Relevant bibliographies by topics / Symmetry

Contents

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

Academic literature on the topic 'Symmetry'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 July 2024

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Journal articles on the topic "Symmetry"

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Ubaidillah, Firdaus. "FUNGSI SIMETRI TERHADAP GARIS x = a DAN SIFAT-SIFATNYA." Majalah Ilmiah Matematika dan Statistika 20, no. 2 (September 29, 2020): 45. http://dx.doi.org/10.19184/mims.v20i2.19623.

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An even function is a function with a graph that is symmetric with respect to the y-axis or the line x = 0. In this paper, we will introduce a more general function of the even function, we call it as symmetry function with respect to the line x = a, which is a function whose graph is symmetric with respect to the line x = a. This paper discusses the properties of the symmetry function with respect to the line x = a, which is derived from the pre-existing properties of the even function. Some of the results obtained above, the linear combination of the symmetry functions with respect to the line x = a is a symmetry function with respect to the line x = a and the composition of any function with a symmety function with respect to the line x = a is a symmetry function with respect to the line x = a. Keywords: Even function, a symmetry function with respect to the line x=a, symmetric graph
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Li, Chunbiao, Zhinan Li, Yicheng Jiang, Tengfei Lei, and Xiong Wang. "Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry." Symmetry 15, no. 8 (August 10, 2023): 1564. http://dx.doi.org/10.3390/sym15081564.

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A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications.
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KANEHISA, Hirotada. "Symmetric Instability without Symmetry." Journal of the Meteorological Society of Japan 83, no. 1 (2005): 129–34. http://dx.doi.org/10.2151/jmsj.83.129.

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Mirenkov, Valery. "DEFORMATION AS A PREPARING PROCESS FOR DESTRUCTION." Interexpo GEO-Siberia 2, no. 4 (2019): 170–75. http://dx.doi.org/10.33764/2618-981x-2019-2-4-170-175.

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Actual mining is accompanied with stress increasing and as a result increasing of developed space causes to deformation of rock with specialties, which brake the symmetry, obtained after statistic calculation. For horizontal working classic approach leads to calculation of symmetric relatively coordinate axes deformation. In that case boundary conditions and mechanical quantities, related to soling containing development, are sized in an arbitrary way. However, it is well known from in-situ observations that braking the symmetry and as a result caving starting happen in the most stressed point. According to used physical and mechanical laws, destruction occurs quite unpredictable and does not have single before determined behavior. As it supposed in the context of symmetric calculation, trying certainly carry out the destruction. Kinematic calculation of displacements, considering weight of rocks, has allowed to brake classic symmetry at calculation of roof and floor displacements and to get closer to understanding of mechanism of the deformation process. In the work isotropic solid with horizontal sunken working, which provides the most deformation symmetry at classic calculation, is considered. Introduction into consideration of dynamic of process of actual mining totally destroys built symmery of possible deformation providing destruction starting in the most stressed point. Dynamic is considered after single advance of support, sum of which additionally provides absence of the symmetry in the destruction process.
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Wang, Yifeng. "Symmetry and symmetric transformations in mathematical imaging." Theoretical and Natural Science 31, no. 1 (April 2, 2024): 320–23. http://dx.doi.org/10.54254/2753-8818/31/20241037.

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The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of polynomial equations. Galois theory, a cornerstone of modern algebra, connects symmetries, permutations, and solvability of equations. Group theory finds practical applications in cryptography, physics, and coding theory. Sophus Lie extends group theory to continuous spaces with Lie Group Theory, offering a powerful framework for studying continuous symmetries. Lie groups find applications in robotics and control theory, streamlining the representation of transformations. Benoit Mandelbrots fractal geometry, introduced in the late 20th century, provides a mathematical framework for understanding complex, self-similar shapes. The applications of fractal geometry range from computer graphics to financial modeling. Symmetrys practical applications extend to data visualization and cryptography. The article concludes by emphasizing symmetrys foundational role in physics, chemistry, computer graphics, and beyond. A deeper understanding of symmetry not only enriches perspectives across scientific disciplines but also fosters interdisciplinary collaborations, unveiling hidden order and structure in the natural and designed world. The exploration of symmetry promises ongoing discoveries at the intersection of mathematics and diverse fields of study.
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YUE, Y., J. H. XIE, and X. J. GAO. "CAPTURING THE SYMMETRY OF ATTRACTORS AND THE TRANSITION TO SYMMETRIC CHAOS IN A VIBRO-IMPACT SYSTEM." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250109. http://dx.doi.org/10.1142/s021812741250109x.

