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Journal articles on the topic 'Symmetrisk relation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Spelsberg-Korspeter, G., D. Hochlenert, and P. Hagedorn. "Non-linear investigation of an asymmetric disk brake model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 10 (July 6, 2011): 2325–32. http://dx.doi.org/10.1177/0954406211408531.

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Among design engineers, it is known that breaking symmetries of a brake rotor can help to prevent squeal. From a modelling point of view, in the literature brake squeal is almost exclusively treated using models with a symmetric brake rotor, which are capable of explaining the excitation mechanism but yield no insight into the relation between rotor asymmetry and stability. In previous work, it has been demonstrated with linear models that the breaking of symmetries of the brake rotor has a stabilizing effect. The equations of motion for this case have periodic coefficients with respect to time and are therefore more difficult to analyse than in the symmetric case. The goal of this article is to investigate whether due to the breaking of symmetries also, the non-linear behaviour of the brake changes qualitatively compared to the symmetric case.

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2

Dresselhaus, M. S., and G. Dresselhaus. "Note on sufficient symmetry conditions for isotropy of the elastic moduli tensor." Journal of Materials Research 6, no. 5 (May 1991): 1114–18. http://dx.doi.org/10.1557/jmr.1991.1114.

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Group theoretical methods are used to obtain the form of the elastic moduli matrices and the number of independent parameters for various symmetries. Particular attention is given to symmetry groups for which 3D and 2D isotropy is found for the stress-strain tensor relation. The number of independent parameters is given by the number of times the fully symmetric representation is contained in the direct product of the irreducible representations for two symmetrical second rank tensors. The basis functions for the lower symmetry groups are found from the compatibility relations and are explicitly related to the elastic moduli. These types of symmetry arguments should be generally useful in treating the elastic properties of solids and composites.

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Khan, Madad, Muhammad Zeeshan, Seok-Zun Song, and Sohail Iqbal. "Types of Complex Fuzzy Relations with Applications in Future Commission Market." Journal of Mathematics 2021 (March 27, 2021): 1–14. http://dx.doi.org/10.1155/2021/6685977.

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In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

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Lee, Jeong-Gon, and Kul Hur. "Bipolar Fuzzy Relations." Mathematics 7, no. 11 (November 3, 2019): 1044. http://dx.doi.org/10.3390/math7111044.

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We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

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LORENZ, KUNO. "Reflections on the concept of symmetry." European Review 13, S2 (August 22, 2005): 3–11. http://dx.doi.org/10.1017/s1062798705000621.

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The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, ‘being symmetric’ in general usage is synonymous with ‘being harmonious’, and in technical usage, as in Euclid's Elements, it is synonymous with ‘commensurable’. Due to the second meaning, which is close to the etymology of συ´μμετρoς, ‘with measure’ has likewise to be read as ‘being [in] rational [ratios]’ and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.

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BUSTINCE, H., and P. BURILLO. "PERTURBATION OF INTUITIONISTIC FUZZY RELATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 01 (February 2001): 81–103. http://dx.doi.org/10.1142/s0218488501000648.

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In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations afterward obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another also intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the conditions there must be for the new intuitionistic fuzzy relation to maintain the original properties.

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7

ROSSI, MAURO. "Value and Preference Relations: Are They Symmetric?" Utilitas 28, no. 3 (September 21, 2015): 239–53. http://dx.doi.org/10.1017/s0953820815000369.

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According to Wlodek Rabinowicz's fitting-attitude analysis of comparative value, it is possible to analyse both standard and non-standard value relations in terms of the standard preference relations and two levels of normativity. In a recent article, however, Johan Gustafsson has argued that Rabinowicz's analysis violates a principle of value–preference symmetry, according to which for any value relation, there is a corresponding preference relation. Gustafsson has proposed an alternative analysis which respects this principle and which allegedly accounts for the idea that originally motivated Rabinowicz's analysis, namely, that in some cases different preference relations between a pair of items are equally permissible. The goal of my article is to show that the arguments offered by Gustafsson in favour of his account do not succeed. In particular, I argue that Gustafsson faces a dilemma: either he abandons the principle of value–preference symmetry or he cannot make conceptual room for multiple permissible preferences.

