scholarly journals ON THE SYMMETRY PROPERTIES OF POWERS OF REPRESENTATIONS OF THE TWO-DIMENSIONAL UNIMODULAR UNITARY GROUP

1954 ◽  
Vol 40 (9) ◽  
pp. 822-825 ◽  
Author(s):  
F. D. Murnaghan
Keyword(s):  
Unitary Group ◽  
Two Dimensional ◽  
Symmetry Properties

Three and Four Centre Oscillators and Their Application in Nuclear Physics

1974 ◽  
Vol 29 (7) ◽  
pp. 1003-1010 ◽  
Author(s):  
Peter Bergmann ◽  
Hans-Joachim Scheefer
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Nuclear Physics ◽  
Schrodinger Equation ◽  
Numerical Procedure ◽  
Orthogonal Basis ◽  
Two Dimensional ◽  
Schmidt's Method ◽  
Symmetry Properties

The extension of the nuclear two-centre-oscillator to three and four centres is investigated. Some special symmetry-properties are required. In two cases an analytical solution of the Schrödinger equation is possible. A numerical procedure is developed which enables the diagonalization of the Hamiltonian in a non-orthogonal basis without applying Schmidt's method of orthonormalization. This is important for calculations of arbitrary two-dimensional arrangements of the centres.

scholarly journals Realizable response matrices of multi-terminal electrical, acoustic and elastodynamic networks at a given frequency

2008 ◽  
Vol 464 (2092) ◽  
pp. 967-986 ◽  
Author(s):  
Graeme W Milton ◽  
Pierre Seppecher
Keyword(s):  
Three Dimensional ◽  
Complete Characterization ◽  
Two Dimensional ◽  
Response Matrix ◽  
Electrical Networks ◽  
Fixed Frequency ◽  
Symmetry Properties ◽  
Acoustic Networks ◽  
Mathematical Equivalence

We give a complete characterization of the possible response matrices at a fixed frequency of n -terminal electrical networks of inductors, capacitors, resistors and grounds, and of n -terminal discrete linear elastodynamic networks of springs and point masses, both in three-dimensional and two-dimensional cases. Specifically, we construct networks that realize any response matrix that is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Owing to a mathematical equivalence, we also obtain a characterization of the response matrices of discrete acoustic networks.

scholarly journals Generating Reflections For U(2, p2n). II, p = 2

1964 ◽  
Vol 7 (2) ◽  
pp. 213-217 ◽  
Author(s):  
D. W. Crowe
Keyword(s):  
Unit Circle ◽  
Unitary Group ◽  
Final Section ◽  
Present Note ◽  
Two Dimensional

It is known [4] that the finite two- dimensional unitary group U(2, p2n) is generated by two reflections if p ≠ 2. The present note completes that result by giving two generating reflections for U(2, 22n), n > 1. As in [4] this implies that the points of the "unit circle " in the unitary plane over GF(22n), n > 1, are the vertices of a "regular unitary polygon" whose group of auto- 2n morphisms is U(2, 22n).The final section gives abstract definitions for the particular groups U(2,24) and U(2,52) in terms of their generating reflections.

scholarly journals Similarity in Symmetry Groups of Ornaments as a Measure for Cultural Interactions in Medieval Times

2020 ◽  
Author(s):  
Mehmet Erbudak ◽  
Selim Onat
Keyword(s):  
Systematic Approach ◽  
Symmetry Groups ◽  
Two Dimensional ◽  
Mathematical Methods ◽  
Symmetry Properties ◽  
Art Practices ◽  
Euclidean Distances ◽  
Similarities And Differences ◽  
Wallpaper Groups ◽  
Cultural Interactions

The symmetry properties of an ornament contain information about its civilisation and its interactions with other cultural sources. Two-dimensional periodic ornaments can be strictly classified into a limited set of 17 mathematical symmetry groups, also known as wallpaper groups. The collection of ornaments thus classified for a civilisation is characteristic of the cultural group and serves as a fingerprint to identify that group. If the distribution of wallpaper groups is available for several societies, mathematical methods can be applied to determine similarities and differences between the art practices of these communities. This method allows a systematic approach to the general ornamental practices within a culture and their interactions in the form of similarity of fingerprints. We test the feasibility of the method on examples of medieval Armenians, Byzantium, Seljuks first in Persia and then in Anatolia and among Arabs in the Middle East. For this purpose we present the distribution of the planar ornaments and calculate the Euclidean distances in pairs. We tested to what extend geographical and religious factors could account for the observed similarity of ornamental groups between cultures. The results suggest an intensive interaction between the Seljuk Turks and Arab craftsmen who produced the ornaments. Therefore the cultural interactions are religiously motivated.