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A three-degree-of-freedom vibro-impact system with symmetric two-sided constraints is considered. The system is strongly nonlinear and symmetric. The symmetric fixed point of the Poincaré map is deduced analytically, and the existence conditions of the symmetric fixed point are obtained. The six-dimensional Poincaré map can be expressed as the second iteration of another unsymmetric implicit map, which implies the symmetry of the Poincaré map. When the control parameter changes successively, symmetry-breaking bifurcation and symmetry-restoring bifurcation will occur at some point, and the attractor may change between symmetry and antisymmetry repeatedly. When a symmetry breaking bifurcation occurs, the symmetry is still the intrinsic property of the vibro-impact system. Here the Poincaré map cannot reflect the symmetry itself. However, the unsymmetric implicit map can capture a pair of antisymmetric ω-limit sets, which reflects the symmetry of the vibro-impact system. Different Poincaré sections are locally conjugate about a diffeomorphism. Therefore, as long as the perturbation is sufficiently small, changing the Poincaré section does not have any effect on the dynamical behavior. The transition to symmetric chaos is represented by numerical simulations.
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Shi, Zeyun, Jinkeng Lin, Jiong Chen, Yao Jin, and Jin Huang. "Symmetry Based Material Optimization." Symmetry 13, no. 2 (February 14, 2021): 315. http://dx.doi.org/10.3390/sym13020315.

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Many man-made or natural objects are composed of symmetric parts and possess symmetric physical behavior. Although its shape can exactly follow a symmetry in the designing or modeling stage, its discretized mesh in the analysis stage may be asymmetric because generating a mesh exactly following the symmetry is usually costly. As a consequence, the expected symmetric physical behavior may not be faithfully reproduced due to the asymmetry of the mesh. To solve this problem, we propose to optimize the material parameters of the mesh for static and kinematic symmetry behavior. Specifically, under the situation of static equilibrium, Young’s modulus is properly scaled so that a symmetric force field leads to symmetric displacement. For kinematics, the mass is optimized to reproduce symmetric acceleration under a symmetric force field. To efficiently measure the deviation from symmetry, we formulate a linear operator whose kernel contains all the symmetric vector fields, which helps to characterize the asymmetry error via a simple ℓ2 norm. To make the resulting material suitable for the general situation, the symmetric training force fields are derived from modal analysis in the above kernel space. Results show that our optimized material significantly reduces the asymmetric error on an asymmetric mesh in both static and dynamic simulations.
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MELKEMI, MAHMOUD, FREDERIC CORDIER, and NICKOLAS S. SAPIDIS. "A PROVABLE ALGORITHM TO DETECT WEAK SYMMETRY IN A POLYGON." International Journal of Image and Graphics 13, no. 01 (January 2013): 1350002. http://dx.doi.org/10.1142/s0219467813500022.

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This paper deals with the problem of detecting "weak symmetry" in a polygon, which is a special bijective and continuous mapping between the vertices of the given polygon. An application of this work is the automatic reconstruction of 3D polygons symmetric with respect to a plane from free-hand sketches of weakly-symmetric 2D polygons. We formalize the weak-symmetry notion and highlight its many properties which lead to an algorithm detecting it. The closest research work to the proposed approach is the detection of skewed symmetry. Skewed symmetry detection deals only with reconstruction of planar mirror-symmetric 3D polygons while our method is able to identify symmetry in projections of planar as well as nonplanar mirror-symmetric 3D polygons.
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Walsh, Toby. "Symmetry Breaking Constraints: Recent Results." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 2192–98. http://dx.doi.org/10.1609/aaai.v26i1.8437.

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Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetry.
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Narechania, Tejas. "Symmetry and (Network) Neutrality." Michigan Law Review Online, no. 119 (2020): 46. http://dx.doi.org/10.36644/mlr.online.119.46.symmetry.

