Academic literature on the topic 'Triangle'

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Journal articles on the topic "Triangle"

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Mui, Grace, and Jennifer Mailley. "A tale of two triangles: comparing the Fraud Triangle with criminology’s Crime Triangle." Accounting Research Journal 28, no. 1 (2015): 45–58. http://dx.doi.org/10.1108/arj-10-2014-0092.

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Purpose – This paper aims to propose the application of the Crime Triangle of Routine Activity Theory to fraud events as a complement to the universally accepted Fraud Triangle. Design/methodology/approach – The application of the Crime Triangle is illustrated using scenarios of asset misappropriations by type of perpetrator: external perpetrator, employee, management and the board and its governing bodies. Findings – The Crime Triangle complements the Fraud Triangle’s perpetrator-centric focus by examining the environment where fraud occurs and the relevant parties that play their role in pre
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Odehnal, Boris. "Two Convergent Triangle Tunnels." KoG, no. 22 (2018): 3–11. http://dx.doi.org/10.31896/k.22.1.

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A semi-orthogonal path is a polygon inscribed into a given polygon such that the $i$-th side of the path is orthogonal to the $i$-th side of the given polygon. Especially in the case of triangles, the closed semi-orthogonal paths are triangles which turn out to be similar to the given triangle. The iteration of the construction of semi-orthogonal paths in triangles yields infinite sequences of nested and similar triangles. We show that these two different sequences converge towards the bicentric pair of the triangle's Brocard points. Furthermore, the relation to discrete logarithmic spirals al
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Jurkin, Ema. "Poncelet Porisms and Loci of Centers in the Isotropic Plane." Mathematics 12, no. 4 (2024): 618. http://dx.doi.org/10.3390/math12040618.

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Any triangle in an isotropic plane has a circumcircle u and incircle i. It turns out that there are infinitely many triangles with the same circumcircle u and incircle i. This one-parameter family of triangles is called a poristic system of triangles. We study the trace of the centroid, the Feuerbach point, the symmedian point, the Gergonne point, the Steiner point and the Brocard points for such a system of triangles. We also study the traces of some further points associated with the triangles of the poristic family, and we prove that the vertices of the contact triangle, tangential triangle
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Norihiro, Someyama. "Qualitative Properties on Bulging Triangles and Their Original Triangles." Journal of Advanced Studies in Topology 12, no. 1-2 (2022): 57–65. https://doi.org/10.5281/zenodo.7458250.

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We consider bulging triangles introduced by the author \cite{So1} and study their qualitative properties. We focus on the triangle consisting of edge-centers of a bulging triangle, ``edge-central triangle.'' In addition, we investigate the similarity to bulging triangles and centroids of their original triangles and edge-central triangles.
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Hikmatovich, Ibragimov Husniddin. "Connection Between A Right Triangle And An Equal Side Triangle." American Journal of Interdisciplinary Innovations and Research 02, no. 11 (2020): 105–14. http://dx.doi.org/10.37547/tajiir/volume02issue11-20.

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There is some evidence that a right triangle and an equilateral triangle are related. Information about Pythagorean numbers is given. The geometric meaning of the relationship between right triangles and equilateral triangles is shown. The geometric meaning of the relationship between an equilateral triangle and an equilateral triangle is shown.
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Wysiadecki, Grzegorz, Maciej Radek, R. Shane Tubbs, et al. "Microsurgical Anatomy of the Inferomedial Paraclival Triangle: Contents, Topographical Relationships and Anatomical Variations." Brain Sciences 11, no. 5 (2021): 596. http://dx.doi.org/10.3390/brainsci11050596.

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The inferomedial triangle is one of the two surgical triangles in the paraclival subregion of the skull base. It is delineated by the posterior clinoid process, the dural entrance of the trochlear nerve and the dural entrance of the abducens nerve. The aim of the present article is to describe the anatomical variations within the inferomedial triangle. Measurements of the triangle’s borders and area were supplemented by detailed observations of the topographical anatomy and various arrangements of its contents. Nine adult cadaveric heads (18 sides) and 28 sagittal head sections were studied. T
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Čerin, Zvonko. "On Napoleon triangles and propeller theorems." Mathematical Gazette 87, no. 508 (2003): 42–50. http://dx.doi.org/10.1017/s0025557200172092.

