Relevant bibliographies by topics / Rectangle

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Rectangle'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Rectangle"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Rectangle"

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Mahmood, Abdullah-Al. "Approximation Algorithms for Rectangle Piercing Problems." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1025.

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Piercing problems arise often in facility location, which is a well-studied area of computational geometry. The general form of the piercing problem discussed in this dissertation asks for the minimum number of facilities for a set of given rectangular demand regions such that each region has at least one facility located within it. It has been shown that even if all regions are uniform sized squares, the problem is NP-hard. Therefore we concentrate on approximation algorithms for the problem. As the known approximation ratio for arbitrarily sized rectangles is poor, we restrict our
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Song, In-Ok. "Infrared emission bands of the Red Rectangle." Thesis, University of Nottingham, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.416304.

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Chung, Yau-lin, and 鍾有蓮. "Optimality and approximability of the rectangle covering problem." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30294873.

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Forsman, Anna. "-those complete strangers- an investigation of the rectangle." Thesis, Högskolan i Borås, Institutionen Textilhögskolan, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-20702.

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An report about investigating the rectangular shape in the relation between the stiff and the soft in drapings. The investigation have been made in the field fashion and garments.<br>Program: Modedesignutbildningen
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Thomas, Joshua David. "Spectroscopic Analysis and Modeling of the Red Rectangle." University of Toledo / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1341345222.

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LeBlanc, Denyse I. "Congelation d'un aliment ayant la forme d'un parallelepipede rectangle." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63893.

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Silvanus, Jannik [Verfasser]. "Improved Cardinality Bounds for Rectangle Packing Representations / Jannik Silvanus." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1188726226/34.

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Theise, Helena. "F ME F YOU : an investigation of the expressional potential of rectangular pattern construction in relation to print." Thesis, Högskolan i Borås, Akademin för textil, teknik och ekonomi, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-11118.

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This work is exploring the rectangle as a pattern construction. It is the most recognised geometric shape, can it still provide us with new expressions in fashion? This project is conducted through clear restrictions in the method, and through draping translated into garments through flat pattern construction. The result is a collection with a complex expression, mixing poetic shapes with playful prints full of contrast, which signifes harmony but does not follow the classical notions of beauty. The value of this work lies in the finding of new expressions in fashion, proposing that it is of u
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Stylianopoulos, Nikalaos Stavros. "A domain decomposition method for numerical conformal mapping onto a rectangle." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257545.

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Topalović, Radmila. "Infrared and optical emission bands of the Red Rectangle and other objects." Thesis, University of Nottingham, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.438417.

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Books on the topic "Rectangle"

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Jean, Robertson J., ed. ?Un cuadrado? ! Un rectangulo! =: A square? A rectangle! Rourke Pub., 2009.

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contributor, Carusi Camilla, Bianchi Amos contributor, and Tattoni Guido editor, eds. The electric rectangle. Quodlibet, 2021.

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Jean, Robertson J., ed. A square? a rectangle! Rourke Pub., 2009.

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Oberto, Varinia. Un rectangle de plaisir: Roman. Presses de la Renaissance, 1988.

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Atallah, Mikhail J. Output-sensitive hidden surface elimination for rectangles. Research Institute for Advanced Computer Science, 1989.

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Atallah, Mikhail J. Output-sensitive hidden surface elimination for rectangles. Research Institute for Advanced Computer Science, 1989.

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Oksana, Bulgakowa, ed. The white rectangle: Writings on film. Potemkin Press, 2003.

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Detambel, Régine. La lune dans le rectangle du patio. Gallimard, 1994.

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Liba, Opher, and Bat-Sheva Ilany. From the Golden Rectangle to the Fibonacci Sequences. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-030-97600-2.

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Csirik, J. Two dimensional rectangle packing: On-line methods and results. European Institute for Advanced Studies in Management, 1990.

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Book chapters on the topic "Rectangle"

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Zambon, Giulio. "Implementing “Rectangle”." In Sudoku Programming with C. Apress, 2015. http://dx.doi.org/10.1007/978-1-4842-0995-0_12.

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Golub, Spencer. "Page (Rectangle)." In Heidegger and Future Presencing (The Black Pages). Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31889-5_1.

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Kwok, Sun. "Red Rectangle." In Encyclopedia of Astrobiology. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-44185-5_5076.

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Stemkoski, Lee, and Evan Leider. "Rectangle Destroyer." In Game Development with Construct 2. Apress, 2017. http://dx.doi.org/10.1007/978-1-4842-2784-8_8.

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Shekhar, Shashi, and Hui Xiong. "Rectangle, Hyper-." In Encyclopedia of GIS. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_1093.

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Kwok, Sun. "Red Rectangle." In Encyclopedia of Astrobiology. Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-65093-6_5076.

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Loryś, Krzysztof, and Katarzyna Paluch. "Rectangle Tiling." In Approximation Algorithms for Combinatorial Optimization. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44436-x_21.

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Chazal, Frédéric, Vin de Silva, Marc Glisse, and Steve Oudot. "Rectangle Measures." In The Structure and Stability of Persistence Modules. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42545-0_3.

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Kwok, Sun. "Red Rectangle." In Encyclopedia of Astrobiology. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-27833-4_5076-6.

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Jukna, Stasys. "Rectangle Bounds." In SpringerBriefs in Mathematics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-42354-3_3.

