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Journal articles on the topic 'Rectangle'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Kwon, Bo-Hyun, and Jung Hoon Lee. "Properties of Casson–Gordon’s rectangle condition." Journal of Knot Theory and Its Ramifications 29, no. 12 (2020): 2050083. http://dx.doi.org/10.1142/s0218216520500832.

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For a Heegaard splitting of a [Formula: see text]-manifold, Casson–Gordon’s rectangle condition, simply rectangle condition, is a condition on its Heegaard diagram that guarantees the strong irreducibility of the splitting; it requires nine types of rectangles for every combination of two pairs of pants from opposite sides. The rectangle condition is also applied to bridge decompositions of knots. We give examples of [Formula: see text]-bridge decompositions of knots admitting a diagram with eight types of rectangles, which are not strongly irreducible. This says that the rectangle condition i

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2

Huang, Eric, and Richard Korf. "Optimal Rectangle Packing on Non-Square Benchmarks." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (2010): 83–88. http://dx.doi.org/10.1609/aaai.v24i1.7538.

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The rectangle packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. We propose two new benchmarks, one where the orientation of the rectangles is fixed and one where it is free, that include rectangles of various aspect ratios. The new benchmarks avoid certain properties of easy instances, which we identify as instances where rectangles have dimensions in common or where a few rectangles occupy most of the area. Our benchmarks are much more difficult for the previous state-of-the-art solver, requiring orders of m

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3

Ellard, Richard, and Des MacHale. "Packing a rectangle with m x (m + 1) rectangles." Mathematical Gazette 100, no. 547 (2016): 34–47. http://dx.doi.org/10.1017/mag.2016.6.

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We consider the packing of rectangles of dimension m x (m + 1) — where m is a natural number — into a larger rectangle. More specifically, we consider the following problem: What is the smallest area of a rectangle into which rectangles of dimensions 1 x 2, 2 x 3, 3 x 4,…, n x (n + 1) will fit without overlap? Unlike the corresponding problem for squares of areas 12, 22, 32, …, n2(see [1]), where there is no known non-trivial example of an exact fit into a rectangle, in many cases we can achieve an exact fit for our set of m x (m + 1) rectangles. Intuitively, this is because each m x (m + 1) r

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4

NAGAMOCHI, HIROSHI. "PACKING SOFT RECTANGLES." International Journal of Foundations of Computer Science 17, no. 05 (2006): 1165–78. http://dx.doi.org/10.1142/s0129054106004327.

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Let R be a rectangle with given area a(R), height h(R) and width w(R), and r1, r2, …, rn be n soft rectangles, where we mean by a soft rectangle a rectangle r whose area a(r) is prescribed but whose aspect ratio ρ(r) is allowed to be changed. In this paper, we consider the problem of packing n soft rectangles r1, r2, …, rn into R. We prove that, if a(R) ≥ Σ1≤i≤n a(ri) + 0.10103amax and amax ≤ 3( min {h(R), w(R)})2 hold for a amax = max 1≤i≤n a(ri), then these n soft rectangles can be packed inside R so that the apect ratio of each rectangle ri is at most 3.

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5

Savic, Aleksandar, Jozef Kratica, and Vladimir Filipovic. "A new nonlinear model for the two-dimensional rectangle packing problem." Publications de l'Institut Math?matique (Belgrade) 93, no. 107 (2013): 95–107. http://dx.doi.org/10.2298/pim1307095s.

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This paper deals with the rectangle packing problem, of filling a big rectangle with smaller rectangles, while the rectangle dimensions are real numbers. A new nonlinear programming formulation is presented and the validity of the formulation is proved. In addition, two cases of the problem are presented, with and without rotation of smaller rectangles by 90?. The mixed integer piecewise linear formulation derived from the model is given, but with a simple form of the objective function.

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6

KIM, SANG-SUB, SANG WON BAE, and HEE-KAP AHN. "COVERING A POINT SET BY TWO DISJOINT RECTANGLES." International Journal of Computational Geometry & Applications 21, no. 03 (2011): 313–30. http://dx.doi.org/10.1142/s0218195911003676.

