The quasilinear second order differential equation .. x + (1 + p (x, t)) . x + p (x, t) x = f (x, t) where p, f ∈ C (D,R) , D = Ix×I, Ix ⊆ R open set, I = 〈 t,∞ 〉 is under consideration. The paper presents some results on the existence and behavior of parameter classes of solutions of this equation. The qualitative analysis theory and topological retraction method are used. The general results are presented and subsequently certain examples are considered.

This paper presents sufficient conditions for the existence of solutions for certain classes of Cauchy’s solutions of the Lagerstrom equation as well as their behavior. Behavior of integral curves in the neighborhoods of an arbitrary or integral curve are considered. The obtained results contain the answer to the question on approximation of solutions whose existence is established. The errors of the approximation are defined by functions that can be sufficiently small. The theory of qualitative analysis of differential equations and topological retraction method are used.

In this paper analyses of the current state of the thermal insulation of walls without styrofoam and existing windows of Alipasino polje buildings in Sarajevo, Bosnia and Herzegovina, which is powered boiler K-5 through its substations, and current fuel consumption is performed. Research results lead to the conclusion that it is worth to consider insulation of buildings, i.e., simulation of adding styrofoam and new windows on the existing structure in order to reduce heat losses and thus reduce fuel consumption and gas emissions. Savings obtained by this simulation are over 30%. Surface area of buildings subject to the installation of the insulation is obtained on the basis of projects from the district heating system Toplane Sarajevo. Styrofoam thickness is determined by optimizing reduction of the payback period. Prediction of fuel consumption was evaluated for the existing and projected future depending on outside temperature. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of DAAAM International Vienna.

Laser beam machining (LBM) is one of the most widely used thermal energy based non-contact type advance machining process which can be applied for almost whole range of materials. This paper defines mathematical models for surface roughness prediction (Ra, μm) and width of heat affected zone (HAZ, mm) during laser cutting of alloy steels 1.4571 and 1.4828 with nitrogen as assist gas. For defining appropriate mathematical models multiple regression analysis is used with four independent variables. Following parameters are varied: cutting speed, focus position, nitrogen assist gas pressure and stand-off. Obtained mathematical models describe dependence of Ra and HAZ from varied process parameters. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of DAAAM International Vienna.

This paper deals with certain classes of Cauchy’s solutions of quasilinear second order differential equations in general form, Van der Pol's differential equation, which is used in the theory of electric circuits, and Lagerstorm's differential equations, which is used in asymptotic treatment of viscous flow past a solid at low Reynolds number. Behaviour of integral curves in the neighbourhoods of an arbitrary or integral curve is considered. Obtained results establish sufficient conditions for the existence and asymptotic behaviour of the observed equations. The obtained results contain the answer to the question on approximation of solutions whose existence is established. The errors of the approximation are defined by functions that can be sufficiently small. The qualitative analysis theory and topological retraction methods were used. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of DAAAM International Vienna.

The aim of this paper is to establish the existence, behavior and approximation of certain classes of solutions of the quasilinear systems of differential equations. Behavior of integral curves in neighborhoods of an arbitrary or certain curve is considered. The approximate solutions with precise error estimates are determined. The theory of qualitative analysis of differential equations and topological retraction method are used.

The present paper deals with the nonlinear systems of differential equations of Volterra type regarding to the existence, behaviour, approximation and stability of their definite solutions, all solutions in a corresponding region or parametric classes of solutions on unbounded interval. The approximate solutions with precise error estimates are determined. The theory of qualitative analysis of differential equations and topological retraction method are used.