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Page 2764 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
Full and quarter plane complete infinite Latin squares. (English summary) Discrete Math. 159 (1996), no. 1-3, 251-253.  ...  Thus, C is a complete infinite Latin square. A similar result is given for an infinite full plane Latin square D.” 97e:05050 05B15 Chopra, D.  ... 

Infinite Latin Squares: Neighbor Balance and Orthogonality [article]

Anthony B. Evans, Gage N. Martin, Kaethe Minden, M. A. Ollis
2018 arXiv   pre-print
Regarding neighbor balance, we consider natural generalizations of D-complete Latin squares and Vatican squares from the finite to the infinite.  ...  We show that an infinite group G with |G|-many square elements has a strong complete mapping; and, with some possible exceptions, infinite abelian groups have a strong complete mapping.  ...  Acknowledgements This work was partly funded by a Marlboro College Faculty Professional Development Grant and a Marlboro College Town Meeting Scholarship Fund award.  ... 
arXiv:1807.08580v1 fatcat:rh5rwsymhrgndlaoauqr6fdkg4

Infinite Latin Squares: Neighbor Balance and Orthogonality

Anthony B. Evans, Gage N. Martin, Kaethe Minden, M. A. Ollis
2020 Electronic Journal of Combinatorics  
Regarding neighbor balance, we consider natural generalizations of $D$-complete Latin squares and Vatican squares from the finite to the infinite.  ...  We show that an infinite group $G$ with $|G|$-many square elements has a strong complete mapping; and, with some possible exceptions, infinite abelian groups have a strong complete mapping.  ...  Acknowledgements This work was partly funded by a Marlboro College Faculty Professional Development Grant (4th author) and a Marlboro College Town Meeting Scholarship Fund award (2nd author).  ... 
doi:10.37236/8020 fatcat:hoxbczett5b5tcgimydt5i6sza

A 2-Categorical Approach to Composing Quantum Structures

David Reutter, Jamie Vicary, Marc Herbstritt
2017 Conference on Algebra and Coalgebra in Computer Science  
We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously  ...  However, our exposition will be elementary, and we will not assume knowledge of these ideas.  ...  Early versions of these results were presented at WIP 2016 and QIP 2017, and we are grateful to the organizers of these events.  ... 
doi:10.4230/lipics.calco.2017.20 dblp:conf/calco/ReutterV17a fatcat:ft7plzsahfcxffnjhvmhdy2tva

MUBs, Polytopes, and Finite Geometries

Ingemar Bengtsson
2005 AIP Conference Proceedings  
They mesh naturally with finite affine planes of order N, that exist when N = p^k. The existence of MUBs for other values of N is an open question, and the same is true for finite affine planes.  ...  I explore the question whether the existence of complete sets of MUBs is directly related to the existence of finite affine planes.  ...  Acknowledgement: I thank Gunnar Björk and Bengt Nagel for discussions, andÅsa Ericsson and Ninos Poli for many discussions-and of course Andrei Khrennikov for inviting me to visit Småland.  ... 
doi:10.1063/1.1874558 fatcat:b27gblxyhzeo7owpkfkfm7a4p4

Biunitary constructions in quantum information [article]

David J. Reutter, Jamie Vicary
2019 arXiv   pre-print
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described.  ...  Early versions of these results were presented at WIP 2016, QIP 2017, CALCO 2017 and QPL 2017, and we are grateful to the organizers of these events, and to the audience for useful feedback.  ...  Acknowledgements We are grateful to Bruce Bartlett, André Henriques, Scott Morrison, Benjamin Musto and Dominic Verdon for useful discussions.  ... 
arXiv:1609.07775v4 fatcat:amg7kj5tnretfblao5u4fi55ga

Gravity and Light in the Newtonian Universe of Stars

Michael Hoskin
2008 Journal for the History of Astronomy  
Edmond Halley disputed this in print, but mistakenly, and later discussions of such a universe led to 'Olbers's Paradox'.  ...  Descartes's universe was a plenum, completely full of matter, and Newton spent a lot of effort trying to understand how planets might move in accordance with Kepler's laws in such a plenum.  ...  Influenced by the book on the magnet published by William Gilbert in 1600, the Gresham circle -and Robert Hooke in particular -held that the universe, far from being completely full, was nearly empty;  ... 
doi:10.1177/002182860803900206 fatcat:htemub2xtrcybdt5tfo6nbdyei

Relative Performance of Three Mesh-Reduction Methods in Predicting Mode III Crack-Tip Singularity

