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Covering tori with squares

Robert J McEliece, Herbert Taylor
1973 Journal of combinatorial theory. Series A  
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]

Angel Pardo
2016 arXiv   pre-print
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]

Sunrose T. Shrestha, Jane Wang
2019 arXiv   pre-print
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]

Alastair N. Fletcher, Daniel Stoertz
2021 arXiv   pre-print
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

I. R. Aitchison, J. H. Rubinstein
1999 Bulletin of the London Mathematical Society  
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


1928 Monthly Weather Review  
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 fatcat:rrf4ygbdhbap7esjnopzp653wy

An Application of Hypergeometric Functions to Heat Kernels on Rectangular and Hexagonal Tori and a "Weltkonstante" – Or – How Ramanujan Split Temperatures [article]

Markus Faulhuber
2019 arXiv   pre-print
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  
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

Robert F. Williams
2020 Science China Mathematics  
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  
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

Indumathi Sivakumar, Faculty of Dentistry, SEGi University, Selangor, Malaysia., Rachel Chua Hui Shien, Nur Lyanna Mahfuzah Binti Mohamad Johar, Sham Wern Xuan, Sin Pi Xian, Klinik Pergigian Sultan Ismail Hospital, Johor, Malaysia, Klinik Pergigian Kota Samarahan, Sarawak, Malaysia, Klinik Pergigian Hospital Kuala Lumpur, Federal Territory of Kuala Lumpur, Malaysia, Klinik Pergigian Simpang Lima, Klinik Pergigian Simpang Lima, Selangor, Malaysia
2021 Journal of Oral Research  
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  
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  
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  
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]

Lynn Heller, Franz Pedit
2017 arXiv   pre-print
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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