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Journal articles on the topic 'Anti-symmetric'

Author: Grafiati

Published: 5 June 2025

Last updated: 8 July 2025

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1

Hossein, Sk M., K. Paul, L. Debnath, and K. C. Das. "Symmetric anti-eigenvalue and symmetric anti-eigenvector." Journal of Mathematical Analysis and Applications 345, no. 2 (2008): 771–76. http://dx.doi.org/10.1016/j.jmaa.2008.04.061.

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2

Han, Jiequn, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, and Linfeng Zhang. "Universal approximation of symmetric and anti-symmetric functions." Communications in Mathematical Sciences 20, no. 5 (2022): 1397–408. http://dx.doi.org/10.4310/cms.2022.v20.n5.a8.

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3

Kim, Namkeun, Kenji Homma, and Sunil Puria. "Inertial Bone Conduction: Symmetric and Anti-Symmetric Components." Journal of the Association for Research in Otolaryngology 12, no. 3 (2011): 261–79. http://dx.doi.org/10.1007/s10162-011-0258-3.

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4

Liu, Zhaofeng, Siwei Tang, Zengrun Wen, Yuanmei Gao, Yangjian Cai, and Liren Zheng. "Talbot effect in anti-PT symmetric synthetic photonic lattices." Chinese Optics Letters 22, no. 3 (2024): 031901. http://dx.doi.org/10.3788/col202422.031901.

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5

Dehghan, Mehdi, and Masoud Hajarian. "Iterative algorithms for the generalized centro‐symmetric and central anti‐symmetric solutions of general coupled matrix equations." Engineering Computations 29, no. 5 (2012): 528–60. http://dx.doi.org/10.1108/02644401211235870.

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PurposeThe purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.Design/methodology/approachBy extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.FindingsWhen the general coupled matrix equations are consistent over the generalized centro‐symmetric and central anti‐symmetric matrices, the generalized centro‐symmetric and central anti‐symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti‐symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti‐symmetric solutions to given generalized centro‐symmetric and central anti‐symmetric matrices can be obtained by finding the least Frobenius norm generalized centro‐symmetric and central anti‐symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous‐time algebraic Lyapunov equations (GCALE).Originality/valueBy the algorithms, the solvability of the general coupled matrix equations over generalized centro‐symmetric and central anti‐symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods.

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6

Zhang, Huilai, Meiyu Peng, Xun-Wei Xu, and Hui Jing. "Anti- APT -symmetric Kerr gyroscope." Chinese Physics B 31, no. 1 (2022): 014215. http://dx.doi.org/10.1088/1674-1056/ac3988.

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Non-Hermitian systems can exhibit unconventional spectral singularities called exceptional points (EPs). Various EP sensors have been fabricated in recent years, showing strong spectral responses to external signals. Here we propose how to achieve a nonlinear anti-parity-time ( A P T ) gyroscope by spinning an optical resonator. We show that, in the absence of any nonlinearity, the sensitivity or optical mode splitting of the linear device can be magnified up to 3 orders compared to that of the conventional device without EPs. Remarkably, the A P T symmetry can be broken when including the Kerr nonlinearity of the materials and, as a result, the detection threshold can be significantly lowered, i.e., much weaker rotations which are well beyond the ability of a linear gyroscope can now be detected with the nonlinear device. Our work shows the powerful ability of A P T gyroscopes in practice to achieve ultrasensitive rotation measurement.

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7

Clark, T. E., C. H. Lee, and S. T. Love. "Anti-symmetric tensor gauge theories." Nuclear Physics B 308, no. 2-3 (1988): 379–96. http://dx.doi.org/10.1016/0550-3213(88)90569-x.

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8

Gallian, Joseph A., and Matthew D. Mullin. "Groups with anti-symmetric mappings." Archiv der Mathematik 65, no. 4 (1995): 273–80. http://dx.doi.org/10.1007/bf01195537.

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9

Wang, X. P., P. Jiang, T. N. Chen, and K. Bao. "Lamb wave band structure in phononic crystal composed of multiple square stubs symmetric or anti-symmetric deposited on a homogeneous plate." International Journal of Modern Physics B 29, no. 16 (2015): 1550106. http://dx.doi.org/10.1142/s0217979215501064.

