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An extension of the Neumann-Minnigerode-Curie principle☆

TLDR
In this article, the NMC principle is extended to non-totally symmetric irreducible representations of the point group to enable the selection rules for the physical properties from the symmetry of the object in question.
Abstract
The Neumann-Minnigerode-Curie Principle (NMC Principle) which enables one to derive the selection rules for the physical properties from the symmetry of the object in question is given for the totally symmetric representation of the point group and thus for the static properties of the object. Its dynamical properties, however, are described by the non-totally symmetric irreducible representations of the point group to which the NMC Principle can be extended.

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Integrable (2+1)-dimensional and (3+1)-dimensional breaking soliton equations

TL;DR: In this article, the modified form of Hirota's bilinear method, established by Hereman, is applied to derive multiple soliton solutions and multiple singular solutions for each model.
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Bell-polynomial construction of Bäcklund transformations with auxiliary independent variable for some soliton equations with one Tau-function

TL;DR: In this article, the Bell-polynomial-typed Backlund transformations (BTs) are constructed for bilinearizable nonlinear evolution equations including the shallow water wave equation, Lax fifth-order KdV equation, and (2+1)- and (3+1)dimensional breaking soliton equations.
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Shedding light on non-Ising polar domain walls: Insight from second harmonic generation microscopy and polarimetry analysis

TL;DR: In this article, the authors highlight the capabilities of non-linear optics to probe these newly discovered aspects in polar non-Ising type domain walls through the second-harmonic generation (SHG) process.
Journal ArticleDOI

Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

TL;DR: Symmetry and orderliness of two-dimensional levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM).
Journal ArticleDOI

Chirality: The Backbone of Chemistry as a Natural Science

Josep M. Ribó
- 01 Nov 2020 - 
TL;DR: Chemistry should express chirality not only as molecular structural dissymmetry that at the present is described in chemical curricula by quite effective pedagogical arguments, but also as a cosmological phenomenon, to a necessarily better understanding of the boundaries of chemistry with physics and biology.