Journal articles: 'Symmetry (Mathematics)'

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Nityananda, Rajaram. "Symmetry and mathematics." Resonance 20, no. 3 (March 2015): 264–76. http://dx.doi.org/10.1007/s12045-015-0182-7.

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Hilton, Peter, and Jean Pedersen. "Symmetry in mathematics." Computers & Mathematics with Applications 12, no. 1-2 (January 1986): 315–28. http://dx.doi.org/10.1016/0898-1221(86)90157-4.

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Varadarajan, V. S. "Symmetry in mathematics." Computers & Mathematics with Applications 24, no. 3 (August 1992): 37–44. http://dx.doi.org/10.1016/0898-1221(92)90212-z.

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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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Miller, Catherine M. "Kaleidoscopes and Mathematics: An Elegant Connection." Mathematics Teaching in the Middle School 22, no. 9 (May 2017): 559–66. http://dx.doi.org/10.5951/mathteacmiddscho.22.9.0559.

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Symmetry is used to create mathematically inspiring images in three-mirror kaleidoscopes. A project outlines how students can build their own kaleidoscopes having mathematically exact symmetric images.

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Brasili, Simone. "Symmetry in Mathematics Education." Symmetry: Culture and Science 34, no. 3 (2023): 213–16. http://dx.doi.org/10.26830/symmetry_2023_3_213.

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VAN SCHAFTINGEN, JEAN. "SYMMETRIZATION AND MINIMAX PRINCIPLES." Communications in Contemporary Mathematics 07, no. 04 (August 2005): 463–81. http://dx.doi.org/10.1142/s0219199705001817.

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We develop a method to prove that some critical levels for functionals invariant by symmetry obtained by minimax methods without any symmetry constraint are attained by symmetric critical points. It is used to investigate the symmetry properties of solutions of elliptic partial differential equations with Dirichlet or Neumann boundary conditions. It is also an alternative to concentration-compactness for some symmetric elliptic problems.

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Burby, J. W., N. Kallinikos, and R. S. MacKay. "Some mathematics for quasi-symmetry." Journal of Mathematical Physics 61, no. 9 (September 1, 2020): 093503. http://dx.doi.org/10.1063/1.5142487.

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Radovic, Ljiljana, and Slavik Jablan. "Visual communication through visual mathematics." Filomat 23, no. 2 (2009): 56–67. http://dx.doi.org/10.2298/fil0902056r.

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In this paper we present some possibilities how different areas of visual mathematics (symmetry in art and science, isometric symmetry groups, similarity symmetry, modularity, antisymmetry, tessellations, theory of proportions, theory of visual perception, perspective, anamorphoses, visual illusions, ethnomathematics, mirror curves, optiles, fractal structures) can be used as a tool of visual communication. The paper also contains (in parts) a description of the course 'Visual Mathematics and Design' organized at the Faculty of Information Technologies (Belgrade).

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Brasili, Simone, and Johan Gielis. "Interdisciplinary insights and inspirations of symmetry." Symmetry: Culture and Science 35, no. 2 (2024): 117–18. http://dx.doi.org/10.26830/symmetry_2024_2_117.

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The second issue of Volume 35 of the Symmetry: Culture and Science journal arrives shortly before the Symmetry Festival 2024, marking its debut in Italy, in the historic city of Pisa, from July 17 to July 20. This event will be a tribute to the founder of the International Symmetry Association and a friend to many of our readers, György Darvas, who passed away in late 2023. In Volume 35, Number 2, we celebrate Darvas’s ongoing legacy of symmetry as a unifying principle across diverse disciplines. This issue presents a diverse range of interdisciplinary research in mathematics, science, art, education, and architecture, emphasizing the interconnectedness inherent in symmetry. We hope these contributions inspire further exploration and appreciation of symmetry’s multifaceted nature.

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Bornemann, Folkmar, and Peter J. Forrester. "Singular values and evenness symmetry in random matrix theory." Forum Mathematicum 28, no. 5 (September 1, 2016): 873–91. http://dx.doi.org/10.1515/forum-2015-0055.

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AbstractComplex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two independent eigenvalue sequences distributed according to particular matrix ensembles with chiral unitary symmetry. We give decompositions of the distribution of singular values, and the decimation of the singular values – whereby only even, or odd, labels are observed – for real symmetric random matrices with an orthogonal symmetry, and even weight. This requires further specifying the functional form of the weight to one of three types – Gauss, symmetric Jacobi or Cauchy. Inter-relations between gap probabilities with orthogonal and unitary symmetry follow as a corollary. The Gauss case has appeared in a recent work of Bornemann and La Croix. The Cauchy case, when appropriately specialised and upon stereographic projection, gives decompositions for the analogue of the singular values for the circular unitary and circular orthogonal ensembles.

