This paper studies the mutual arrangements of multidimensional vectors with coordinates that are consecutive natural numbers and the maximum of which coincides with the dimension of the corresponding Euclidean space. The set of all such vectors is called an ensemble of integer vectors. Since the membership of a vector in an ensemble means that its coordinates are some permutation of coordinates of any other vectors of the ensemble, all these vectors have the same length and, when they are placed at the origin, all their ends are lying on a sphere with a radius equal to this length. The vector (1, 2, ..., n) is considered as the main vector of the ensemble. All possible angles that can be formed by the vectors of an integer ensemble are studied. In particular, authors are looking for the number of those that form angles of equal magnitude with the main vector. Obtained results can be used in the construction of the exact distribution of the rank correlation coefficient. In conclusion, the application of this distribution to one of the problems of differential diagnosis in the analysis of deep vein thrombosis and pulmonary artery thromboembolism is considered.

Venous thromboembolic complications (VTEC) are acute and time-limited diseases. However, the recurrence rate after a first episode of VTEC is high and potentially life-threatening. Developed deep vein thrombosis (DVT) and thromboembolism of pulmonary artery (TEPA) are inevitably associated with use of anticoagulant therapy (ACT). A peculiarity of the modern clinical management of patients with VTEC is determination of duration of ACT. Aim. To study possibilities of prolonged anticoagulation therapy and secondary prevention of venous thromboembolic complications taking into consideration modern variants of drug therapy, on the basis of literature data. Search for literature was conducted in Medline and Elibrary databases including materials published in 2020. Randomized clinical and observational studies and meta-analyses, concerning prolonged therapy and secondary prevention of VTEC with vitamin K antagonists (VKA), peroral anticoagulants (POAC), sulodexide and aspirin, were analyzed. As it is evidenced by patho-physiological and epidemiological data, risk of VTEC recurrence in most patients is not resolved after the first 6 months of treatment with anticoagulants. In such situations it is reasonable to prolong anticoagulation for an indefinite period of time. However, sometimes a limiting factor for prolonged therapy with anticoagulants is bleedings caused by prolonged anticoagulation, sometimes leading to lethal outcome. Therefore, duration of treatment in the long-term period after an acute episode may rest on the balance between the risk of development of recurrence of venous thrombosis and bleeding, evaluated with the help of scales. The main achievement of recent years regarding prolonged therapy and secondary prevention of VTEC, are POAC, which in fact are new and alternative drugs that permitted the emergence of serious evidential basis in the range of means for treatment of this category of patients, sulodexide drug has appeared characterized by the minimal rate of development of large and clinically significant bleedings. Conclusion. The emergence of serious evidential basis for POAC with improved safety profiles, different pharmacokinetic profiles and dosage regimens, including sulodexide that has been actively used in recent years for secondary prevention of VTEC, will permit clinicians to differentially approach treatment of different clinical variants of venous thrombosis, to improve the results of therapy taking into account evaluation of the individual risk and comorbid diseases, and compliance of patients.