Symmetry

210 KiB

Open AccessArticle

Phase Diffusion of a q-Deformed Oscillator

by Turan Birol and Özgür Esat Müstecaplıoğlu

Symmetry 2009, 1(2), 240-251; https://doi.org/10.3390/sym1020240 - 21 Dec 2009

Cited by 3 | Viewed by 6696

We examine the problem of phase diffusion rate in a U(1) global phase symmetry broken system, from the perspective of q-deformed oscillators where the deformation parameter represents the anharmonicity. It is shown that broken phase symmetry states, described by deformed coherent states, suffer [...] Read more.

We examine the problem of phase diffusion rate in a U(1) global phase symmetry broken system, from the perspective of q-deformed oscillators where the deformation parameter represents the anharmonicity. It is shown that broken phase symmetry states, described by deformed coherent states, suffer phase diffusion at a rate determined by the deformation parameter. Analytical discussions are given for the case of weak deformations, while detailed numerical results are presented when strong anharmonicity is present in the system. Full article

(This article belongs to the Special Issue Symmetry Breaking Phenomena)

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5410 KiB

Open AccessArticle

Polyhedral Phenylacetylenes: The Interplay of Aromaticity and Antiaromaticity in Convex Graphyne Substructures

by Daniel Sebastiani and Matt A. Parker

Symmetry 2009, 1(2), 226-239; https://doi.org/10.3390/sym1020226 - 11 Dec 2009

Cited by 9 | Viewed by 7235

Abstract

We have studied a series of bridged phenylacetylene macrocycles with topologies based on Platonic and Archimedean polyhedra, using density functional calculations to determine both their molecular structure and their electronic response to external magnetic fields (NICS maps). We are able to elucidate the [...] Read more.

We have studied a series of bridged phenylacetylene macrocycles with topologies based on Platonic and Archimedean polyhedra, using density functional calculations to determine both their molecular structure and their electronic response to external magnetic fields (NICS maps). We are able to elucidate the interplay of aromaticity and anti-aromaticity as a function of structural parameters, in particular the symmetry properties of the intramolecular bond connectivities, in these compounds. Full article

(This article belongs to the Special Issue Aromaticity and Molecular Symmetry)

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163 KiB

Open AccessArticle

Symmetry in Infancy: Analysis of Motor Development in Autism Spectrum Disorders

by Gianluca Esposito and Paola Venuti

Symmetry 2009, 1(2), 215-225; https://doi.org/10.3390/sym1020215 - 10 Dec 2009

Cited by 25 | Viewed by 10184

Abstract

Motor asymmetry, defined as the lack of symmetry in movements or postures, is often observed briefly in many typically developing children. However, if such asymmetry persists, it may be a sign of neurological disease. Recent studies have suggested that motor asymmetries may be [...] Read more.

Motor asymmetry, defined as the lack of symmetry in movements or postures, is often observed briefly in many typically developing children. However, if such asymmetry persists, it may be a sign of neurological disease. Recent studies have suggested that motor asymmetries may be an early symptom of Autism Spectrum Disorders (ASD). ASD involve a range of social, cognitive, and behavioral problems, at different degrees of functioning, which are thought to be the final common pathway of multiple etiological mechanisms. Furthermore, early identification of ASD has been recognized as a critical aspect for treatment. Our study aims to analyze symmetry in the motor milestones of infants with ASD compared with typically developing infants (TD) or infants with other developmental delay (DD) during the first year of life. Our results highlight that there are different patterns of motor symmetry in the groups. In particular, infants with ASD scored significantly poorer (higher levels of asymmetry) then the TD and DD infants. We also identified two subgroups of infants with ASD, one with a typical level and the other with a lower level of motor functioning. Implications of the study for diagnosis and treatment are described. Full article

(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)

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250 KiB

Open AccessArticle

On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities

by Antonio Di Crescenzo and Barbara Martinucci

Symmetry 2009, 1(2), 201-214; https://doi.org/10.3390/sym1020201 - 26 Nov 2009

Cited by 12 | Viewed by 6407

Abstract

We consider a bilateral birth-death process having sigmoidal-type rates. A thorough discussion on its transient behaviour is given, which includes studying symmetry properties of the transition probabilities, finding conditions leading to their bimodality, determining mean and variance of the process, and analyzing absorption [...] Read more.

We consider a bilateral birth-death process having sigmoidal-type rates. A thorough discussion on its transient behaviour is given, which includes studying symmetry properties of the transition probabilities, finding conditions leading to their bimodality, determining mean and variance of the process, and analyzing absorption problems in the presence of 1 or 2 boundaries. In particular, thanks to the symmetry properties we obtain the avoiding transition probabilities in the presence of a pair of absorbing boundaries, expressed as a series. Full article

(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)

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305 KiB

Open AccessArticle

Testing Group Symmetry of a Multivariate Distribution

by Lyudmila Sakhanenko

Symmetry 2009, 1(2), 180-200; https://doi.org/10.3390/sym1020180 - 26 Nov 2009

Cited by 4 | Viewed by 5424

Abstract

We propose and study a general class of tests for group symmetry of a multivariate distribution, which encompasses different types of symmetry, such as ellipsoidal and permutation symmetries among others. Our approach is based on supremum norms of special empirical processes combined with [...] Read more.