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This paper theoretically investigates the propagation of Lamb waves in a two-dimensional (2D) phononic crystal (PC) structure composed of multiple square stubs symmetric or anti-symmetric deposited on a thin homogeneous plate. The dispersion relations, the power transmission spectra and the displacement fields of the eigenmodes are studied by using the finite-element method (FEM). We investigate the effect of the distance between adjacent square stubs on the band gaps (BGs). The results show that the distance between adjacent square stubs can remarkably change the location and the width of the BGs. Meanwhile, we conducted a numerically study on the different results between the anti-symmetric and symmetric distribution of the scatterers. The band structure of the anti-symmetric structure PC is significantly different from the symmetric structure. In general, the distribution of the square stubs has an influence on the band structures. We further identify the physical mechanism of the distinction in the formation of the BG between the anti-symmetric and the symmetric model through the displacement fields of the eigenmodes. In addition, we find that the variation of the PC BGs in anti-symmetric and symmetric structure are sensitive to the distance between adjacent square stubs, which could be indispensable to practical applications such as BG tuning.

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10

Forrester, P., and E. Nordenstam. "The Anti-Symmetric GUE Minor Process." Moscow Mathematical Journal 9, no. 4 (2009): 749–74. http://dx.doi.org/10.17323/1609-4514-2009-9-4-749-774.

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11

Choi, Seul Hee, Jongwoo Lee, and Ki-Bong Nam. "Algebra Versus Its Anti-symmetric Algebra." Algebra Colloquium 16, no. 04 (2009): 661–68. http://dx.doi.org/10.1142/s1005386709000625.

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For a given algebra A= 〈A,+,·〉, we can define its anti-symmetric algebra A-= 〈A-,+,[ , ]〉 using the commutator [ , ] of A, where the sets A and A- are the same. We show that there are isomorphic algebras A1 and A2 such that their anti-symmetric algebras are not isomorphic. We define a special type Lie algebra and show that it is simple.

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12

Antonosyan, Diana A., Alexander S. Solntsev, and Andrey A. Sukhorukov. "Parity-time anti-symmetric parametric amplifier." Optics Letters 40, no. 20 (2015): 4575. http://dx.doi.org/10.1364/ol.40.004575.

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13

Sun, Min, Huping Zhou, Chongjie Liao, et al. "Stable Characteristics Optimization of Anti-Symmetric Cylindrical Shell with Laminated Carbon Fiber Composite." Materials 15, no. 3 (2022): 933. http://dx.doi.org/10.3390/ma15030933.

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This paper proposes a multi-objective optimization model for anti-symmetric cylindrical shell in the bionic gripper structure. Here, the response surface method is used to establish multiple surrogate models of the anti-symmetric cylindrical shell, and the non-dominated sorting genetic algorithm-II (NSGA-II) is used to optimize the design space of the anti-symmetric cylindrical shell; the design points of the anti-symmetric cylindrical shell are verified by experimental methods. The optimization goals are that the first steady state transition load (the transition process of the bionic gripper structure from the open state to the closed state) of the anti-symmetric cylindrical shell is minimized, and the second steady state transition load (the transition process of the bionic gripper structure from the closed state to the open state) is the largest. At the same time, in order to prevent stable instability caused by stress concentration in the second steady state of the anti-symmetric cylindrical shell, the maximum principal plane stress is given as the constraint condition. The validity of the optimization results is verified by finite element and experimental methods. Due to the stable transition load of the anti-symmetric cylindrical shell being significantly larger than that of the orthogonal laminated plate, therefore, the anti-symmetric cylindrical shell has potential application prospects in the application of deformable structures and bionic structures that require composite functions such as having light weight, high strength, and large clamping force. The novelty of this paper lies in the multi-objective optimization of the application of the antisymmetric bistable cylindrical shell in the bionic gripper structure.

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14

Xue, Jianghong, and Michelle S. Hoo Fatt. "Symmetric and anti-symmetric buckle propagation modes in subsea corroded pipelines." Marine Structures 18, no. 1 (2005): 43–61. http://dx.doi.org/10.1016/j.marstruc.2005.08.001.

