scholarly journals Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

2004 ◽  
Vol 16 (1) ◽  
pp. 125-149 ◽  
Author(s):  
Jean-Pierre Gazeau ◽  
Jean-Louis Verger-Gaugry
Keyword(s):  
Perron Number ◽  
Geometric Study

scholarly journals Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris ◽  
Kangning Wei ◽  
René Zander
Keyword(s):  
Integrable Systems ◽  
Geometric Description ◽  
Discrete Integrable Systems ◽  
Birational Maps ◽  
Base Points ◽  
Special Geometry ◽  
Low Degree ◽  
Geometric Study

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

scholarly journals A Geometric Study of Wasserstein Spaces: Isometric Rigidity in Negative Curvature

2015 ◽  
Vol 2016 (5) ◽  
pp. 1368-1386 ◽  
Author(s):  
Jérôme Bertrand ◽  
Benoît R. Kloeckner
Keyword(s):  
Negative Curvature ◽  
Geometric Study

Geometric Study of Various Chimney Graft Configurations in an In Vitro Juxtarenal Aneurysm Model

2013 ◽  
Vol 20 (2) ◽  
pp. 184-190 ◽  
Author(s):  
Jorg L. de Bruin ◽  
Kak K. Yeung ◽  
Wouter W. Niepoth ◽  
Rutger J. Lely ◽  
Qingfeng Cheung ◽  
...  
Keyword(s):  
Juxtarenal Aneurysm ◽  
Chimney Graft ◽  
Aneurysm Model ◽  
Geometric Study

scholarly journals Hydrodynamics Around a Deep-Draft Semi-Submersible With Various Corner Shapes

2018 ◽  
Author(s):  
Yibo Liang ◽  
Longbin Tao
Keyword(s):  
Numerical Model ◽  
Experimental Test ◽  
Numerical Study ◽  
Water Channel ◽  
Hydrodynamic Characteristics ◽  
Shape Design ◽  
Circulating Water ◽  
Fluid Physics ◽  
Shape Effects ◽  
Geometric Study

A numerical study on flow over a stationary deep-draft semi-submersible (DDS) with various corner shapes was carried out to investigate the corner shape effects on the overall hydrodynamics. Three models based on a typical DDS design with different corner shapes were numerically investigated under 45° incidence. The present numerical model has been validated by an experimental test carried out in a circulating water channel. It is demonstrated that, as the corner shape design changed, the hydrodynamic characteristics alter drastically. In addition, the flow patterns were examined to reveal some insights of the fluid physics due to the changing of different corner shape designs. The detailed numerical results from the geometric study will provide a good guidance for future practical designs.

scholarly journals Non-negative integral matrices with given spectral radius and controlled dimension

2021 ◽  
pp. 1-24
Author(s):  
MEHDI YAZDI
Keyword(s):  
Spectral Radius ◽  
Positive Real Number ◽  
Algebraic Integer ◽  
Log P ◽  
Irreducible Matrix ◽  
Positive Real ◽  
Shift Of Finite Type ◽  
Primitive Matrix ◽  
Integral Matrices ◽  
Perron Number

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius of some integral primitive matrix, if and only if, it is a Perron algebraic integer. Given a Perron number p, we prove that there is an integral irreducible matrix with spectral radius p, and with dimension bounded above in terms of the algebraic degree, the ratio of the first two largest Galois conjugates, and arithmetic information about the ring of integers of its number field. This arithmetic information can be taken to be either the discriminant or the minimal Hermite-like thickness. Equivalently, given a Perron number p, there is an irreducible shift of finite type with entropy $\log (p)$ defined as an edge shift on a graph whose number of vertices is bounded above in terms of the aforementioned data.

scholarly journals Negative curvature in graph braid groups

2020 ◽  
pp. 1-36
Author(s):  
Anthony Genevois
Keyword(s):  
Braid Group ◽  
Negative Curvature ◽  
Braid Groups ◽  
Gromov Hyperbolic ◽  
Relatively Hyperbolic ◽  
Geometric Study

In this paper, we initiate a geometric study of graph braid groups. More precisely, by applying the formalism of special colorings introduced in a previous paper, we determine precisely when a graph braid group is Gromov-hyperbolic, toral relatively hyperbolic and acylindrically hyperbolic.

scholarly journals Dynamical degrees of affine-triangular automorphisms of affine spaces

2021 ◽  
pp. 1-42
Author(s):  
JÉRÉMY BLANC ◽  
IMMANUEL VAN SANTEN
Keyword(s):  
Affine Space ◽  
Affine Spaces ◽  
Dynamical Degree ◽  
Perron Number ◽  
Dynamical Degrees ◽  
Affine Automorphism

Abstract We study the possible dynamical degrees of automorphisms of the affine space $\mathbb {A}^n$ . In dimension $n=3$ , we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This generalizes the easier case of shift-like automorphisms which can be studied in any dimension. We also prove that each weak Perron number is the dynamical degree of an affine-triangular automorphism of the affine space $\mathbb {A}^n$ for some n, and we give the best possible n for quadratic integers, which is either $3$ or $4$ .

Application of nanofluid to improve the thermal performance of horizontal spiral coil utilized in solar ponds: Geometric study

2018 ◽  
Vol 122 ◽  
pp. 1-16 ◽  
Author(s):  
Erfan Khodabandeh ◽  
Mohammad Reza Safaei ◽  
Soheil Akbari ◽  
Omid Ali Akbari ◽  
Abdullah A.A.A. Alrashed
Keyword(s):  
Thermal Performance ◽  
Spiral Coil ◽  
Solar Ponds ◽  
Geometric Study
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