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Journal articles on the topic 'Symmetry center'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

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1

Krivoshein, A. V. "Multivariate symmetric refinable functions and function vectors." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 05 (2016): 1650034. http://dx.doi.org/10.1142/s021969131650034x.

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For any symmetry group [Formula: see text], any appropriate matrix dilation (compatible with [Formula: see text]) and any appropriate symmetry center [Formula: see text] we give an explicit method for the construction of [Formula: see text]-symmetric with respect to the center [Formula: see text] refinable masks which have sum rule of an arbitrary order [Formula: see text]. Moreover, we give a description of all these masks. For any symmetry group [Formula: see text], any appropriate matrix dilation (compatible with [Formula: see text]) and any appropriate row of symmetry centers [Formula: see text] we give two explicit methods for the construction of [Formula: see text]-symmetric with respect to the row of centers [Formula: see text] refinable matrix masks which have sum rule of an arbitrary order [Formula: see text]. A description of all such matrix masks is also presented.

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2

Sercel, Peter C., Andrew Shabaev, and Alexander L. Efros. "Symmetry Breaking Induced Activation of Nanocrystal Optical Transitions." MRS Advances 3, no. 14 (2018): 711–16. http://dx.doi.org/10.1557/adv.2018.19.

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ABSTRACTWe have analysed the effect of symmetry breaking on the optical properties of semiconductor nanocrystals due to doping by charged impurities. Using doped CdSe nanocrystals as an example, we show the effects of a Coulomb center on the exciton fine-structure and optical selection rules using symmetry theory and then quantify the effect of symmetry breaking on the exciton fine structure, modelling the charged center using a multipole expansion. The model shows that the presence of a Coulomb center breaks the nanocrystal symmetry and affects its optical properties through mixing and shifting of the hole spin and parity sublevels. This symmetry breaking, particularly for positively charged centers, shortens the radiative lifetime of CdSe nanocrystals even at room temperature, in qualitative agreement with the increase in PL efficiency observed in CdSe nanocrystals doped with positive Ag charge centers [A. Sahu et.al., Nano Lett. 12, 2587, (2012)]. The effect of the charged center on the photoluminescence and the absorption spectra is shown, with and without the presence of compensating charges on the nanocrystal surface. While spectra of individual nanocrystals are expected to shift and broaden with the introduction of a charged center, configuration averaging and inhomogeneous broadening are shown to wash out these effects. The presence of compensating charges at the NC surface also serves to stabilize the band edge transition energies relative to NCs with no charge centers.

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3

Dakić, Vedran, Mario Kovač, and Josip Knezović. "Improving Infrastructure Cluster Design by Using Symmetry." Symmetry 17, no. 3 (2025): 357. https://doi.org/10.3390/sym17030357.

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Symmetry in IT system design is essential for improving efficiency, consistency, and manageability in data center operations. Symmetry guarantees that all system elements—be it hardware, software, or network configurations—are crafted to be consistent, thereby minimizing variability and streamlining operations. This principle is especially pertinent in cluster computing, where uniform server configurations facilitate efficient maintenance and consistent system performance. Symmetric designs reduce variations among nodes, alleviating performance discrepancies and resource imbalances commonly encountered in heterogeneous environments. This paper examines the advantages of symmetric configurations via an experimental analysis of the lifecycle management process. The findings indicate that clusters constructed with a symmetric server architecture enhance operational efficiency. From a lifecycle management standpoint, symmetry streamlines hardware provisioning and maintenance, diminishing complexities related to Day-1 and Day-2 operations. Furthermore, by guaranteeing consistent performance across all servers, symmetric designs facilitate a more predictable quality of service (QoS), reducing bottlenecks and improving overall system stability. Experimental results indicate that, when properly configured, symmetric clusters surpass asymmetric configurations in sustaining QoS, especially during peak loads or hardware failures, owing to their enhanced resource allocation and failover mechanisms. This research highlights the significance of symmetry as a fundamental principle in cluster-based data center architecture.

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4

DZHUNUSHALIEV, V., H. J. SCHMIDT, and O. RURENKO. "SPHERICALLY SYMMETRIC SOLUTIONS IN MULTIDIMENSIONAL GRAVITY WITH THE SU(2) GAUGE GROUP AS THE EXTRA DIMENSIONS." International Journal of Modern Physics D 11, no. 05 (2002): 685–701. http://dx.doi.org/10.1142/s0218271802001925.

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The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the "SU(2) gauge potential" (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed.

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5

KOZAMEH, CARLOS, RAUL ORTEGA, and TERESITA ROJAS. "CENTER OF MASS AND SPIN FOR AXIALLY SYMMETRIC SPACETIMES." International Journal of Modern Physics D 20, no. 05 (2011): 717–28. http://dx.doi.org/10.1142/s0218271811019050.