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Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are allowed to be reoriented freely while restricting them to be parallel to each other, and (2) one rectangle is restricted to be axis-parallel but the other rectangle is allowed to be reoriented freely. For both of the problems, we present O(n2 log n)-time algorithms using O(n) space.

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7

S., Vidhyalakshmi M.A. Gopalan S. Aarthy Thangam and J. Srilekha. "Special characterizations of rectangles in connection with trimorphic numbers." Annals of Communications in Mathematics 2, no. 1 (2019): 17–23. https://doi.org/10.5281/zenodo.10041575.

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This paper consists of two sections A and B. Section A exhibits rectangles, where, in each rectangle, the area added with its semi-perimeter is a Trimorphic number. Section B presents rectangles, where, in each rectangle, the area minus its semi-perimeter is a Trimorphic number

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8

BIRD, RICHARD S. "Building a consensus: A rectangle covering problem." Journal of Functional Programming 21, no. 2 (2011): 119–28. http://dx.doi.org/10.1017/s0956796810000316.

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The other day, over a very pleasant lunch in the restaurant of Oxford's recently renovated Ashmolean Museum, Oege de Moor gave me a problem about rectangles. The problem is explained more fully later, but roughly speaking one is given a finite set of rectangles RS and a rectangle R completely covered by RS. The task is to construct a single rectangle covering R among the elements of a larger set of rectangles associated with RS, called the saturation of RS. The saturation of RS is the closure of RS under so-called consensus operations, a term coined in (Quine, 1959), in which two rectangles ar

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9

Kaleeswari, K., J. Kannan, A. Deepshika, and M. Mahalakshmi. "Computations of Exponential Diophantine Rectangles over Gnomonic Numbers using Python." Indian Journal Of Science And Technology 17, no. 42 (2024): 4449–53. http://dx.doi.org/10.17485/ijst/v17i42.3491.

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Objective: The main objective of this paper is to define and collect a new type of rectangle called the Exponential Diophantine Rectangle over Gnomonic numbers (figurate numbers that take the form 𝑛2 − (𝑛 − 1)2, 𝑛 ∈ 𝑁). Methods: It is done by solving the two exponential Diophantine equations using Mihailescu’s theorem, binomial expansion, and the basic theory of congruences. Findings: Here, it is proven that there are only four exponential Diophantine rectangles over Gnomonic numbers. Finally, it is validated using Python programming for a specific limit. Novelty: The concept of solving an exp

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10

Huang, Eric, and Richard Korf. "Optimal Packing of High-Precision Rectangles." Proceedings of the International Symposium on Combinatorial Search 2, no. 1 (2021): 195–96. http://dx.doi.org/10.1609/socs.v2i1.18211.

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The rectangle-packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, a problem for the previous state-of-the-art, which enumerates all locations for placing rectangles. We instead limit these locations and bounding box dimensions to the set of subset sums of the rectangles' dimensions, allowing us to test 4,500 times fewer bounding boxes and solve N=9 over two orders of magnitude faster. Finally, on the open problem of the feasibility of packi

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11

Zavagno, D. "Some New Effects: Phenomenal Glare, Luminous ‘Mist’ and Dark ‘Smoke’." Perception 26, no. 1_suppl (1997): 58. http://dx.doi.org/10.1068/v970247.

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The impression of glare is caused by a very intense light source. However, here I show that this impression can also be generated with normal light intensities. The strength of the effect depends on the number of elements used to produce it. The elements are 2 cm × 5 cm rectangles. A single horizontal achromatic rectangle is first used on a homogeneous white or black background. From left to right, the brightness of the rectangle varies smoothly from black to white. The left part of the rectangle appears to progressively bend toward the background when the background is black, while the rectan

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12

K, Kaleeswari, Kannan J, Deepshika A, and Mahalakshmi M. "Computations of Exponential Diophantine Rectangles over Gnomonic Numbers using Python." Indian Journal of Science and Technology 17, no. 42 (2024): 4449–53. https://doi.org/10.17485/IJST/v17i42.3491.