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Moyer, Patricia S. "Patterns and Symmetry: Reflections of Culture." Teaching Children Mathematics 8, no. 3 (November 2001): 140–44. http://dx.doi.org/10.5951/tcm.8.3.0140.

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Many contributions of diverse cultures foster a rich understanding of mathematics. Knowing how one's culture has contributed to mathematics and how these contributions enhance our cultural environment supports the acquisition of mathematical power. However, discussing culture in mathematics classrooms for a one-week celebration of women in mathematics or a one-month recognition of the contributions of African Americans is not enough. Cultural learning that recognizes race, ethnicity, gender, and social class should be woven into the fabric of mathematics lessons throughout the year. Yet many teachers have limited backgrounds in promoting culturally relevant mathematics in meaningful ways.

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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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Gao, Xinyan, Yingcai Ding, Wenbo Liu, Kaidi Zheng, Siyu Huang, Ning Zhou, and Dakui Li. "Unified Mathematical Framework for Slicing and Symmetry Reduction over Event Structures." Journal of Applied Mathematics 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/352152.

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Nonclassical slicing and symmetry reduction can act as efficient structural abstract methods for pruning state space when dealing with verification problems. In this paper, we mainly address theoretical and algorithmic aspects for nonclassical slicing and symmetry reduction over prime event structures. We propose sliced and symmetric quotient reduction models of event structures and present their corresponding algorithms. To construct the underlying foundation of the proposed methodologies, we introduce strong and weak conflict concepts and a pair of mutually inverse operators and extend permutation group based symmetry notion of event structures. We have established a unified mathematical framework for slicing and symmetry reduction, and further investigated the translation, isomorphism, and equivalence relationship and other related basic facts from a theoretical point of view. The framework may provide useful guidance and theoretical exploration for overcoming verification challenges. This paper also demonstrates their practical applications by two cases.

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Zlatanovic, Milan, and Svetislav Mincic. "Identities for curvature tensors in generalized Finsler space." Filomat 23, no. 2 (2009): 34–42. http://dx.doi.org/10.2298/fil0902034z.

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In the some previous works we have obtained several curvature tensors in the generalized Finsler space GFN (the space with non-symmetric basic tensor and non-symmetric connection in Rund's sence). In this work we study identities for the mentioned tensors (the antisymmetriy with respect of two indices, the cyclic symmetry, the symmetry with respect of pairs of indices).

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Fečkan, Michal. "Invariant curves from symmetry." Mathematica Bohemica 118, no. 2 (1993): 171–74. http://dx.doi.org/10.21136/mb.1993.126048.

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Bangu, Sorin. "Reifying mathematics? Prediction and symmetry classification." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39, no. 2 (May 2008): 239–58. http://dx.doi.org/10.1016/j.shpsb.2007.09.003.

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Yanofsky, Noson S., and Mark Zelcer. "The Role of Symmetry in Mathematics." Foundations of Science 22, no. 3 (March 7, 2016): 495–515. http://dx.doi.org/10.1007/s10699-016-9486-7.

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Whitman, Nancy. "Activities: Line and Rotational Symmetry." Mathematics Teacher 84, no. 4 (April 1991): 296–302. http://dx.doi.org/10.5951/mt.84.4.0296.

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Introduction: The NCTM's Curriculum and Evaluation Standards (NCTM 1989) recom- mends that teachers connect mathematics to the world outside the classroom. Classroom activities should afford students the opportunity to work individually as well as in small- and large-group arrangements. Teachers should furnish experiences that enhance students' ability to communicate in mathematics and that integrate the students' cultural background into the learning of mathematics. The activities described in this article respond to these recommendations. They were designed for students in Hawaii, but all students can benefit from doing them.

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Evered, Lisa J. "Folded Fashions: Symmetry in Clothing Design." Arithmetic Teacher 40, no. 4 (December 1992): 204–6. http://dx.doi.org/10.5951/at.40.4.0204.