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We give equations of motion for the center of mass and intrinsic angular momentum of axially symmetric sources that emit gravitational radiation. This symmetry is used to uniquely define the notion of total angular momentum. The center of mass then singles out the intrinsic angular momentum of the system.

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6

Reiersolmoen, Ann Christin, Stefano Battaglia, Sigurd Oien-Odegaard, et al. "Symmetry of Three-Center, Four-Electron Bonds." Chemical Science 11 (May 30, 2020): 7979–90. https://doi.org/10.5281/zenodo.3866337.

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7

Faber, M., and R. Höllwieser. "Center Vortices and Chiral Symmetry Breaking." Nuclear Physics B - Proceedings Supplements 245 (December 2013): 9–16. http://dx.doi.org/10.1016/j.nuclphysbps.2013.10.003.

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8

Wang, Xing-Xiang, and Xiao Hu. "Reconfigurable topological waveguide based on honeycomb lattice of dielectric cuboids." Nanophotonics 9, no. 10 (2020): 3451–58. http://dx.doi.org/10.1515/nanoph-2020-0146.

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AbstractWe show that the photonic crystal (PhC) made of dielectric cuboids with their centers forming a honeycomb lattice is characterized by a ${\mathbb{&#x2124;}}_{2}$ topological index when the longer sides of six cuboids point towards the center of hexagonal unit cell. While the C6v symmetry regarding the center of unit cell is preserved, the C3 symmetry regarding honeycomb sites is broken, which opens a bandgap in the Dirac dispersion of honeycomb structure and induces a band inversion between p modes and d modes. Rotating cuboids around their individual centers closes the bandgap and reopens a trivial bandgap. We discuss that this feature can be exploited for realizing a reconfigurable topological waveguide.

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9

Estrozi, Leandro Farias, Stefano Trapani, and Jorge Navaza. "SCA: Symmetry-based center assignment of 2D projections of symmetric 3D objects." Journal of Structural Biology 157, no. 2 (2007): 339–47. http://dx.doi.org/10.1016/j.jsb.2006.08.004.

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10

Bingham, Geoffrey P., and Michael M. Muchisky. "Center of mass perception: Perturbation of symmetry." Perception & Psychophysics 54, no. 5 (1993): 633–39. http://dx.doi.org/10.3758/bf03211786.

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11

BAGRAEV, N. T. "SYMMETRY OF THE EL2 CENTER IN GaAs." Modern Physics Letters B 05, no. 29 (1991): 1925–31. http://dx.doi.org/10.1142/s0217984991002318.

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Optical absorption measurements on uniaxially stressed GaAs single crystals point to the C3v symmetry for the D0, D+, and D++ charge states of the EL2 double donor and allow to assign these states respectively to the L, Γ, and X valleys of the conduction band.

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12

Debbio, Luigi Del, and Agostino Patella. "Center symmetry and the orientifold planar equivalence." Journal of High Energy Physics 2009, no. 03 (2009): 071. http://dx.doi.org/10.1088/1126-6708/2009/03/071.

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13

Reiersølmoen, Ann Christin, Stefano Battaglia, Sigurd Øien-Ødegaard, et al. "Symmetry of three-center, four-electron bonds." Chemical Science 11, no. 30 (2020): 7979–90. http://dx.doi.org/10.1039/d0sc02076a.

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14

Basile, Ivano, and Pouya Golmohammadi. "Center Symmetry Breaking in Calabi–Yau Compactifications." Symmetry 17, no. 4 (2025): 490. https://doi.org/10.3390/sym17040490.

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It is widely believed that global symmetries must be broken in Quantum Gravity. This includes higher-form symmetries, which are commonplace in supergravity coupled to vector multiplets. Recently, a quantitative criterion for the breaking of (higher-form) symmetries in effective field theories of gravity has been proposed. We studied this criterion in the context of center one-form symmetries broken by BPS states in Calabi–Yau compactifications of type IIA string theory and M-theory. In a simple toy model, we evaluated the parameters quantifying the extent of symmetry breaking for large and small values of the moduli, comparing the scales of significant breaking with other relevant physical scales.

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15

Clemente, Dore Augusto, and Armando Marzotto. "30 Space-group corrections: two examples of false polymorphism and one of incorrect interpretation of the fine details of an IR spectrum." Acta Crystallographica Section B Structural Science 60, no. 3 (2004): 287–92. http://dx.doi.org/10.1107/s0108768104006391.

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Revised structures are reported for 30 crystalline compounds, based on space groups of higher symmetry than originally reported. In 18 cases the Laue class is revised, in seven cases the center of symmetry is added, in two cases the Laue class change is coupled with the addition of the center of symmetry, in two cases the addition of the center of symmetry also requires the addition of systematic absences and, finally, one case of the addition of systematic absences without changing the Laue group is reported. Two examples (CSD refcodes: DAMLIM and ABPZCU01) of false polymorphism and one (PAVJUR) of the erroneous interpretation of the fine details of IR spectra, owing to incorrect space-group determination, have been detected.