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Abstract <strong>Objective:</strong> The main objective of this paper is to define and collect a new type of rectangle called the Exponential Diophantine Rectangle over Gnomonic numbers (figurate numbers that take the form 𝑛2 − (𝑛 − 1)2, 𝑛 ∈ 𝑁). <strong>Methods:</strong> It is done by solving the two exponential Diophantine equations using Mihailescu’s theorem, binomial expansion, and the basic theory of congruences. <strong>Findings:</strong> Here, it is proven that there are only four exponential Diophantine rectangles over Gnomonic numbers. Fi

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13

Alon, Noga, and Daniel J. Kleitman. "Partitioning a rectangle into small perimeter rectangles." Discrete Mathematics 103, no. 2 (1992): 111–19. http://dx.doi.org/10.1016/0012-365x(92)90261-d.

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14

Joós, Antal. "On packing of rectangles in a rectangle." Discrete Mathematics 341, no. 9 (2018): 2544–52. http://dx.doi.org/10.1016/j.disc.2018.06.007.

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15

White, Peter A. "Visual Impressions of Interactions between Objects When the Causal Object Does Not Move." Perception 34, no. 4 (2005): 491–500. http://dx.doi.org/10.1068/p3263.

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Stimuli were presented that consisted of a stationary row of black-bordered white rectangles. As observers watched, each rectangle in turn from left to right changed from white to black. The final rectangle did not change colour but moved off from left to right. The sequential colour change suggested motion from left to right, and observers reliably reported a visual impression that this illusory motion kicked or bumped the last rectangle, thereby making it move. The impression was stronger when the sequential colour change was faster, but was not significantly affected by the number of the re

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16

Jia, Jie, Yong Jun Yang, Yi Ming Hou, Xiang Yang Zhang, and He Huang. "Adaboost Classification-Based Object Tracking Method for Sequence Images." Applied Mechanics and Materials 44-47 (December 2010): 3902–6. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3902.

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An object tracking framework based on adaboost and Mean-Shift for image sequence was proposed in the manuscript. The object rectangle and scene rectangle in the initial image of the sequence were drawn and then, labeled the pixel data in the two rectangles with 1 and 0. Trained the adaboost classifier by the pixel data and the corresponding labels. The obtained classifier was improved to be a 5 class classifier and employed to classify the data in the same scene region of next image. The confidence map including 5 values was got. The Mean-Shift algorithm is performed in the confidence map area

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17

CHEN, DUANBING, and WENQI HUANG. "A NEW HEURISTIC ALGORITHM FOR CONSTRAINED RECTANGLE-PACKING PROBLEM." Asia-Pacific Journal of Operational Research 24, no. 04 (2007): 463–78. http://dx.doi.org/10.1142/s0217595907001334.

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The constrained rectangle-packing problem is the problem of packing a subset of rectangles into a larger rectangular container, with the objective of maximizing the layout value. It has many industrial applications such as shipping, wood and glass cutting, etc. Many algorithms have been proposed to solve it, for example, simulated annealing, genetic algorithm and other heuristic algorithms. In this paper a new heuristic algorithm is proposed based on two strategies: the rectangle selecting strategy and the rectangle packing strategy. We have applied the algorithm to 21 smaller, 630 larger and

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18

Snay, R. A., H. C. Neugebauer, and W. H. Prescott. "Horizontal deformation associated with the Loma Prieta earthquake." Bulletin of the Seismological Society of America 81, no. 5 (1991): 1647–59. http://dx.doi.org/10.1785/bssa0810051647.

