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Content available remote Unification in some substructural logics of BL-algebras and hoops
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Abstract. It is shown that substructural logics of k- potent BL-algebras and k-potent hoops have unitary unification (in fact, transparent unifiers) while Basic Fuzzy Logic, BL (the logic of BL-algebras), and infinity-valued Lukasiewicz logic (the logic of MV-algebras) do not have unitary unification. It follows that every k-potent substructural logic containing BL is structurally complete in the restricted sense, but Basic Logic itself is not.
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Content available remote Extensions of the Grzegorczyk Logic Determined by Some Countable Boolean Algebras
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EN
It is shown that a chain of type of w + 1 of modal logics: Tr = Grz + B1 ⊃ Grz + B2 ⊃ Grz + B3 ⊃...⊃ Grz (all of them are extensions of the Grzegorczyk logic Grz), contains all and only such modal logics which can be obtained as sets of formulae that are valid in the Stone spaces of countable superatomic Boolean algebras. Some topological conditions which correspond to the Grzegorczyk logic are presented.
EN
A logical systems is structurally complete (or smooth) if structural and admissible rules are derivable in it. It is shown that if some peculiar "omitting" rules are neglected then classical predicate logic L2 is structurally complete. A unique structural and structurally complete extension of L2 is described. Next, it is shown that among negation-free intermediate predicate logics, there are chains of type ? ? + 1 of such logics (extension of Gödel-Dummett logic) which are hereditarily structurally complete. This is in contrast with the case of prepositional logics.
EN
Intervention vaccinations were undertaken after 2.5 weeks since the first cases of abortions, i.e. when the percentage of abortions was 23. There were used the following vaccines: Equivac RP, Prevaccinol and RPK. Immunizations were performed on 3 groups of mares: group A comprised 19 animals vaccinated once with Equivac at months 8—9 or 9—10 of pragnancy. Group В containing 29 pregnant mares was immunized 3 times: at first (9 animals) in the 2—3 month, 10 animals in the 4—5th month and 9 animals in the 5—6th month, then for the second time in the months 4—5, 6—7 and 7—8, and for the third time in months 6—7, 8—9 and 9—10. The third group (C) was immunized for the first time when the mares were not pregnant, then in the 3—4 and 7—8th month of pregnancy. The percentage of abortion was 94.7% (group A), 10.3% (group B) and 0% (group C). Only three fold vaccinations protected mares from abortions in the infected environment.
EN
The purpose of the work was to determine the percentage of infections with arteritis virus and the analysis of epizootiological state in the stud of horses in the Upper Silesia. In the first period of studies the percentage of mares with specific antibodies was 58.3 per cent and after 6 months it increased by 79 per cent. It was lowest in young mares aged 3—4 years. The SN titres against EAV ranged between 4—512. In most cases they fluctuated between 32—256. The titre in one stallion was 128—256 while in another one no antibodies were found at all. Sera of mares without antibodies at day of mating showed the presence of the antibodies after three weeks following mating by a stallion serologically positive; that was not observed in case of mating by a stallion serologically negative. The findings indicated that in the horses under study equine arteritis virus was transmitted through the genital system during mating and the stallion’s semen was the source of infection.
EN
The examinations comprised all the mares and stallions of the stud K in the period from January 1989 to February 1991. Mares aged 6—12 months to 12 years were divided into 13 groups (from A to M). Serological tests were performed three times (I, II, III) at intervals of 1 years. The percentage of mares with neutralizing antibodies against EAV was 53.3, 67.5 and 48.5 (consecutive years). The titers of the antibodies ranged from 4 to ≥ 512. In the course of examinations the titers were 64—128, 32—64 and 16—32. In 24 of 27 fresh cases of infections between the first and second examination the appearance of specific antibodies was observed at week 3 after covering by a stallion with antibodies against EAV. In the same period there was noticed also a significant per cent of infections in 6—12 old mares of the group A (50%) and L (27.7%) being in contact with the mares covered by an infected stallion. After elimination of that stallion from the stud the number of new infections decreased markedly and only two cases were found in that time (between the second and third examination). The findings indicate that the primary transmission of EAV in the stud K took place through the genital tract due to infection by the infected stallion, and the secondary — by the respiratory tract.
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