The paper proposes a method for calculating the area of a flat area from a photograph based on the use of mathematical analysis methods. To calculate the area, a curved integral of the second kind is used along a closed contour bounding the area under consideration. Defining the boundary in the form of a Bezier spline reduces the calculation of a curved integral to the calculation of several definite integrals from the Bernstein basis polynomials. An explicit form is obtained for integrals of Bernstein basis polynomials. For a third-order Bezier spline, a formula is derived for calculating the area of the area in terms of the coordinates of the reference points of the Bezier curves.

Keywords: cubic spline, Bernstein basis polynomials. Bezier curve, Bezier spline, Green's formula, beta function, gamma function

Article focuses on the use of statistical models to predict tolerability surgery using intracavitary hyperthermic chemotherapy (IHCT) and the definition of indications and contraindications to perform operations and tolerability for patients with cancer based on the hemostatic patient. This technique allows a high enough accuracy to prediction portability planned surgery, duration of disease-free period, the period and quality of life in the immediate and late postoperative period.Improve treatment of patients with malignant tumors of the abdomen and pelvis, is one of the priorities of modern health care. Relevance of various parameters of immunity, clinical and biological parameters of homeostasis and prognosis of malignant disease in humans will significantly reduce the proportion of late diagnoses of relapses. Recently there has been increased research to find a method of complex cytoreductive surgery and the use of cytotoxic drugs, and physical therapies, one of which is a local intraoperative hyperthermic chemotherapy. With the help of statistical methods has been studied the degree of influence on the parameters IHCT immunity and an estimate of the nature of the immunological changes in different types of surgery. Methods of binary logistic regression analysis was calculated diskriminatnogo forecast portability operation - patient survival probability. Based on the method of multiple regression were obtained algorithms calculate the duration of life of patients after surgery, and the duration of DFS. Studies based on the factor analysis showed that the main factors affecting the prognosis of disease-free period and the period of life are the morphological structure of the tumor volume cytoreduction, the sum of your immune system and cancer markers. Peritoneal cancer index, sex and age of the patient does not have a significant effect on these parameters. Thus, the introduction into clinical practice of the proposed computer systems and statistical forecasting models allow physicians to objectively evaluate the performance of homeostasis, the portability of the planned surgery, more accurately predict the course of the cancer disease and the likelihood of recurrence of the disease and the duration and quality of life.

Keywords: statistics, modeling, forecasting, surgery, colorectal cancer, disease-free life expectancy, tolerance of surgery, immunological parameters, factor analysis, regression equation