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8

Chajda, Ivan. "Varieties with modular and distributive lattices of symmetric or reflexive relations." Czechoslovak Mathematical Journal 42, no. 4 (1992): 623–30. http://dx.doi.org/10.21136/cmj.1992.128357.

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9

Parreño, Assumpta, Martin J. Savage, Brian C. Tiburzi, Jonas Wilhelm, Emmanuel Chang, William Detmold, and Kostas Orginos. "Baryon magnetic moments: Symmetries and relations." EPJ Web of Conferences 175 (2018): 06001. http://dx.doi.org/10.1051/epjconf/201817506001.

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Magnetic moments of the octet baryons are computed using lattice QCD in background magnetic fields, including the first treatment of the magnetically coupled ∑0- ⋀ system. Although the computations are performed for relatively large values of the up and down quark masses, we gain new insight into the symmetries and relations between magnetic moments by working at a three-flavor mass-symmetric point. While the spinflavor symmetry in the large Nc limit of QCD is shared by the naïve constituent quark model, we find instances where quark model predictions are considerably favored over those emerging in the large Nc limit. We suggest further calculations that would shed light on the curious patterns of baryon magnetic moments.

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10

Galas, David, and Nikita Sakhanenko. "Symmetries among Multivariate Information Measures Explored Using Möbius Operators." Entropy 21, no. 1 (January 18, 2019): 88. http://dx.doi.org/10.3390/e21010088.

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Relations between common information measures include the duality relations based on Möbius inversion on lattices, which are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). In this paper we use the lattice and functional symmetries to provide a unifying formalism that reveals some new relations and systematizes the symmetries of the information functions. To our knowledge, this is the first systematic examination of the full range of relationships of this class of functions. We define operators on functions on these lattices based on the Möbius inversions that map functions into one another, which we call Möbius operators, and show that they form a simple group isomorphic to the symmetric group S3. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, when applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is then naturally generalized which yields an even wider range of new relationships.

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11

Chen, Xueyou. "The Lattice Structure of L-Contact Relations." Advances in Fuzzy Systems 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/3942416.

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From the point of view of graded truth approach, we define the notion of a contact relation on the collection of allL-sets, discuss the connection to the set of all close, reflexive, and symmetric relations on allL-ultrafilters onX, and investigate the algebraic structure of allL-contact relations.

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12

Vetterlein, Thomas. "Orthogonality spaces of finite rank and the complex Hilbert spaces." International Journal of Geometric Methods in Modern Physics 16, no. 05 (May 2019): 1950080. http://dx.doi.org/10.1142/s0219887819500804.

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An orthogonality space is a set endowed with a symmetric, irreflexive binary relation. By means of the usual orthogonality relation, each anisotropic quadratic space gives rise to such a structure. We investigate in this paper the question to which extent this strong abstraction suffices to characterize complex Hilbert spaces, which play a central role in quantum physics. To this end, we consider postulates concerning the nature and existence of symmetries. Together with a further postulate excluding the existence of nontrivial quotients, we establish a representation theorem for finite-dimensional orthomodular spaces over a dense subfield of [Formula: see text].

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BOIXADER, D., J. JACAS, and J. RECASENS. "THE LENGTH AND BETWEENNESS RELATIONS OF INDISTINGUISHABILITY OPERATORS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 07, no. 03 (June 1999): 203–12. http://dx.doi.org/10.1142/s0218488599000143.

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The most common ways used to generate indistinguishability operators, namely as transitive closure of reflexive and symmetric fuzzy relation, via the Representation Theorem and as decomposable relations, are related for archimedean t-norms introducing the notion of length of indistinguishability operators.

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14

Lewis, Joel Brewster. "Affine symmetric group." WikiJournal of Science 4, no. 1 (2021): 3. http://dx.doi.org/10.15347/wjs/2021.003.

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The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tesselation of the plane, as well as related higher dimensional objects. It is an infinite extension of the symmetric group, which consists of all permutations (rearrangements) of a finite set. In additition to its geometric description, the affine symmetric group may be defined as the collection of permutations of the integers (..., −2, −1, 0, 1, 2, ...) that are periodic in a certain sense, or in purely algebraic terms as a group with certain generators and relations. These different definitions allow for the extension of many important properties of the finite symmetric group to the infinite setting, and are studied as part of the fields of combinatorics and representation theory.