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Abstract Co-seismic horizontal displacements for the 1989 Loma Prieta earthquake were derived from preseismic triangulation/trilateration observations and post-seismic GPS observations. As part of this process, the empirical model entitled TDP-H91 was applied to “correct” the preseismic measurements for the crustal motion that occurred during the seven decades spanned by these data. These newly derived displacements were combined with previously documented geodetic results to generate a dislocation model for the earthquake. Our preferred model consists of a vertically segmented rupture surface

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19

HÄGGKVIST, ROLAND, and ANDERS JOHANSSON. "Orthogonal Latin Rectangles." Combinatorics, Probability and Computing 17, no. 4 (2008): 519–36. http://dx.doi.org/10.1017/s0963548307008590.

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We use a greedy probabilistic method to prove that, for every ε > 0, every m × n Latin rectangle on n symbols has an orthogonal mate, where m = (1 − ε)n. That is, we show the existence of a second Latin rectangle such that no pair of the mn cells receives the same pair of symbols in the two rectangles.

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20

Zaidi, Abdelhamid. "Mathematical Methods for IoT-Based Annotating Object Datasets with Bounding Boxes." Mathematical Problems in Engineering 2022 (August 23, 2022): 1–16. http://dx.doi.org/10.1155/2022/3001939.

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Object datasets used in the construction of object detectors are typically annotated with horizontal or oriented bounding rectangles for IoT-based. The optimality of an annotation is obtained by fulfilling two conditions: (i) the rectangle covers the whole object and (ii) the area of the rectangle is minimal. Building a large-scale object dataset requires annotators with equal manual dexterity to carry out this tedious work. When an object is horizontal for IoT-based, it is easy for the annotator to reach the optimal bounding box within a reasonable time. However, if the object is oriented, th

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21

Erb, Christopher D., Jeff Moher, Joo-Hyun Song, and David M. Sobel. "Numerical cognition in action: Reaching behavior reveals numerical distance effects in 5- to 6-year-olds." Journal of Numerical Cognition 4, no. 2 (2018): 286–96. http://dx.doi.org/10.5964/jnc.v4i2.122.

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This study investigates how children’s numerical cognition is reflected in their unfolding actions. Five- and 6-year-olds (N = 34) completed a numerical comparison task by reaching to touch one of three rectangles arranged horizontally on a digital display. A number from 1 to 9 appeared in the center rectangle on each trial. Participants were instructed to touch the left rectangle for numbers 1-4, the center rectangle for 5, and the right rectangle for 6-9. Reach trajectories were more curved toward the center rectangle for numbers closer to 5 (e.g., 4) than numbers further from 5 (e.g., 1). T

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22

Kumar, Vinod, and Krishnendra Shekhawat. "On the characterization of rectangular duals." Notes on Number Theory and Discrete Mathematics 30, no. 1 (2024): 141–49. http://dx.doi.org/10.7546/nntdm.2024.30.1.141-149.

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A rectangular partition is a partition of a rectangle into a finite number of rectangles. A rectangular partition is generic if no four of its rectangles meet at the same point. A plane graph G is called a rectangularly dualizable graph if G can be represented as a rectangular partition such that each vertex is represented by a rectangle in the partition and each edge is represented by a common boundary segment shared by the corresponding rectangles. Then the rectangular partition is called a rectangular dual of the RDG. In this paper, we have found a minor error in a characterization for rect

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23

Abo-Alsabeh, Rewayda Razaq, Hajem Ati Daham, and Abdellah Salhi. "On the maximum empty hyper-rectangle problem." Journal of Algorithms & Computational Technology 17 (January 2023): 174830262211511. http://dx.doi.org/10.1177/17483026221151197.

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Given a rectangle [Formula: see text] containing points, we consider the problem of detecting the largest rectangle that is totally contained in [Formula: see text] and does not include any of the points. In other words, we want to find the biggest hole in the dataset that can contain the biggest possible rectangle. A new algorithm for dealing with this problem is, therefore, suggested. Existing algorithms are exact but cannot deal efficiently with problems in high dimensions and large instances. In fact, only computing maximum empty rectangles in a set of points in [Formula: see text] has bee

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Zhumabaev, M. J., and A. B. Shyrakbaev. "CYLINDRICAL SHELL WITH FILLER." Bulletin of Dulaty University 14, no. 2 (2024): 268–74. http://dx.doi.org/10.55956/vbne7749.

