Abstract. The complex moment sequence µ(P ) is assigned to a univalent polynomial P (z) by the Cauchy transform of the domain P (D), where D is the unit disk. We establish the representation of the Jacobian det dµ(P ) in terms of roots of the derivative P ′ (z). Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for det dµ(P ), which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in U is contained in the union of three irreducible algebraic surfaces.

Abstract. We study metric and analytic properties of generalized lemniscates Et(f ) = {z ∈ C : ln |f (z)| = t}, where f is an analytic function. Our main result states that the length function |Et(f )| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln |Et(f )| is convex on any interval free of critical points of ln |f |. As another application we deduce explicit formulae of the length function in some special cases.

We studied the effects of SNK-411, a new 5-pyrimidinol derivative, on serum cytokine profile of C57Bl/6 mice with Lewis lung carcinoma. The compound was injected intraperitoneally in doses of 25 and 50 mg/kg. A significant (by 3.5 times) increase in serum IL-4 content was detected in mice with tumors on day 9 of tumor development. In mice receiving SNK-411 in doses of 25 and 50 mg/kg, IL-4 content significantly decreased (by 4.0 and 3.6 times) on days 2-8 of carcinoma development; IL-2 content decreased by 1.4 and 1.2 times and IL-6 content decreased by 2.7 and 1.6 times, respectively, in comparison with control mice with tumors. Injections of SNK-411 in the same doses on days 8-15 of carcinoma development led to a significant decrease in IL-4 levels (by 2.2 and 4.5 times, respectively, in comparison with control mice with tumors) and did not affect serum levels of other cytokines.

Исследовано действие нового производного 5-оксипиримидина СНК-411 в дозах от 1 до 50 мг/кг на параметры иммунной системы у интактных мышей. СНК-411 в дозах 25 мг/кг и 50 мг/кг стимулировал показатели иммунного клеточного ответа в реакции гиперчувствительности замедленного типа и гуморального ответа в реакции пассивной гемагглютинации в среднем в 1,2 раза (p < 0,05). СНК-411 в дозе 50 мг/кг стимулировал фагоцитарную активность перитонеальных макрофагов в 1,2 раза (p < 0,05). СНК-411 в дозе 25 мг/кг увеличивает (p < 0,01) содержание цитотоксических Т-лимфоцитов CD3+CD8+ в крови в 2,3 раза, в дозе 50 мг/кг увеличивает количество CD3+CD8+ в печени и тимусе в 3,3 и 1,4 раза, соответственно (p < 0,01). СНК-411 в дозе 25 мг/кг увеличивает содержание естественных киллеров CD335+ в крови и печени в 1,9 и 1,4 раза, соответственно (p < 0,05).

No abstract