A method, by which the broken edge of mechanical engineering drawings being binarised can be eliminated and the whole edge of mechanical engineering drawing can be got, is given. To all points of a connected area on t...A method, by which the broken edge of mechanical engineering drawings being binarised can be eliminated and the whole edge of mechanical engineering drawing can be got, is given. To all points of a connected area on the image of the modular maximum value of wavelet transform at scale 2 2, the averaging grey value method is used to their grey values, then the edge of the dim place is continuous after the maximum variance threshold method is used. All these methods are fast, they can be used for all linear graphics having nothing to do with the grey value, its application scope is wide.展开更多
Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then trans...Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.展开更多
文摘A method, by which the broken edge of mechanical engineering drawings being binarised can be eliminated and the whole edge of mechanical engineering drawing can be got, is given. To all points of a connected area on the image of the modular maximum value of wavelet transform at scale 2 2, the averaging grey value method is used to their grey values, then the edge of the dim place is continuous after the maximum variance threshold method is used. All these methods are fast, they can be used for all linear graphics having nothing to do with the grey value, its application scope is wide.
文摘Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.