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In the article we will consider cylindrical shells, their definition and properties of cylindrical shells, as well as examples of their application. We will also consider methods for calculating cylindrical shells. A cylindrical shell is a geometric body formed by turning a rectangle around one of its sides. The result is a cylinder whose bases are two parallel and equal rectangles, and the side surface is a surface formed by rotating the rectangle around one of its sides. Cylindrical shells have two main elements – the base and the side surface. The bases of the cylindrical shell are parallel

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STEWART, ROBERT, and HONG ZHANG. "A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE." Bulletin of the Australian Mathematical Society 87, no. 1 (2012): 115–19. http://dx.doi.org/10.1017/s0004972712000421.

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AbstractGiven a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided.

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26

Ren, Hong E., Mian Liu, and Meng Zhu. "Recognition Analysis of Wood Flour Mesh Number Based on External Rectangle Fitting Algorithm." Applied Mechanics and Materials 496-500 (January 2014): 1995–98. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.1995.

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To overcome disadvantages of traditional detection methods of wood flour mesh number, a mesh number recognition algorithm based on external rectangle fitting and morphological characteristics has been studied. It makes use of minimum external rectangle with the boundary points obtained by the preprocessing of microscopic images. The external rectangles length is calculated when the area is the smallest. The experimental results demonstrate that the proposed algorithm has a good fitting accuracy and meets producing demands.

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Recuero, A., M. Álvarez, and O. Río. "Realización de un grafo en recintos rectangulares sobre una planta definida." Informes de la Construcción 47, no. 437 (1995): 63–85. http://dx.doi.org/10.3989/ic.1995.v47.i437.1074.

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28

Wilson, Patricia S., and Verna M. Adams. "A Dynamic Way to Teach Angle and Angle Measure." Arithmetic Teacher 39, no. 5 (1992): 6–13. http://dx.doi.org/10.5951/at.39.5.0006.

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Huang, Eric, and Richard Korf. "Optimal Packing of High-Precision Rectangles." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (2011): 42–47. http://dx.doi.org/10.1609/aaai.v25i1.7814.

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The rectangle-packing problem consists of ﬁnding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, challenging the previous state-of-the-art, which enumerates all locations for placing rectangles, as well as all bounding box widths and heights up to the optimal box. We instead limit the rectangles’ coordinates and bounding box dimensions to the set of subset sums of the rectangles’ dimensions. We also dynamically prune values by learning from infeasible subtrees and constra

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Yee, Wee L. "Three-Dimensional Versus Rectangular Sticky Yellow Traps for Western Cherry Fruit Fly (Diptera: Tephritidae)." Journal of Economic Entomology 112, no. 4 (2019): 1780–88. http://dx.doi.org/10.1093/jee/toz092.

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Abstract The most effective traps tested against western cherry fruit fly, Rhagoletis indifferens Curran, have been the Yellow Sticky Strip (YSS) rectangle made of styrene and the three-dimensional yellow Rebell cross made of polypropylene. However, three-dimensional YSS styrene traps have never been tested against this or any other fruit fly. The main objectives of this study were to determine the efficacies of 1) YSS cross, Rebell cross, YSS cylinder, and YSS rectangle traps, 2) Rebell cross versus Rebell rectangle traps, and 3) YSS tent versus YSS rectangle traps for R. indifferens. For 1),

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31

Ching-yi, Wang. "Does Personality Type Affect People Preference for the Golden Ratio? An Mbti Personality Approach." International Journal of Case Studies 6, no. 1 (2017): 92–104. https://doi.org/10.5281/zenodo.3534697.