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Recent reports supported by research indicate the need to encourage girls as well as boys to continue the study of mathematics. Two reasons often given for the lack of females' interest in mathematics are its perception as a male domain and the scarcity of female role models. These influences appear to be active early in the mathematics curriculum. Despite the efforts of concerned teachers and textbook publishers, the majority of classroom applications of mathematics are oriented more toward males than females. Further, historical references to such female mathematicians such as Hypatia, Kovalevsky, and Noether do little toencouragetoday's young women who may not wish to become mathematicians to choose vocations in which mathematics is important

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Wang, Yaning, and Wenjie Wang. "Curvature properties of almost Kenmotsu manifolds with generalized nullity conditions." Filomat 30, no. 14 (2016): 3807–16. http://dx.doi.org/10.2298/fil1614807w.

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In this paper, it is proved that on a generalized (k,?)'-almost Kenmotsu manifold M2n+1 of dimension 2n + 1, n > 1, the conditions of local symmetry, semi-symmetry, pseudo-symmetry and quasi weak-symmetry are equivalent and this is also equivalent to that M2n+1 is locally isometric to either the hyperbolic space H2n+1(-1) or the Riemannian product Hn+1(-4)xRn. Moreover, we also prove that a generalized (k,?)-almost Kenmotsu manifold of dimension 2n + 1, n > 1, is pseudo-symmetric if and only if it is locally isometric to the hyperbolic space H2n+1(-1).

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Ruch, David K. "Vanishing moments for scaling vectors." International Journal of Mathematics and Mathematical Sciences 2004, no. 36 (2004): 1897–908. http://dx.doi.org/10.1155/s0161171204308215.

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One advantage of scaling vectors over a single scaling function is the compatibility of symmetry and orthogonality. This paper investigates the relationship between symmetry, vanishing moments, orthogonality, and support length for a scaling vectorΦ. Some general results on scaling vectors and vanishing moments are developed, as well as some necessary conditions for the symbol entries of a scaling vector with both symmetry and orthogonality. If orthogonal scaling vectorΦhas some kind of symmetry and a given number of vanishing moments, we can characterize the type of symmetry forΦ, give some information about the form of the symbolP(z), and place some bounds on the support of eachϕi. We then construct anL2(ℝ)orthogonal, symmetric scaling vector with one vanishing moment having minimal support.

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Zheng, Chao. "Quantum simulation of PT-arbitrary-phase–symmetric systems." Europhysics Letters 136, no. 3 (November 1, 2021): 30002. http://dx.doi.org/10.1209/0295-5075/ac3e8b.

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Abstract Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT–symmetric systems and their featured properties have started to be investigated. In this work, we develop the PT and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT-φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT symmetry, unifying the PT and anti-PT symmetries and having intermediate properties between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH system in two dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.

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Guirao, Juan Luis García. "“Mathematics and Symmetry/Asymmetry Section”—Editorial 2020–2021." Symmetry 15, no. 1 (December 26, 2022): 55. http://dx.doi.org/10.3390/sym15010055.

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Li, Chunbiao, Julien Clinton Sprott, Yongjian Liu, Zhenyu Gu, and Jingwei Zhang. "Offset Boosting for Breeding Conditional Symmetry." International Journal of Bifurcation and Chaos 28, no. 14 (December 30, 2018): 1850163. http://dx.doi.org/10.1142/s0218127418501638.

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Symmetry is usually prevented by the broken balance in polarity. If the offset boosting returns the balance of polarity when some of the variables have their polarity reversed, the corresponding system becomes conditionally symmetric and in turn produces coexisting attractors with that type of symmetry. In this paper, offset boosting in one dimension or in two dimensions in a 3D system is made for producing conditional symmetry, where the symmetric pair of coexisting attractors exist from one-dimensional or two-dimensional offset boosting, which is identified by the basin of attraction. The polarity revision from offset boosting provides a general method for constructing chaotic systems with conditional symmetry. Circuit implementation based on FPGA verifies the coexisting attractors with conditional symmetry.

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Caratelli, Diego, Pierpaolo Natalini, and Paolo Emilio Ricci. "Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory." Symmetry 15, no. 10 (October 10, 2023): 1900. http://dx.doi.org/10.3390/sym15101900.

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Bernoulli and Euler numbers and polynomials are well known and find applications in various areas of mathematics, such as number theory, combinatorial mathematics, series expansions, and the theory of special functions. Using fractional exponential functions, we extend the classical Bernoulli and Euler numbers and polynomials to introduce their fractional-index-based types. This reveals a symmetry in relation to the classical numbers and polynomials. We demonstrate some examples of these generalized mathematical entities, which we derive using the computer algebra system Mathematica©.