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Conference papers on the topic "Rectangle"

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Liu, Zhixiong. "A Weighted Surplus Rectangle Algorithm for Rectangle Packing Problem." In 2024 43rd Chinese Control Conference (CCC). IEEE, 2024. http://dx.doi.org/10.23919/ccc63176.2024.10662618.

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Kovács, Kristóf, and Boglárka G.-Tóth. "Rectangle covering." In PROCEEDINGS LEGO – 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP. Author(s), 2019. http://dx.doi.org/10.1063/1.5090003.

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Lohmann, Adolf W., and Stefan Sinzinger. "Improvements of the graphic code of computer generated holograms." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.turr4.

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During recent years, research in the area of computer generated holography (CGH) almost exclusively dealt with the improvement of the algorithms to produce CGHs with enhanced performance. Now we would like to concentrate on improvements of the CGH quality by using certain tricks during the actual manufacturing process. In most CGHs the sampling cells contain one or sometimes two black rectangles. The size of the rectangle is responsible for the local light amplitude. The location of the rectangle determines the phase of the light, which is diffracted at that cell.
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Zhu, Shenglong, Scott J. Emrich, and Danny Z. Chen. "Predicting Local Inversions Using Rectangle Clustering and Representative Rectangle Prediction." In 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). IEEE, 2018. http://dx.doi.org/10.1109/bibm.2018.8621190.

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Dobkin, David P., and Dimitrios Gunopulos. "Computing the rectangle discrepancy." In the tenth annual symposium. ACM Press, 1994. http://dx.doi.org/10.1145/177424.178098.

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Lin, Sching L., and Jonathan Allen. "Minplex---a compactor that minimizes the bounding rectangle and individual rectangles in a layout." In the 23rd ACM/IEEE conference. ACM Press, 1986. http://dx.doi.org/10.1145/318013.318033.

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Lin, S. L., and J. Allen. "Minplex - A Compactor that Minimizes the Bounding Rectangle and Individual Rectangles in a Layout." In 23rd ACM/IEEE Design Automation Conference. IEEE, 1986. http://dx.doi.org/10.1109/dac.1986.1586078.

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Regan, D., and X. H. Hong. "Motion-Defined Letter Reading Test." In Noninvasive Assessment of the Visual System. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/navs.1991.we2.

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We have compared detection and spatial discrimination for motion-defined (MD) and contrast-defined (CD) form in normally-sighted subjects using a hardware stimulus generator of our own design and fabrication.1 The device displays approximately 1000 dots on a Tektronix 608 display with 100 frames/sec. The dot display is superimposed on a uniform patch of light so that dot contrast can be controlled. A new dot pattern can be generated every frame from a very large menu of patterns. The dot pattern contains a rectangular area whose aspect ratio, orientation, size and location can be controlled on
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Jingyu Yang and Zhongyu Jiang. "Rectangle fitting via quadratic programming." In 2015 IEEE 17th International Workshop on Multimedia Signal Processing (MMSP). IEEE, 2015. http://dx.doi.org/10.1109/mmsp.2015.7340875.

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Ralevic, Nebojsa M., Slobodan Drazic, and Radovan Obradovic. "The Hough transformation of rectangle." In 2008 6th International Symposium on Intelligent Systems and Informatics (SISY 2008). IEEE, 2008. http://dx.doi.org/10.1109/sisy.2008.4664906.

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Reports on the topic "Rectangle"

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Silver, G. L. Operational equations for the five-point rectangle. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10185763.

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Walker, J. S. Liquid-metal MHD flow in a duct whose cross section changes from a rectangle to a trapezoid, with applications in fusion blanket designs. Office of Scientific and Technical Information (OSTI), 1986. http://dx.doi.org/10.2172/5409989.

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Danielson, Thomas. A MONTE CARLO RECTANGLE PACKING ALGORITHM FOR IDENTIFYING LIKELY SPATIAL DISTRIBUTIONS OF FINAL CLOSURE CAP SUBSIDENCE IN THE E-AREA LOW-LEVEL WASTE FACILITY. Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1571419.

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Yager, Robert J. Creating, Positioning, and Rotating Rectangles Using C++. Defense Technical Information Center, 2013. http://dx.doi.org/10.21236/ada591373.

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Shiogi, Ann. Connected Painted Rectangles Experiments in Quantitative Shape and Contrasting Elements. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.6553.

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Ponce, Scarlitte. Enumerating Tilings with Thin Rectangles by Use of Independent Sets in Graphs. Iowa State University, 2019. http://dx.doi.org/10.31274/cc-20240624-627.

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Hoover, Donald R. Different Algorithms for Obtaining Upper Bounds to Multivariate Normal Areas Outside of Origin Centered Rectangles Using Joint Marginal Probabilities. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada199772.

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Kao, Sovansophal, Phal Chea, and Sopheak Song. Upper Secondary School Tracking and Major Choices in Higher Education: To Switch or Not to Switch. Cambodia Development Resource Institute, 2022. https://doi.org/10.64202/wp.133.202203.

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Strengthening the quality of education, science and technology education is one of the four strategic rectangles of Rectangular Strategy Phase IV and at the heart of Cambodia’s ambition to achieve higher-middle-income status by 2030 and high-income status by 2050. To that end, increasing attention has been paid to improving both the quantity and quality of science education from secondary school through higher education. Empirically, it has been demonstrated that upper secondary school science can play a significant role in inspiring students to pursue STEM majors in higher education. Yet, the
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