Behavior of Integral Curves of the Quasilinear Second Order Differential Equations

AbstractThis 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

Optimization of Thermal Insulation and Regression Analysis of Fuel Consumption

AbstractIn 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