Families of nested completely regular codes and distance-regular graphs

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended binary) Hamming codes of length $n=2^m-1$ (respectively, $2^m$), where $m=2u$. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter $D$ equal to $3$ or $4$ are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive

On gravitational interactions for massive higher spins in AdS3AdS_3

In this paper we investigate gravitational interactions of massive higher spin fields in three dimensional $AdS$ space with arbitrary value of cosmological constant including flat Minkowski space. We use frame-like gauge description for such massive fields adopted to three-dimensional case. At first, we carefully analyze the procedure of switching on gravitational interactions in the linear approximation on the example of massive spin-3 field and then proceed with the generalization to the case of arbitrary integer spin field. As a result we construct a cubic interaction vertex linear in spin-2 field and quadratic in higher spin field on $AdS_3$ background. As in the massless case the vertex does not contain any higher derivative corrections to the Lagrangian and/or gauge transformations. Thus, even after switching on gravitational interactions, one can freely consider any massless or partially massless limits as well as the flat one.Comment: 21 pages. Some clarifications and 1 new reference added. Version to appear in the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasilie

Conformal self-dual fields

Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal symmetries is obtained. Light-cone gauge Lagrangian is found. Also, we demonstrate use of the light-cone gauge for counting of on-shell degrees of freedom of the conformal self-dual fields.Comment: 28 pages, LaTeX-2e, v3: Discussion of realization of conformal algebra symmetries on field strengths added to Sections 3,5. Appendices B,C,D and one reference added. Typos correcte

Concept of heat treatment and reversed hot strip rolling of magnesium

The production of magnesium strips, based on a twin-roll casting (TRC) and Hot Strip Rolling, has a promising application especially in automobile industry. Recently, the TRC line extends by further rolling mills to produce strips with fewer thicknesses. The additional rolling requires re-heating of the TRC strip coil to improve the deformation properties. The heating process affects the microstructure and final properties of the strips. Therefore, it is important to control the heat treatment process. The aim of this study is to create a bundle of models to calculate the temperature development in process of magnesium strip production. The first model calculates the temperature distribution in the TRC magnesium coils during pre-heating process and after rolling. Furthermore, the extend first model will be included into the Hot Strip Rolling in order to analyze a temperature condition in coil during the rolling process. Additionally, in this modelthe microstructure influencing by deformation and heat treatment process will be furtherincluded. In this article, the concept of the model and current state of the work will be defined