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15

GAETA, GIUSEPPE, PAOLA MORANDO, and OSMAN TEOMAN TURGUT. "SYMMETRY REDUCTION IN THE VARIATIONAL APPROACH TO LIOUVILLE DYNAMICS." International Journal of Geometric Methods in Modern Physics 02, no. 04 (August 2005): 657–74. http://dx.doi.org/10.1142/s0219887805000727.

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In a recent paper, a variational principle for Liouville dynamics (vector fields preserving a volume form) was introduced. In the present paper, we discuss the relation between symmetries and conservation laws in Liouville dynamics. We recall a result by Crampin relating symmetries and conserved quantities in Liouville dynamics, and discuss how symmetry reduction is implemented in the frame of the variational principle for Liouville dynamics.

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Xu, Jiuping, and Kang Xu. "An Approach for Achieving Consistency for Symmetric Trapezoidal Interval Type-2 Fuzzy Sets." Mathematical Problems in Engineering 2019 (March 20, 2019): 1–16. http://dx.doi.org/10.1155/2019/4031485.

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Interval type-2 fuzzy sets (IT2 FSs) are powerful tools for dealing with linguistic information in decision making. However, there is a dearth of research regarding the consistency of preference relations based on IT2 FSs. In this paper, symmetric IT2 FSs and IT2 additive preference relations are defined, whilst at the same time a mapping method is proposed to convert IT2 numbers into the corresponding linguistic terms based on the ranking values for IT2 FSs, and some properties for symmetric IT2 FSs are proved. Then, we discuss the process for achieving consistency for IT2 additive preference relations. An algorithm is developed for the IT2 additive preference relation process for achieving consistency, and some desired algorithmic properties are proved. Finally, an actual case study is used in order to demonstrate the effectiveness of the proposed approach.

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17

AVAN, J., J.-M. MAILLARD, M. TALON, and C. VIALLET. "ALGEBRAIC VARIETIES FOR THE CHIRAL POTTS MODEL." International Journal of Modern Physics B 04, no. 10 (August 1990): 1743–62. http://dx.doi.org/10.1142/s0217979290000875.

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We describe the symmetries of the chiral checkerboard Potts model (duality, inversion relation, …) and write down the algebraic variety corresponding to the integrable case advocated by Baxter, Perk, Au-Yang. We examine some of its subvarieties, in different limits and for various lattices, with a special emphasis on q=3. This yields for q=3, a new algebraic variety where the standard scalar checkerboard Potts model is solvable. By a comparative analysis of the parametrization of the integrable four-state chiral Potts model and the one of the symmetric Ashkin-Teller model, we bring to light algebraic subvarieties for the q-state chiral Potts model which are invariant under the symmetries of the model. We recover in this manner the Fateev-Zamolodchikov points.

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18

BAVARD, CHRISTOPHE. "CLASSES MINIMALES DE RÉSEAUX ET RÉTRACTIONS GÉOMÉTRIQUES ÉQUIVARIANTES DANS LES ESPACES SYMÉTRIQUES." Journal of the London Mathematical Society 64, no. 2 (October 2001): 275–86. http://dx.doi.org/10.1112/s0024610701002319.

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Equivariant and cocompact retractions of certain symmetric spaces are constructed. These retractions are defined using the natural geometry of symmetric spaces and in relation to the theory of lattices of euclidean space. The following cases are considered: the symmetric space corresponding to lattices endowed with a finite group action, from which is obtained some information relating to the classification problem of these lattices, and the Siegel space Sp2g(R)/Ug, for which a natural Sp2g(Z)-equivariant cocompact retract of codimension 1 is obtained.

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19

Des Tombe, Louis. "Is Translation Symmetric?" Meta 37, no. 4 (September 30, 2002): 791–801. http://dx.doi.org/10.7202/004494ar.

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Abstract General properties of the translation relation are of interest to translators, translatologists and machine translation system designers. As translation is somehow related to the intuitive notion “equivalence”, one wonders whether it has the properties of strict mathematical equivalence. Symmetry is one of these. The paper starts out with some definitions, so that the question can he treated in a meaningful way. The answer turns out to be positive for “perfect” but negative for “imperfect” translation#x2009;; the latter because of a tendency of translators to “weaken” claims made in texts. This asymmetric aspect of imperfect translation is explained by relating it to a “monotonie” view of the organization of discourse. The paper ends with a description of a machine translation system designed to produce perfect translation, and draws conclusions about machine translation design.