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15

Yan, Wen, and Tin-Yau Tam. "Anti-diagonals of symmetric and skew symmetric matrices with prescribed eigenvalues." Linear Algebra and its Applications 438, no. 3 (2013): 1446–53. http://dx.doi.org/10.1016/j.laa.2012.08.038.

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16

Marchewka, M., E. M. Sheregii, I. Tralle, et al. "Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells." Physica E: Low-dimensional Systems and Nanostructures 40, no. 4 (2008): 894–906. http://dx.doi.org/10.1016/j.physe.2007.11.020.

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17

MARCHEWKA, M., E. M. SHEREGII, I. TRALLE, G. TOMAKA, and D. PLOCH. "WEAKLY INTERACTING SYMMETRIC AND ANTI-SYMMETRIC STATES IN THE BILAYER SYSTEMS." International Journal of Modern Physics B 21, no. 08n09 (2007): 1511–18. http://dx.doi.org/10.1142/s0217979207043117.

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We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.

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18

DZHUMADIL'DAEV, A. S. "ANTI-COMMUTATIVE ALGEBRAS WITH SKEW-SYMMETRIC IDENTITIES." Journal of Algebra and Its Applications 08, no. 02 (2009): 157–80. http://dx.doi.org/10.1142/s0219498809003230.

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Generalizing Lie algebras, we consider anti-commutative algebras with skew-symmetric identities of degree > 3. Given a skew-symmetric polynomial f, we call an anti-commutative algebra f-Lie if it satisfies the identity f = 0. If sn is a standard skew-symmetric polynomial of degree n, then any s4-Lie algebra is f-Lie if deg f ≥ 4. We describe a free anti-commutative super-algebra with one odd generator. We exhibit various constructions of generalized Lie algebras, for example: given any derivations D, F of an associative commutative algebra U, the algebras (U, D ∧ F) and (U, id ∧ D2) are s4-Lie. An algebra (U, id ∧ D3 - 2D ∧ D2) is s'5-Lie, where s'5 is a non-standard skew-symmetric polynomial of degree 5.

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19

Sosoe, Philippe, and Uzy Smilansky. "On the spectrum of random anti-symmetric and tournament matrices." Random Matrices: Theory and Applications 05, no. 03 (2016): 1650010. http://dx.doi.org/10.1142/s2010326316500106.

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We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the non-Hermitian matrix around any fixed index are interlaced with those of the anti-symmetric matrix. Along the way, we show that some tools recently developed to study the eigenvalue distributions of Hermitian matrices extend to the anti-symmetric setting.

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20

Yu, Lei, Kaiyuan Zhang, and Zhongke Shi. "The solvability conditions for inverse problems of anti-symmetric ortho-symmetric matrices." Journal of Applied Mathematics and Computing 28, no. 1-2 (2008): 225–33. http://dx.doi.org/10.1007/s12190-008-0096-6.

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21

Lianngenga, R., and S. S. Singh. "Symmetric and anti-symmetric vibrations in micropolar thermoelastic materials plate with voids." Applied Mathematical Modelling 76 (December 2019): 856–66. http://dx.doi.org/10.1016/j.apm.2019.07.012.

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22

Yang, Tian-Zhi, and Xiao-Dong Yang. "Exact solution of supercritical axially moving beams: symmetric and anti-symmetric configurations." Archive of Applied Mechanics 83, no. 6 (2012): 899–906. http://dx.doi.org/10.1007/s00419-012-0725-2.

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23

ASAI, MASAHITO, MASAYUKI MINAGAWA, and MICHIO NISHIOKA. "The instability and breakdown of a near-wall low-speed streak." Journal of Fluid Mechanics 455 (March 25, 2002): 289–314. http://dx.doi.org/10.1017/s0022112001007431.

