressed as well, and we provide, in all the cases, an explicit formula of the limit function.

AN AUTOREGRESSIVE APPROACH TO SURFACE TEXTURE ANALYSIS

1994 ◽  
Vol 08 (04) ◽  
pp. 845-857 ◽  
Author(s):  
DINESH P. MITAL ◽  
GOH WEE LENG
Keyword(s):  
Aspect Ratio ◽  
Random Field ◽  
Texture Analysis ◽  
Surface Texture ◽  
Field Model ◽  
Invariant Property ◽  
Circular Area ◽  
Pixel Image ◽  
Rotational Invariant ◽  
Surface Texture Analysis

The use of autoregressive models in textual analysis holds great potential. Coupling the technique to a circular neighbourhood set imparts a rotational invariant property to it. This was demonstrated by Kashyap and Khotanzad in their model called the Circular Symmetric Autogressive (CSAR) Random Field model. The short-coming in this very ingenious proposal is that it is set in a background of square pixels and the rotational invariant property of the model fails in cases when the aspect ratio of the pixels are not at unity. This paper proposes a major modification to the CSAR to render the model rotational invariant under all configurations of pixel implementation. It is based on the area segments covered by a circle set in a 3×3 neighbourhood. We call it the Circular Area Autoregressive (CAAR) model. The results obtained from the CAAR showed much better consistency over that of the CSAR when a non-square pixel image was used.

scholarly journals Phase Inconsistency Error Compensation for Multichannel Spaceborne SAR Based on the Rotation-Invariant Property

2020 ◽  
pp. 1-5
Author(s):  
Heli Gao ◽  
Jie Chen ◽  
Wei Liu ◽  
Chunsheng Li ◽  
Wei Yang
Keyword(s):  
Error Compensation ◽  
Invariant Property ◽  
Rotation Invariant

The slimmest arrangements of hyperplanes: II. Basepointed geometric lattices and Euclidean arrangements

Mathematika ◽  
1981 ◽  
Vol 28 (2) ◽  
pp. 169-190 ◽  
Author(s):  
Thomas Zaslavsky
Keyword(s):  
Arrangements Of Hyperplanes ◽  
Geometric Lattices

Simplicial cells in arrangements of hyperplanes

1979 ◽  
Vol 8 (2) ◽  
Author(s):  
R.W. Shannon
Keyword(s):  
Arrangements Of Hyperplanes

scholarly journals Dynamic point location in arrangements of hyperplanes

1992 ◽  
Vol 8 (3) ◽  
pp. 335-360 ◽  
Author(s):  
Ketan Mulmuley ◽  
Sandeep Sen
Keyword(s):  
Point Location ◽  
Arrangements Of Hyperplanes
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