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In this short Essay, I take the opportunity to highlight one further potential asymmetry that may yet emerge from the Supreme Court’s application of Chevron’s many doctrines. Drawing on then-Judge Kavanaugh’s disdissental from the D.C. Circuit’s decision affirming network neutrality rules, I suggest that there is at least one vote on the Supreme Court—and perhaps more—for an asymmetric approach to the major questions doctrine. Moreover, I demonstrate how asymmetry in this context is deeply irrational. As applied to network neutrality, the asymmetry has at least one of two effects. One, it might simply favor one large industry over another, subjecting one inter-sector wealth transfer to heightened scrutiny, while treating an analogous wealth transfer—in the opposite direction—deferentially. But the judiciary is not typically in the business of favoring one industrial sector over another. Two, it subjects consumer-protection devices to increased regulatory scrutiny, thereby shifting the costs and burdens of overcoming a regulatory default to those entities—consumers—who can likely least afford to bear them. Hence, in more general terms, Justice Kavanaugh’s unbalanced approach to the major questions doctrine tends to undermine many of the values— accountability and expertise, among others—that agency policymaking has long served.
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Dissertations / Theses on the topic "Symmetry"

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Werning, Margaret Elizabeth. "Fearful symmetry." [Ames, Iowa : Iowa State University], 2008.

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Aparício, James Monteiro. "DNA symmetry." Master's thesis, Universidade de Aveiro, 2011. http://hdl.handle.net/10773/8627.

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Mestrado em Engenharia de Computadores e Telemática
A investigação do DNA tem sido uma das áreas de investigação mais exploradas no último século. Desde a sua primeira descrição até à primeira sequência completa do genoma humano muito foi descoberto, mas ainda estamos longe de o compreender completamente. Neste trabalho tentámos explorar a ordem até à qual se verifica a existência de simetria relevante em genomas, e para esse fim, usámos um conjunto de genomas de vários organismos. Tentámos encontar relação entre os vários genomas através das características de simetria. Foram analisados três tipos de simetria: simetria inversa, simetria reversa e simetria complementar. Usámos, ainda, uma nova medida para classificar a simetria: a proporção de pares equivalentes. A natureza das operações envolvidas, o tamanho da memória e a eficiência temporal são factores a ter em conta aquando do desenvolvimento de ferramentas computacionais. Várias soluções foram exploradas tendo como objectivo minimizar a memória utilizada e minimizar o tempo de execução. Confirma-se uma tendência para a existência de simetria inversa no conjunto dos genomas usados e observou-se que existe associação entre os resultados das medidas de simetria e o tamanho dos genomas.
DNA research has been one of the most explored areas in the last century. From its first description to the first complete human genome sequence a lot has been discovered, but we are still far from fully understanding it. With this work we tried to find until which order is relevant symmetry found in genomes and for that purpose, we used several genomes of different organisms. We tried to find a relation between the various genomes by analysing their symmetry characteristics. Three types of symmetry were analysed: complementary symmetry, reverse symmetry, and inverted symmetry. Also, a new symmetry measure was used: the proportion of equivalent pairs. The nature of the operations involved, memory space and time efficiency are important factors to be considered when developing computational tools. A few different solutions are explored in order to minimize memory allocation and minimize runtimes. This work confirms a tendency for the inverted symmetry in the set of genomes used and it was also observed an association between the symmetry measure results and the size of the genomes.
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Power, Christopher. "Probabilistic symmetry reduction." Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3493/.

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Model checking is a technique used for the formal verification of concurrent systems. A major hindrance to model checking is the so-called state space explosion problem where the number of states in a model grows exponentially as variables are added. This means even trivial systems can require millions of states to define and are often too large to feasibly verify. Fortunately, models often exhibit underlying replication which can be exploited to aid in verification. Exploiting this replication is known as symmetry reduction and has yielded considerable success in non probabilistic verification. The main contribution of this thesis is to show how symmetry reduction techniques can be applied to explicit state probabilistic model checking. In probabilistic model checking the need for such techniques is particularly acute since it requires not only an exhaustive state-space exploration, but also a numerical solution phase to compute probabilities or other quantitative values. The approach we take enables the automated detection of arbitrary data and component symmetries from a probabilistic specification. We define new techniques to exploit the identified symmetry and provide efficient generation of the quotient model. We prove the correctness of our approach, and demonstrate its viability by implementing a tool to apply symmetry reduction to an explicit state model checker.
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Breda, d'Azevedo Antonio Joao. "Hypermaps and symmetry." Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303114.