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Mutlu, Ebru, and Asuman Duatepe-Paksu. "Pre-Service Lower Secondary School Mathematics Teachers’ Ability of Drawing the Symmetry of a Figure according to a Line." ITM Web of Conferences 22 (2018): 01038. http://dx.doi.org/10.1051/itmconf/20182201038.

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The aim of the present study is to investigate pre-service lower secondary school mathematics teachers’ ability of drawing a given figure’s symmetry according to the lines in various positions. The sampling of the study comprised eight pre-service mathematics teachers who were attending a mathematics education department and willing to participate in the study. The criterion sampling methods was used. Six open-ended questions were asked to determine the ability of the prospective teachers to take the symmetry of a given figure according to the lines in different situations. Furthermore, interviews were conducted with the participants on their definitions of symmetry and symmetry according to a line. The data of the study were the prospective teachers’ drawing papers and the video recordings of the interviews including the definitions of the concepts of symmetry and symmetry according to a line. Content analysis was used to analyze the data. The findings indicated that the prospective teachers were successful in drawing the symmetry of a given figure according to the vertical, horizontal and oblique lines, and they used an informal language to define the concepts of symmetry and symmetry according to a line.

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Tits, Jacques, and John Stillwell. "Symmetry." American Mathematical Monthly 107, no. 5 (May 2000): 454. http://dx.doi.org/10.2307/2695304.

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Tits, Jacques, and John Stillwell. "Symmetry." American Mathematical Monthly 107, no. 5 (May 2000): 454–61. http://dx.doi.org/10.1080/00029890.2000.12005222.

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Brasili, Simone. "In conversation with Eugen Jost – art, mathematics and symmetry." Symmetry: Culture and Science 35, no. 2 (2024): 221–23. http://dx.doi.org/10.26830/symmetry_2024_2_221.

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In this short conversation, Eugen Jost, a well-known Swiss artist whose work is strongly influenced by mathematics, discusses the role of symmetry in his art. The dialogue sheds light on how symmetry naturally emerges in his artistic expressions through an intricate process of balance and harmony. The interview reveals his relationship between mathematics and art, helping us understand the multifaceted nature of their intricate connection with symmetry expressed in the works as in the Egyptian Triangle: a fascinating testament to the profound interplay between the order and rigor of mathematics and the boundless creativity of art, resulting in stunning works that evoke a sense of wonder and awe.

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Ditasona, Candra. "Exploring Ethnomathematics in Batak Toba Carvings for Locally-based Mathematics Teaching Material." Journal of Education Research and Evaluation 7, no. 3 (August 27, 2023): 399–407. http://dx.doi.org/10.23887/jere.v7i3.66787.

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As one of the traditional ornaments of the Batak Toba tribe, "gorga" carries philosophical meaning and serves to embellish the decoration of traditional houses. The gorga motif has its own distinctive characteristics, with closely arranged patterns and symmetrical designs. This indicates the presence of mathematical aspects within these carved gorga patterns. This research aims to analyze the symmetries embedded in the gorga motifs that can be utilized as locally-based mathematics teaching material. The study is conducted by exploring various gorga motifs and analyzing their types of symmetry. The research is employing an ethnographic research approach. Data is collected through observing buildings adorned with gorga motifs, studying literature, and conducting interviews with gorga carvers. Qualitative data analysis can be started with data reduction, data presentation, drawing conclusions and verification. The research findings reveal the existence of seven types of symmetry obtained from all gorga motifs. These symmetry types include translation symmetry, glide reflect symmetry, vertical symmetry, rotation 180° symmetry, vertical and rotation 180° symmetry, horizontal symmetry, and vertical and horizontal symmetry.

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Brock, Friedemann, Gisella Croce, Olivier Guibé, and Anna Mercaldo. "Symmetry and asymmetry of minimizers of a class of noncoercive functionals." Advances in Calculus of Variations 13, no. 1 (January 1, 2020): 15–32. http://dx.doi.org/10.1515/acv-2017-0005.

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AbstractIn this paper we prove symmetry results for minimizers of a noncoercive functional defined on the class of Sobolev functions with zero mean value. We prove that the minimizers are foliated Schwarz symmetric, i.e., they are axially symmetric with respect to an axis passing through the origin and nonincreasing in the polar angle from this axis. In the two-dimensional case, we show a symmetry breaking.

