In this paper, we introduce $n$-variables mappings which are cubic in each variable. We show that such satisfy a functional equation. The main purpose is to extend the applications of fixed point method establish Hyers-Ulam stability for multi-cubic mappings. As consequence, prove equation can be hyperstable.

We study the bandwidth and the pathwidth of multi-dimensional grids. It can be shown for grids, that these two parameters are equal to a more basic graph parameter, the vertex boundary width. Using this fact, we determine the bandwidth and the pathwidth of three-dimensional grids, which were known only for the cubic case. As a by-product, we also determine the two parameters of multi-dimensiona...

This work presents a new type of polarization-free GaN emitter. The unique aspect of this work is that the ultraviolet and visible emission originates from the cubic phase GaN and the cubic phase InGaN/GaN multi-quantum-wells, respectively. Conventionally, GaN emitters (e.g. light emitting diodes, laser diodes) are wurtzite phase thus strong polarization fields exist across the structure contri...

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the suffi...

We report an observation of uniaxial magnetic anisotropy along the [100] crystallographic direction in crystalline Fe film grown on Ge buffers deposited on a (001) GaAs substrate. As expected, planar Hall resistance (PHR) measurements reveal the presence of four in-plane magnetic easy axes, indicating the dominance of the cubic anisotropy in the film. However, systematic mapping of the PHR hyst...

In this paper, multi-component generalizations to the Camassa–Holm equation, the modified Camassa–Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schrödinger equation, the complex Camassa– Holm equation and the multi-component modified Camassa–Holm equation are provided. It is shown that these equations arise from non-streching invariant c...

Ontology mapping is one of the core tasks for ontology interoperability. It is aimed to find semantic relationships between entities (i.e. concept, attribute, and relation) of two ontologies. It benefits many applications, such as integration of ontology based web data sources, interoperability of agents or web services. To reduce the amount of users’ effort as much as possible, (semi-) automat...

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over Fp into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial homomorphisms in the other cases. Thereby, we follow the classification of cubic surfaces, due to A.Cayley. 1 The quasi group of a cubic surface 1.1. –––– According to Yu. I. ...

In this paper, reference trajectory is designed according to minimum energy consumed for multi-robot system, which nonlinear programming and cubic spline interpolation are adopted. The control strategy is composed of two levels, which lower-level is simple PD control and the upper-level is based on the internal average kinetic energy for multi-robot system in the complex environment with veloci...

This paper considers the implementation of the cubic public-key transformation, a publickey cryptographic scheme that requires sending of additional side-information. A coding scheme for the side-information, based on the residue number system, is presented. In the conventional one-to-one encryption mapping also, such coding can be used to send additional like that of watermarking, which could ...