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20

Hodder, Ian, and Gavin Lucas. "The symmetries and asymmetries of human–thing relations. A dialogue." Archaeological Dialogues 24, no. 2 (December 2017): 119–37. http://dx.doi.org/10.1017/s1380203817000137.

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AbstractThis paper presents a dialogue about the question of symmetry and asymmetry in human–thing relations, and the links between such asymmetries and those encountered in power relations amongst humans. The conversation discusses various issues, such as whether symmetry is possible in any kind of relation, how one defines asymmetry, whether there are different kinds of asymmetry, and how inequality between humans is related to the asymmetries in human–thing entanglements. The last issue is considered especially important in light of the various critiques that have been levelled at actor networks and other relational materialisms for their weakened political stance insofar as sources of inequality and injustice are so widely distributed that they become, in effect, apolitical.

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21

MOSHTAGH, H., and A. RAHNAMAI BARGHI. "A CLASS OF ASSOCIATION SCHEMES IN WHICH ALL BASIS RELATIONS HAVE VALENCY 1 OR λ > 2." Journal of Algebra and Its Applications 12, no. 01 (December 13, 2012): 1250124. http://dx.doi.org/10.1142/s0219498812501241.

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In this paper, we classify the commutative association schemes with both the property that each basis relation has valency either 1 or λ > 2 for some fixed λ and the property that there is a connected, symmetric basis relation R for which R2 contains exactly two basis relations. We show that up to isomorphism, the unique association scheme with these properties is the direct product of the trivial association scheme of order 2 and the trivial association scheme of order λ + 1.

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22

Urbanowski, Krzysztof. "Uncertainty Relations: Curiosities and Inconsistencies." Symmetry 12, no. 10 (October 6, 2020): 1640. http://dx.doi.org/10.3390/sym12101640.

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Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB≥0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied.

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23

KOTLERMAN, LILI, IDO DAGAN, IDAN SZPEKTOR, and MAAYAN ZHITOMIRSKY-GEFFET. "Directional distributional similarity for lexical inference." Natural Language Engineering 16, no. 4 (October 2010): 359–89. http://dx.doi.org/10.1017/s1351324910000124.

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AbstractDistributional word similarity is most commonly perceived as a symmetric relation. Yet, directional relations are abundant in lexical semantics and in many Natural Language Processing (NLP) settings that require lexical inference, making symmetric similarity measures less suitable for their identification. This paper investigates the nature of directional (asymmetric) similarity measures that aim to quantify distributional feature inclusion. We identify desired properties of such measures for lexical inference, specify a particular measure based on Average Precision that addresses these properties, and demonstrate the empirical benefit of directional measures for two different NLP datasets.

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24

MacHale, Des, and Peter MacHale. "Relations on Sets." Mathematical Gazette 97, no. 539 (July 2013): 224–33. http://dx.doi.org/10.1017/s0025557200005817.

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This paper is dedicated to the memory of George Boole FRS (1815-1864), first Professor of Mathematics at University College Cork.A relation on a non-empty set K is any subset W of the cartesian product K × K. If (x, x) ∈ W for every x ∈ K, W is said to be reflexive on K. If for x, y, z ∈ K, (x, y) ∈ W implies that (y, x) ∈ W, W is said to be symmetric on K. If for x, y, z ∈ K (x, y) ∈ W and (y, z) ∈ W together imply that (x, z) ∈ W, W is said to be transitive on K. Finally, if the relation W is reflexive, symmetric and transitive on K, W is said to be an equivalence relation on K. We contend that equivalence relations are of central importance in many areas of mathematics. Many texts on algebra (for example Topics in Algebra [1]) contain as an exercise the following fallacious argument which the reader is challenged to refute.

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25

MARTÍN-DELGADO, M. A. "THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL." International Journal of Modern Physics A 08, no. 06 (March 10, 1993): 1139–52. http://dx.doi.org/10.1142/s0217751x93000461.

