ON STATIONARY MODES OF CYCLIC NEIGHBORHOOD SYSTEMS

В работе устанавливается связь между предельными циклами алгоритма последовательного проектирования, возникающими в случае применения алгоритма к переопределенным системам линейных уравнений, и стационарными режимами динамических окрестностных систем циклического типа. In this paper, a connection is established between the limit cycles of the sequential projection algorithm (that arise when the algorithm is applied to overdetermined systems of linear equations) and the stationary modes of dynamic neighborhood systems of cyclic type.

Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

<abstract><p>The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $ b $-metric spaces. The considered operators are generalized $ \varphi $-contractions and $ \alpha $-$ \varphi $ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.</p></abstract>

General regularities in the development Gzhelian-Asselian conodonts

Subject of study. The features of the evolutionary changing of Gzhelian-Asselian conodonts are examined. Materials. The data on Ural and North American conodonts are used. Results. The cyclic type of change of the Pa-element morphology in the process of the evolutionary development of the representatives of the genus Streptognathodus is established. Morphological evolutionary trends of gradual development alternate with the periods of the rapid appearance of a group of the forms of original constitution. The species of this group are characterized by wide distribution and short lifetime. Such species are used as the markers of the boundaries of stratigraphic subdivisions. Lower boundary of Gzhelian is determined by the appearance of species of the group simulator; the species of group isolatus mark lower boundary of Asselian. Model of the ensemble evolution of the related species is used for explaining the directed change in the morphology of conodonts. The saltational appearance of the determined indication is explained by the phenomenon of evolutionary oscillations. Conclusion. We can make conclusion about the sexual multiplication of this group of the organisms according the established alternation of the periods of the slow and rapid morphological evolution of conodonts.

Some new results on (s,q)-Dass-Gupta-Jaggi type contractive mappings in b-metric-like spaces

In this paper we consider cyclic (s-q)-Dass-Gupta-Jaggi type contractive mapping in b-metric like spaces. By using our new approach for the proof that one Picard?s sequence is Cauchy in the context of b-metric-like space, our results generalize, improve and complement several results in the existing literature. Moreover, we showed that the cyclic type results of Kirk et al. are equivalent with the corresponding usual fixed point ones for Dass-Gupta-Jaggi type contractive mappings. Finally, some examples are presented here to illustrate the usability of the obtained theoretical results.

Quandles of Cyclic Type with Several Fixed Points

A quandle of cyclic type of order $n$ with $f$ (greater than 1) fixed points is such that, by definition, each of its permutations splits into $f$ cycles of length 1 and one cycle of length $n-f$. In this article we prove that there is only one such connected quandle, up to isomorphism. This is a quandle of order 6 and 2 fixed points, known in the literature as octahedron quandle.

Monoidal Categories, 2-Traces, and Cyclic Cohomology

In this paper we show that to a unital associative algebra object (resp. co-unital co-associative co-algebra object) of any abelian monoidal category ( $\mathscr{C},\otimes$ ) endowed with a symmetric 2-trace, i.e., an $F\in \text{Fun}(\mathscr{C},\text{Vec})$ satisfying some natural trace-like conditions, one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra “with coefficients in $F$ ”. Furthermore, we observe that if $\mathscr{M}$ is a $\mathscr{C}$ -bimodule category and $(F,M)$ is a stable central pair, i.e., $F\in \text{Fun}(\mathscr{M},\text{Vec})$ and $M\in \mathscr{M}$ satisfy certain conditions, then $\mathscr{C}$ acquires a symmetric 2-trace. The dual notions of symmetric 2-contratraces and stable central contrapairs are derived as well. As an application we can recover all Hopf cyclic type (co)homology theories.