Документация

$${\rho }_{mix}={\rho }_{L0}\cdot e^{\left(p-p_0\right)/{\beta }_L}$$

$$\frac{\partial {\rho }_{mix}}{\partial p}=\frac{{\rho }_{L0}}{{\beta }_L}{e}^{\left(p-p_0\right)/{\beta }_L}$$

$${\beta }_{mix}={\beta }_L$$

$${\rho }_{mix}={\rho }_{L0}{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{1/K_{\beta p}}$$

$$\frac{\partial {\rho }_{mix}}{\partial p}=\frac{{\rho }_{L0}}{{\beta }_{L0}}{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{1/K_{\beta p}-1}$$

$${\beta }_{mix}={\beta }_{L0}+K_{\beta p}\left(p-p_0\right)$$

$${\rho }_{mix}=\frac{{\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}}{e^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}}$$

$$\frac{\partial {\rho }_{mix}}{\partial p}=\frac{\left({\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}\right)\left(\frac{1}{{\beta }_L}{e}^{-\left(p-p_0\right)/{\beta }_L}+\frac{1}{n}\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right)\left(\frac{p_0^{1/n}}{p^{1/n+1}}\right)\right)}{{\left(e^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\right)}^2}$$

$${\beta }_{mix}={\beta }_L\frac{e^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}}{e^{-\left(p-p_0\right)/{\beta }_L}+{\beta }_L\frac{1}{n}\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right)\left(\frac{p_0^{1/n}}{p^{1/n+1}}\right)}$$

$${\rho }_{mix}=\frac{{\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}}{{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}}$$

$$\frac{\partial {\rho }_{mix}}{\partial p}=\frac{\left({\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}\right)\left(\frac{1}{{\beta }_L}{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}-1}+\frac{1}{n}\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right)\left(\frac{p_0^{1/n}}{p^{1/n+1}}\right)\right)}{{\left({\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\right)}^2}$$

$${\beta }_{mix}={\beta }_L\frac{{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}}{{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}-1}+{\beta }_L\frac{1}{n}\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right)\left(\frac{p_0^{1/n}}{p^{1/n+1}}\right)}$$

$${\rho }_{mix}=\frac{{\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}}{e^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\theta (p)}$$

$$\frac{\partial {\rho }_{mix}}{\partial p}=\frac{\left({\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}\right)\left(\frac{1}{{\beta }_L}{e}^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\left(\frac{\theta (p)}{np}-\frac{d\theta (p)}{dp}\right)\right)}{{\left(e^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\theta (p)\right)}^2}$$

$${\beta }_{mix}={\beta }_L\frac{e^{-\left(p-p_0\right)/{\beta }_L}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\theta (p)}{e^{-\left(p-p_0\right)/{\beta }_L}+{\beta }_L\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\left(\frac{\theta (p)}{np}-\frac{d\theta (p)}{dp}\right)}$$

$${\rho }_{mix}=\frac{{\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}}{{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\theta \left(p\right)}$$

$$\frac{\partial {\rho }_{mix}}{\partial p}=\frac{\left({\rho }_{L0}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\rho }_{g0}\right)\left(\frac{1}{{\beta }_L}{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}-1}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\left(\frac{\theta (p)}{np}-\frac{d\theta (p)}{dp}\right)\right)}{{\left({\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\theta (p)\right)}^2}$$

$${\beta }_{mix}={\beta }_L\frac{{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}}+\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\theta (p)}{{\left(1+\frac{K_{\beta p}}{{\beta }_{L0}}\left(p-p_0\right)\right)}^{-1/K_{\beta p}-1}+{\beta }_L\left(\frac{{\alpha }_0}{1-{\alpha }_0}\right){\left(\frac{p_0}{p}\right)}^{1/n}\left(\frac{\theta (p)}{np}-\frac{d\theta (p)}{dp}\right)}$$