Browsing by Subject "Smoothness of functions."

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Open Access
Implementation of a continuation method for nonlinear complementarity problems via normal maps
(1997) Erkan, Ali
In this thesis, a continuation method for nonlinear complementarity problems via normal maps that is developed by Chen, Harker and Pinar [8] is implemented. This continuation method uses the smooth function to approximate the normal map reformulation of nonlinear complementarity problems. The algorithm is implemented and tested with two different plussmoothing functions namely interior point plus-smooth function and piecewise quadratic plus-smoothing function. These two functions are compared. Testing of the algorithm is made with several known problems.
Open Access
Smoothness of the green function for some special compact sets
(2010) Çelik, Serkan
Smoothness of the Green functions for some special compact sets, which are sequences of closed intervals with certain parameters, is described in terms of the function ϕ(δ) = 1 log 1 δ that gives the logarithmic measure of sets. As a tool, we use the so-called nearly Chebyshev polynomials and Lagrange interpolation. Moreover, some concepts of potential theory are explained with illustrative examples.
Open Access
Smoothness properties of Green's functions
(2014) Türkün, Can
Basic notions of potential theory are explained with illustrative examples. Many important properties, including the characteristic ones, of Green’s functions that are defined by the help of equilibrium measures are given. It is discussed that for what kind of sets they are continuous. Then, it is analyzed how good their continuity can be, how smooth they can be. Examples are given for the optimal smoothness. Besides, many other examples with diverse moduli of continuity are considered. Recent developments and articles in this field are introduced in details. Finally, an open problem about finding a Cantor type set K(γ) for preassigned smoothness of Green’s function is presented.