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Packing Rectangles into the Unit Square
Geometriae Dedicata, 2000\textit{L. Moser} and \textit{J. W. Moon} [Colloq. Math. 17, 103-110 (1967; Zbl 0152.39502)] proved that every sequence of squares whose total area is not more than 1/2 can be packed (using isometries) into a unit square. Now Januszewski generalizes this to: a sequence of rectangles of side length at most 1 and total area at most 1/2 can be packed into
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On the Bit Complexity of Sum-of-Squares Proofs
International Colloquium on Automata, Languages and Programming, 2017It has often been claimed in recent papers that one can find a degree d Sum-of-Squares proof if one exists via the Ellipsoid algorithm. In a recent paper, Ryan O'Donnell notes this widely quoted claim is not necessarily true.
P. Raghavendra, Benjamin Weitz
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Discrete unit square cover problem
Discrete Mathematics, Algorithms and Applications, 2018In this paper, we consider the discrete unit square cover (DUSC) problem as follows: given a set [Formula: see text] of [Formula: see text] points and a set [Formula: see text] of [Formula: see text] axis-aligned unit squares in [Formula: see text], the objective is (i) to check whether the union of the squares in [Formula: see text] covers all the ...
Manjanna Basappa, Gautam K. Das
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BIO-INSPIRED auxetic mechanical metamaterials evolved from rotating squares unit
Mechanics of materials (Print), 2022A. Sorrentino +3 more
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Packing of non-blocking squares into the unit square
Colloquium MathematicumLet \(S_n\) be a square, for \(n = 1, 2,\dots\), and let \(I\) be a square of sidelength 1. We say that the squares \(S_1\), \(S_2\), \(\dots\) can be \textit{packed} into \(I\) if it is possible to apply translations and rotations to the sets \(S_n\) so that the resulting translated and rotated squares are contained in \(I\) and have mutually disjoint
Januszewski, Janusz, Zielonka, Łukasz
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Youden Square with Split Units
2013In this chapter we present the most important problems connected with the design of experiments using Youden squares with split units. In fact we consider two types of designs. The first is connected with different arrangements of subplot treatments on the units of Youden squares.
Stanisław Franciszek Mejza +1 more
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Gated Dual Attention Unit Neural Networks for Remaining Useful Life Prediction of Rolling Bearings
IEEE Transactions on Industrial Informatics, 2021Yi Qin +3 more
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Critical care management of chimeric antigen receptor T‐cell therapy recipients
Ca-A Cancer Journal for Clinicians, 2022Alexander Shimabukuro-Vornhagen +2 more
exaly
Visualising Conditional Probabilities—Three Perspectives on Unit Squares and Tree Diagrams
, 2018Katharina Böcherer-Linder +2 more
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