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This study investigates whether personality type affects one’s ratio preference by classifying people into different personality types based on the MBTI test from developmental psychology. 749 subjects were initially surveyed in this study. Of these subjects, 656 (270 designers and 386 novices) with a single personality type participated in an additional survey. 15 rectangle ratios were tested, including horizontal and vertical samples. Subjects were asked to evaluate their preferences for each rectangle using a Likert scale ranging from 1 to 5. The results were concluded that both perso

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Richter, David. "Some notes on generic rectangulations." Contributions to Discrete Mathematics 17, no. 2 (2022): 41–66. http://dx.doi.org/10.55016/ojs/cdm.v17i2.72522.

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A rectangulation is a subdivision of a rectangle into rectangles. A generic rectangulation is a rectangulation that has no crossing segments. We explain several observations and pose some questions about generic rectangulations. In particular, we show how one may "centrally invert" a generic rectangulation about any given rectangle, analogous to reflection across a circle in classical geometry. We also explore 3-dimensional orthogonal polytopes related to "marked" rectangulations and drawings of planar maps. These observations arise from viewing a generic rectangulation as topologically equiva

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Oh, Eunjin, and Hee-Kap Ahn. "Finding pairwise intersections of rectangles in a query rectangle." Computational Geometry 85 (December 2019): 101576. http://dx.doi.org/10.1016/j.comgeo.2019.101576.

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DINITZ, YEFIM, MATTHEW J. KATZ, and ROI KRAKOVSKI. "GUARDING RECTANGULAR PARTITIONS." International Journal of Computational Geometry & Applications 19, no. 06 (2009): 579–94. http://dx.doi.org/10.1142/s0218195909003131.

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A rectangular partition is a partition of a rectangle into non-overlapping rectangles, such that no four rectangles meet at a common point. A vertex guard is a guard located at a vertex of the partition (i.e., at a corner of a rectangle); it guards the rectangles that meet at this vertex. An edge guard is a guard that patrols along an edge of the partition, and is thus equivalent to two adjacent vertex guards. We consider the problem of finding a minimum-cardinality guarding set for the rectangles of the partition. For vertex guards, we prove that guarding a given subset of the rectangles is N

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Huang, E., and R. E. Korf. "Optimal Rectangle Packing: An Absolute Placement Approach." Journal of Artificial Intelligence Research 46 (January 23, 2013): 47–87. http://dx.doi.org/10.1613/jair.3735.

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We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We then transform the problem into a perfect-packing problem with no empty space by adding additional rectangles. To determine the y-coordinates, we branch on the different rectangles that can be placed in each empty position. Our packer allows us to extend the known solutions for a consecutive-square benchmark from 27 to 32 squares. We also introduce three ne

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Li, Ziqiang, Xianfeng Wang, Jiyang Tan, and Yishou Wang. "A Quasiphysical and Dynamic Adjustment Approach for Packing the Orthogonal Unequal Rectangles in a Circle with a Mass Balance: Satellite Payload Packing." Mathematical Problems in Engineering 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/657170.

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Packing orthogonal unequal rectangles in a circle with a mass balance (BCOURP) is a typical combinational optimization problem with the NP-hard nature. This paper proposes an effective quasiphysical and dynamic adjustment approach (QPDAA). Two embedded degree functions between two orthogonal rectangles and between an orthogonal rectangle and the container are defined, respectively, and the extruded potential energy function and extruded resultant force formula are constructed based on them. By an elimination of the extruded resultant force, the dynamic rectangle adjustment, and an iteration of

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Sari, Siska Nurmala. "HUBUNGAN ANTARA HIMPUNAN KUBIK ASIKLIK DENGAN RECTANGLE." Jurnal Matematika UNAND 3, no. 1 (2014): 53. http://dx.doi.org/10.25077/jmu.3.1.53-57.2014.

