surface

The Bosphorus (Istanbul Strait) that connects the continents of Europe and Asia is too complex due to geographical conditions and have a continuously increasing maritime traffic. The length of the Bosphorus which connect the Black Sea and the  Marmara Sea is 29.9 km. The number of ships (Tanker, general Cargo and bulk carrier) passing through the Istanbul strait was recorded as 42553 in 2016 and these transit ships cause more than half of the amount total ship emissions in the Bosphorus. The aim of this study is to estimate the PM amounts emitted from transit vessels passing through the Bosphorus by using fuzzy inference system in MATLAB. Total emissions from ships are expressed by surfaces allowing the analysis of the data according to the gross tonnage and the types of ships.

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman''s and Skrypnik''s variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik''s method, described in cite{vyr3}. In local coordinates, equilibrium points satisfy an elliptic boundary value problem.