Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Empirical therapy for vulvovaginitis in reproductive-aged women in routine clinical practice

Objective. To evaluate the efficiency of empirical therapy with tergynan in reproductive-aged women in routine clinical practice. Subjects and methods. The TERRA multicenter post-registration observational study enrolled 430 reproductive-aged patients diagnosed with acute vulvovaginitis. Based on their complaints, clinical symptoms, and objective examination, the patients received empirical therapy with the combination antimicrobial drug Tergynan as a single vaginal tablet once daily for 10 days. Gynecological examination, pH-metry, and bacterioscopic and bacteriological examinations of discharge (Femoflor-16) were performed, and the time course of changes in clinical symptoms evaluated. Results. There was less vaginal discharge, a complete disappearance of unpleasant odor, and a feeling of vaginal itching and burning (74.5 and 67.1%, respectively). There were increases in the detection rate of Lactobacillus spp. by 2 times with a dissemination level of 106-107 CFU/ml, in the suppression of obligate anaerobic representatives (associations of Gardnerella vaginalis + Prevotella bivia + Porphyromonas spp., as well as Eubacterium spp.) by 5 times, facultative anaerobic bacteria (Enterobacteriaceae and Streptococcus spp.) by 3 times, and yeast-like fungi of the genus Candida by 2 times. Conclusion. This investigation demonstrated the high clinical (96.5%) and microbiological (97.3%) efficiency of empirical therapy with tergynan in 430 reproductive-aged women with acute nonspecific vulvovaginitis. © 2020, Bionika Media Ltd. All rights reserved