Faisal M. Mukhtar
2017 Latin American Journal of Solids and Structures  
Consequently, the BEM formulation is not altered in any way, and modifications to both the RBF and MFS are limited to enrichment by the addition of, at most, one singular term and/or the domain-decomposition  ...  The present study assesses the applicability and relative performance of three such mesh-reduction methods, namely the radial basis function (RBF) method, the boundary element method (BEM), and the method  ...  Figure 14 : 14 Figure 14: Plate with two parallel cracks: (a) Full model (b) Quarter model due to symmetry.  ... 
doi:10.1590/1679-78253656 fatcat:qd5uba3mnbfcxjasn64klailte

Master index of volumes 151–160

1997 Discrete Mathematics  
., Full and quarter plane complete infinite latin squares (Note) Ceccherini, P.V., see G. Burosch Cerdeira, J.O. and P. Barcia, Ordered matroids and regular Chen, J., S.P. Kanchi and J.L.  ...  Janssen, All-even latin squares Hamburger, P., see L.W. Beineke Hamidoune, Y.O., AS. Llad6 and 0. Serra, Small cutsets in quasiminimal Cayley graphs Hammer, P.L., see P.C. Fishburn Han, Z.  ... 
doi:10.1016/s0012-365x(97)90002-9 fatcat:jhdpq4lxr5cz5ctggxfuouj6ti

Wallis on Indivisibles [chapter]

Antoni Malet, Marco Panza
2015 Seventeenth-Century Indivisibles Revisited  
Likely, the De Sectionibus Conicis was already completed in 1652, while the Arithmetica infinitorum was begun during the same year, but concluded later.  ...  The present chapter is devoted, first, to discuss in detail the structure and results of Wallis's major and most influential mathematical work, the Arithmetica Infinitorum ([51]).  ...  Let ABC be a quarter of circle of centre A and radius AB ( fig. 7) . Suppose this radius be divided in an infinity of parts by points T.  ... 
doi:10.1007/978-3-319-00131-9_14 fatcat:5g7x54e4y5hofcjb7w2twpafy4

Chapter 6 [chapter]

Ekkehard Kopp
2020 Making up Numbers  
as Latin.  ...  So we can write 1, 250, 000 ('one-and-a-quarter million') as 1.25 × 10 6 , for example.  ...  That said, what David Hume, who so clearly abhorred 'horn angles' (see the end of Chapter 5), might have thought about the infinitely many different orders of infinitesimals now made possible, must remain  ... 
doi:10.11647/obp.0236.06 fatcat:v22whoog6bgzjfevq2dd74g35a

Geometric Methods of the 1500s for Laying Out the Ionic Volute

Denise Andrey, Mirko Galli
2004 Nexus Network journal  
Authors Denise Andrey and Mirko Galli compare and contrast three methods by Sebastiano Serlio, Giuseppe Salviati and by Philandrier for laying out the Ionic volute.  ...  In addition to studies of its proportions, research focused on the search for a sure and elegant method for laying out the volute.  ...  Salviati's volute is constituted of twelve quarter-circles, the centers of which are situated inside the eye, along the diagonal of a square that is inscribed both within the and within a larger square  ... 
doi:10.1007/s00004-004-0017-4 fatcat:mv5ifjunjbe7xeiwrfc7yhz3mq

THE PHILOSOPHICAL FOUNDATIONS OF MATHEMATICS. I. HISTORICAL INTRODUCTION

Paul Carus
1903 The Monist  
investigated ; they require a special name, and therefore these manifoldnesses in which the square of the line-element may be expressed as the sum of the squares of complete differentials I will  ...  by " In the extension of space-construction to the infinitely great, we must distin guish between unboundedness and infinite extent ; the former belongs to the extent-relations, the latter to  ... 
fatcat:6w536pzgpfbpxmppzbxx4btotu

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity

Elena Atroshchenko, Stéphane P. A. Bordas
2015 Proceedings of the Royal Society A  
Introduction This paper presents both a complete derivation of the fundamental solutions arising in plane Cosserat elasticity and a demonstration of their use within a boundary element framework based  ...  The plane strain state is described by two in-plane displacements u 1 , u 2 and one out-of-plane microrotation φ 3 .  ... 
doi:10.1098/rspa.2015.0216 pmid:26345089 pmcid:PMC4528668 fatcat:e5fxe34iavcadenstrjqoqkurq

Notes

1904 Bulletin of the American Mathematical Society  
OSGOOD : Calculus (second course) ; f Infinite series and products ; and either f Galois's theory of equations, or f Riemann's theory of functions. -By Professor M.  ...  GMEINER, of the German University of Prague, and K. ZINDLER, of the University of Innsbruck, have been promoted to full professorships. PROFESSOR H.  ... 
doi:10.1090/s0002-9904-1904-01145-3 fatcat:37ktgppxv5hc7babcord5endau
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