In this paper we will look at the one system of ODE and analyze it. We aim to determine the points of equilibrium; examine their character and establish the existence of a bifurcation for the corresponding parameter value. A detailed analysis of local stability was performed for all values of the given parameter. For a certain value of the parameter, the existence of supercritical Hopf bifurcation of the observed system of differential equations has been proved. Also, the existence of a limit cycle that is always stable has been proved.

This study investigated the correlation between bone characteristics, the design of orthodontic mini-implants, the pull-out force, and primary stability. This experimental in vitro study has examined commercial orthodontic mini-implants of different sizes and designs, produced by two manufacturers: Tomas-pin SD (Dentaurum, Ispringen, Germany) and Perfect Anchor (Hubit, Seoul, Korea). The total number of 40 mini-implants were tested. There are two properties that are common to all tested implants—one is the material of which they are made (titanium alloy Ti-6Al-4V), and the other is the method of their insertion. The main difference between the mini-implants, which is why they have been selected as the subject of research in the first place, is reflected in their geometry or design. Regardless of the type of implant, the average pull-out forces were found to be higher for a cortical bone thickness (CBTC) of 0.62–0.67 mm on average, compared to the CBTC < 0.62 mm, where the measured force averages were found to be lower. The analysis of variance tested the impact of the mini-implant geometry on the pull-out force and proved that there is a statistically significant impact (p < 0.015) of all three analyzed geometric factors on the pull-out force of the implant. The design of the mini-implant affects its primary stability. The design of the mini-implant affects the pulling force. The bone quality at the implant insertion point is important for primary stability; thus, the increase in the cortical bone thickness increases the value of the pulling force significantly.

In this paper we will present the Julia set and the global behavior of a polynomial second-order difference equation of type xn+1 = axmn xx-1 + axm+1 n-1 + bxn-1 where m ? N, a > 0 and b ? 0 with non-negative initial conditions.

The research deals with the optimisation of CNC turning process parameters to determine the optimal parametric combination that provides the minimal surface roughness (Ra) and maximal material removal rate. The experiment was conducted by the CNC turning process of S355J2 carbon steel. Data from the Taguchi design of experiments were the subject of analysis with Grey Relational Analysis (GRA) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In the present study, three process parameters, such as cutting speed, feed rate and depth of cut, were chosen for the experimentation. It was found that 250 m/min cutting speed, 0.10 mm/rev feed rate and 1.8 mm depth of cut presented the optimal parametric combination by both used multi-objective optimisation methods. Analysis of variance (ANOVA) at a 95 % confidence level was used to determine the most significant parameters. Finally, the accuracy of GRA and TOPSIS results were validated by confirmation experiments.

Car jack is the basic equipment of every car. To replace the tires or to repair a specific defect on the car it is necessary to have a car jack. A modern way of creating the complex mechanical structures is described in this paper, which allows for rapid change of parameters and therefore of the whole design, i.e. the parameterized car jack model was developed. Also, the goal of this research is to carry out kinematic analysis of a car jack design. Parametric model is developed in such a way that all parameters of design are in correlations to one main parameter. The angle of thread spindle is chosen for main parameter. Usually, main parameter should be chosen as one of the parameters from power input elements. Car jack has a human hand power which is applied on car jack handle and because of that, the angle of rotation of thread spindle is the best for main parameter.

This paper presents the methodology for the development of an optimization model for the optimization of the cross-section dimensions of a bridge crane girder designed as a welded I-profile. To carry out this optimization, the CAD/CAE software package CATIA V5 was used. In order to develop an optimization model, a CAD geometrical model and structural analysis model were developed. Optimization was carried out by the iterative method using a simulated hardening algorithm. Additionally, the optimization process is carried out by using the PEO (Product Engineering Optimization) CATIA module that contains tools for setting the optimization criteria, design parameters, constraints, and algorithms. The goal of the optimization is to achieve the minimal mass of the girder, while satisfying all functional and geometrical constraints. As a result of the optimization process, minimal girder dimensions were obtained and due to that, a minimal amount of material can be used for the manufacturing of the girder.

In general, polynomial difference equations and polynomial maps in the plane have been studied in both the real and complex domains (see [8, 9]). First results on quadratic polynomial difference equation have been obtained in [1, 2] but these results gave us only a part of the basins of attraction of equilibrium points and period-two solutions. In [4], the general second order difference equation is completely investigated and described the regions of initial conditions in the first quadrant for which all solutions tend to equilibrium points, period-two solutions, or the point at infinity, except for the case of infinitely many period-two solutions. In [3], case of infinitely many period-two solutions is completely investigated. Our results are based on the theorems which hold for monotone difference equations. Our principal tool is the theory of monotone maps, and in particular cooperative maps, which guarantee the existence and uniqueness of the stable and unstable invariant manifolds for the fixed points and periodic points (see [5]). Consider the difference equation

A novel method for indoor air quality monitoring is presented in this paper. It is based on the network of smart sensors permanently connected to the cloud. The prototype system, consisting of 10 smart sensors is evaluated in laboratory and real use. Each smart sensor was able to measure air temperature, relative humidity, particulate matter concentration, and carbon dioxide concentration. The cloud-based architecture of the system is explained, followed by the calibration method and real scenario results. The system proved to be suitable for real-time monitoring of indoor air quality parameters for large buildings.