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The instability of the three-dimensional high-shear layer associated with a near-wall low-speed streak is investigated experimentally. A single low-speed streak, not unlike the near-wall low-speed streaks in transitional and turbulent flows, is produced in a laminar boundary layer by using a small piece of screen set normal to the wall. In order to excite symmetric and anti-symmetric modes separately, well-controlled external disturbances are introduced into the laminar low-speed streak through small holes drilled behind the screen. The growth of the excited symmetric varicose mode is essentially governed by the Kelvin–Helmholtz instability of the in ectional velocity profiles across the streak in the normal-to-wall direction and it can occur when the streak width is larger than the shear-layer thickness. The spatial growth rate of the symmetric mode is very sensitive to the streak width and is rapidly reduced as the velocity defect decreases flowing to the momentum transfer by viscous stresses. By contrast, the anti-symmetric sinuous mode that causes the streak meandering is dominated by the wake-type instability of spanwise velocity distributions across the streak. As far as the linear instability is concerned, the growth rate of the anti-symmetric mode is not so strongly affected by the decrease in the streak width, and its exponential growth may continue further downstream than that of the symmetric mode. As for the mode competition, it is important to note that when the streak width is narrow and comparable with the shear-layer thickness, the low-speed streak becomes more unstable to the anti-symmetric modes than to the symmetric modes. It is clearly demonstrated that the growth of the symmetric mode leads to the formation of hairpin vortices with a pair of counter-rotating streamwise vortices, while the anti-symmetric mode evolves into a train of quasi-streamwise vortices with vorticity of alternate sign.

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24

Doria, M. M., F. Parage, and O. Buisson. "Anti-symmetric plasma mode in superconducting films." Europhysics Letters (EPL) 35, no. 6 (1996): 445–50. http://dx.doi.org/10.1209/epl/i1996-00100-3.

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25

Wong, K. J., X. J. Gong, S. Aivazzadeh, and M. N. Tamin. "Tensile behaviour of anti-symmetric CFRP composite." Procedia Engineering 10 (2011): 1865–70. http://dx.doi.org/10.1016/j.proeng.2011.04.310.

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26

Gao, Yuan, Tao Zhu, and Yu Bai. "Anti-symmetric Plane Anti-symmetric Arch Cable-stayed Bridge abutment Joint Stress Analysis based on Finite Element Method." Journal of Physics: Conference Series 1744, no. 4 (2021): 042173. http://dx.doi.org/10.1088/1742-6596/1744/4/042173.

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27

Zhang, Haixiao, Xiaoli Liu, Yu Bao, Yiwei Zhang, and Jinyu Zhao. "Scattering Properties of an Acoustic Anti-Parity-Time-Symmetric System and Related Fabry–Perot Resonance Mode." Symmetry 14, no. 5 (2022): 965. http://dx.doi.org/10.3390/sym14050965.

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The pursuit of artificial structures exhibiting unusual acoustic properties is a major scientific endeavor, in which anti-parity-time (PT) symmetry has been coming into view recent years. At the same time, with the emergence of new acoustic metamaterials, the classical Fabry–Perot resonance mode also exhibits fascinating scattering features similar to those of the anti-PT-symmetric system. We derive the generalized relation for the scattering parameters of an acoustic anti-PT-symmetric system with a transfer matrix, including conjugate bidirectional reflection coefficients and pure real feature of transmission coefficient. In the absence of the real or the imaginary (representing gain/loss) part of the refractive index, the anti-PT-symmetric system degrades into a pair of complementary media, resulting in the bidirectional total transmission. Moreover, a Fabry–Perot resonance mode exhibiting conjugate bidirectional reflection coefficients and a pure imaginary transmission coefficient has been demonstrated. Our results are meaningful for guiding the experimental test of an acoustic anti-PT-symmetric system and the design of associated bidirectional response prototype devices.

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28

ZHANG, ZHENG, HELONG WU, HUAPING WU, XIAOQIAO HE, YUMEI BAO, and GUOZHONG CHAI. "BISTABLE CHARACTERISTICS OF IRREGULAR ANTI-SYMMETRIC LAY-UP COMPOSITE CYLINDRICAL SHELLS." International Journal of Structural Stability and Dynamics 13, no. 06 (2013): 1350029. http://dx.doi.org/10.1142/s0219455413500296.

