Symmetry, Volume 6, Issue 2

The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of...

Bilateral symmetry is an extremely salient feature for the human visual system. An interesting issue is whether the perceptual salience of symmetry is rooted in normal visual development. In this review, we discuss empirical work on visual and tactil...

An innovative classification and back-propagation-network tree (CABPN tree) approach is proposed in this study to estimate the cycle time of a job in a wafer fabrication factory, which is one of the most important tasks in controlling the wafer fabri...

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear a...

In this review article, I report our recent studies on spectroscopic visualizations of macroscopic helical alignments of nanofibers in vortex flows. Our designed supramolecular nanofibers, formed through self-assemblies of dye molecules, helically al...

Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence o...

Several dynamic processes, including tautomerism and macrocyclic inversion, in ¹H-NMR prochiral solvating agents (pro-CSAs) are investigated. Various features of pro-CSA, including modes of interaction for complex formation, stoichiometry, binding st...

We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not su...

A crystallographic bar-joint framework, C in R^d, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω (C), is a singleton. Moreover, the a...

Supramolecular chirality, being an intelligent combination of supramolecular chemistry and chiral science, plays a decisive role in the functioning of various natural assemblies and has attracted much attention from the scientific community, due to d...

In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum feature...

Visual symmetry has been found to be preferred to asymmetry in a variety of domains and across species. A number of theories propose to explain why symmetry is preferred. In this article, I compare a perceptual bias view, in which symmetry is preferr...

We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transformat...

Symmetry plays a fundamental role in chiral recognition and enantioselective catalysis. Porphyrins possess a number of structural features that make them attractive for the stereocontrol of chiral recognition and metal-catalyzed asymmetric reactions....

Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R³. In this paper, we determine for each complete graph K_n with n ≤ 6, wh...

An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also use...

I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the me...