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In this paper we shall consider two situations in triangle geometry when equilateral triangles appear and then show that they are closely related.In the first (known as the Napoleon theorem) equilateral triangles BCAT, CABT, and ABCT, are built on the sides of an arbitrary triangle ABC and their centroids are (almost always) vertices of an equilateral triangle ANBNCN (known as a Napoleon triangle of ABC; see Figure 1).
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Kodrnja, Iva, and Helena Koncul. "The Loci of Vertices of Nedian Triangles." KoG, no. 21 (2017): 19–25. http://dx.doi.org/10.31896/k.21.5.

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In this article we observe nedians and nedian triangles of ratio $\eta$ for a given triangle. The locus of vertices of the nedian triangles for $\eta\in\mathbb{R}$ is found and its correlation with isotomic conjugates of the given triangle is shown. Furthermore, the curve on which lie vertices of a nedian triangle for fixed $\eta$, when we iterate nedian triangles, is found.
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ISMAIL, SHAHRINA. "PERFECT TRIANGLES ON THE CURVE." Journal of the Australian Mathematical Society 109, no. 1 (2019): 68–80. http://dx.doi.org/10.1017/s144678871900003x.

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A Heron triangle is a triangle that has three rational sides $(a,b,c)$ and a rational area, whereas a perfect triangle is a Heron triangle that has three rational medians $(k,l,m)$. Finding a perfect triangle was stated as an open problem by Richard Guy [Unsolved Problems in Number Theory (Springer, New York, 1981)]. Heron triangles with two rational medians are parametrized by the eight curves $C_{1},\ldots ,C_{8}$ mentioned in Buchholz and Rathbun [‘An infinite set of heron triangles with two rational medians’, Amer. Math. Monthly 104(2) (1997), 106–115; ‘Heron triangles and elliptic curves’
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Hidayatin, Nur, and Frida Murtinasari. "Generalisasi Ketaksamaan Sinus pada Segitiga." Jurnal Axioma : Jurnal Matematika dan Pembelajaran 7, no. 1 (2022): 72–78. http://dx.doi.org/10.56013/axi.v7i1.1195.

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This study aims to find a generalization of the sine inequality of any triangles. This generalization is the general form of the sine inequality in a triangle when the angles given are not angles of the triangle, i.e. when the sum of the three angles is not equal to . The sine inequality that will be studied focuses on the inequalities of the sum and multiplication of sine in triangles. In the process, qualitative research methods are carried out in the form of literature review, namely studying the sum and the multiplication inequalities of sine in triangles which will then be developed and o
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Dissertations / Theses on the topic "Triangle"

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Peters, Joyana. "Triangle." ScholarWorks@UNO, 2014. http://scholarworks.uno.edu/td/1830.

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Abstract In the Lower East Side of New York City from 1909 through 1911 a fight for change was taking place. Jewish immigrant girls put their safety on the line and brought attention to the abuse taking place in factories across the country. They first spoke out and led the Ladies' Garment Worker strike bringing attention to their cause. But it was ultimately their untimely deaths in one of the most tragic workplace disasters ever in history that finally spurred the country to action in passing new fire safety and child labor laws. Historical Fiction, Immigration Story, 1911, Triangle Shirtwai
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Saucedo, Antonio Jr. "Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/855.

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Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.
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James, Lacey Taylor. "Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/835.

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This paper will discuss the analogues between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya's perspective. The topics presented in this paper will show that Pascal's triangle and Leibniz's triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal's Arithmetic Triangle can
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Davila, Rosa. "Tribonacci Convolution Triangle." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/883.

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A lot has been said about the Fibonacci Convolution Triangle, but not much has been said about the Tribonacci Convolution Triangle. There are a few ways to generate the Fibonacci Convolution Triangle. Proven through generating functions, Koshy has discovered the Fibonacci Convolution Triangle in Pascal's Triangle, Pell numbers, and even Tribonacci numbers. The goal of this project is to find inspiration in the Fibonacci Convolution Triangle to prove patterns that we observe in the Tribonacci Convolution Triangle. We start this by bringing in all the information that will be useful in construct
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Thompson, James Matthew. "Complex hyperbolic triangle groups." Thesis, Durham University, 2010. http://etheses.dur.ac.uk/478/.