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The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

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ALCALDE, CRISTINA, ANA BURUSCO, and RAMÓN FUENTES-GONZÁLEZ. "ANALYSIS OF CERTAIN L-FUZZY RELATIONAL EQUATIONS AND THE STUDY OF ITS SOLUTIONS BY MEANS OF THE L-FUZZY CONCEPT THEORY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 01 (February 2012): 21–40. http://dx.doi.org/10.1142/s021848851250002x.

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Given a Brouwerian complete lattice (L,≤) and two referential sets K and E, and using a fuzzy relation R ∈ LE×E which is reflexive and symmetric, certain fuzzy relations [Formula: see text] are characterized as solutions of X ⊲ R = X, proving that they play the role of the blocks in the context of crisp tolerance relations. Moreover, it is verified that these new fuzzy blocks [Formula: see text] can be determinated by means of the L-fuzzy concepts associated with the K -labeled L-fuzzy context (L,K,E,E,R).

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27

Huang, Yong-Chang, Syeda Tehreem Iqbal, and Wen-Yu Wang. "New symmetric relations among lepton masses and prediction of lepton masses of the fourth generation." Modern Physics Letters A 31, no. 18 (June 14, 2016): 1650115. http://dx.doi.org/10.1142/s0217732316501157.

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The presence of more than three generation of particles, predicted by various models beyond Standard Model (SM), can be the answer to several unanswered questions. In this paper, we discover a mass space by generalizing the Koide’s relation over the leptons section of SM and deduce some new symmetric relations. By using the magnitude dilation and angular rotation ratio between these relations, we predict the masses of the fourth generation particles. Also, this model constraints the existence of fifth generation leptons which up to now no theory can do.

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HANSEL, DAVID, JEAN-MARIE MAILLARD, and PÁL RUJÁN. "A STEP-BY-STEP APPROACH TO INTEGRABILITY." International Journal of Modern Physics B 03, no. 10 (October 1989): 1539–59. http://dx.doi.org/10.1142/s0217979289000993.

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We try to elucidate the role played by different symmetries in simple models of statistical mechanics. Starting with obvious symmetries for the partition function and combining them with duality relations we obtain a set of constraints on the possible algebraic varieties relevant for the integrable manifolds and the phase diagram of the lattice model. When imposing in addition the inversion relation special polynomials are obtained, which are close and sometimes identical to the set of equations defining the parameter subspace of the integrable models. Our procedure is detailed on the q-state chiral Potts models on a square lattice, in particular for q=3 and 4.

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Khan, Waseem, and Divesh Srivastava. "On the generalized Apostol-type Frobenius-Genocchi polynomials." Filomat 33, no. 7 (2019): 1967–77. http://dx.doi.org/10.2298/fil1907967k.

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The main object of this work is to introduce a new class of the generalized Apostol-type Frobenius-Genocchi polynomials and is to investigate some properties and relations of them. We derive implicit summation formulae and symmetric identities by applying the generating functions. In addition a relation in between Array-type polynomials, Apostol-Bernoulli polynomials and generalized Apostol-type Frobenius-Genocchi polynomials is also given.

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Huang, Yong-Chang, Syeda Tehreem Iqbal, Zhen Lei, and Wen-Yu Wang. "Some new symmetric relations and prediction of left- and right-handed neutrino masses using Koide’s relation." Chinese Physics C 41, no. 4 (April 2017): 043104. http://dx.doi.org/10.1088/1674-1137/41/4/043104.

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31

Kehagias, A., H. Perrier, and A. Riotto. "Equal-time consistency relations in the large-scale structure of the universe." Modern Physics Letters A 29, no. 29 (September 21, 2014): 1450152. http://dx.doi.org/10.1142/s0217732314501521.

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Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities have been recently obtained, thanks to the symmetries enjoyed by the Newtonian equations of motion describing the dark matter and galaxy fluids coupled through gravity. Via an appropriate change of coordinates, the symmetries allow to go to a frame where the zero mode and the first spatial gradient of the long and linear wavelength mode of the gravitational potential have been removed. In such a case, the response of the system on short scales is a uniform displacement leading to the vanishing of the correlators in the soft limit at the equal-time. In this paper, we show that equal-time consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter can be obtained if there is a well-defined relation between the linear growth factor D(a) and the abundance of dark matter Ω, [Formula: see text]. We also discuss the consequences of the consistency relations for the halo model.

