Equations of the set of all possible rotations of the three-dimensional space (with both zero and nonzero centers) which translate the given initial point to the final one were obtained using the spinor representation of the orthogonal transformations of rotation. An equation of the plane where the centers of these rotations are situated was obtained. Relations between the elements of the complex unitary matrices of the second order and the real orthogonal rotation matrices of the third order as well as expressions for calculation of the Euler angles from the coordinates of the initial and final rotation points were derived. The latter play an important part in the control of spatial rotations of the mechanical plants.
Introduction. Congenital portosystemic shunt (SPSS) is a congenital anomaly of the portal system. Blood from the portal system, bypassing the hepatic bloodstream, enters the systemic venous bloodflow. Clinical manifestations are not specific. SPSS can be suspected in patients with arterial hypoxemia and intrapulmonary vascular dilatation, in patients with foci of nodular hyperplasia in the liver, with carbohydrate metabolism disorders in the form of hyperinsulinemia and hypoglycemia, hepatic encephalopathy, hyperammoniemia. Material and methods. Nine patients ( five boys and four girls) , aged 7.7 ± 5.2, were treated in our clinic. All patients had hyperammonemia before surgery 124.5 ± 24.7 μmol / L. Five patients had endovascular SPSS occlusion. Four patients had open SPSS ligation. Results. An immediate technical success was achieved in all patients. There were no complications after endovascular treatment. There was one relapse which required a repeated endovascular occlusion. After endovascular occlusion, the length of hospital stay was shorter, postoperative period was much easier; there were no serious complications compared with the open SPSS ligation. Blood ammonia returned to normal levels in eight patients. In one patient who had multiple shunts and incomplete occlusion, blood ammonia level decreased by twice, up to 82 μmol / L. Conclusion. If SPSS is revealed, a surgical intervention is recommended to separate the portal and systemic venous blood flow. In the surgical treatment for SPSS, X-ray surgical endovascular occlusion is more preferable. If this technique was not possible, surgeons performed open surgical intervention.
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