This article is concerned with the construction of the general algorithm for evaluating twocenter, two-and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function rt derived in Part I of this series for k = -1,O, 1,2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculaticns for different types of the two-and threeelectron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.

is greater than energy expenditure, causing both the hyperplasia and the hypertrophy of adipocytes. Adipocyte hypertrophy has negative consequences connected with insulin resistance and chronAccording to the World Health Organization (WHO), obesity is related to an excessive accumulation of adipose tissue, which may result in health deterioration [1]. This occurs when energy input AbstractBackground. The most common cause of death among people with obesity are cardiovascular complications as a result of a hypercoagulability state. Objectives. The purpose of the study was to assess the potential of coagulation system activation depending on the tissue factor and to analyze of the influence of a 3-week low-calorie diet and balneological treatment on selected coagulation parameters in morbidly obese patients. Material and Methods. The study included 36 patients (28 females and 8 males; mean age 46) with the value of BMI > 40 kg/m 2 . The study was designed in two stages: baseline and after 21-days. The evaluation of tissue factor (TF), tissue factor pathway inhibitor (TFPI), von Willebrand factor (vWF), fibrinogen, D-dimer, thrombin--antithrombin complexes (TAT), and the activity of antithrombin (AT) was performed in patients before and after the treatment. The control group consisted of 24 healthy volunteers (16 females and 8 males) at a mean age of 39 with BMI ≤ 24.9 kg/m 2 . Results. There were significantly higher levels of TF, TFPI, fibrinogen, TAT complexes and D-dimer in the study group as compared to the controls. Moreover, there were no significant changes in the parameters studied before and after the treatment. In the group of obese patients, there were significant positive correlations between the concentrations of vWF and BMI and BMI changes and a significant negative correlation between the WHR changes and TFPI concentration. Conclusions. The study confirmed that morbidly obese patients represent a high risk of hypercoagulability state, despite no clinical evidence, which could be due to the great inhibitory potential of TFPI in suppressing the extrinsic pathway of the coagulation system. However, the lack of effect of the 3-week exposure to the LCD and balneological treatment in morbidly obese subjects indicates that substantial fat mass must be reduced before adequate hemostasis is re-established (Adv Clin Exp Med 2016, 25, 4, 755-761).

Introduction of a modified correlation factor in the place of r: eliminates the problem of multiple infinite summations in Hamiltonian matrix elements. Calculations performed for several He states show that the introduction of the modified correlation factor does not change energies of the states by more than 1 cm-'.

Numerical verification of the algorithm for evaluation of the two-center, two-and three-electron integrals with the correlation factors of the type ri2, elaborated by us previously is presented. The influence of different parameters on the accuracy of the expressions for evaluating the integrals is discussed on the basis of the numerical results obtained.