To simplify the assessment method of soy protein isolate （SPI） functionalities, the viscosity and functionalities of commercial SPI products were studied. Viscosity value （y） increases With increasing concentrati...To simplify the assessment method of soy protein isolate （SPI） functionalities, the viscosity and functionalities of commercial SPI products were studied. Viscosity value （y） increases With increasing concentration （x） and exhibits a highly significant correlation with the exponential equation y = a. ebx. The b values of products are gradually enhanced from dispersion, emulsion and injected to gel type. Products with low b values （〈0.2）, and high dispersivity were dispersion-type. Products having high b values （〉0.4） and gel springiness were gel-type. The other products with centered b value （0.2-0.4）, high solubility and emulsifying capacity were emulsion-type.展开更多
This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, w...This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.展开更多
基金supported by the National Key Technologies Research and Development Program(No. 2012BAD34B04)Ministry of Science and Technology of the People's Republic of China
文摘To simplify the assessment method of soy protein isolate （SPI） functionalities, the viscosity and functionalities of commercial SPI products were studied. Viscosity value （y） increases With increasing concentration （x） and exhibits a highly significant correlation with the exponential equation y = a. ebx. The b values of products are gradually enhanced from dispersion, emulsion and injected to gel type. Products with low b values （〈0.2）, and high dispersivity were dispersion-type. Products having high b values （〉0.4） and gel springiness were gel-type. The other products with centered b value （0.2-0.4）, high solubility and emulsifying capacity were emulsion-type.
文摘This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.
