We have selected problems that may not yet be well known, but have the potential to push the research in interesting directions. In particular, we state problems that do not require specific knowledge outside the standard circle of ideas in discrete geometry. Despite the relatively simple statements, these problems are related to current research and their solutions are likely to require new ideas and approaches. We have chosen problems from different fields to make this short paper attractive to a wide range of specialists.

The article is published in the author’s wording.

Relaxation oscillations in a first order differential equation with two delays are considered. On the basis of a special asymptotic big parameter method the problem of studying dynamics of an equation is reduced to the analysis of nonlinear mappings. Each cycle of these mappings corresponds to a periodic solution of the initial equation with the same stability.

In the article the complex Hutchinson equation is studied. New results on numerically observable space-inhomogenious solutions are obtained.

A nanoscale model of surface erosion, simulating the process of surface shaping under ion bombardment is considered. The possibility of a ripple topography is demonstrated by means of bifurcations theory methods for dynamical systems with an infinite dimensional space of initial data. In particular, we use the normal form of Poincare–Dulak.

The problem of constructing and classifying stationary and translating configurations of point vortices with an arbitrary choice of circulations is studied. The polynomial method enabling one to find any such configuration is described in detail. Stationary configurations for vortex systems with circulations Γ, −µΓ are classified in the case of integer µ. New configurations are obtained.

Bifurcation analysis of dynamic system modeling the array of coupled ocillators in the experience of Scott are presented. The non-resonant cases are considered.

This paper is dedicated to the study of ideals in semi-lattice of the enumeration degrees.

The article is devoted to the methods of proving parallel programs correctness that are based on the axiomatic approach. Formal system for functional data-flow parallel programming language Pifagor is described. On the basis of this system programs correctness could be proved.

Algebraic program models with procedures are designed to analyze program semantic properties on their models called program schemes. The concepts that give foundation to the theory of such models are stated along with a description of their implementation. The key point of the theory is the equivalence of program schemes that belong to a particular model. A class of special algebraic models with procedures, called gateway models, is studied. Necessary and sufficient conditions of the equivalence problem decidability in such models are proposed.

Nested Petri nets (NP-nets) are an extension of Petri net formalism within the “netswithin-nets” approach, when tokens in a marking are Petri nets, which have an autonomous behavior and are synchronized with the system net. The formalism of NP-nets allows modeling multi-level multi-agent systems with dynamic structure in a natural way. Currently, there is no tool for supporting NP-nets simulation and analysis. The paper proposes the translation of NP-nets into Colored Petri nets and the use of CPN Tools as a virtual machine for NP-nets modeling, simulation and automatic verification.

The paper describes implementation of dataflow networks based on Smart-M3 platform for use cases related to the Internet of Things. The mechanism for automatic substitution of computational agents created on top of Smart-M3 platform is described. The paper reviews concurrency issues of the developed solution regarding Smart-M3 platform, as well as in the broader context of the Internet of Things.

The article describes TCP TIPS, the transport level protocol, which aim is to effi- ciently use the available bandwidth. This protocol implements the proactive methods for congestion avoidance. These methods allow TCP TIPS to yield the required amount of bandwidth to high-priority flows with realtime data and to use this amount, when it becomes available.