The aim of this study was to investigate hemocompatibility and cytotoxicity properties of synthetic polymer coatings containing various unsaturated carbonic acids with vinylacetate. Co-polymers of vinylacetate and crotonic acid (CA), maleic acid (MA), and itaconic acid (IA) were made. The materials were characterized in terms of their adhesion to metal supports (titanium and stainless steel) as well as hemocompatibility (% hemolysis, wettability, erythrocyte aggregation, hemoglobin content, thrombocyte count and lipid peroxidation levels) and cytotoxicity (human endothelial cell activity in vitro and chromosome aberrations, bone marrow proliferation and cell ploidy in rats). Co-polymers of unsaturated carbonic acids with vinylacetate exhibited good hemocompatibility properties, as opposed to vinylacetate homopolymer for which substantial levels of hemolysis were observed. By coating the metal supports with co-polymers the cytotoxic effects associated with the bare metal samples were markedly reduced. MA samples showed excellent hemocompatibility and no cytotoxicity, yet they lacked good adhesion properties to metal substrate, probably due to high water content. CA samples, having the highest density of carboxylic groups among the samples under investigation, showed increased bone marrow proliferation activity and cell ploidy in rats, as compared to controls. The most promising results in the present study were obtained for the samples with IA, which showed good adhesion to metal substrates, good hemocompatibility and low cytotoxicity. Thus, co-polymers of vinylacetate and IA rich in carboxylic groups are promising materials for the design of novel drug-eluting stents.

KEY WORDS: random polynomials, sub-Gaussian random variable, Littlewood's conjecture. For independent random variables r0, ... ,r,,-I taking values +1 or -1 with probability 1/2, we consider the probability .1 I) P(u) = P,,(u) = P(min ~-' rjexp(ijx) > u , u ~_ O. k zET ~0 Littlewood [1] conjectured that P(r ~ 0 as n ---* oo for any r > 0. Kashin [2] proved this conjecture; moreover, he studied the minimum of the values of the polynomial not on the entire torus T but on a certain subset of points from the interval [0, ~r]. More precisely, he proved that .... Io(o.)l > n'/2(log-) -1/3) 0 as n --* o~, where 0v = 2r-2 -v for u --1, 2,... , and n--I

Theorem 2. Let fl = [0,M] x w, and let u E [H2,p(n)] k be a solution of the problem a(a2, u + Au) + -~a,u -f(u, t) = g(t), uL_0 =u0, =0, uL_M Then one .has the estimate [lu, ~TII2,p < R(lluollvo)X(To -T) + R(IlUMIIVo)X(T -M + To) + R(lgl,).

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