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16

Wu, Yang, Wenquan Liu, Jianpei Geng, et al. "Observation of parity-time symmetry breaking in a single-spin system." Science 364, no. 6443 (2019): 878–80. http://dx.doi.org/10.1126/science.aaw8205.

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Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time–symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time–symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken PT symmetry have been observed with a single nitrogen-vacancy center in diamond. Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.

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17

Zhukov, Dmitry O., Elena G. Andrianova, and Sergey A. Lesko. "The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold." Symmetry 11, no. 7 (2019): 920. http://dx.doi.org/10.3390/sym11070920.

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Analyses of the processes of information transfer within network structures shows that the conductivity and percolation threshold of the network depend not only on its density (average number of links per node), but also on its spatial symmetry groups and topological dimension. The results presented in this paper regarding conductivity simulation in network structures show that, for regular and random 2D and 3D networks, an increase in the number of links (density) per node reduces their percolation threshold value. At the same network density, the percolation threshold value is less for 3D than for 2D networks, whatever their structure and symmetry may be. Regardless of the type of networks and their symmetry, transition from 2D to 3D structures engenders a change of percolation threshold by a value exp{−(d − 1)} that is invariant for transition between structures, for any kind of network (d being topological dimension). It is observed that in 2D or 3D networks, which can be mutually transformed by deformation without breaking and forming new links, symmetry of similarity is observed, and the networks have the same percolation threshold. The presence of symmetry axes and corresponding number of symmetry planes in which they lie affects the percolation threshold value. For transition between orders of symmetry axes, in the presence of the corresponding planes of symmetry, an invariant exists which contributes to the percolation threshold value. Inversion centers also influence the value of the percolation threshold. Moreover, the greater the number of pairs of elements of the structure which have inversion, the more they contribute to the fraction of the percolation threshold in the presence of such a center of symmetry. However, if the center of symmetry lies in the plane of mirror symmetry separating the layers of the 3D structure, the mutual presence of this group of symmetry elements do not affect the percolation threshold value. The scientific novelty of the obtained results is that for different network structures, it was shown that the percolation threshold for the blocking of nodes problem could be represented as an additive set of invariant values, that is, as an algebraic sum, the value of the members of which is stored in the transition from one structure to another. The invariant values are network density, topological dimension, and some of the elements of symmetry (axes of symmetry and the corresponding number of symmetry planes in which they lie, centers of inversion).

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18

Lee, Seungeun, and Jaehoon Yim. "Students’ Understanding of Figures with Point Symmetry and Its Educational Implications." Korean Society of Educational Studies in Mathematics - Journal of Educational Research in Mathematics 33, no. 2 (2023): 245–65. http://dx.doi.org/10.29275/jerm.2023.33.2.245.

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This paper examines students’ thoughts and the difficulties faced while learning figures with point symmetry. This study was conducted with a class of 5th grade students. We identified the difficulties encountered by them as: confusing the center of a figure with the center of rotation, confusing rotating a figure 180° with moving a figure in the opposite direction, difficulty in specifying and explaining the amount of rotation, tendency to use the property of corresponding sides instead of the property of corresponding points when completing a figure with point symmetry, and difficulty in dealing with both horizontal and vertical directions on grid paper. These findings suggest that the following experiences should be provided while learning figures with point symmetry: distinguishing the center of a figure from the center of rotation, understanding the difference between rotating by 180° and moving in the opposite direction, specifying and measuring the amount of rotation in circular motion, exploring figures with point symmetry on a polar grid, understanding the rotation of a figure in connection with the rotation of its components, dealing with information of both directions in grids, and drawing figures with point symmetry on non-grid as well as grid paper.

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19

Kaczmarek, Slawomir M., Grzegorz Leniec, Tomasz Bodziony, et al. "BaWO4:Ce Single Crystals Codoped with Na Ions." Crystals 9, no. 1 (2019): 28. http://dx.doi.org/10.3390/cryst9010028.

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Single crystals of BaWO4, BaWO4: 0.5 at. % Ce; BaWO4: 1 at. % Ce; BaWO4: 0.5 at. % Ce, 1 at. % Na; and BaWO4: 1 at. % Ce, 2 at. % Na were grown from an inductively heated iridium crucible by the Czochralski method on a Malvern MSR4 puller. They were investigated using Electron Paramagnetic Resonance (EPR) spectroscopy at helium temperatures. One isolated center of high (D2d or S4) symmetry was found and two or more other centers of lower symmetry were identified, depending on crystal doping. From the fitting using the EPR-NMR program, the following parameters of g-matrix for the high symmetry center were found: gx = 1.505, gy = 1.505, and gz = 2.731. The linewidth vs. temperature revealed an increasing exponential tendency with increasing temperature. It showed one phonon at the lower temperatures and a Raman + Orbach effect at the higher temperatures. Radioluminescence and pulse height spectra showed rather poor scintillation properties, without any contribution from cerium emission.