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32

MAINZER, KLAUS. "Symmetry and complexity in dynamical systems." European Review 13, S2 (August 22, 2005): 29–48. http://dx.doi.org/10.1017/s1062798705000645.

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Historically, static symmetric bodies and ornaments are geometric idealizations in the Platonic tradition. Actually, symmetries are locally and globally broken by phase transitions of instability in dynamical systems generating a variety of new order and partial symmetries with increasing complexity. The states of complex dynamical systems can refer to, for example, atomic clusters, crystals, biomolecules, organisms and brains, social and economic systems. The paper discusses dynamical balance as dynamical symmetry in dynamical systems, which can be simulated by computational systems. Its emergence is an interdisciplinary challenge of nonlinear systems science. The philosophy of science analyses the common methodological framework of symmetry and complexity.

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Hjorth, G. "Actions by the classical Banach spaces." Journal of Symbolic Logic 65, no. 1 (March 2000): 392–420. http://dx.doi.org/10.2307/2586545.

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The study of continuous group actions is ubiquitous in mathematics, and perhaps the most general kinds of actions for which we can hope to prove theorems in just ZFC are those where a Polish group acts on a Polish space.For this general class we can find works such as [29] that build on ideas from ergodic theory and examine actions of locally compact groups in both the measure theoretic and topological contexts. On the other hand a text in model theory, such as [12], will typically consider issues bearing on the actions by the symmetric group of all permutations of the integers. More generally [1] shows that the orbit equivalence relations induced by closed subgroups of the infinite symmetric group can be reduced to the isomorphism relation on corresponding classes of countable models.This paper considers a third category formed by the continuous actions of separable Banach spaces on Polish spaces. These examples cannot be subsumed under the two earlier headings, and it is known from [10] that theBorel cardinalitiesof the quotient spaces that arise from such actions are incomparable with the equivalence relations induced by the symmetric group or any locally compact Polish group action.One of the first things to be addressed concerns the complexity of these equivalence relations. This question forappears in [1].

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Lee, Jen-Chi, and Yi Yang. "Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory." Symmetry 11, no. 8 (August 13, 2019): 1045. http://dx.doi.org/10.3390/sym11081045.

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In this paper, we studied symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the ifinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. We showed that all the high energy string amplitudes can be solved using the linear or recurrence relations, so that all the string amplitudes can be expressed in terms of a single string amplitude. We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes. Finally, we reviewed the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known S L ( K + 3 , C ) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory.

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35

Chapman, C. J., and S. V. Sorokin. "The deferred limit method for long waves in a curved waveguide." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160900. http://dx.doi.org/10.1098/rspa.2016.0900.

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This paper presents a technique, based on a deferred approach to a limit, for analysing the dispersion relation for propagation of long waves in a curved waveguide. The technique involves the concept of an analytically satisfactory pair of Bessel functions, which is different from the concept of a numerically satisfactory pair, and simplifies the dispersion relations for curved waveguide problems. Details are presented for long elastic waves in a curved layer, for which symmetric and antisymmetric waves are strongly coupled. The technique gives high-order corrections to a widely used approximate dispersion relation based a kinematic hypothesis, and determines rigorously which of its coefficients are exact.

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Jianan Xue and Kai Yang. "Symmetric relations in multistate systems." IEEE Transactions on Reliability 44, no. 4 (1995): 689–93. http://dx.doi.org/10.1109/24.476003.

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Dijksma, A., H. S. V. de Snoo, and A. V. Štraus. "Symmetric relations and module spaces." Integral Equations and Operator Theory 18, no. 2 (June 1994): 154–65. http://dx.doi.org/10.1007/bf01192457.

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38

Mainetti, Matteo. "Symmetric Operations on Equivalence Relations." Annals of Combinatorics 7, no. 3 (December 1, 2003): 325–48. http://dx.doi.org/10.1007/s00026-003-0189-8.

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39

CHEN, YI-XIN, ZHONG-SHUI MA, and ZHAO-BIN SU. "W INFINITE SYMMETRIES IN THE HIERARCHICAL QUASIPARTICLE STATES (LOWEST LANDAU LEVEL STATES) OF THE FRACTIONAL QUANTUM HALL SYSTEMS." International Journal of Modern Physics B 09, no. 02 (January 20, 1995): 195–219. http://dx.doi.org/10.1142/s0217979295000112.

