Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic setvalued functional equation, a generalized quadratic set-valued functional equation and a Jensen type cubic set-valued functional equation. Mathematics Subject Classification 2010: 47H10; 54C60; 39B52; 47H04; 91B44.
Climate change is found to be one of the main catastrophes to which human encountered. It serves as a threat to the Planet Earth and to predict its components has great deal of importance to planning on irrigation, controlling pests and diseases, drought as well as crisis management among many others. Since both temperature and humidity are the most important meteorological parameters so that other atmospheric changes are function of these two parameters, the present research tries to put forward appropriate prediction on them by using models of nonlinear Autoregressive Neural Network and Autoregressive Network with Exogenous inputs (NARX). For this purpose, metrological data for Bushehr province in south of Iran for the years 2012-2013 and model performance criteria including R 2 , RMSE and NRMSE were used. Different architectures for dynamic artificial neural network models were investigated through comparing the root mean square error. Models of performance validation suggested that Nonlinear Autoregressive Exogenous (NARX) forecasts temperature and humidity more accurate than Nonlinear Autoregressive Neural Network (NAR).
An analysis for the mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet is carried out via symmetry analysis. By employing Lie group method to the given system of nonlinear partial differential equations, we can obtain information about the invariants and symmetries of these equations. This information can be used to determine the similarity variables that will reduce the number of independent variables in the system. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using fifth-order Improved Runge-Kutta Method (IRK5) coupled with shooting method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. This paper' results in comparison with known results are excellent.
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