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20

Eppel, Sagi, and Joel Bernstein. "Statistical survey of hydrogen-bond motifs in crystallographic special symmetry positions, and the influence of chirality of molecules in the crystal on the formation of hydrogen-bond ring motifs." Acta Crystallographica Section B Structural Science 64, no. 1 (2008): 50–56. http://dx.doi.org/10.1107/s0108768107059629.

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A statistical survey was carried out to examine the connection between hydrogen-bond ring motifs (synthons) and crystallographic special symmetry positions. In the first part, the probability of common hydrogen-bond ring motifs to occupy specific crystallographic symmetry positions of inversion centers, rotation axes and mirror planes was examined. In the second part the probability of the occurrence of hydrogen-bond ring motifs was compared between crystals of chiral molecules (which cannot form inversion or mirror symmetry) to crystals of achiral molecules and racemic crystals. The results show that the crystallographic inversion center is a very significant component in the formation of hydrogen-bond ring motifs.

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21

Wang, Qiang, Guowei Li, Weitong Jin, Shurui Zhang, and Weixing Sheng. "A Variable Structure Multiple-Model Estimation Algorithm Aided by Center Scaling." Electronics 12, no. 10 (2023): 2257. http://dx.doi.org/10.3390/electronics12102257.

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The accuracy for target tracking using a conventional interacting multiple-model algorithm (IMM) is limited. In this paper, a new variable structure of interacting multiple-model (VSIMM) algorithm aided by center scaling (VSIMM-CS) is proposed to solve this problem. The novel VSIMM-CS has two main steps. Firstly, we estimate the approximate location of the true model. This is aided by the expected-mode augmentation algorithm (EMA), and a new method—namely, the expected model optimization method—is proposed to further enhance the accuracy of EMA. Secondly, we change the original model set to ensure the current true model as the symmetry center of the current model set, and the model set is scaled down by a certain percentage. Considering the symmetry and linearity of the system, the errors produced by symmetrical models can be well offset. Furthermore, narrowing the distance between the true model and the default model is another effective method to reduce the error. The second step is based on two theories: symmetric model set optimization method and proportional reduction optimization method. All proposed theories aim to minimize errors as much as possible, and simulation results highlight the correctness and effectiveness of the proposed methods.

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22

Höllwieser, R. "Center Vortices, Topological Charge and Chiral Symmetry Breaking." Acta Physica Polonica B Proceedings Supplement 10, no. 4 (2017): 1001. http://dx.doi.org/10.5506/aphyspolbsupp.10.1001.

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23

Bagraev, Nikolai T. "The El2 Center in GaAs: Symmetry and Metastability." Defect and Diffusion Forum 103-105 (January 1993): 67–84. http://dx.doi.org/10.4028/www.scientific.net/ddf.103-105.67.

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24

Bagraev, N. T. "The EL2 center in GaAs: symmetry and metastability." Journal de Physique I 1, no. 10 (1991): 1511–27. http://dx.doi.org/10.1051/jp1:1991223.

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25

Rose, Kristie N., Michaele J. Hardie, Jerry L. Atwood, and Colin L. Raston. "Oxygen-center laden C2h symmetry resorcin[4]arenes." Journal of Supramolecular Chemistry 1, no. 1 (2001): 35–38. http://dx.doi.org/10.1016/s1472-7862(01)00006-5.

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26

Koiller, Jair, Sônia Pinto De Carvalho, Ronaldo Rodrigues Da Silva, and Luis Carlos Gonçalves De Oliveira. "On Aref's vortex motions with a symmetry center." Physica D: Nonlinear Phenomena 16, no. 1 (1985): 27–61. http://dx.doi.org/10.1016/0167-2789(85)90084-3.

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27

Ogilvie, Michael C. "Center symmetry and abelian projection at finite temperature." Nuclear Physics B - Proceedings Supplements 119 (May 2003): 709–11. http://dx.doi.org/10.1016/s0920-5632(03)80460-7.

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28

Saraste, Jaakko, and Bruno Goud. "Functional Symmetry of Endomembranes." Molecular Biology of the Cell 18, no. 4 (2007): 1430–36. http://dx.doi.org/10.1091/mbc.e06-10-0933.

