---

Although chemotherapy is one of the effective methods in cancer treatment its effects may be moderated due to drug resistance. The main objective of this paper is to propose optimal finite cancer treatment duration. In this paper, a mathematical model of tumor growth by adding radiotherapy, chemotherapy and metastasis of cancer cells terms is extended. Stability analysis shows that the tumor free equilibrium point is unstable. Hence, changing the dynamics of the system around this equilibrium point for achieving finite duration treatment method is essential. Therefore, the effects of chemotherapy drug are considered not only on cells populations but also on the dynamics of the system. For this purposes, State Dependent Riccati Equation (SDRE) based optimal control is used. So chemotherapy agent is used as the control input to the extended cancer nonlinear model. Then, in order to show the flexibility in design, two different types of input weighting matrices are selected. Moreover, the robustness of this control method is investigated by simulation. Results show that changing the dynamics of the system is necessary for finite duration cancer treatment method.

---

Milk fat, one of the expensive fatty matters, might be sometimes adulterated with other edible fats, particularly palm oil or its fractions, which can be a major problem for the dairy industry, especially in Iran. The aim of this study was to investigate the adulteration of milk fat based on some minor components present in unsaponifiable matters, namely, sterols and squalene. Different concentrations of palm oil and its fractions (0, 1, 2, 5, 10, 20, 50, and 100%) were added to pure milk fat. Sterol and squalene contents were determined by the application of GC and HPLC, respectively. The experimental data showed that β-sitosterol was the main phytosterol in palm oils and it could be a good indicator for detection of adulteration by palm oil as low as 5%. The result also indicated that squalene was not identified in milk fat, so, it can be considered as a good indicator to show the presence of palm oil as low as 1%. According to the results, it might be concluded that sterols and squalene could be used as important indicators to find the presence of palm oil and its fractions in milk fat.