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Matheson, A. "Chiral symmetry breaking." Thesis, University of Cambridge, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234997.

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Ismael, Jenann. "Essays on symmetry /." New York ; London : Garland, 2001. http://catalogue.bnf.fr/ark:/12148/cb388115162.

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Nivens, Ryan Andrew. "Fonts and Symmetry." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etsu-works/227.

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Using fonts as a context, we will analyze symmetry of fi gures. Diff erent letters and numbers will be measured, and participants will describe items that possess vertical, horizontal, and rotational symmetry. Our discussion and activity will focus on the mathematics of fonts and the presence and absence of symmetry in their design.
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Nivens, Ryan Andrew. "Fonts and Symmetry." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etsu-works/224.

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Using fonts as a context, we will analyze symmetry of fi gures. Diff erent letters and numbers will be measured, and participants will describe items that possess vertical, horizontal, and rotational symmetry. Our discussion and activity will focus on the mathematics of fonts and the presence and absence of symmetry in their design.
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Cassart, Delphine. "Optimal tests for symmetry." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210693.

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Dans ce travail, nous proposons des procédures de test paramétriques et nonparamétrique localement et asymptotiquement optimales au sens de Hajek et Le Cam, pour trois modèles d'asymétrie.

La construction de modèles d'asymétrie est un sujet de recherche qui a connu un grand développement ces dernières années, et l'obtention des tests optimaux (pour trois modèles différents) est une étape essentielle en vue de leur mise en application.

Notre approche est fondée sur la théorie de Le Cam d'une part, pour obtenir les propriétés de normalité asymptotique, bases de la construction des tests paramétriques optimaux, et la théorie de Hajek d'autre part, qui, via un principe d'invariance permet d'obtenir les procédures non-paramétriques.

Nous considérons dans ce travail deux classes de distributions univariées asymétriques, l'une fondée sur un développement d'Edgeworth (décrit dans le Chapitre 1), et l'autre construite en utilisant un paramètre d'échelle différent pour les valeurs positives et négatives (le modèle de Fechner, décrit dans le Chapitre 2).

Le modèle d'asymétrie elliptique étudié dans le dernier chapitre est une généralisation multivariée du modèle du Chapitre 2.

Pour chacun de ces modèles, nous proposons de tester l'hypothèse de symétrie par rapport à un centre fixé, puis par rapport à un centre non spécifié.

Après avoir décrit le modèle pour lequel nous construisons les procédures optimales, nous obtenons la propriété de normalité locale asymptotique. A partir de ce résultat, nous sommes capable de construire les tests paramétriques localement et asymptotiquement optimaux. Ces tests ne sont toutefois valides que si la densité sous-jacente f est correctement spécifiée. Ils ont donc le mérite de déterminer les bornes d'efficacité paramétrique, mais sont difficilement applicables.

Nous adaptons donc ces tests afin de pouvoir tester les hypothèses de symétrie par rapport à un centre fixé ou non, lorsque la densité sous-jacente est considérée comme un paramètre de nuisance.

Les tests que nous obtenons restent localement et asymptotiquement optimaux sous f, mais restent valides sous une large classe de densités.

A partir des propriétés d'invariance du sous-modèle identifié par l'hypothèse nulle, nous obtenons les tests de rangs signés localement et asymptotiquement optimaux sous f, et valide sous une vaste classe de densité. Nous présentons en particulier, les tests fondés sur les scores normaux (ou tests de van der Waerden), qui sont optimaux sous des hypothèses Gaussiennes, tout en étant valides si cette hypothèse n'est pas vérifiée.