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In higher eukaryotic cells pleiomorphic compartments composed of vacuoles, tubules and vesicles move from the endoplasmic reticulum (ER) and the plasma membrane to the cell center, operating in early biosynthetic trafficking and endocytosis, respectively. Besides transporting cargo to the Golgi apparatus and lysosomes, a major task of these compartments is to promote extensive membrane recycling. The endocytic membrane system is traditionally divided into early (sorting) endosomes, late endosomes and the endocytic recycling compartment (ERC). Recent studies on the intermediate compartment (IC) between the ER and the Golgi apparatus suggest that it also consists of peripheral (“early”) and centralized (“late”) structures, as well as a third component, designated here as the biosynthetic recycling compartment (BRC). We propose that the ERC and the BRC exist as long-lived “mirror compartments” at the cell center that also share the ability to expand and become mobilized during cell activation. These considerations emphasize the functional symmetry of endomembrane compartments, which provides a basis for the membrane rearrangements taking place during cell division, polarization, and differentiation.

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29

Polikanova, I. V. "Central Symmetry of Star-Shaped Flat Bodies." Izvestiya of Altai State University, no. 1(111) (March 6, 2020): 119–23. http://dx.doi.org/10.14258/izvasu(2020)1-20.

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Well-known criteria for the central symmetry are formulated for convex bodies. This study relates to a broader class of star-shaped bodies but is limited by the dimension of 2. The paper introduces the concepts of a sector and a segment of a flat star-shaped body.The basic result is the following. Let a flat body K be star-shaped with respect to its interior point o. On the set of sectors and segments of K, a simply additive, monotonic, and invariant with respect to central symmetry with the center o functional F is given. The body K is centrally symmetric with respect to the center o if and only if every chord passing through the point o divides K into two sectors with equal values of the functional F.The method of proof is — "on the contrary".When considering quantities having geometric meaning (central geometric moments, area) as such functionals, we get both new and known (for an area) statements for flat convex bodies. A slight modification of the proof allows us to obtain a similar statement for the perimeter (an additive functional, but simply not an additive functional on the set of convex flat bodies): flat convex body has its central symmetry if and only if all the chords, dividing the perimeter into halves, pass through one point.

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30

KIMPARA, Hiroaki. "HemipolyhedrHemipolyhedrHemipolyhedrHemipolyhedra and their Dualsa and their Dualsa and their Dualsa and their Dualsa and their Dualsa and their Dualsa and their Dualsa and their Dualsa." International Journal of Mathematics and Statistics Invention 12, no. 6 (2024): 01–05. https://doi.org/10.35629/4767-12060105.

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There exist 9 nonconvex uniform polyhedra whose name includes “hemi”. They are called hemipolyhedra. The duals of these hemipolyhedra share a unique feature, i.e. they are represented by a compound of prisms interpenetrating the center of symmetry. The number of these prisms corresponds to the number of facial planes passing through the center of symmetry of the original hemipolyhedron and the cross section of the prisms is the same as the shape of these planes that pass through the center of symmetry. A symmetry of points and lines arises in a projective plane: just as a pair of points determine a line, so a pair of lines determine a point. The existence of parallel lines leads to establishing a point at infinity which represents the intersection of these parallels. Thus, the lateral faces of the prism are considered to converge at infinity, becoming the vertices which correspond to the original hemipolyhedron’s facial planes passing through the center of symmetry. All these are already known and not new. However, the way to identify the vertices corresponding to the other facial planes of the original hemipolyhedron in question has not yet been clearly established. The author gave a consideration to this point and found a simple proper way to enable it. The purpose of this paper is to explain it in an easy-tounderstand manner.

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31

Thanh, Nguyen Thi Viet, Thorsten Könekamp, Daniela Hanke, Franziska Löwer, Tobias Borrmann, and Franz-Peter Montforts. "Synthesis of a cofacial chlorin dimer of defined symmetry." Journal of Porphyrins and Phthalocyanines 16, no. 05n06 (2012): 626–32. http://dx.doi.org/10.1142/s1088424612500666.

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Special pair chlorophylls arranged in a cofacial dimeric structure play an important role in the initial step of light induced electron transfer of photosynthetic reaction centers of bacteria and plants. For mimicking the natural photosynthetic reaction center we aimed on synthesis of an artificial special pair 13 constructed from two chlorin subunits 5a, b and a rigid biphenylene spacer moiety 11. Due to the reduced C2h symmetry of the chlorin units compared with so far used D4h porphyrins and due to the rigid spacer a cofacial dimer of defined symmetry and distance was obtained.

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32

Dobretsova, Elena, Olimkhon Alimov, Sergey Rusanov, Vitaly Kashin, and Vladimir Tsvetkov. "Selective Laser Spectroscopy of the Bixbyite-Type Yttrium Scandate Doped by Rare-Earth Ions." Materials 16, no. 21 (2023): 6829. http://dx.doi.org/10.3390/ma16216829.

