A mathematical model for melting processes of solid particles immersed in metal baths has been develOPed, which includes the cases with the melting point of solid particles greater than, equal to, and lower than freez...A mathematical model for melting processes of solid particles immersed in metal baths has been develOPed, which includes the cases with the melting point of solid particles greater than, equal to, and lower than freezing point of the bath. Experiments are performed on the melting of ice spheres in water at different temperature. The model is validated by experimental data for melting of ice spheres submerged in water and aluminum spheres immersed in aluminum melt. Finally, the parometers affecting particles melting time such as particle size, bath temperature, and slip velocity are analyzed.展开更多
This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second ...This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.展开更多
文摘A mathematical model for melting processes of solid particles immersed in metal baths has been develOPed, which includes the cases with the melting point of solid particles greater than, equal to, and lower than freezing point of the bath. Experiments are performed on the melting of ice spheres in water at different temperature. The model is validated by experimental data for melting of ice spheres submerged in water and aluminum spheres immersed in aluminum melt. Finally, the parometers affecting particles melting time such as particle size, bath temperature, and slip velocity are analyzed.
文摘This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.