Afin de comparer les performances des tests paramétriques et non paramétriques présentés, nous calculons les efficacités asymptotiques relatives des tests non paramétriques par rapport aux tests pseudo-Gaussiens, sous une vaste classe de densités non-Gaussiennes, et nous proposons quelques simulations.
Doctorat en sciences, Orientation statistique
info:eu-repo/semantics/nonPublished

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Kiziltan, Zeynep. "Symmetry Breaking Ordering Constraints." Doctoral thesis, Uppsala : Univ., Department of Information Science, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3991.

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Books on the topic "Symmetry"

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István, Hargittai, ed. Fivefold symmetry. Singapore: World Scientific, 1992.

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Walser, Hans. Symmetry. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/spec/090.

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Tapp, Kristopher. Symmetry. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-51669-7.

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Tapp, Kristopher. Symmetry. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-0299-2.

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John, Hilton Peter, Pedersen Jean, and Mathematical Association of America, eds. Symmetry. [Washington, D.C.]: Mathematical Association of America, 2000.

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Peppas, Lynn. Symmetry. New York: Crabtree Pub., 2010.

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Bell, Alan. Symmetry. Derby: Association of Teachers of Mathematics, 1985.

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Sautoy, Marcus Du. Symmetry. New York: HarperCollins, 2008.

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Zhao, Xuezhuang. Molecular symmetry and fuzzy symmetry. Hauppauge, N.Y: Nova Science Publishers, 2011.

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Hönerlage, Bernd, and Ivan Pelant. Symmetry and Symmetry-Breaking in Semiconductors. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94235-3.

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Book chapters on the topic "Symmetry"

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Tapp, Kristopher. "Introduction to Symmetry." In Symmetry, 1–16. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_1.

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Tapp, Kristopher. "What Is a Number?" In Symmetry, 149–65. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_10.

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Tapp, Kristopher. "Cantor’s Infinity." In Symmetry, 167–78. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_11.

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Tapp, Kristopher. "Euclidean Space." In Symmetry, 179–97. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_12.

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Tapp, Kristopher. "Symmetry and Matrices." In Symmetry, 199–211. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_13.

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Tapp, Kristopher. "The Algebra of Symmetry." In Symmetry, 17–33. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_2.

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Tapp, Kristopher. "Isomorphism." In Symmetry, 35–50. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_3.

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Tapp, Kristopher. "The Classification Theorems." In Symmetry, 51–62. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_4.

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Tapp, Kristopher. "Subgroups and Product Groups." In Symmetry, 63–74. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_5.

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Tapp, Kristopher. "Permutations." In Symmetry, 75–86. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0299-2_6.

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Conference papers on the topic "Symmetry"

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Honda, Tomonori, Fabien Nicaise, and Erik K. Antonsson. "Synthesis of Structural Symmetry Driven by Cost Savings." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85111.

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An engineer presented with a design challenge often creates a symmetric solution. For instance, consider a table (front-back and left-right symmetry), a car (left and right symmetry), a bridge (front-back and left-right symmetry), or the space shuttle (left-right) symmetry. These examples may not be 100% symmetric, but their overriding features are remarkably similar. The reasons for the design of symmetric structures is not always clear. In some cases, like the table, symmetry may be a tradition. Similarly, the symmetry may be for aesthetic reasons. However in automated design algorithms, especially stochastic techniques, the output is often largely asymmetric, One reason for this is that fitness functions are not rewarded for symmetry. A possible resolution to this is to add a reward function for symmetry. Unfortunately, this approach is computationally intractable as well as arbitrary. In this paper a Genetic Algorithm based method is presented that rewards re-use of parts. The method is applied to a simple, idealized situation as well as to real design case. The results show that in some situations, symmetry naturally emerges from the synthesis, but that it does not provide clear performance advantages over asymmetric configurations.
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Cho, Minsu, and Kyoung Mu Lee. "Bilateral Symmetry Detection via Symmetry-Growing." In British Machine Vision Conference 2009. British Machine Vision Association, 2009. http://dx.doi.org/10.5244/c.23.4.

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Li, Ling-Fong. "Spontaneous symmetry breaking and chiral symmetry." In PARTICLES AND FIELDS: Seventh Mexican Workshop. American Institute of Physics, 2000. http://dx.doi.org/10.1063/1.1315030.

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Pietralla, N. "Mixed Symmetry in the Symmetry Triangle." In MAPPING THE TRIANGLE: International Conference on Nuclear Structure. AIP, 2002. http://dx.doi.org/10.1063/1.1517931.