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Yttrium scandate crystals doped by Nd3+ and Tm3+ ions have been successfully grown in the form of fibers using the laser-heated pedestal growth (LHPG) technique. The selective laser spectroscopy methods have identified and distinguished three distinct types of optically active centers associated with Nd3+ and Tm3+ ions. The substitution of Y3+ and Sc3+ for rare-earth ions in the C2 structural site leads to the formation of two distinct basic long-time centers. In Nd3+:YScO3, another type of center (a short-lifetime one) is formed known as the Nd3+–Nd3+ aggregate pair. This center arises from the substitution of Y3+ or Sc3+ for Nd3+ cation in the adjacent MO6 polyhedra that share an edge. In Tm3+:YScO3, the third optical center is formed as a result of the substitution of Y3+ or Sc3+ for Tm3+ in the MO6 octahedra with the C3i site symmetry. The fluorescence decay lifetimes of Nd3+ and Tm3+ ions in the YScO3 crystal structure have been accurately measured and estimated. A Stark level diagram illustrating the splitting of 4F3/2, 4I11/2, and 4I9/2 multiplets of Nd3+ ions has been constructed to show features of the active optical centers with the C2 site symmetry.

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33

Prof.S.Subbulakshmi. "Mathematics and Barathanatyam." Global Journal of Research in Humanities & Cultural Studies 3, no. 1 (2023): 28–32. https://doi.org/10.5281/zenodo.7700028.

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Mathematics is the Science and the study of quality, structure, space and change. It is an area of knowledge that includes the topics of number, formulas and related structures, shapes, logic quality and arrangements. Mathematic skill is a skill which deals with number sense , special sense , measurement sense, Estimation sense , Pattern sense ,Problem solving sense and so on . The quality of stability, equilibrium, Repose and Perfect Symmetry are essential in Indian Arts particularly Dance, Painting and Sculpture. Geometrical formations like circle , square , Triangles, straight lines , angles, shape , size ,relative position and perfect symmetry are very essential in these Indian arts ,which are highly mathematical aspects.. Dance geometry and numbers have a fascinating relationship. Distinguished poses like straight line pattern, circular patterns and symmetry in posture development are all important features of dance. Like in Geometry certain poses provide a lovely symmetry that adds tidy elegance and greatness to the performance. Angasudhi in Dance is the result of a combination of proper posture, balance centered symmetry. In Araimandai the body is split into a sequence of triangles. The angle plays an important role for Abinaya, Adavu, Stage lighting, Dance Drama and so on.  

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Conti, Sergio, Heiner Olbermann, and Ian Tobasco. "Symmetry breaking in indented elastic cones." Mathematical Models and Methods in Applied Sciences 27, no. 02 (2017): 291–321. http://dx.doi.org/10.1142/s0218202517500026.

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Motivated by simulations of carbon nanocones (see [S. P. Jordan and V. H. Crespi, Theory of carbon nanocones: Mechanical chiral inversion of a micron-scale three-dimensional object, Phys. Rev. Lett. 93 (2004) 255504]), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry, and modeling the compression by suitable Dirichlet boundary conditions at the center and the boundary of the sheet, we identify the energy scaling law in the von Kármán plate model. Specifically, we find that three different regimes arise with increasing indentation [Formula: see text]: initially the energetic cost of the logarithmic singularity dominates, then there is a linear response corresponding to a moderate deformation close to the boundary of the cone, and for larger [Formula: see text] a localized inversion takes place in the central region. Then, we show that for large enough indentations minimizers of the elastic energy cannot be radially symmetric. We do so by an explicit construction that achieves lower elastic energy than the minimum amount possible for radially symmetric deformations.

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35

Iacopetti, Alessandro, and Giusi Vaira. "Sign-changing tower of bubbles for the Brezis–Nirenberg problem." Communications in Contemporary Mathematics 18, no. 01 (2016): 1550036. http://dx.doi.org/10.1142/s0219199715500364.

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In this paper, we prove that the Brezis–Nirenberg problem: [Formula: see text] where [Formula: see text] is a symmetric bounded smooth domain in [Formula: see text], [Formula: see text] and [Formula: see text], has a solution with the shape of a tower of two bubbles with alternate signs, centered at the center of symmetry of the domain, for all [Formula: see text] sufficiently small.

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36

Evidente, Imogene, Rene Felix, and Manuel Joseph Loquias. "Color Symmetry of Certain Tilings with a Singular Center." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1425. http://dx.doi.org/10.1107/s205327331408574x.

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"Tilings with singular points, or tilings that are not locally finite, are classified in [1] among tilings that are not ""well-behaved"". In [2], colorings of tilings with a singular center were obtained from certain colorings of regular Euclidean tilings. It was observed that not all such colorings could be transformed into colorings of tilings with a singularity. Moreover, the existence of maximum color indexes was surmised. In this paper, we provide a mathematical basis for the said observations by utilizing conformal maps that distort a regular Euclidean tiling into a tiling with a singular center. That is, we determine conditions so that a coloring of a regular Euclidean tiling can be transformed into a coloring of a tiling with a singular center. In addition, we establish that a maximum number of colors exists. Finally, we give conditions so that the symmetry group of the tiling with a singular center induces a permutation of the colors."