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We investigate the W infinite symmetries in the theory of general fractional quantum Hall effects by using the lowest Landau level constraint approach. We find that there does exist a W infinite symmetric algebra for the fractional quantum Hall system with all the quasiparticles being restricted to the lowest Landau level. The corresponding generators can be used to generate the new degenerate wavefunctions of the lowest Landau level states by means of Laughlin and Halperin wavefunctions. Meanwhile, we find there still exists another W infinite symmetric algebra in the system, whose generators are used to generate the degenerate wavefunctions of the lowest Landau level for the anti-quasiparticles. We conclude that the FQH system can effectively be described by quasiparticle features or anti-quasiparticle features. We also show that the local part of the W infinite symmetric algebras is the magnetic translation operator of the general fractional quantum Hall system. We finally construct the operators of the single mode wave density excitations in the system and discuss their operator product relations.

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POPOV, A. D. "SELF-DUAL YANG–MILLS: SYMMETRIES AND MODULI SPACE." Reviews in Mathematical Physics 11, no. 09 (October 1999): 1091–149. http://dx.doi.org/10.1142/s0129055x99000350.

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Geometry of the solution space of the self-dual Yang–Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of the SDYM equations and its action on the space of local solutions to the field equations. It is argued that owing to the relation to a holomorphic analogue of the Chern–Simons theory, the SDYM theory may be as solvable as 2D rational conformal field theories, and successful nonperturbative quantization may be developed. An algebra acting on the space of self-dual conformal structures on a 4-space (an analogue of the Virasoro algebra) and an algebra acting on the space of self-dual connections (an analogue of affine Lie algebras) are described. Relations to problems of topological and N=2 strings are briefly discussed.

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41

Christensen, Jesper Højbjerg. "Public relations i et overkommunikeret samfund." MedieKultur: Journal of media and communication research 9, no. 20 (September 1, 1993): 7. http://dx.doi.org/10.7146/mediekultur.v9i20.963.

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Vi har aldrig før været så overfodret med kommunikation. Jesper Højbjerg Christensen, direktør for Advice Ledelses- og Kommuni- kationsrådgivning A/S, diskuterer i artiklen som praktiker med kom- munikationsreoretisk baggrund, hvordan det kan sikres, at man inden for kommunikations- og public relations-branchen ikke bare kommunikerer som propagandamaskiner - mere og mere - men hellere går i dialog og kommunikerer mindre, og bedre. Han peger på, at vi i fremtiden, bl.a. takket være sammenhængne mellem høj uddannelse og avanceret teknologi, får mulighed for at udfolde mere symmetriske kommunikationsformer og konsensus-funderet dialog. Som sit bidrag til at udrydde forvirringen om, hvad public relation egentlig er, opstiller han - uden større tiltro til, at man kan skabe en "teori" om PR - ud fra praksis fire forskellige måder at dyrke public relations på.

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Blažić, Novica, and Neda Bokan. "Projective and affine transformations of a complex symmetric connection." Bulletin of the Australian Mathematical Society 50, no. 2 (October 1994): 337–47. http://dx.doi.org/10.1017/s0004972700013794.

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Let M be a compact complex manifold and ∇ an arbitrary complex (not necessarily Riemannian) connection. In this paper we study the relation between the geometry of (M, ∇) and the topology of M, that is, we are interested in the following problem: To what extent does the topology of M determine the relations between the group of holomorphically projective transformations, the group of projective transformations and the group of affine transformations on M? Under assumptions on the Ricci-type tensors of ∇ and Chern numbers of M we show that a holomorphically projective transformation and a projective transformation are in fact affine transformations on M. A family of interesting examples of connections of this kind are constructed. Also, the case when M is a Kähler manifold is studied.

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KOLLAR, MARCUS. "CONSTRUCTION OF A DISPERSION RELATION FROM AN ARBITRARY DENSITY OF STATES." International Journal of Modern Physics B 16, no. 23 (September 10, 2002): 3491–501. http://dx.doi.org/10.1142/s0217979202011937.

