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Covering tori with squares
1973
Journal of combinatorial theory. Series A
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Another possible question is: "What about packing tori with cubes?" ...
In the next section we will give a very simple construction which covers T2 with [~-'[e-'jl squares from 5$*. By Theorem 1 this shows that Z,? can be covered with ["/k[n/kl] squares from Ykz. ...
doi:10.1016/0097-3165(73)90069-1
fatcat:tq2u4z777vejlh5tgn7a6gurgm
Number of cyclic square-tiled tori
[article]
2016
arXiv
pre-print
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We also give the asymptotic proportion of cyclic square-tiled tori over all square-tiled tori. ...
We study cyclic square-tiled tori in H(0), answering a question by M. Bolognesi (by personal communication to A. Zorich). We give the exact number of cyclic tori tiled by n∈N squares. ...
Introduction In this note we count cyclic square-tiled surfaces in the stratum H(0), the well known moduli space of translation surfaces of genus one (flat tori) with a marked point. ...
arXiv:1506.02826v2
fatcat:53xmcw5byrbzvmkihr6rg6rinu
Statistics of Square-tiled Surfaces: Symmetry and Short Loops
[article]
2019
arXiv
pre-print
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Square-tiled surfaces are a class of translation surfaces that are of particular interest in geometry and dynamics because, as covers of the square torus, they share some of its simplicity and structure ...
In this paper, we study counting problems that result from focusing on properties of the square torus one by one. ...
A square-tiled surface is called reduced if the only genus one square-tiled surface that it covers (branched over a single point) is the torus with only one square. ...
arXiv:1902.08214v2
fatcat:uleps2s7e5byvormmeehfm6o3a
Genus 2 Cantor sets
[article]
2021
arXiv
pre-print
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Choose four square tori, call them T 1 , . . . , T 4 with square core curves γ 1 , . . . , γ 4 , respectively. ...
Recall the following notation from Section 3: • We have square solid tori X 1 0 and X 2 0 with square core curves γ 1 0 and γ 2 0 , respectively. ...
Since the standard defining sequence consists entirely of double tori, g(X) ≤ 2, and hence g(X) = 2. ...
arXiv:2009.12427v2
fatcat:6z4rwv74azfovkq6iy2itzx6aq
Polyhedral Metrics and 3-Manifolds which are Virtual Bundles
1999
Bulletin of the London Mathematical Society
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tori. ...
So the link of each vertex is a tetrahedron with the six edges being shared by four hexagons and two squares. The square edges form an opposite pair of edges in the tetrahedron. ...
doi:10.1112/s0024609398004974
fatcat:ogtejvesdrcunetenygd2gc27q
SOLAR AND SKY RADIATION MEASUREMENTS DURING DECEMBER, 1928
1928
Monthly Weather Review
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At Madison no measurements were obtained during the month, as most of the time the ground was covered with snow.
TaBLeE 1. ...
Dec. 3 (Naval Observa- tory). ‘
COreoo BGHrOD
Dec. 4 (Naval Observa- tory).
Dec. 5 (Naval Observa- tory).
Qeee wow
Dec. 6 (Naval Observs- tory). ...
doi:10.1175/1520-0493(1928)56<514a:sasrmd>2.0.co;2
fatcat:rrf4ygbdhbap7esjnopzp653wy
An Application of Hypergeometric Functions to Heat Kernels on Rectangular and Hexagonal Tori and a "Weltkonstante" – Or – How Ramanujan Split Temperatures
[article]
2019
arXiv
pre-print
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We compute the minimum and the maximum of the temperature on rectangular tori of fixed area by means of Gauss' hypergeometric function _2F_1 and the elliptic modulus. ...
Also, we investigate the temperature distribution of the heat kernel on hexagonal tori and use Ramanujan's corresponding theory of signature 3 to derive analogous results to the rectangular case. ...
However, we do not follow the suggestion to study heat kernels on tori with fixed covering radius, but rather tori of fixed surface area. ...
arXiv:1901.01218v2
fatcat:6ai7zxmmwbeshdn6jcihfufb2m
Page 374 of De Bow's Review : Devoted to the Restoration of the Southern States Vol. 1, Issue 3
[page]
1858
De Bow's Review : Devoted to the Restoration of the Southern States
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In 1815, therefore, the States and Terri- tories covered 759,864 square miles, while in 1858 they cover 8,268,000 square miles, an area four times and one-third larger now than in 18165.
was our true policy ...
