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Diagonally cyclic equitable rectangles

Anthony B. Evans, David Fear, Rebecca J. Stones
2014 Designs, Codes and Cryptography  
We give a constructive proof of necessary and sufficient conditions for the existence of a diagonally cyclic equitable (r, c; v)-rectangle.  ...  We call L diagonally cyclic if l (i+1)( j+1) = l i j + 1, where the rows are indexed by Z r and columns indexed by Z c .  ...  Then we call L diagonally cyclic. We will be interested in the case of diagonally cyclic equitable (r, c; v)-rectangles, or (r, c; v)-DCERs for short.  ... 
doi:10.1007/s10623-014-9977-x fatcat:hpmlhy57yzcsrodlo5ghvuuhcy

Generalized Latin rectangles I: Construction and decomposition

L.D. Andersen, A.J.W. Hilton
1980 Discrete Mathematics  
We exploit the close correspondence between (p, q, x)-latin rectangles and equitable edge-colourings of certain graphs.  ...  This paper contains results on existence and various forms of decomposition of such rectangles. In a sequel paper embedding is considered.  ...  Example 1 shows a cyclic exac: generalized latin rectangle and square, respectively, the first bemg with repetition, the second without. Example 1.  ... 
doi:10.1016/0012-365x(80)90030-8 fatcat:ypcj3e7kznbfjapfswsynpon6i

K-plex 2-Erasure Codes and Blackburn Partial Latin Squares

Rebecca J. Stones
2020 IEEE Transactions on Information Theory  
It may also be interesting to consider weakening the "partial Latin square" property, and replace it with the "equitable rectangle" property (where we allow repeated symbols in rows and columns, but ensure  ...  If any cell (i, j) is good in a diagonally cyclic k-plex, we construct a diagonally cyclic strong (k+1)-plex by defining l ij = 0, and further defining l (i+t)(j+t) = t for all t ∈ Z n , i.e., cyclically  ... 
doi:10.1109/tit.2020.2967758 fatcat:raeu37nn3jfx3fosbvkqflwetu

Compact localized states and flat bands from local symmetry partitioning

M. Röntgen, C. V. Morfonios, P. Schmelcher
2018 Physical review B  
The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states.  ...  This permutation S : {1, . . . , 10} → {1, . . . 10} is commonly written in the socalled cyclic notation S = (2)(5)(7)(8)(9)(10)(1, 3)(4, 6).  ...  Figure 6 . 6 (a1) Unit cell (indicated by dotted rectangle) of a periodic setup, with a local symmetry under the permutation S: 1 ↔ 3, 2 ↔ 4 leading to CLSs at two energies E1, E2, and (a2) corresponding  ... 
doi:10.1103/physrevb.97.035161 fatcat:5wuq4hpm5bcjzgmfcyvj3qo6f4

MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES), vol. 1 / 2018

Linfan Mao
2018 Figshare  
Suppose that [M D ] has exactly one entry 1 in each odd diagonal lines and all the diagonal entries are zero in the even diagonal lines including the main diagonal.  ...  Then [M D ] has exactly one entry one in each diagonal line except the main diagonal line.  ... 
doi:10.6084/m9.figshare.7076639 fatcat:st2yba5vtrbybprfygfwmt2oji

INTERNATIONAL JOURNAL OF MATHEMATICAL COMBINATORICS, vol. 1 / 2018

Linfan Mao
2018 Figshare  
Suppose that [M D ] has exactly one entry 1 in each odd diagonal lines and all the diagonal entries are zero in the even diagonal lines including the main diagonal.  ...  Then [M D ] has exactly one entry one in each diagonal line except the main diagonal line.  ... 
doi:10.6084/m9.figshare.7076618.v1 fatcat:eitikmxxozhqvdc7wney2pll74

Algebraic framework for determining laminar pattern bifurcations by lateral-inhibition in 2D and 3D bilayer geometries [article]

Joshua W. Moore, Trevor C. Dale, Thomas E. Woolley
2021 arXiv   pre-print
(a) Membrane bound Delta ligands (purple rectangles) on a signal sending cell bind to membrane bound Notch receptors (green rectangles) on a receiving cell.  ...  Let G be an undirected, cyclic, connected graph with equitable partitions PL and PB , such that the reduced graphs GL and GB are bipartite, where GL contains the set of vertices representing luminal cells  ... 
arXiv:2104.12142v2 fatcat:wifdcmnxqndora7t6eefsnzan4

