On the maximal number of cubic subwords in a string

We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are produced in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares $xx$ such that $x$ is not a primitive word (nonprimitive squares) in a word of length $n$ is exactly $\lfloor \frac{n}{2}\rfloor - 1$, and the maximum number of subwords of the form $x^k$, for $k\ge 3$, is exactly $n-2$. In particular, the maximum number of cubes in a word is not greater than $n-2$ either. Using very technical properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length $n$ is between $(1/2)n$ and $(4/5)n$. (In particular, we improve the lower bound from the conference version of the paper.)Comment: 14 page

PROPERTIES OF NATIVE PROTEIN-CONTAINING ANTIGENS OF STREPTOCOCCUS PNEUMONIAE

Aim. The study of immunochemical and immunobiological properties of native protein-containing antigens of pneumococcus. Materials and methods. The study was carried out on the strains of the Collective Usage Center «Collection of Mechnikov Res. Inst. for Vaccine and Sera». In the work studied the chemical composition, the molecular weight of the obtained antigens in SDS-electrophoresis and antibody titers in ELISA. Protective activity of protein-containing antigens of pneumococcus was determined in experiments of active protection of mice. Results. Protein-containing antigens of pneumococcus were isolated from S. pneumoniae serotypes 3, 6B, 10A, 14, 19F, 23F and 36. The chemical composition of the preparations contained from 16 to 35% protein. In SDS-electrophoresis in polyacrylamide gel it was established that the molecular weight of protein-containing antigens of pneumococcus ranged from 14 to 116 kDa. Using ELISA shows the cross-activity of native antigens. Virtually all drugs reacted with antimicrobial rabbit serum obtained to serotype 19F (p≤0.05). Serotype serum 14 was less active and only protein-containing pneumococcal antigens obtained from 14 and 19F serotypes (p≤0.05) interacted with it. In the precipitation test according to Ouchterlony it was confirmed that preparations of serotypes 3, 6B, 14, 19F and 36 reacted with rabbit immune serum obtained for S. pneumoniae 19F serotype. In immunoblotting it was found that protein-containing antigens of pneumococcus isolated from serotypes 3, 6B, 10A, 14, 19F and 36 were associated with monoclonal antibodies to pneumococcal protein — pneumolysin. In vivo experiments it was shown that protein-containing antigens of pneumococcus protected animals from intraperitoneal infection of S. pneumoniae in homologous and heterologous systems (p≤0.05). Conclusion. The revealed immunochemical and cross-protective activity of protein-containing antigens of pneumococcus in vitro and in vivo experiments allows to select drugs derived from serotypes 6B, 10A, 19F and 36, as the most promising for further study of the intraspecific protective activity of individual native proteins of pneumococcus

Effects of fungicidal protection programs on the development of fusarium head blight and the accumulation of mycotoxins in winter wheat

Fusarium head blight (FHB) of cereals is one of the most important pre-harvest diseases worldwide. One possible method to reduce the intensity of FHB and mycotoxin levels is to apply fungicides to wheat at the flowering stage. This paper reports the efficacy of fungicides to control FHB and reduce the associated mycotoxin biosynthesis. In a two-year experiment eight combinations of fungicides were tested. Ear inoculation with a suspension of conidia of Fusarium culmorum representing the DON chemotype, confirmed by PCR assay, was conducted during anthesis. All fungicides significantly reduced FHB severity. The best control and the highest wheat yield were obtained after the application of spiroxamine + prothioconazole at GS 29-32, combined with prothioconazole + fluoxastrobin at GS 49-55 (yield 166.5% of the control) or tebuconazole and prothioconazole (165.8%). All the other protection programs resulted in higher yields (117.1–138.5% of the control). A clear relation was observed between the disease intensity and mycotoxin concentrations