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Dalam artikel ini akan dipelajari hubungan antara himpunan kubik asiklik dengan rectangle. Diberikan suatu kubus dasar Q yang merupakan suatu hasil kaliberhingga dari interval-interval dasar I = [l, l +1] atau I = [l, l] untuk suatu l ∈ Z. suatuhimpunan kubik X adalah gabungan berhingga dari kubus-kubus dasar Q. Himpunankubik dengan bentuk X = [k 1 , l 1 ] × [k 2 , l 2] × · · · × [kn , ln] ⊂ Rn disebut rectangle, dimanaki , li adalah bilangan bulat dan ki ≤ li. Selanjutnya diperoleh bahwa sebarang rectangleX adalah asiklik, dengan kata lain Hk(X) isomorfik dengan Z jika k = 0, dan Hk(X)isomorf

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Virk, Amandeep K., and Kawaljeet Singh. "On Performance of Binary Flower Pollination Algorithm for Rectangular Packing Problem." Recent Advances in Computer Science and Communications 13, no. 1 (2020): 22–34. http://dx.doi.org/10.2174/2213275911666181114143239.

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Background: Metaheuristic algorithms are optimization algorithms capable of finding near-optimal solutions for real world problems. Rectangle Packing Problem is a widely used industrial problem in which a number of small rectangles are placed into a large rectangular sheet to maximize the total area usage of the rectangular sheet. Metaheuristics have been widely used to solve the Rectangle Packing Problem. Objective: A recent metaheuristic approach, Binary Flower Pollination Algorithm, has been used to solve for rectangle packing optimization problem and its performance has been assessed. Meth

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39

Feldman, Jacob, and Whitman Richards. "Mapping the Mental Space of Rectangles." Perception 27, no. 10 (1998): 1191–202. http://dx.doi.org/10.1068/p271191.

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The cognitive structure of a shape space—the space of rectangles—is explored by a nonmetric scaling technique. Our experiment was designed to extract the major transformational paths or ‘modes’ that characterize the mental shape space. Earlier studies of rectangle similarities using multidimensional scaling have provided conflicting evidence about whether the coordinate system of the mental rectangle space is based on height and width or on area and shape (ie aspect ratio). Our study reveals shape to be the single dominant factor. We suspected that earlier evidence for a height – width paramet

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Suryaningrum, Christine Wulandari, Purwanto Purwanto, Subanji Subanji, Hery Susanto, Yoga Dwi Windy Kusuma Ningtyas, and Muhammad Irfan. "SEMIOTIC REASONING EMERGES IN CONSTRUCTING PROPERTIES OF A RECTANGLE: A STUDY OF ADVERSITY QUOTIENT." Journal on Mathematics Education 11, no. 1 (2020): 95–110. http://dx.doi.org/10.22342/jme.11.1.9766.95-110.

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Semiotics is simply defined as the sign-using to represent a mathematical concept in a problem-solving. Semiotic reasoning of constructing concept is a process of drawing a conclusion based on object, representamen (sign), and interpretant. This paper aims to describe the phases of semiotic reasoning of elementary students in constructing the properties of a rectangle. The participants of the present qualitative study are three elementary students classified into three levels of Adversity Quotient (AQ): quitter/AQ low, champer/AQ medium, and climber/AQ high. The results show three participants

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ANZAI, SHINYA, JINHEE CHUN, RYOSEI KASAI, MATIAS KORMAN, and TAKESHI TOKUYAMA. "EFFECT OF CORNER INFORMATION IN SIMULTANEOUS PLACEMENT OF k RECTANGLES AND TABLEAUX." Discrete Mathematics, Algorithms and Applications 02, no. 04 (2010): 527–37. http://dx.doi.org/10.1142/s1793830910000863.

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We consider the optimization problem of finding k nonintersecting rectangles and tableaux in n × n pixel plane where each pixel has a real valued weight. We discuss existence of efficient algorithms if a corner point of each rectangle/tableau is specified.

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Liu, Hong Hai, and Xiang Hua Hou. "The Face Detection Research Based on Multi-Scale and Rectangle Feature." Applied Mechanics and Materials 198-199 (September 2012): 1383–88. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.1383.

