In this paper, we introduce the concept of a quasi-metric-like space, and by defining the w-compatibility of two mappings, we obtain multidimensional coincidence point and multidimensional fixed point theorems for generalized ψ-quasi-contractions in quasi-metric-like spaces. Our results extend the fixed point theorems in Vetro and
Steady-state responses of the boost converter operating in discontinuous conduction mode of operation are identified by using bifurcation diagrams as a typical simulation tool for identification of steady-state responses. The structure of simulated bifurcation diagrams is dependent on the initial period of sampling and the initial instant of sampling. The influence of these parameters on calculation of bifurcation diagrams was studied. Some possible issues, pitfalls and misinterpretations are commented as well as some recommendations about steady-state response identification are given
The paper gives a systematic overview of literature sources who consider impacts critical damage of mechanical, corrosive and thermal nature which may occur on railway axles during operation and which may be the causes of their fracture. The results of the research of the mechanisms that cause cracks, crack propagation and final fracture of the railway vehicle axle, such as material fatigue and the appearance of localized notches caused by paint (coating) separation, damage from ballast impact and pitting corrosion are presented. The influence of high temperatures and overheating on the axles was analyzed and an excerpt from the research published in one research report was given. Some significant suggestions for optimizing the design of the axles are highlighted which would take into account the analysis of time-varying axle stresses, stress spectrum in operation, axle tolerance to damage and the existence of residual surface stresses. The reliefs of the fracture surfaces of the axle after the railway incidents and the derailment of the rail vehicle from the rails are presented and explained.
Steady-state responses of the boost converter by change of input voltage are experimentally identified. In a part of parameter space hysteretic behaviour of steadystate responses by varying input voltage in different tendency of change is noticed. Procedure for studying steady-state responses of the boost converter is proposed by using one-parameter and two-parameter bifurcation diagrams as simulation result. It is shown that the initial condition of bifurcation parameters affects steady-state responses inside hysteretic region. There is a variety of combinations of initial inductor current and initial capacitor voltage which cause particular steady-state. Therefore, hysteretic bifurcation model of the boost converter is proposed and verified by simulations and measurement outside hysteretic region.
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