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The dispersion relations of energy bands in solids are characterized by their density of states, but a given density of states may originate from various band structures. We show how a spherically symmetric dispersion can be constructed for any one-band density of states. This method is applied to one-, two- and three-dimensional systems. It also serves to establish that any one-band spectrum with finite bandwidth can be obtained from a properly scaled dispersion relation in the limit of infinite dimensions.

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Chantraine, Baptiste. "Lagrangian concordance is not a symmetric relation." Quantum Topology 6, no. 3 (2015): 451–74. http://dx.doi.org/10.4171/qt/68.

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Huang, Tian-yi, Chang-bin Wang, and Zhang-yin Zhao. "The relation between symmetric and symplectic methods." Chinese Astronomy and Astrophysics 22, no. 1 (January 1998): 101–12. http://dx.doi.org/10.1016/s0275-1062(98)00015-0.

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Margańska, Magdalena, Marek Szopa, and Eldot zbieta Zipper. "Symmetric and asymmetric dispersion relation in graphene." Journal of Physics: Conference Series 30 (February 28, 2006): 302–6. http://dx.doi.org/10.1088/1742-6596/30/1/036.

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Kolmykov, V. A. "The Commutativity Relation in the Symmetric Semigroup." Siberian Mathematical Journal 45, no. 5 (September 2004): 931–34. http://dx.doi.org/10.1023/b:simj.0000042480.17442.5b.

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48

Arora, Kushal, Aishik Chakraborty, and Jackie C. K. Cheung. "Learning Lexical Subspaces in a Distributional Vector Space." Transactions of the Association for Computational Linguistics 8 (July 2020): 311–29. http://dx.doi.org/10.1162/tacl_a_00316.

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In this paper, we propose LexSub, a novel approach towards unifying lexical and distributional semantics. We inject knowledge about lexical-semantic relations into distributional word embeddings by defining subspaces of the distributional vector space in which a lexical relation should hold. Our framework can handle symmetric attract and repel relations (e.g., synonymy and antonymy, respectively), as well as asymmetric relations (e.g., hypernymy and meronomy). In a suite of intrinsic benchmarks, we show that our model outperforms previous approaches on relatedness tasks and on hypernymy classification and detection, while being competitive on word similarity tasks. It also outperforms previous systems on extrinsic classification tasks that benefit from exploiting lexical relational cues. We perform a series of analyses to understand the behaviors of our model. 1 Code available at https://github.com/aishikchakraborty/LexSub .

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BERGSHOEFF, ERIC, STEFAN VANDOREN, and ANTOINE VAN PROEYEN. "THE IDENTIFICATION OF CONFORMAL HYPERCOMPLEX AND QUATERNIONIC MANIFOLDS." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 913–32. http://dx.doi.org/10.1142/s0219887806001521.

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We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. "conformal hypercomplex" manifolds) and quaternionic manifolds of one dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between the structure of these manifolds is presented, including curvatures and symmetries. An important role is played by "ξ transformations," relating connections on quaternionic manifolds, and a new type "[Formula: see text] transformations" relating complex structures on conformal hypercomplex manifolds. In this map, the subclass of conformal hyper-Kähler manifolds is mapped to quaternionic-Kähler manifolds.

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Bremner, Murray, and Vladimir Dotsenko. "Classification of Regular Parametrized One-relation Operads." Canadian Journal of Mathematics 69, no. 5 (October 1, 2017): 992–1035. http://dx.doi.org/10.4153/cjm-2017-018-3.

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AbstractJean-Louis Loday introduced a class of symmetric operads generated by one bilinear operation subject to one relation making each left-normed product of three elements equal to a linear combination of right-normed products: . Such an operad is called a parametrized one-relation operad. For a particular choice of parameters {xσ}, this operad is said to be regular if each of its components is the regular representation of the symmetric group; equivalently, the corresponding free algebra on a vector space V is, as a graded vector space, isomorphic to the tensor algebra of V. We classify, over an algebraically closed field of characteristic zero, all regular parametrized one-relation operads. In fact, we prove that each such operad is isomorphic to one of the following ûve operads: the left-nilpotent operad defined by the relation ((a1a2)a3) = 0, the associative operad, the Leibniz operad, the dual Leibniz (Zinbiel) operad, and the Poisson operad. Our computationalmethods combine linear algebra over polynomial rings, representation theory of the symmetric group, and Gröbner bases for determinantal ideals and their radicals.

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