We propose and study a general class of tests for group symmetry of a multivariate distribution, which encompasses different types of symmetry, such as ellipsoidal and permutation symmetries among others. Our approach is based on supremum norms of special empirical processes combined with bootstrap. We show that these tests are consistent against any fixed alternative. This work generalizes the methodology of Koltchinskii and Sakhanenko [7], developed for ellipsoidal symmetry to the case of group symmetry. It also provides a unified approach to testing different types of symmetry of a multivariate distribution. Full article

271 KiB

Open AccessArticle

Tetraquark Spectroscopy: A Symmetry Analysis

by Javier Vijande and Alfredo Valcarce

Symmetry 2009, 1(2), 155-179; https://doi.org/10.3390/sym1020155 - 23 Nov 2009

Cited by 29 | Viewed by 6797

Abstract

We present a detailed analysis of the symmetry properties of a four-quark wave function and its solution by means of a variational approach for simple Hamiltonians. We discuss several examples in the light and heavy-light meson sector. Full article

(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)

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15 KiB

Open AccessNew Book Received

Visual Symmetry. By Magdolna Hargittai and István Hargittai, World Scientific Publishing, 2009; 224 pages. Price: US48 / £ 36 ISBN 978-981-283-531-4

by Shu-Kun Lin

Symmetry 2009, 1(2), 153-154; https://doi.org/10.3390/sym1020153 - 23 Oct 2009

Viewed by 5606

Abstract

Symmetry is as simple or as complicated as we are ready to absorb it in everything around us. From flowers to bridges, buildings, coke machines, and snowflakes; from molecules to walnuts, fences, pine cones, and sunflowers; from music to children's drawings; from hubcaps [...] Read more.

Symmetry is as simple or as complicated as we are ready to absorb it in everything around us. From flowers to bridges, buildings, coke machines, and snowflakes; from molecules to walnuts, fences, pine cones, and sunflowers; from music to children's drawings; from hubcaps to bank logos, propellers, wallpaper decorations, and pavements, we recognize it if we walk around with open eyes and an open mind. This book provides aesthetic pleasure and covert education, immersing the reader in both the familiar and the unknown and leading always to unexpected discoveries. [...] Full article

168 KiB

Open AccessArticle

On the Symmetry of a Zig-Zag and an Armchair Polyhex Carbon Nanotorus

by Morteza Yavari and Ali Reza Ashrafi

Symmetry 2009, 1(2), 145-152; https://doi.org/10.3390/sym1020145 - 08 Oct 2009

Cited by 5 | Viewed by 6437

Abstract

A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [d_ij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix d_ii [...] Read more.

A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [d_ij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix d_ii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. The aim of this paper is to compute the automorphism group of the Euclidean graph of a carbon nanotorus. We prove that this group is a semidirect product of a dihedral group by a group of order 2. Full article

(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)

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266 KiB

Open AccessReview

Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions

by Axel Schulze-Halberg and Juan M. Carballo Jimenez

Symmetry 2009, 1(2), 115-144; https://doi.org/10.3390/sym1020115 - 06 Oct 2009

Cited by 9 | Viewed by 6346

Abstract

We review recent results on how to extend the supersymmetry SUSY normalism in Quantum Mechanics to linear generalizations of the time-dependent Schrödinger equation in (1+1) dimensions. The class of equations we consider contains many known cases, such as the Schrödinger equation for position-dependent [...] Read more.

We review recent results on how to extend the supersymmetry SUSY normalism in Quantum Mechanics to linear generalizations of the time-dependent Schrödinger equation in (1+1) dimensions. The class of equations we consider contains many known cases, such as the Schrödinger equation for position-dependent mass. By evaluating intertwining relations, we obtain explicit formulas for the interrelations between the supersymmetric partner potentials and their corresponding solutions. We review reality conditions for the partner potentials and show how our SUSY formalism can be extended to the Fokker-Planck and thenonhomogeneous Burgers equation. Full article

(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)

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98 KiB

Open AccessArticle

The Relationship Between Morphological Symmetry and Immune Response in Wild-Caught Adult Bush-Crickets

by Åsa Berggren and Matthew Low

Symmetry 2009, 1(2), 106-114; https://doi.org/10.3390/sym1020106 - 28 Sep 2009

Cited by 1 | Viewed by 6187

Abstract

Despite interest in the relationship between fluctuating asymmetry (FA), immune response and ecological factors in insects, little data are available from wild populations. In this study we measured FA and immune response in 370 wild-caught male bush-crickets, Metrioptera roeseli, from 20 experimentally introduced [...] Read more.

Despite interest in the relationship between fluctuating asymmetry (FA), immune response and ecological factors in insects, little data are available from wild populations. In this study we measured FA and immune response in 370 wild-caught male bush-crickets, Metrioptera roeseli, from 20 experimentally introduced populations in southern-central Sweden. Individuals with more-symmetric wings had a higher immune response as measured by the cellular encapsulation of a surgically-implanted nylon monofilament. However, we found no relationship between measures of FA in other organs (i.e. tibia and maxillary palp) and immune response, suggesting that this pattern may reflect differing selection pressures. Full article

(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)

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Symmetry, Volume 1, Issue 2 (December 2009) – 10 articles , Pages 106-251

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