XXI. A freehand graphic way of determining stream lines and equipotentials

L.F. Richardson
1908 The London Edinburgh and Dublin Philosophical Magazine and Journal of Science  
)otentials. 269 sheet of tracing-paper, and drawing the diagonals of the chequers formed by the intersecting contours.  ...  By symmetry V wiil be equal to ~ along the diagonals. And again by symmetry, the lines joining mid-points of opposite sides will be normal to the contours of V.  ... 
doi:10.1080/14786440809463764 fatcat:a5owfakxnfcfbg23m7sdopeh7a

The Fifth Epoch: Socio-Economic Approach to Sustainable Capitalism

David M. Boje, Yue Cai Hillon
2017 Markets, Globalization & Development Review: The Official Journal of the International Society of Markets and Development  
Diagonals trace the disjunctions or contradictory relationships.  ...  Wegner (2009) expanded that thought by overlaying the Greimas semiotic rectangle from top to bottom with Lacan's symbolic, imaginary, and real.  ... 
doi:10.23860/mgdr-2017-02-01-02 fatcat:leaxclsosnc55knhbz2pxizvpq

Packing and Covering in Combinatorics

R. A. Cuninghame-Green, A. Schrijver
1980 Journal of the Operational Research Society  
Colour the squares of the box (rectangle) with a 1 colours in a cyclic manner: let the colours be O, ...  ...  Now B' E PSD and therefore all diagonal elements of B' are positive. Let D be the diagonal matrix having diagonal equal to the diagonal of B. Define B' := D-~B'D-~ -I.  ... 
doi:10.2307/2581088 fatcat:szdtpgrkzrfvvehhovqz3r6vxq

Subject Index Volumes 1–200

2001 Discrete Mathematics  
, 4067 chromatic number, 4446 equitable colouring, 4446 conjecture, 4446 equitable edge colouring, 439, 1033, 4067 n-colouring, 439 equitably coloured, 4446 equitiling of the plane, 3280 equivalence  ...  group, 599, 2003, 2502, 5602 map, 3214, 3230 partition, 2715, 4127 problem, 5681 subgroup, 5409 Frobenius, G, 2206 Frolík, 3494 Frolík, Z, 3471, 3476, 3479, 3485, 3490, 3492, 3493, 3504 front diagonal  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

A comparison of blindpulling and blindwalking as measures of perceived absolute distance

John W. Philbeck, Adam J. Woods, Carly Kontra, Petra Zdenkova
2010 Behavior Research Methods  
As with blindwalking, this response requires integration of cyclical, bilateral limb movements over time.  ...  In dark trials, the stimulus appeared as a glowing rectangle at eye level. When ready, the experimenter signaled the participant to raise the blindfold.  ... 
doi:10.3758/brm.42.1.148 pmid:20160295 pmcid:PMC2883722 fatcat:izzemsfwibdw7i6tfv6td5oauy

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
Falcón, Colouring games based on autotopisms of Latin hyper-rectangles, preprint.[3] R. M.  ...  In this talk, we consider orthogonal matrices whose diagonal entries are zero and offdiagonal entries are non-zero.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby

Is spring starting earlier?

R. Thompson, R.M. Clark
2008 The Holocene  
Amplitude of annual carbon dioxide cycle It is important when studying cyclic behaviour to consider both phase and amplitude.  ...  (Figure 1 1 Extra rectangle that gets added, or subtracted, to the triangle beta according to the duration of chilling. Area = λ times γ i .)  ... 
doi:10.1177/0959683607085599 fatcat:pw477tyczzelzahjkcmj4bzrbm

Calibration of the continuous surface cap model for concrete

Hua Jiang, Jidong Zhao
2015 Finite elements in analysis and design  
Strain softening corresponds to a post-peak decrease in strength and modulus reduction denotes a reduction of elastic modulus in cyclic loading case.  ...  Note: a linear fit is used for other size of aggregate, the fit equitation is G F0 ¼0.021þ 5.357 Â 10 À 4 d max. From Eq. (29), B þ can be obtained by Fig. 11 .  ...  Input parameter card for the MAT 145 Note: Parameters marked in rectangle are important parameters calibrated in this paper. Parameters marked in ellipse are ignored parameters with default value.  ... 
doi:10.1016/j.finel.2014.12.002 fatcat:adv57uasabcfxprfrwn7zboxym
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