Given two structures ${\cal M}$ and ${\cal N}$ on the same domain, we say that ${\cal N}$ is a reduct of ${\cal M}$ if all $\emptyset$-definable relations of ${\cal N}$ are $\emptyset$-definable in ${\cal M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are ${\aleph _0}$-categorical, determining their reducts is equivalent to determining the closed supergroups G ≤ Sym(ℕ) of their automorphism groups.

A consequence of the classification is that there are ${2^{{\aleph _0}}}$ pairwise noninterdefinable Henson digraphs which have no proper nontrivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are ${2^{{\aleph _0}}}$ pairwise nonconjugate maximal-closed subgroups of Sym(ℕ). By the reconstruction results of Rubin, these groups are also nonisomorphic as abstract groups.

There are specific problems of databases in meteor science such as making meteor databases into the modern research tools. Special institutes and virtual observatories exist for the meteor data storage where the data is online and in open access. However, there are also numerous databases without the open access, such as for example, three radar databases: Kharkiv database with 250,000 meteor orbits in Ukraine, New Zealand database with 500,000 meteor orbits, and Canadian database with more than 3 million meteor orbits. One of the reasons the open access is absent for these databases could be the complexity in the copyright compliance. In the framework of the creation of the modern effective research tool in the meteor science, we discuss here the case of the Kharkiv meteor database.

This paper presents applications of group theory tools to simplify the analysis of kinematic chains associated with mechanisms and parallel manipulators. For the purpose of this analysis, a kinematic chain is described by its properties, i.e. degrees-of-control, connectivity and redundancy matrices. In number synthesis, kinematic chains are represented by graphs, and thus the symmetry of a kinematic chain is the same as the symmetry of its graph. We present a formal definition of symmetry in kinematic chains based on the automorphism group of its associated graph. The symmetry group of the graph is associated with the graph symmetry. By using the group structure induced by the symmetry of the kinematic chain, we prove that degrees-of-control, connectivity and redundancy are invariants by the action of the automorphism group of the graph. Consequently, it is shown that it is possible to reduce the size of these matrices and thus reduce the complexity of the kinematic analysis of mechanisms and parallel manipulators in early stages of mechanisms design.

We give some extension to theorems of Jiménez López and Soler López concerning the topological characterization for limit sets of continuous flows on closed orientable surfaces.

Given a finite field 𝔽p={0,…,p−1} of p elements, where p is a prime, we consider the distribution of elements in the orbits of a transformation ξ↦ψ(ξ) associated with a rational function ψ∈𝔽p(X). We use bounds of exponential sums to show that if N≥p1/2+ε for some fixed ε then no N distinct consecutive elements of such an orbit are contained in any short interval, improving the trivial lower bound N on the length of such intervals. In the case of linear fractional functions we use a different approach, based on some results of additive combinatorics due to Bourgain, that gives a nontrivial lower bound for essentially any admissible value of N.

Let $\mathcal{F}$ be a family of vector fields on a manifold or a subcartesian space spanning a distribution $D.$ We prove that an orbit $O$ of $\mathcal{F}$ is an integral manifold of $D$ if $D$ is involutive on $O$ and it has constant rank on $O$. This result implies Frobenius’ theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.

In this study, a method is presented to maintain real-time positioning at the decimetre-level accuracy during breaks in reception of the measurement corrections from multiple reference stations. The method is implemented at the rover by estimating prediction coefficients of the corrections during normal RTK positioning, and uses these coefficients to predict the corrections when reception of the corrections is temporarily lost. The paper focuses on one segment of this method, the on-the-fly prediction of orbital corrections. Frequently, only a few minutes of data representing short orbit ‘arcs’ are available to the user before losing radio transmission. Thus, it would be hard for the rover to predict the satellite positions using equations of motion. An alternative method is proposed. In this method, GPS orbital corrections are predicted as a time series and are added to the initial positions computed from the broadcast ephemeris to compute relatively accurate satellite positions. Different prediction approaches were investigated. Results show that the double exponential smoothing method and Winters' method can be successfully applied. The latter, however, has a better performance. The impact of the data length used for estimation of the prediction coefficients and the selection of seasonal lengths in Winters' method were investigated and some values were recommended. In general, the method can give orbital correction estimation accuracy of less than 5 cm after 15 minutes of prediction. This will result in a positioning accuracy better than 5 cm.

The evolution of a barred galactic potential containing a central mass concentration is examined by means of a self-consistent 2-D N-body simulation. It is found that the bar weakens as the central mass grows and eventually dissolves, in agreement with earlier orbital studies of this problem.