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Wang, Hong-ren, Xue Yang, and Xue Yang. "Rotating-symmetric solutions for nonlinear systems with symmetry." Acta Mathematicae Applicatae Sinica, English Series 31, no. 2 (June 2015): 307–12. http://dx.doi.org/10.1007/s10255-015-0484-2.

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Lev, Felix M. "Symmetries in Foundation of Quantum Theory and Mathematics." Symmetry 12, no. 3 (March 4, 2020): 409. http://dx.doi.org/10.3390/sym12030409.

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In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

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Boyd, J. N., R. G. Hudepohl, and P. N. Raychowdhury. "Breaking the symmetry of a circular system of coupled harmonic oscillators." International Journal of Mathematics and Mathematical Sciences 29, no. 11 (2002): 665–74. http://dx.doi.org/10.1155/s0161171202006014.

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First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for2,3,5, and6particles are given.

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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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Gorini, Catherine. "Symmetry: A Link Between Mathematics and Life." Humanistic Mathematics Network Journal 1, no. 13 (May 1996): 19–22. http://dx.doi.org/10.5642/hmnj.199601.13.08.

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Mostow, G. D. "A brief survey of symmetry in mathematics." Proceedings of the National Academy of Sciences 93, no. 25 (December 10, 1996): 14233–37. http://dx.doi.org/10.1073/pnas.93.25.14233.

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Zamani, Yousef, and Esmaeil Babaei. "SYMMETRY CLASSES OF POLYNOMIALS ASSOCIATED WITH THE DICYCLIC GROUP." Asian-European Journal of Mathematics 06, no. 03 (September 2013): 1350033. http://dx.doi.org/10.1142/s1793557113500332.

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In this paper, we obtain the dimensions of symmetry classes of polynomials with respect to the irreducible characters of the dicyclic group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes. In particular, the existence of o-basis of symmetry classes of polynomials with respect to the irreducible characters of the generalized quaternion group are concluded.

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Chaubey, Yogendra P., Govind S. Mudholkar, and M. C. Jones. "Reciprocal symmetry, unimodality and Khintchine’s theorem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (February 15, 2010): 2079–96. http://dx.doi.org/10.1098/rspa.2009.0482.

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The symmetric distributions on the real line and their multi-variate extensions play a central role in statistical theory and many of its applications. Furthermore, data in practice often consist of non-negative measurements. Reciprocally symmetric distributions defined on the positive real line may be considered analogous to symmetric distributions on the real line. Hence, it is useful to investigate reciprocal symmetry in general, and Mudholkar and Wang’s notion of R-symmetry in particular. In this paper, we shall explore a number of interesting results and interplays involving reciprocal symmetry, unimodality and Khintchine’s theorem with particular emphasis on R-symmetry. They bear on the important practical analogies between the Gaussian and inverse Gaussian distributions.

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Torrisi, Mariano. "Editorial of Papers Published in 2020–2021 in the Mathematics and Symmetry/Asymmetry Section." Symmetry 15, no. 1 (December 30, 2022): 105. http://dx.doi.org/10.3390/sym15010105.

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JIANG, QINGTANG. "BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (September 2011): 773–812. http://dx.doi.org/10.1142/s0219691311004316.

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This paper discusses the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently, hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hexagonal data also have high symmetry which is pertinent to the symmetric structure of the hexagonal lattice. The high symmetry of filter banks and wavelets not only leads to simpler algorithms and efficient computations, it also has the potential application for the texture segmentation of hexagonal data. While in the field of computer-aided geometric design (CAGD), when the filter banks are used for surface multiresolution processing, it is required that the corresponding decomposition and reconstruction algorithms for regular vertices have high symmetry, which make it possible to design the corresponding multiresolution algorithms for extraordinary vertices. In this paper we study the construction of six-fold axial symmetric biorthogonal filter banks and the associated wavelets, with both the dyadic and [Formula: see text]-refinements. The constructed filter banks have the desirable symmetry for hexagonal data processing. By associating the outputs (after one-level multiresolution decomposition) appropriately with the nodes of the regular triangular mesh with which the input data is associated (sampled), we represent multiresolution analysis and synthesis algorithms as templates. The six-fold axial symmetric filter banks constructed in this paper result in algorithm templates with desirable symmetry for triangle surface processing.

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Lu, Tianai, Chunbiao Li, Sajad Jafari, and Fuhong Min. "Controlling Coexisting Attractors of Conditional Symmetry." International Journal of Bifurcation and Chaos 29, no. 14 (December 26, 2019): 1950207. http://dx.doi.org/10.1142/s0218127419502079.

