In the light of the guiding methodical role of anharmonic oscillators in field theory we communicate the observation that their " first nontrivial " PT −symmetric cubic Hamiltonians H ± = p 2 ± m 2 x 2 + i f x 3 with opposite sign of mass term are, up to a constant shift, isospectral.

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x + 3y) + f(x− 3y) = 9(f(x + y) + f(x− y))− 16f(x).

The relation between the uniformizing equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces and an AppellLauricella hypergeometric system in nine variables is clarified.

A bicontinuous lyotropic cubic phase, composed of the nonionic surfactant

The circular ow number F c (G) of a graph G = (V; E) is the minimum r 2 Q such that G admits a ow with 1 (e) r ? 1, for each e 2 E. We determine the circular ow number of some regular multigraphs. In particular, we characterize the bipartite (2t + 1)-regular graphs (t 1). Our results imply that there are gaps for possible circular ow numbers for (2t + 1)-regular graphs, e.g. there is no cubic g...

We describe a general theory for the stability of the laminated microstructure for martensitic crystals. Our theory has been applied to the orthorhombic to monoclinic transformation, the cubic to tetragonal transformation, the tetragonal to monoclinic transformation, and the cubic to orthorhombic transformation.

A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.

This paper presents a practical representation containing a parameter of rational cubic conic sections and research’s deeply the inner properties. Firstly, the parameter how to affect the control points, inner weights and shoulder point is discussed. Secondly, the inner relation between the parameter and the weights of the nonstandard-form quadratic rational conic sections is analyzed in detail...