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37

Huang, Ting, Jieping Gu, Yuting Ouyang, and Wentao Huang. "Bifurcation of Limit Cycles and Center in 3D Cubic Systems with Z3-Equivariant Symmetry." Mathematics 11, no. 11 (2023): 2563. http://dx.doi.org/10.3390/math11112563.

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This paper focuses on investigating the bifurcation of limit cycles and centers within a specific class of three-dimensional cubic systems possessing Z3-equivariant symmetry. By calculating the singular point values of the systems, we obtain a necessary condition for a singular point to be a center. Subsequently, the Darboux integral method is employed to demonstrate that this condition is also sufficient. Additionally, we demonstrate that the system can bifurcate 15 small amplitude limit cycles with a distribution pattern of 5−5−5 originating from the singular points after proper perturbation. This finding represents a novel contribution to the understanding of the number of limit cycles present in three-dimensional cubic systems with Z3-equivariant symmetry.

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38

Kapustin, A. D., and S. A. Paston. "Analytical analysis of the origin of core-cusp matter density distributions in galaxies." Journal of Cosmology and Astroparticle Physics 2022, no. 11 (2022): 025. http://dx.doi.org/10.1088/1475-7516/2022/11/025.

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Abstract We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the central slope of density profile and the near-origin behavior of the angular momentum distribution function. We consider both a spherically symmetric (on average) matter distribution as well as deviations from it. If the density profile forms in a background of spherical gravitation potential then a core-type distribution arises. A regular matter may behave in such way if the background potential was formed by the dark matter. In the presence of deviation from spherical symmetry the formation of cusp-type distribution is possible. Moreover, a reduction of spherical symmetry to the axial one leads to a less steep cusp profile. The complete symmetry breaking (which corresponds, in particular, to the common setup of numerical simulations), leads to a steeper cusp profile.

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39

Chehlarova, Toni. "Game with center of central symmetry in the plane." Symmetry: Culture and Science 32, no. 2 (2021): 277–80. http://dx.doi.org/10.26830/symmetry_2021_2_277.

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40

Astafiev, S. B., V. M. Fridkin, V. G. Lazarev, and A. L. Shlensky. "Magnetophotovoltaic effect in crystals without a center of symmetry." Ferroelectrics 83, no. 1 (1988): 3–18. http://dx.doi.org/10.1080/00150198808235444.

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41

Magomadov, R. M. "Kinetic phenomena in environments without a center of symmetry." Ferroelectrics 567, no. 1 (2020): 206–22. http://dx.doi.org/10.1080/00150193.2020.1791607.

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42

Fridkin, V. M. "Magnetophotovoltaic Effects in Crystals without a Center of Symmetry." Crystallography Reports 63, no. 6 (2018): 969–70. http://dx.doi.org/10.1134/s1063774518060123.

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43

Sochava, L. S., S. A. Basun, V. É. Bursian, et al. "Low-symmetry paramagnetic center in a KTaO3: Ni crystal." Physics of the Solid State 49, no. 3 (2007): 460–62. http://dx.doi.org/10.1134/s1063783407030110.

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44

Hsieh, Fushing. "A regression approach for estimating the center of symmetry." Statistics & Probability Letters 22, no. 2 (1995): 157–60. http://dx.doi.org/10.1016/0167-7152(94)00062-d.

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45

Mirescu, Constantin Radu, and Gabriela Roșca. "A Precise Algorithm for Known Spherical Marker Position Retrieval Using an Ideal Pinhole Camera in a Diffuse Light Scene." Applied Mechanics and Materials 859 (December 2016): 93–98. http://dx.doi.org/10.4028/www.scientific.net/amm.859.93.

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The exact marker image was computed for various positions in the workspace and for each image was computed back the approximation of the marker position based on it. The position computation used the symmetry of the scene and the particular characteristics of the ellipse marker projection. Was established that the center of symmetry of the marker projection is different than the projection of the marker center itself and the the relation between two was found using the Dandeline Spheres. For a given marker radius the ratio between the area of the right cone base that contains the marker center projection and the area of the marker projection was expressed as a law based only on the angle of the line passing through the focal point and the symmetry center of the marker projection and the view axis. Based on all these intermediary results was obtained an algorithm with a precision under 0.04 mm in sagital plane, and under 0.1 mm on the depth view axis with a modest 1920x1680 camera resolution.

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46

Valiev, Kh F., and A. N. Kraiko. "Self-Similar Flows with a Shock Wave Advancing toward the Center or Axis of Symmetry." Fluid Dynamics 58, no. 5 (2023): 864–72. http://dx.doi.org/10.1134/s001546282370009x.

