A variant of the large sieve inequality with explicit constants

We give an effective version with explicit constants of the large sieve inequality for imaginary quadratic fields. Explicit results of this kind are useful for estimating the computational complexity of algorithms which generate elements, whose norm is a rational prime, in an arithmetic progression of the corresponding ring of integers.

ENERGY METHOD BASED ON THE STABILITY OF THE FLAT SHAPE OF THE CANTILEVER STRIP BEND TAKING INTO ACCOUNT ITS OWN WEIGHT

the problem of bending a strip by a force applied at the end is not of practical interest. Such method of loading and securing the ends is interesting only because it is most convenient to implement it on experience, which makes it possible to verify the Prandtl theory. When conducting experiments, there is a need for two corrections: it is necessary to evaluate the influence of the self-weight of the strip and the effect of increasing or decreasing the point of force application. As we are talking about small corrections, it is quite enough to use only the first approximation for calculations. An effective version of the energy method is recommended. It is used to calculate rectangular cantilever strips for stability of a flat bending shape, taking into account its own weight. The essence of this variant of the method is to use the Lagrange variational principle instead of the condition for equality of the potential strain energy and the work of external forces. The proposed approach allows us to perform machine implementation of calculations and take into account an arbitrary number of members of the series. The presented solution of the problem for the cantilever beam takes into account its own weight and the action of concentrated force.

Control systems for unmanned combine harvester

Nowadays, there are many technical and technological solutions to increase productivity in agriculture. One of such solutions is the use of the latest robotic mobile systems that can increase agricultural productivity. For the implementation of these decisions, sound concepts are needed to create control systems for agricultural unmanned mobile energy devices based on an analysis of current trends in the development of robotic mobile energy devices. This paper discusses various areas of the concept of creating unmanned control systems for a mobile energy device - a combine harvester, ensuring high-quality performance of technological operations of harvesting, including the directional stability of the combine harvester. The most effective version of the concept of creating a control system was selected.

The mini-neutron monitor: a new approach in neutron monitor design

The near-Earth cosmic ray flux has been monitored for more than 70 years by a network of ground-based neutron monitors (NMs). With the ever-increasing importance of quantifying the radiation risk and effects of cosmic rays for, e.g., air and space-travel, it is essential to continue operating the existing NM stations, while expanding this crucial network. In this paper, we discuss a smaller and cost-effective version of the traditional NM, the mini-NM. These monitors can be deployed with ease, even to extremely remote locations, where they operate in a semi-autonomous fashion. We believe that the mini-NM, therefore, offers the opportunity to increase the sensitivity and expand the coverage of the existing NM network, making this network more suitable to near-real-time monitoring for space weather applications. In this paper, we present the technical details of the mini-NM’s design and operation, and present a summary of the initial tests and science results.

A short proof of the deformation property of Bridgeland stability conditions

The key result in the theory of Bridgeland stability conditions is the property that they form a complex manifold. This comes from the fact that given any small deformation of the central charge, there is a unique way to correspondingly deform the stability condition. We give a short direct proof of an effective version of this deformation property.

Error Detection and Correction On-Board Nanosatellites Using Hamming Codes

The field of nanosatellites is constantly evolving and growing at a very fast speed. This creates a growing demand for more advanced and reliable EDAC systems that are capable of protecting all memory aspects of satellites. The Hamming code was identified as a suitable EDAC scheme for the prevention of single event effects on-board a nanosatellite in LEO. In this paper, three variations of Hamming codes are tested both in Matlab and VHDL. The most effective version was Hamming [16, 11, 4]2. This code guarantees single-error correction and double-error detection. All developed Hamming codes are suited for FPGA implementation, for which they are tested thoroughly using simulation software and optimized.

Cuspidal curves, minimal models and Zaidenberg’s finiteness conjecture

Let {E\subseteq\mathbb{P}^{2}} be a complex rational cuspidal curve and let {(X,D)\to(\mathbb{P}^{2},E)} be the minimal log resolution of singularities. We prove that E has at most six cusps and we establish an effective version of the Zaidenberg finiteness conjecture (1994) concerning Eisenbud–Neumann diagrams of E. This is done by analyzing the Minimal Model Program run for the pair {(X,\frac{1}{2}D)} . Namely, we show that {\mathbb{P}^{2}\setminus E} is {\mathbb{C}^{**}} -fibred or for the log resolution of the minimal model the Picard rank, the number of boundary components and their self-intersections are bounded.