scholarly journals Horocycle flow orbits and lattice surface characterizations

2017 ◽  
Vol 39 (06) ◽  
pp. 1441-1461
Author(s):  
JON CHAIKA ◽  
KATHRYN LINDSEY
Keyword(s):  
Translation Surface ◽  
Orbit Closure ◽  
Horocycle Flow ◽  
Lattice Surface

The orbit closure of any translation surface under the horocycle flow in almost any direction equals its $\text{SL}_{2}(\mathbb{R})$ orbit closure. This result gives rise to new characterizations of lattice surfaces in terms of the horocycle flow.

scholarly journals Ergodicity for infinite periodic translation surfaces

2013 ◽  
Vol 149 (8) ◽  
pp. 1364-1380 ◽  
Author(s):  
Pascal Hubert ◽  
Barak Weiss
Keyword(s):  
Translation Surface ◽  
Translation Surfaces ◽  
Lattice Surface

AbstractFor a $ \mathbb{Z} $-cover $\widetilde {M} \rightarrow M$ of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.

Investigation of Lattice Surface Layers by Scanning Probe Microscopy

1993 ◽  
pp. 243-256
Author(s):  
Max Firtel ◽  
Gordon Southam ◽  
Terry J. Beveridge ◽  
Wei Xu ◽  
Manfred H. Jericho ◽  
...  
Keyword(s):  
Scanning Probe Microscopy ◽  
Scanning Probe ◽  
Surface Layers ◽  
Probe Microscopy ◽  
Lattice Surface

scholarly journals Algorithms for orbit closure separation for invariants and semi-invariants of matrices

2020 ◽  
Vol 14 (10) ◽  
pp. 2791-2813
Author(s):  
Harm Derksen ◽  
Visu Makam
Keyword(s):  
Orbit Closure

scholarly journals Poincaré polynomials of generic torus orbit closures in Schubert varieties

2021 ◽  
pp. 189-208
Author(s):  
Eunjeong Lee ◽  
Mikiya Masuda ◽  
Seonjeong Park ◽  
Jongbaek Song
Keyword(s):  
Schubert Variety ◽  
Flag Variety ◽  
Schubert Varieties ◽  
Orbit Closure ◽  
Poincaré Polynomial ◽  
Content Type ◽  
Eulerian Polynomial ◽  
Orbit Closures

The closure of a generic torus orbit in the flag variety G / B G/B of type  A A is known to be a permutohedral variety, and its Poincaré polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincaré polynomial of a generic torus orbit closure in a Schubert variety in  G / B G/B . When the generic torus orbit closure in a Schubert variety is smooth, its Poincaré polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.

Generalized heredity in ℬ-free systems

2021 ◽  
pp. 2140008
Author(s):  
Gerhard Keller
Keyword(s):  
Orbit Closure ◽  
Light Tails ◽  
Free Sets

Let [Formula: see text] be a primitive set, [Formula: see text], [Formula: see text], and denote by [Formula: see text] the orbit closure of [Formula: see text] under the shift. We complement results on heredity of [Formula: see text] from [Dymek et al., [Formula: see text]-free sets and dynamics, Trans. Amer. Math. Soc. 370 (2018) 5425–5489] in two directions: In the proximal case we prove that a certain subshift [Formula: see text], which coincides with [Formula: see text] when [Formula: see text] is taut, is always hereditary. (In particular there is no need for the stronger assumption that the set [Formula: see text] has light tails, as in [Dymek et al., [Formula: see text]-free sets and dynamics, Trans. Amer. Math. Soc. 370 (2018) 5425–5489].) We also generalize the concept of heredity to include the non-proximal (and hence non-hereditary) case by proving that [Formula: see text] is always “hereditary above its unique minimal (Toeplitz) subsystem”. Finally, we characterize this Toeplitz subsystem as being a set [Formula: see text], where [Formula: see text] for a set [Formula: see text] that can be derived from [Formula: see text], and draw some further conclusions from this characterization. Throughout results from [Kasjan et al., Dynamics of [Formula: see text]-free sets: A view through the window, Int. Math. Res. Not. 2019 (2019) 2690–2734] are heavily used.

Rule based Translation Surface for Telugu Nouns

2023 ◽  
Vol 12 (5) ◽  
pp. 1
Author(s):  
Phani Kumar S ◽  
Prasad Rao P
Keyword(s):  
Translation Surface ◽  
Rule Based

Asymptotic Formulae for the Lattice Point Enumerator

1999 ◽  
Vol 51 (2) ◽  
pp. 225-249 ◽  
Author(s):  
U. Betke ◽  
K. Böröczky
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Positive Curvature ◽  
Convex Bodies ◽  
Mixed Volume ◽  
Lattice Points ◽  
Asymptotic Formulae ◽  
General Convex ◽  
Lattice Surface ◽  
Small Deformations

AbstractLet M be a convex body such that the boundary has positive curvature. Then by a well developed theory dating back to Landau and Hlawka for large λ the number of lattice points in λM is given by G(λM) = V(λM) + O(λd−1−ε(d)) for some positive ε(d). Here we give for general convex bodies the weaker estimatewhere SZd (M) denotes the lattice surface area of M. The term SZd is optimal for all convex bodies and o(λd−1) cannot be improved in general. We prove that the same estimate even holds if we allow small deformations of M.Further we deal with families {Pλ} of convex bodies where the only condition is that the inradius tends to infinity. Here we havewhere the convex body K satisfies some simple condition, V(Pλ; K; 1) is some mixed volume and S(Pλ) is the surface area of Pλ.

A Critical Review on Energy Conversion and Environmental Remediation of Photocatalysts with Remodeling Crystal Lattice, Surface, and Interface

ACS Nano ◽  
2019 ◽  
Vol 13 (9) ◽  
pp. 9811-9840 ◽  
Author(s):  
Jinming Luo ◽  
Shuqu Zhang ◽  
Meng Sun ◽  
Lixia Yang ◽  
Shenglian Luo ◽  
...  
Keyword(s):  
Energy Conversion ◽  
Crystal Lattice ◽  
Critical Review ◽  
Environmental Remediation ◽  
Surface And Interface ◽  
Lattice Surface
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