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We prove several discreteness and non-discreteness results about complex hyperbolic triangle groups and discover two new lattices. These results use geometric (explicit construction of a fundamental domain), group theoretic and arithmetic methods.
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Rabemanambola, Maholy Félicien. "Le "triangle laitier" malgache." Clermont-Ferrand 2, 2007. http://www.theses.fr/2007CLF20007.

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L'essentiel de la production laitière de Madagascar est issu d'un "triangle" situé au coeur de l'île. Depuis des décennies, les régimes successifs ont toujours intégré le développement laitier dans leur programmes de développement respectifs, même si l'approche a souvent varié d'un régime à l'autre, les uns cherchant à privilégier la paysannerie, les autres misant sur le développement de grandes structures " modernes" et étrangères aux campagnes. Aujourd'hui, l'adoption de l'innovation par les paysans bute toujours sur certains obstacles majeurs. Les exploitations agricoles essentiellement con
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Monaghan, Andrew. "Complex hyperbolic triangle groups." Thesis, University of Liverpool, 2013. http://livrepository.liverpool.ac.uk/14033/.

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In this thesis we study the discreteness criteria for complex hyperbolic triangle groups, generated by reflections in the complex hyperbolic 2-space. A complex hyperbolic triangle group is a group of isometries of the complex hyperbolic plane generated by three complex reflections. We study discreteness of some of these groups using arithmetic and geometric methods. We show that certain complex hyperbolic triangle groups of signature (p,p,2p) and (p,q,pq/(q-p)) are not discrete. The arithmetic methods we use are those studied by Conway and Jones and Parker. We also extend these results further
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Správka, Petr. "stragická průmyslová zóna triangle." Master's thesis, Vysoká škola ekonomická v Praze, 2006. http://www.nusl.cz/ntk/nusl-494.

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Baker, Charla Bezdek András. "Triangle centers and Kiepert's hyperbola." Auburn, Ala., 2006. http://repo.lib.auburn.edu/2006%20Fall/Theses/BAKER_CHARLA_6.pdf.

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Williams, Alun G. T. "Studies on generalised triangle groups." Thesis, Heriot-Watt University, 2000. http://hdl.handle.net/10399/580.

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Books on the topic "Triangle"

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Weber, Katharine. Triangle. Farrar, Straus and Giroux, 2006.

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Weber, Katharine. Triangle. Farrar, Straus and Giroux, 2006.

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Weber, Katharine. Triangle. Farrar, Straus and Giroux, 2006.

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Ripslinger, Jon. Triangle. Harcourt Brace, 1994.

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Weber, Katharine. Triangle. Farrar, Straus and Giroux, 2006.

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Kimberling, Clark. Triangle centers and central triangles: By Clark Kimberling. Utilitas Mathematica Publishing, 1998.

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Bingham, Jane. Bermuda Triangle. Capstone Raintree, 2013.

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Ylonka Nacidit-Perdomo. Triangulo en Trebol/Triangle in Trefoil. CCLEH, 2001.

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Gopalakrishnan, Devika, and Gopeka Krishnan. Triangle. Independently Published, 2019.

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Matsuura, Hisaki, and David Karashima. Triangle. Dalkey Archive Press, 2014.

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Book chapters on the topic "Triangle"

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Johnson, D. L. "Triangle Groups." In Springer Undergraduate Mathematics Series. Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0243-4_11.

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Gottschalk, Petter. "Convenience Triangle." In The Convenience of White-Collar Crime in Business. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37990-2_5.

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Mitrinović, D. S., J. E. Pečarić, and A. M. Fink. "Triangle Inequalities." In Classical and New Inequalities in Analysis. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1043-5_17.

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Kao, Ming-Yang. "Triangle Finding." In Encyclopedia of Algorithms. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-30162-4_432.