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The bistable characteristics of the irregular anti-symmetric cylindrical shell (IACS), such as [+α1/ -α2/ +α2/ -α1] lay-up, are presented using theoretical methodology and finite element (FE) analysis. A novel approach named two points loading method is used to induce a snap-through of the shell in FE analysis. Unlike regular [+α/ -α/ +α/ -α] lay-up anti-symmetric cylindrical shells, two or more different ply angles are included in the irregular anti-symmetric lay-up. Besides ply angles, the bistable characteristics of composite cylindrical shells with irregular anti-symmetric lay-ups are also affected by the sequence of lay-ups. Both analytical and FE results show that IACS with different bistable behaviors can be obtained by changing the ply angles or sequence of the lay-ups. It is very useful for the design and manufacture of the bistable structure. There is a reasonable agreement between analytical and FE predictions; possible reasons of differences between analytical and FE results are given.

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29

Yang, Jie, Maoxiong Zhao, Liang Liu, Hong Xiang, and Dezhuan Han. "Analysis of the Symmetric and Anti-Symmetric Modes in Spoof–Insulator–Spoof Waveguides." Journal of the Physical Society of Japan 86, no. 6 (2017): 064401. http://dx.doi.org/10.7566/jpsj.86.064401.

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30

Yacoby, Itamar, Nathan Paldor, and Hezi Gildor. "Geostrophic adjustment on the f-plane: Symmetric versus anti-symmetric initial height distributions." Physics of Fluids 33, no. 7 (2021): 076607. http://dx.doi.org/10.1063/5.0056592.

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31

Li, Youfa, and Shouzhi Yang. "Construction of symmetric or anti-symmetric B-spline wavelets and their dual wavelets." International Journal of Computer Mathematics 88, no. 5 (2011): 1024–34. http://dx.doi.org/10.1080/00207160.2010.492213.

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32

He, Zhihui, Chunjiang Li, Zhenxiong Li, Weiwei Xue, and Wei Cui. "Nonlinear radiation oscillator theory for symmetric and anti-symmetric damping graphene coupled metamaterials." New Journal of Physics 22, no. 9 (2020): 093043. http://dx.doi.org/10.1088/1367-2630/abb0fc.

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33

Ceruti, Gianluca, and Christian Lubich. "Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors." BIT Numerical Mathematics 60, no. 3 (2020): 591–614. http://dx.doi.org/10.1007/s10543-019-00799-8.

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34

Yong, Li, Hou Zhi-Lin, Fu Xiu-Jun, and Badreddine M. Assouar. "Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate." Chinese Physics Letters 27, no. 7 (2010): 074303. http://dx.doi.org/10.1088/0256-307x/27/7/074303.

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35

Rasid, Zainudin A., Saiful Amri Mazlan, Ayob Amran, Rizal Zahari, Dayang Laila Majid, and Azmin Shakrine Mohd Rafie. "The Strain Energy Tuning of the Shape Memory Alloy on the Post-Buckling of Composite Plates Using Finite Element Method." Advanced Materials Research 445 (January 2012): 577–82. http://dx.doi.org/10.4028/www.scientific.net/amr.445.577.

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This paper presents a geometric non-linear finite element model of shape memory alloy composite plates and its source code in order to determine critical loads and to trace post-buckling paths of the composite plates. A numerical study was conducted on symmetric and anti-symmetric angle-ply and cross-ply composite plates. Buckling and post-buckling improvements of composite plates due to the shape memory effect behaviour of shape memory alloy were carried out. The pre-strained shape memory alloy wires were embedded within laminated composite plates so that recovery stress could be induced with the heated wires. The methods of active property tuning and active strain energy tuning were applied to show the various effects of the shape memory alloy on the studied behaviour. The result showed that significant improvements occurred in the critical loads and the post-buckling paths of the symmetric and anti-symmetric angle-ply and the symmetric cross-ply composite plates due to the active strain energy tuning method. In the case of the anti-symmetric cross-ply composite plate where bifurcation point did not exist, the post-buckling path was substantially improved.

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36

Klimek, Małgorzata. "On reflection symmetry and its application to the Euler–Lagrange equations in fractional mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1990 (2013): 20120145. http://dx.doi.org/10.1098/rsta.2012.0145.

