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Yayın Hybrid high dimensional model representation (HHDMR) on the partitioned data(Elsevier B.V., 2006-01-01) Tunga, Mehmet Alper; Demiralp, MetinA multivariate interpolation problem is generally constructed for appropriate determination of a multivariate function whose values are given at a finite number of nodes of a multivariate grid. One way to construct the solution of this problem is to partition the given multivariate data into low-variate data. High dimensional model representation (HDMR) and generalized high dimensional model representation (GHDMR) methods are used to make this partitioning. Using the components of the HDMR or the GHDMR expansions the multivariate data can be partitioned. When a cartesian product set in the space of the independent variables is given, the HDMR expansion is used. On the other band, if the nodes are the elements of a random discrete data the GHDMR expansion is used instead of HDMR. These two expansions work well for the multivariate data that have the additive nature. If the data have multiplicative nature then factorized high dimensional model representation (FHDMR) is used. But in most cases the nature of the given multivariate data and the sought multivariate function have neither additive nor multiplicative nature. They have a hybrid nature. So, a new method is developed to obtain better results and it is called hybrid high dimensional model representation (HHDMR). This new expansion includes both the HDMR (or GHDMR) and the FHDMR expansions through a hybridity parameter. In this work, the general structure of this hybrid expansion is given. It has tried to obtain the best value for the hybridity parameter. According to this value the analytical structure of the sought multivariate function can be determined via HHDMR.Yayın Waves in fluid-filled elastic tubes with a stenosis: Variable coefficients KdV equations(Elsevier B.V., 2007-05-15) Demiray, HilmiIn the present work, by treating the arteries as thin-walled prestressed elastic tubes with a stenosis and the blood as an inviscid fluid we have studied the propagation of weakly nonlinear waves in such a medium, in the longwave approximation, by employing the reductive perturbation method. The variable coefficients KdV and modified KdV equations are obtained depending on the balance between the nonlinearity and the dispersion. By seeking a localized progressive wave type of solution to these evolution equations, we observed that the wave speeds takes their maximum values at the center of stenosis and gets smaller and smaller as one goes away from the stenosis. Such a result seems to reasonable from the physical point of view.