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Bottema, O., and Reinie Erne. "Morley’s Triangle." In Topics in Elementary Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_10.

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Deza, Michel Marie, and Monique Laurent. "Triangle Inequalities." In Algorithms and Combinatorics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-04295-9_27.

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Wilkinson, Tolbert S. "Submental Triangle." In Practical Procedures in Aesthetic Plastic Surgery. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2594-2_5.

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Shichor, Yitzhak. "Fluid Triangle." In East-West Asia Relations in the 21st Century. Routledge, 2023. http://dx.doi.org/10.4324/9781003326595-4.

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Barnes, John. "Pascal’s Triangle." In Nice Numbers. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46831-0_12.

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Fulton, Kristy. "Pascal's Triangle." In More Math Puzzles and Patterns For Kids. Routledge, 2021. http://dx.doi.org/10.4324/9781003236733-6.

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Conference papers on the topic "Triangle"

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Garau, Luca, Riccardo Scateni, and Gianmarco Cherchi. "Triangle-triangle intersections with different numerical representations." In 2025 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW). IEEE, 2025. https://doi.org/10.1109/vrw66409.2025.00092.

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Mata Hernández, Gloria. "THE TRIANGLE OF EFFECTIVE LEARNING." In 19th International Technology, Education and Development Conference. IATED, 2025. https://doi.org/10.21125/inted.2025.1687.

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L. Sabharwal, Chaman, and Jennifer L. Leopold. "A Trianlge-Triangle Intersection Algorithm." In Seventh International Conference on Wireless & Mobile Network. Academy & Industry Research Collaboration Center (AIRCC), 2015. http://dx.doi.org/10.5121/csit.2015.51003.

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Williams, Virginia Vassilevska, and Yinzhan Xu. "Monochromatic Triangles, Triangle Listing and APSP." In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2020. http://dx.doi.org/10.1109/focs46700.2020.00078.

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Amarasinghe, G. W. Indika Shameera. "The Geometry Involving a Right-Cevian Triangle." In SLIIT INTERNATIONAL CONFERENCE ON ADVANCEMENTS IN SCIENCES AND HUMANITIES. Faculty of Humanities & Sciences, SLIIT, 2024. https://doi.org/10.54389/cxcc3246.

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This paper presents some significant theorems and corollaries prevailed, involving the cevian triangles, in particular, on right cevian triangles. Some useful corollaries are presented including a main theorem on right cevian triangles with detailed proofs, involving the ratios generated by the end points of internal cevians drawn to the side lengths of a triangle, adducing more generalized formulas for the different cevians of triangles around the right cevian triangle to fulfil the existing significant research gap in cevian geometry, particularly on cevian triangles. This paper presents pur
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Botler, Fábio, Cristina G. Fernandes, and Juan Gutiérrez. "On Tuza's conjecture for graphs with treewidth at most 6." In III Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2018. http://dx.doi.org/10.5753/etc.2018.3141.

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Tuza (1981) conjectured that the size τ (G) of a minimum set of edges that meets every triangle of a graph G is at most twice the size ν(G) of a maximum set of edge-disjoint triangles of G. In this paper we verify this conjecture for graphs with treewidth at most 6. In this paper, all graphs considered are simple and the notation and terminology are standard. A triangle transversal of a graph G is a set of edges of G whose deletion results in a triangle-free graph; and a triangle packing of G is a set of edge-disjoint triangles of G. We denote by τ (G) (resp. ν(G)) the size of a minimum triang
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Spremić, Siniša. "NOVE GRANICE UNAPREĐENOG TROUGLA ZA ANALIZU GASOVA RASTVORENIH U ULJU SA PRIMERIMA KVAROVA." In 36. Savetovanja CIGRE Srbija 2023 Fleksibilnost elektroenergetskog sistema. Srpski nacionalni komitet Međunarodnog saveta za velike električne mreže CIGRE Srbija, 2023. http://dx.doi.org/10.46793/cigre36.0135s.