REPRESENTATIONS OF THE UNITARY GROUP AND WAVE FUNCTIONS

1961 ◽  
Vol 39 (4) ◽  
pp. 510-513
Author(s):  
H. A. Venables
Keyword(s):  
Spherical Harmonics ◽  
Unitary Group ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Two Dimensional

A number of wave functions besides the spherical harmonics are obtainable from the irreducible representations of the two-dimensional unitary group.

SPATIAL, TEMPORAL, AND GLOBAL MODE ENTROPY IN A THALAMO–CORTICAL NETWORK

1993 ◽  
Vol 03 (06) ◽  
pp. 1487-1501 ◽  
Author(s):  
GENE V. WALLENSTEIN
Keyword(s):  
Cortical Neurons ◽  
Space Time ◽  
Time Behavior ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Cortical Cells ◽  
Global Mode ◽  
Time Symmetry ◽  
Symmetry Properties ◽  
Cortical System

We employ an orthogonal decomposition technique with unique space–time symmetry properties to analyze a network of thalamo–cortical oscillators. A small number of thalamic "cells" are used to drive a network of cortical cells structured on a two-dimensional lattice. Two Bonhoeffer–van der Pol (BVP) based models of cortical neurons are compared at the network level in an attempt to reproduce some features of the thalamo–cortical system. It is shown that with the addition of a slowly varying term to the classical two-dimensional BVP model, the network can exhibit both periodic and irregular space–time behavior, along with changes in the temporal coherence and spatial frequency resembling the 8–12 Hz alpha rhythm.

Piezoelectricity in Monolayers and Bilayers of Inorganic Two-Dimensional Crystals

2013 ◽  
Vol 1556 ◽  
Author(s):  
Karel-Alexander N. Duerloo ◽  
Mitchell T. Ong ◽  
Evan J. Reed
Keyword(s):  
Density Functional ◽  
Electromechanical Coupling ◽  
Three Dimensional ◽  
Single Layer ◽  
Elastic Model ◽  
Two Dimensional ◽  
Functional Theory ◽  
Symmetry Properties ◽  
Electromechanical Effects ◽  
Out Of Plane

ABSTRACTThe symmetry properties of many inorganic two-dimensional monolayer crystals make them piezoelectric, whereas their three-dimensional parent crystals are not. The emergence of piezoelectricity in the single-layer limit points toward intriguing electromechanical effects and applications in the single- or few-layer regime. We use density functional theory to calculate the piezoelectric coefficients of BN, MoS2, MoSe2, MoTe2, WS2, WSe2 and WTe2. These coefficients are found to be comparable to, and in some cases greater than those of commonly used wurtzite piezoelectrics. The centrosymmetry of a BN bilayer prevents a piezoelectric effect for this structure. However, by developing an elastic model, we find that the bilayer exhibits an unusual electromechanical coupling to the curvature, similar to that of a bimorph. A BN bilayer is found to amplify the constituent monolayers’ in-plane piezoelectric displacements by factors on the order of 103-104 into out-of plane deflections.

The Duschinsky Effect and Optical Spectra

1983 ◽  
Vol 38 (8) ◽  
pp. 937-946
Author(s):  
G. Olbrich ◽  
H. Kupka
Keyword(s):  
Electronic Spectra ◽  
Emission Band ◽  
Electronic States ◽  
Polyatomic Molecules ◽  
Two Dimensional ◽  
Molecular Electronic ◽  
Quadratic Interaction ◽  
Symmetry Properties ◽  
Emission And Absorption Spectra ◽  
Weakly Linear

Abstract The influence of the normal mode rotation (i.e. the Duschinsky mixing) on the molecular electronic spectra in polyatomic molecules is treated by means of multidimensional intramolecular distributions (MID). It is shown that symmetry properties of the two-dimensional MID which relate emission and absorption spectra or pertain to the exchange of modes do not exist if the number of non-separable modes exceeds 2. Specific examples of emission band shapes are calculated for weakly (linear) coupled electronic states for both, zero and finite temperatures. The strength of the mixed quadratic interaction parameter is shown to influence the shape considerably.

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