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We study the properties of fractional differentiation with respect to the reflection symmetry in a finite interval. The representation and integration formulae are derived for symmetric and anti-symmetric fractional derivatives, both of the Riemann–Liouville and Caputo type. The action dependent on the left-sided Caputo derivatives of orders in the range (1,2) is considered and we derive the Euler–Lagrange equations for the symmetric and anti-symmetric part of the trajectory. The procedure is illustrated with an example of the action dependent linearly on fractional velocities. For the obtained Euler–Lagrange system, we discuss its localization resulting from the subsequent symmetrization of the action.

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37

Zheng, Chao, Jin Tian, Daili Li, Jingwei Wen, Shijie Wei, and Yansong Li. "Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System." Entropy 22, no. 8 (2020): 812. http://dx.doi.org/10.3390/e22080812.

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Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

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38

RIETDIJK, R. H. "CLASSICAL AND QUANTUM MECHANICS OF A SPINNING PARTICLE INTERACTING WITH ANTI-SYMMETRIC NON-ABELIAN TENSOR FIELDS." Modern Physics Letters A 07, no. 10 (1992): 881–92. http://dx.doi.org/10.1142/s0217732392003529.

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We study the spinning particle interacting in a supersymmetric and gauge invariant way with anti-symmetric non-Abelian tensor fields. A quantum theory is presented. We calculate the Witten index for the corresponding Dirac operator and conclude that the anti-symmetric non-Abelian tensor fields do not give any contribution to it.

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39

YANG, SHOUZHI, and YANMEI XUE. "CONSTRUCTION OF COMPACTLY SUPPORTED CONJUGATE SYMMETRIC COMPLEX TIGHT WAVELET FRAMES." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 06 (2010): 861–74. http://dx.doi.org/10.1142/s0219691310003857.

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Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function ϕ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function ϕ is compactly supported conjugate symmetric, then we prove that there exists a compactly supported conjugate symmetric/anti-symmetric complex tight wavelet frame Ψ = {ψ1, ψ2, ψ3} associated with ϕ. Secondly, under the conditions that both the low-pass filters and high-pass filters are unknown, we give a parametric formula for constructing a class of smooth conjugate symmetric/anti-symmetric complex tight wavelet frames. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames.

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40

Wang, Ben-Xin, Chongyang Xu, Haiquan Zhou, and Guiyuan Duan. "Realization of broadband terahertz metamaterial absorber using an anti-symmetric resonator consisting of two mutually perpendicular metallic strips." APL Materials 10, no. 5 (2022): 050701. http://dx.doi.org/10.1063/5.0092958.

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This paper presents a scheme to achieve a broadband metamaterial absorber in the terahertz region, which is consisted of an anti-symmetric T-shaped resonator (formed by two mutually perpendicular metallic strips) on top of a metallic back layer separated by an insulator dielectric layer. The anti-symmetric T-shaped resonator can have a strong electromagnetic interaction with the incident beam, resulting in four different absorption peaks having adjacent frequencies, and the superposition effect of these adjacent peaks produces a broadband absorption. The resonance bandwidth of greater than 80% absorption can have 0.58 THz ranging from 1.54 to 2.12 THz, and its relative resonance bandwidth is 31.69%. The resonance bandwidth and relative resonance bandwidth can be scaled by controlling the parameters of two mutually perpendicular metallic strips in the anti-symmetric T-shaped resonator. Moreover, the parameter optimization of the anti-symmetric T-shaped resonator can realize five discrete absorption peaks with adjacent frequencies, and their combined effect can obtain not only broadband absorption but also a greater absorption bandwidth compared with the case of broadband absorption having four absorption peaks.

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41

Forrester, Peter J., Jesper R. Ipsen, Dang-Zheng Liu, and Lun Zhang. "Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles." Random Matrices: Theory and Applications 08, no. 04 (2019): 1950015. http://dx.doi.org/10.1142/s2010326319500151.