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For many years, various methods have been used for the dissolved gas in oil analysis: Dernenburg, Rogers relations, MSS (Mueller, Schliesinger and Soldner), Duval triangles, Duval pentagons, Universal triangle, Key gas, Logarithmic nomograph, IEC relations, Gas pattern analysis method, Japan ETRA diagnostic diagram, Heptagon... Basically most methods deal with single or pure faults. The Duval Triangle has had significant changes in the boundaries between all areas with the appearance of areas of multiple faults of electrical discharge and overheating (DT) in the existing Duval Triangle 1. A ne
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Tomaz, G., M. I. Falcão, and H. R. Malonek. "Pascal's triangle and other number triangles in Clifford analysis." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756125.

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Lou, Fangyuan, and Nicole L. Key. "On Choosing the Optimal Impeller Exit Velocity Triangles in Preliminary Design." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59210.

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Abstract Impeller discharge flow plays an important role in centrifugal compressor performance and operability for two reasons. First, it determines the work factor and relative diffusion for the impeller. Second, it sets the flow into the downstream stationary diffusion system. The choice made in the preliminary design phase for the impeller exit velocity triangle is crucial for a successful design. The state-of-the-art design approach for determining the impeller exit velocity triangle in the preliminary design phase relies on several empirical guidelines, i.e. maximum work factor and diffus
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Strothoff, Sven, Dimitar Valkov, and Klaus Hinrichs. "Triangle cursor." In the ACM International Conference. ACM Press, 2011. http://dx.doi.org/10.1145/2076354.2076377.

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Reports on the topic "Triangle"

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Ungar, Abraham A. The Hyperbolic Triangle Defect. GIQ, 2012. http://dx.doi.org/10.7546/giq-5-2004-225-236.

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Sinn, Hans-Werner. The Vanishing Harberger Triangle. National Bureau of Economic Research, 1990. http://dx.doi.org/10.3386/w3225.

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Shapira, Yair. Multigrid for refined triangle meshes. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/431152.

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Hanmer, S. Geology, East Athabasca Mylonite Triangle, Saskatchewan. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1994. http://dx.doi.org/10.4095/194845.

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Farzan, Yasaman. Leptonic Unitarity Triangle and CP-Violation. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/798993.

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Eigen, G. Probing the CKM Triangle at BABAR. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/826748.

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ชวนชื่น, รุ่งทิพย์, พรเพ็ญ พัฒนโสภณ та ศุภชัย เนื้อนวลสุวรรณ. การเฝ้าระวังการดื้อต่อยาฆ่าเชื้อและยาปฏิชีวนะของ Salmonella spp. และ Escherichia coli ในสายพันธุ์ที่แยกได้ในประเทศไทย : รายงานการวิจัย. จุฬาลงกรณ์มหาวิทยาลัย, 2006. https://doi.org/10.58837/chula.res.2006.87.

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แยก Salmonella enterica จำนวน 257 isolates และ Escherichia coli จำนวน 60 isolates จากตัวอย่างที่ได้จาก ไก่ สุกรและสิ่งแวดล้อมในฟาร์ม ทำการหาค่า minimal inhibitory concentration (MIC) ต่อยาปฏิชีวนะและยาฆ่าเชื้อ ได้แก่ ampicillin (AMP) chloramphenicol (CHP) ciprofloxacin (CIP) erythromycin (ERY) gentamycin (GEN) tetracycline (TET) trmethoprim (TRI) benzalkonium chloride (BKC) chlorhexidine (CHX), copper sulfate (CuSO4) และ zinc chloride (ZnCl2) พบว่า salmonella 162 isolates (63.04%) และ E. coli 50 isolates (83.33%) ดื้อต่อยาปฏิชีวนะอย่างน้อยหนึ่งชนิด ค่า MIC ต่อ BKC, CHX, CUSO4 และ ZnCl2 เกาะกัน
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Heron, Scott. Sea Surface Temperature in the Coral Triangle. The Nature Conservancy, 2010. http://dx.doi.org/10.3411/col.07070329.

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Stacy, Jerry. The Last B-2s: A Wobbly Iron Triangle. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada441380.

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Arabio, Alexandra C. Quantifying Writer Variance Through Rainbow Triangle Feature Extraction. Iowa State University, 2024. https://doi.org/10.31274/cc-20250502-124.

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