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Abstract We study one-dimensional flows of an ideal (inviscid and non-heat-conducting) perfect gas with an adiabatic exponent γ behind a shock wave moving toward the center (ν = 3) or axis (ν = 2) of symmetry in a cold gas at rest. Flows with a reflected shock wave and flows terminating with simultaneous arrival of a shock wave and a piston, which has compressed the gas into a point or line, to the center of symmetry are admitted.

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47

KEDKAEW, CHITTRA, PICHET LIMSUWAN, KANPHOT THONGCHAM, and SIWAPORN MEEJOO. "THE SPIN HAMILTONIAN PARAMETERS CALCULATION OF 14N AND 15N IN NATURAL TYPE I DIAMOND." International Journal of Modern Physics B 22, no. 25n26 (2008): 4740–48. http://dx.doi.org/10.1142/s0217979208050498.

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The main purpose of this work is to present the ESR spectra and calculate the spin Hamiltonian parameters of 14 N and 15 N impurities in natural diamond. The ESR spectra of diamond crystal were measured on ESR spectrometer operating at X-band microwave frequency. The results of ESR spectra show that the diamond has a P1 center. This center gives rise to three strong resonance absorption peaks at θ = 90°, φ = 0° due to hyperfine interaction between electron spin and nuclear spin of 14 N . The ESR spectra of 15 N impurity consist of two satellites at the same rotation angle (φ). The effects of isolated substitution nitrogen on carbon atom produced a symmetric distortion from Td to C3V symmetry. According to this symmetry, the resonance magnetic field positions of ESR spectra for the rotation angles of 0°, 90° and 180° are almost overlap. The g-factor values and spin Hamiltonian parameters of 14 N and 15 N are: g = 2.0019, A⊥ = 29.73, A‖ = 40.24 and g = 2.0019, A⊥ = −39.90, A‖ = −57.05, respectively.

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48

Palmer, Stephen E., and Stefano Guidi. "Mapping the Perceptual Structure of Rectangles through Goodness-of-Fit Ratings." Perception 40, no. 12 (2011): 1428–46. http://dx.doi.org/10.1068/p7021.

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Three experiments were carried out to investigate the internal structure of a rectangular frame to test Arnheim's (1974 Art and Visual Perception, 1988 The Power of the Center) proposals about its ‘structural skeleton’. Observers made subjective ratings of how well a small probe circle fit within a rectangle at different interior positions. In experiment 1, ratings of 77 locations were highest in the center, decreased with distance from the center, greatly elevated along vertical and horizontal symmetry axes, and somewhat elevated along the local symmetry axes. A linear regression model with six symmetry-related factors accounted for 95% of the variance. In experiment 2 we measured perceived fit along local symmetry axes versus global diagonals near the corners to determine which factor was relevant. 2AFC probabilities were elevated only along the local symmetry axes and were higher when the probe was closer to the vertex. In experiment 3 we examined the effect of dividing a rectangular frame into two rectangular ‘subframes’ using an additional line. The results show that the primary determinant of good fit is the position of the target circle within the local subframes. In general, the results are consistent with Arnheim's proposals about the internal structure of a rectangular frame, but an alternative interpretation is offered in terms of the Gestalt concept of figural goodness.

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Shih, W. Y., L. Kudryavtsev, and K. K. Wang. "Elastic Buckling of a Circular Disk due to Internal Membrane Forces." Journal of Applied Mechanics 62, no. 3 (1995): 813–16. http://dx.doi.org/10.1115/1.2777115.

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Residual internal stresses often remain in materials after thermal-mechanical processes. Considerable deformation, such as elastic buckling, may result from such stresses. Some cases of circular-plate buckling due to internal membrane forces are analyzed in this work. The internal membrane-force field is introduced with a nonuniform radial temperature distribution in the disk. Detailed analysis is performed and critical buckling criteria are tabulated for some specific sets of parameters. Although the membrane force in the plate is axially symmetric, symmetry breaking is found at buckling. When the temperature is higher at the disk center, the first buckling mode is domeshaped, which maintains the polar symmetry. The mode of buckling, however, changes to a saddle shape when the radial temperature distribution is reversed.

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50

Kudo, Masafumi, Shohei O. Shingu, Tsuyoshi Imazu, Jun Goryo, and Yoshiki Imai. "Possible pairing symmetries in the ordered honeycomb network superconductor BaPtSb." Journal of Physics: Conference Series 2164, no. 1 (2022): 012015. http://dx.doi.org/10.1088/1742-6596/2164/1/012015.

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Abstract We investigate the pairing symmetry of the ordered honeycomb network superconductor BaPtSb, which has a crystal structure without inversion center. There is a preliminary μSR report which implies the broken time-reversal symmetry in the superconducting state. In this paper, we classify the pairing symmetry and examine the pairing instability. Among the unconventional states with time-reversal symmetry breaking, we find that the state with a gap structure compatible with Fermi surfaces is the spin-triplet chiral p-wave state.

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