We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and d...We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and decomposition of semi-algebraic set, etc., we deal with the dimension of the real piecewise algebraic variety and real Nullstellensatz in Cμ spline ring.展开更多
Phase behavior of scCO2 microemul- sion formed with food grade surfactant sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) was studied Critical microemulsion concentration (cμc) was de- duced from the dependence of pre...Phase behavior of scCO2 microemul- sion formed with food grade surfactant sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) was studied Critical microemulsion concentration (cμc) was de- duced from the dependence of pressure of cloud points on the concentration of surfactant AOT at con- stant temperature and water concentration. The re- sults show that there are transition points on the cloud point curve in a very narrow range of concen- tration of surfactant AOT. The transition points were changed with the temperature and water concentra- tion. These phenomena show that lower temperature is suitable to forming microemulsion droplet and the microemulsion with high water concentration is likely to absorb more surfactants to structure the interface.展开更多
基金Project supported by The National Natural Science Foundation of China No.69973010,19871010 and10271022.
文摘We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and decomposition of semi-algebraic set, etc., we deal with the dimension of the real piecewise algebraic variety and real Nullstellensatz in Cμ spline ring.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 20573056, 20473035 and 20273032）the New Technique Foundation of Jiangsu Province （Grant No. BG-2005041）.
文摘Phase behavior of scCO2 microemul- sion formed with food grade surfactant sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) was studied Critical microemulsion concentration (cμc) was de- duced from the dependence of pressure of cloud points on the concentration of surfactant AOT at con- stant temperature and water concentration. The re- sults show that there are transition points on the cloud point curve in a very narrow range of concen- tration of surfactant AOT. The transition points were changed with the temperature and water concentra- tion. These phenomena show that lower temperature is suitable to forming microemulsion droplet and the microemulsion with high water concentration is likely to absorb more surfactants to structure the interface.