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Conditional symmetry is known as a new regime for providing coexisting duplicate oscillations with opposite polarity. Polarity balance can be obtained from a function for hosting conditional symmetry. In this paper, new cases of chaotic systems with conditional symmetry are coined from 1D and 2D offset boosting based on a suitable polarity adjustment. Conditional symmetric attractors are controlled effectively by a simple absolute value function, where the distance between two coexisting attractors of conditional symmetry is modified linearly by the offset boosting constant, meanwhile the size of the coexisting attractors gets controlled by the slope. Coexisting attractors of conditional symmetry are thereafter implemented based on the develop kit of STM32.

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Kruglikov, Boris, and Henrik Winther. "Submaximally symmetric quaternion Hermitian structures." International Journal of Mathematics 31, no. 11 (September 3, 2020): 2050084. http://dx.doi.org/10.1142/s0129167x20500846.

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We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian manifolds. We classify all structures with such symmetry dimensions. Geometric properties of the submaximally symmetric spaces are studied, in particular, we identify locally conformally quaternion-Kähler structures as well as quaternion-Kähler with torsion.

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Li, Chunbiao, Julien Clinton Sprott, Xin Zhang, Lin Chai, and Zuohua Liu. "Constructing conditional symmetry in symmetric chaotic systems." Chaos, Solitons & Fractals 155 (February 2022): 111723. http://dx.doi.org/10.1016/j.chaos.2021.111723.

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Liang, Xiquan, and Tao Wang. "Some Basic Properties of Some Special Matrices. Part III." Formalized Mathematics 20, no. 1 (January 1, 2012): 73–77. http://dx.doi.org/10.2478/v10037-012-0010-4.

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Some Basic Properties of Some Special Matrices. Part III This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.

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BUI, HUY DUONG. "ON DUALITY, SYMMETRY AND SYMMETRY LOST IN SOLID MECHANICS." International Journal of Computational Methods 11, no. 03 (June 2014): 1343004. http://dx.doi.org/10.1142/s0219876213430044.

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The paper recalls the concept of duality in mathematics and extends it to solid mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical formulation of boundary value problems (finite element method). Usually, conservation laws in fracture mechanics make use of the current fields, displacement and stress. Many conservation laws of this type are not free of the source term. Consequently, one cannot derive path-independent integrals for use in fracture mechanics. The introduction of variables and dual or adjoint variables leads to true path-independent integrals. Duality also introduces some anti-symmetry in current fields and adjoint ones for some boundary value problems. The symmetry is lost between fields and adjoint fields. The last notion enables us to derive new variational formulation on dual subspaces and to exactly solve inverse problems for detecting cracks and volume defects.

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Douglas, Michael R. "Mathematics for string phenomenology." International Journal of Modern Physics A 30, no. 03 (January 30, 2015): 1530018. http://dx.doi.org/10.1142/s0217751x15300185.

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We survey some of the basic mathematical ideas and techniques which are used in string phenomenology, such as constructions of Calabi–Yau manifolds, singularities and orbifolds, toric geometry, variation of complex structure, and mirror symmetry.

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HORNOS, JOSÉ EDUARDO M., YVONE M. M. HORNOS, and MICHAEL FORGER. "SYMMETRY AND SYMMETRY BREAKING: AN ALGEBRAIC APPROACH TO THE GENETIC CODE." International Journal of Modern Physics B 13, no. 23 (September 20, 1999): 2795–885. http://dx.doi.org/10.1142/s021797929900268x.

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We give a comprehensive review of the algebraic approach to the genetic code originally proposed by two of the present authors, which aims at explaining the degeneracies encountered in the genetic code as the result of a sequence of symmetry breakings that have occurred during its evolution. We present the relevant background material from molecular biology and from mathematics, including the representation theory of (semi) simple Lie groups/algebras, together with considerations of general nature.

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Gravel, P., and C. Gauthier. "Mirror symmetry and conformal flatness in general Relativity." International Journal of Mathematics and Mathematical Sciences 2004, no. 41 (2004): 2205–8. http://dx.doi.org/10.1155/s0161171204309038.

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Using symmetry arguments only, we show that every spacetime with mirror-symmetric spatial sections is necessarily conformally flat. The general form of the Ricci tensor of such spacetimes is also determined.

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Journal articles on the topic 'Symmetry (Mathematics)'

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