1858 we have thirty- two States, covering an area of 1,602,- 000 square miles, six organized Terri- tories, (exclusive of the District of Columbia, ) covering an area of 1,401,- 000 sqare miles. ...
Anosov and expanding attractors
2020
Science China Mathematics
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Some time ago I found a putative counter example to Conjecture 0.2, constructed as the union of two tori: ...
There exists g ′ M , with M being a manifold, with g ′ (shift) equivalent to g, and (thus) having inverse limit conjugate to that of g. It was proved by Wen [4] in a special case. ...
Making an example with two tori Suppose X = T 1 ∪ T 2 with T 1 and T 2 being two tori, g X is an onto immersion and the branch set is B = T 1 ∩ T 2 , which are tangent where they intersect. ...
doi:10.1007/s11425-019-9565-y
fatcat:uiq2oy7bxfeg7klwnh2zl7mv7u
Page 8 of Book News Monthly Vol. 20, Issue 230
[page]
1901
Book News Monthly
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Illustrated, with decorative cover. Square 12mo, 85 cents, et ; postpaid, 95 cents.
The story of two small girls, one a princess, the other a porter’s child. ...
With illus- trations and a decorative cover. Square I2mo, 85 cents, met; postpaid, 95 cents.
_A charming story of a little girl on a plan- tation in one of the Gulf States. ...
Evaluation of oral stereognosis in completely edentulous patients with palatal tori
Evaluación de la estereognosia oral en pacientes completamente edéntulos con toros palatinos
2021
Journal of Oral Research
Evaluación de la estereognosia oral en pacientes completamente edéntulos con toros palatinos
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The corollary is not investigated in the completely edentulous patients with palatal tori. ...
Material and Methods: Thirty-four completely edentulous patients aged 50 to 89 years were allocated to Group 1 (without palatal tori, n=18) and Group 2 (with palatal tori, n=16). ...
Patients with torus palatinus are reported to have questionable satisfaction with complete dentures owing to trauma or ulceration of the mucosa covering the tori, speech difficulties due to limited tongue ...
doi:10.17126/joralres.2021.009
fatcat:df54gr6gb5ferdw2gq3emabl7q
Page 544 of McBride's Magazine Vol. 23, Issue
[page]
1879
McBride's Magazine
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The country around the fac- tory is one immense swamp, level as a floor, thickly covered with bushes and dotted here and there with pine trees, while the winter extends through eight months of the year ...
By the middle of the month the still waters of the swamps and marshes are frozen over and the ground is covered with snow. ...
Page 96 of American Journal of Veterinary Research Vol. 7, Issue 23
[page]
1946
American Journal of Veterinary Research
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One side of this cover slide was marked with a diamond glass cutter with thin lines sub- dividing it into 16 equal squares. ...
In covering the sample, the side containing the squares was placed in contact with the fluid to be ex- amined. ...
Page 392 of Potter's American Monthly Vol. 6, Issue 53
[page]
1876
Potter's American Monthly
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On the north and south sides of this principal room are four forcing- houses for the propa- gation of young plants, each of them 100 by 30 feet, covered with curved roofs of iron and glass. ...
These external galleries | are connected with a grand promenade, formed by the roofs of the rooms on the ground floor, which has a superficial | area of 1,880 square yards. ...
Towards a constrained Willmore conjecture
[article]
2017
arXiv
pre-print
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The horizontal axis measures the rectangular conformal type, starting at the square structure for ξ g,1 on the right and degenerating to the twice covered equatorial 2-sphere at the origin. constructed ...
≤ b ≤ √ 3 and the 2-lobed Delaunay tori in a 3-sphere for b > √ 3 limiting to a twice covered equatorial 2-sphere as b → ∞ (see Figure 2 ). ...
arXiv:1705.03217v1
fatcat:5zimw2vrnbacti43qsqvnro4qm
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