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In this paper, we highlight the role played by orthogonal and symplectic Harish-Chandra integrals in the study of real-valued matrix product ensembles. By making use of these integrals and the matrix-valued Fourier-Laplace transform, we find the explicit eigenvalue distributions for particular Hermitian anti-symmetric matrices and Hermitian anti-self dual matrices, involving both sums and products. As a consequence of these results, the eigenvalue probability density function of the random product structure [Formula: see text], where each [Formula: see text] is a standard real Gaussian matrix, and [Formula: see text] is a real anti-symmetric matrix can be determined. For [Formula: see text] and [Formula: see text] the bidiagonal anti-symmetric matrix with 1’s above the diagonal, this reclaims results of Defosseux. For general [Formula: see text], and this choice of [Formula: see text], or [Formula: see text] itself a standard Gaussian anti-symmetric matrix, the eigenvalue distribution is shown to coincide with that of the squared singular values for the product of certain complex Gaussian matrices first studied by Akemann et al. As a point of independent interest, we also include a self-contained diffusion equation derivation of the orthogonal and symplectic Harish-Chandra integrals.

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42

Tang, Xiaomin, and Yu Yang. "Biderivations of the higher rank Witt algebra without anti-symmetric condition." Open Mathematics 16, no. 1 (2018): 447–52. http://dx.doi.org/10.1515/math-2018-0042.

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AbstractThe Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

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43

Calvetti, Daniela, and Lothar Reichel. "Symmetric Gauss–Lobatto and Modified Anti-Gauss Rules." BIT Numerical Mathematics 43, no. 3 (2003): 541–54. http://dx.doi.org/10.1023/b:bitn.0000007053.03860.c0.

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44

Landsteiner, Karl, Calin Iuliu Lazaroiu, and Radu Tatar. "(Anti)symmetric matter and superpotentials from IIB orientifolds." Journal of High Energy Physics 2003, no. 11 (2003): 044. http://dx.doi.org/10.1088/1126-6708/2003/11/044.

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45

Ekambaram, K., and A. S. Vytheeswaran. "Interacting Non-Abelian Anti-Symmetric Tensor Field Theories." Journal of Physics: Conference Series 1000 (April 2018): 012141. http://dx.doi.org/10.1088/1742-6596/1000/1/012141.

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46

Addya, Subhankar, and Sabitabrta Dey. "Anti-symmetric quadruple ring resonator based optical filter." Optik 126, no. 24 (2015): 5865–69. http://dx.doi.org/10.1016/j.ijleo.2015.08.212.

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47

Kabir, H. R. H. "Anti-symmetric angle-ply laminated thick cylindrical panels." International Journal of Solids and Structures 35, no. 28-29 (1998): 3717–35. http://dx.doi.org/10.1016/s0020-7683(97)00234-5.

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48

Halpern, Federico D. "Anti-symmetric representation of the extended magnetohydrodynamic equations." Physics of Plasmas 27, no. 4 (2020): 042303. http://dx.doi.org/10.1063/5.0002345.

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49

Song, Yiling, Shaolin Ke, Yuelan Chen, and Mingfeng Wang. "Mode-locking in anti-PT symmetric frequency lattices." Applied Physics Letters 122, no. 15 (2023): 151106. http://dx.doi.org/10.1063/5.0146246.

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Active mode-locking (ML) is an important technique in laser science, which greatly shortens the laser pulse. Here, we construct an anti-parity-time (anti-PT) symmetric Su–Schrieffer–Heeger frequency lattice by two ring resonators with antisymmetric amplitude (AM) modulations. We find that the temporal width of the generated pulse can be greatly shortened by the phase-mismatching of the AM modulations. In addition, the pulse shortening shows extremely high sensitivity to the phase transition point, at which the anti-PT symmetry of the system is completely broken. This work exploits the concept of anti-PT symmetry in a laser field to realize ML, and will have broad application prospects in ultrafast spectroscopy and ultra-high sensitive sensors.

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Narwariya, Manoj, Avadesh K. Sharma, Vinod Patidar, and Premanand S. Chauhan. "Harmonic Analysis of symmetric and anti-symmetric laminated skew plate using finite element method." IOP Conference Series: Materials Science and Engineering 691 (December 11, 2019): 012007. http://dx.doi.org/10.1088/1757-899x/691/1/012007.

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