Symmetry, Volume 4, Issue 3

This paper describes 4-valent tiling-like structures, called pseudotilings, composed of barrel tiles and apeirogonal pseudotiles in Euclidean 3-space. These (frequently face-to-face) pseudotilings naturally rise in columns above 3-valent plane tiling...

The structure of β-Mn crystallizes in space group P4132. The pseudo 8-fold nature of the 41 axes makes it constitute an approximant to the octagonal quasicrystals. In this paper we analyze why a five-dimensional super space group containing mutually...

An exciting subject in string theory is to consider some applications of the AdS/CFT correspondence to realistic systems like condensed matter systems. Since most of such systems are non-relativistic, an anisotropic scaling symmetry with the general...

This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler g...

In order to investigate why crystal symmetry lowers with increasing temperature by phase transition of TII–III (=369 K) in Cs3H(SeO4)2, in spite of the fact that crystal symmetry in the high-temperature phase of many ionic conductors becomes higher b...

We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent p...

We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain suc...

In the present paper we study subsolutions of the Dirac and Duffin–Kemmer–Petiau equations in the interacting case. It is shown that the Dirac equation in longitudinal external fields can be split into two covariant subequations (Dirac equations with...

Two-dimensional (2D) functions with wallpaper group symmetry can be written as Fourier series displaying both translational and point-group symmetry. We elaborate the symmetry-adapted Fourier series for each of the 17 wallpaper groups. The symmetry m...

Using an x-y-z coordinate system, the equations of the superspheres have been extended to describe intermediate shapes between a sphere and various convex polyhedra. Near-polyhedral shapes composed of {100}, {111} and {110} surfaces with round edges...