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When extracting the face image features based on pixel distribution in face image, there always exist large amount of calculation and high dimensions of feature sector generated after feature extraction. This paper puts forward a feature extraction method based on prior knowledge of face and Haar feature. Firstly, the Haar feature expressions of face images are classified and the face features are decomposed into edge feature, line feature and center-surround feature, which are further concluded into the expressions of two rectangles, three rectangles and four rectangles. In addition, each rec

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Jansen, Klaus, and Guochuan Zhang. "Maximizing the Total Profit of Rectangles Packed into a Rectangle." Algorithmica 47, no. 3 (2007): 323–42. http://dx.doi.org/10.1007/s00453-006-0194-5.

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Kong, T. Y., David M. Mount, and A. W. Roscoe. "The Decomposition of a Rectangle into Rectangles of Minimal Perimeter." SIAM Journal on Computing 17, no. 6 (1988): 1215–31. http://dx.doi.org/10.1137/0217077.

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Alsaydalani, Majed O. A. "Discharge Coefficient of a Two-Rectangle Compound Weir combined with a Semicircular Gate beneath it under Various Hydraulic and Geometric Conditions." Engineering, Technology & Applied Science Research 14, no. 1 (2024): 12587–94. http://dx.doi.org/10.48084/etasr.6605.

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Two-component composite hydraulic structures are commonly employed in irrigation systems. The first component, responsible for managing the overflow, is represented by a weir consisting of two rectangles. The second component, responsible for regulating the underflow, is represented by a semicircular gate. Both components are essential for measuring, directing, and controlling the flow. In this study, we experimentally investigated the flow through a combined two-rectangle sharp-crested weir with a semicircular gate placed across the channel as a control structure. The upper rectangle of the w

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Yildiz, Gizem Y., Bailey G. Evans, and Philippe A. Chouinard. "The Effects of Adding Pictorial Depth Cues to the Poggendorff Illusion." Vision 6, no. 3 (2022): 44. http://dx.doi.org/10.3390/vision6030044.

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We tested if the misapplication of perceptual constancy mechanisms might explain the perceived misalignment of the oblique lines in the Poggendorff illusion. Specifically, whether these mechanisms might treat the rectangle in the middle portion of the Poggendorff stimulus as an occluder in front of one long line appearing on either side, causing an apparent decrease in the rectangle’s width and an apparent increase in the misalignment of the oblique lines. The study aimed to examine these possibilities by examining the effects of adding pictorial depth cues. In experiments 1 and 2, we presente

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Plewa, Julian, Małgorzata Płońska, and Grzegorz Junak. "Studies of Auxetic Structures Assembled from Rotating Rectangles." Materials 17, no. 3 (2024): 731. http://dx.doi.org/10.3390/ma17030731.

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The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson’s ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure’s linear dimensions and Poisson’s ratio. The obtained findings suggest that Poisson’s r

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Steele, Kenneth M., Mary Ellen Dello Stritto, and Willard L. Brigner. "A Looming-Recession Threshold." Perceptual and Motor Skills 82, no. 2 (1996): 604–6. http://dx.doi.org/10.2466/pms.1996.82.2.604.

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When the origin of magnification-minification of an outline rectangle had a horizontal locus which exceeded one-fourth of the rectangle's horizontal dimension, 16 observers of 21 reported apparent depth characteristic of looming and recession.

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Ridley, J. N. "Rectangles and spirals." Mathematical Gazette 105, no. 564 (2021): 416–24. http://dx.doi.org/10.1017/mag.2021.108.

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Every reader knows about the Golden Rectangle (see [1, pp. 85, 119], [2, 3]), and that it can be subdivided into a square and a smaller copy of itself, and that this process can be continued indefinitely, converging towards the intersection point of diagonals of any two successive rectangles in the sequence. The circumscribed logarithmic spiral passing through the vertices and converging to the same point is also familiar (see [3, 4]), and is analogous to the circumcircle of a regular polygon or a triangle. The approximate logarithmic spiral obtained by drawing a quarter-circle inside each of

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Chen, Kaizhi, Jiahao Zhuang, Shangping Zhong, and Song Zheng. "Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate." Mathematics 8, no. 11 (2020): 1914. http://dx.doi.org/10.3390/math8111914.

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Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL)

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