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Feng, Z. C., and Mahmoud Almasri. "Amplitude Modulation and Symmetry Breaking Bifurcation in Micro Devices." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70146.

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Designs of many micro devices take advantage of the symmetry for better performance, immunity to noise, and for simpler analysis. When a symmetric structure is subjected to symmetric forcing, the symmetric response can become unstable leading to asymmetric responses. The occurrence of symmetry breaking bifurcation leads to complicated dynamic responses which often result in less desirable performances. In this paper, we obtain analytical criteria for the onset of symmetry breaking bifurcations. We also conduct numerical simulations to demonstrate different types of asymmetric dynamic responses resulting from the symmetry breaking bifurcation. In particular, we show the occurrence of amplitude modulated motions in such systems.
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Zang, Hongyan, Shourong Zhang, Tingyan Yan, Lili Huang, You Zhou, and Xin Zhang. "Conditional symmetry of symmetric systems with hidden attractors." In 2022 China Automation Congress (CAC). IEEE, 2022. http://dx.doi.org/10.1109/cac57257.2022.10055486.

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GINOCCHIO, JOSEPH N. "PSEUDOSPIN SYMMETRY: A RELATIVISTIC SYMMETRY IN NUCLEI." In Proceedings of the 7th International Spring Seminar on Nuclear Physics. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778383_0025.

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Ginocchio, Joseph N. "Pseudospin Symmetry: A Relativistic Symmetry in Nuclei." In MAPPING THE TRIANGLE: International Conference on Nuclear Structure. AIP, 2002. http://dx.doi.org/10.1063/1.1517961.

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Ginocchio, Joseph N. "Pseudospin symmetry: A relativistic symmetry in nuclei." In NUCLEAR PHYSICS IN THE 21st CENTURY:International Nuclear Physics Conference INPC 2001. AIP, 2002. http://dx.doi.org/10.1063/1.1470057.

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Funk, Christopher, and Yanxi Liu. "Symmetry reCAPTCHA." In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2016. http://dx.doi.org/10.1109/cvpr.2016.558.

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Reports on the topic "Symmetry"

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Choi, Sun Young. Infinite symmetry. Ames: Iowa State University, Digital Repository, September 2016. http://dx.doi.org/10.31274/itaa_proceedings-180814-1591.

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Zwart, P. H., R. W. Grosse-Kunstleve, and P. D. Adams. Exploring Metric Symmetry. Office of Scientific and Technical Information (OSTI), July 2006. http://dx.doi.org/10.2172/926901.

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Jensen, David W., and Robert G. Harvey. Plane Symmetry Groups. Fort Belvoir, VA: Defense Technical Information Center, June 1988. http://dx.doi.org/10.21236/ada198952.

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Leder, Erik. Symmetry, Symmetry Breaking, and the Current View of the Dirac Monopole. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.7261.

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Koch, Volker. Introduction to Chiral Symmetry. Office of Scientific and Technical Information (OSTI), May 2017. http://dx.doi.org/10.2172/1414767.

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Zhang, Y., and S. Mahajan. On broken ballooning symmetry. Office of Scientific and Technical Information (OSTI), March 1991. http://dx.doi.org/10.2172/5996019.

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MADLAND, D. G., and J. L. FRIAR. CHIRAL SYMMETRY IN FINITE NUCLEI. Office of Scientific and Technical Information (OSTI), November 1999. http://dx.doi.org/10.2172/787258.

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Albright, Eric Jason, and James David McHardy. Symmetry Analysis Using Symbolic Computation. Office of Scientific and Technical Information (OSTI), July 2018. http://dx.doi.org/10.2172/1460673.

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Kachru, Shamit. Mirror Symmetry for Open Strings. Office of Scientific and Technical Information (OSTI), June 2000. http://dx.doi.org/10.2172/763790.

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Glans, P., K. Gunnelin, and J. Guo. Probing symmetry and symmetry breaking in resonant soft-x-ray fluorescence spectra of molecules. Office of Scientific and Technical Information (OSTI), April 1997. http://dx.doi.org/10.2172/603533.

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