2013/1

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    Some applications of infinitary logical languages in universal algebra
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2013) Pinus, Aleksandr G.
    Some examples are given of applications of an in nite logical language in universal algebra, in the algebraic geometry of universal algebras, in the theory of implicit operations on algebras, in the Galois theory between automorphisms of universal algebras and its subalgebras of xed points, in the theory of Hamiltonian closure of subalgebras and other areas.
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    The Baker-Campbell-Hausdorff formula and the Zassenhaus formula in synthetic differential geometry
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2013) Nishimura, Hirokazu
    After the torch of Anders Kock [6], we will establish the Baker-Campbell- Hausdor formula as well as the Zassenhaus formula in the theory of Lie groups.
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    Axiomatic differential geometry II-2 - differential forms
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2013) Nishimura, Hirokazu
    We refurbish our axiomatics of di erential geometry introduced in [5]. Then the notion of Euclideaness can naturally be formulated. The principal ob- jective of this paper is to present an adaptation of our theory of di erential forms developed in [3] to our present axiomatic framework.
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    Some Wolstenholme type congruences
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2013) Meštrović, Romeo
    In this paper we give an extension and another proof of the following Wolstenholme's type curious congruence established in 2008 by J. Zhao. Let s and l be two positive integers and let p be a prime such that p ls + 3. Then H(fsgl; p􀀀1) S(fsgl; p􀀀1) 8>>< >>: 􀀀 s(ls + 1)p2 2(ls + 2) Bp􀀀ls􀀀2 (mod p3) if 2 - ls (􀀀1)l􀀀1 sp ls + 1 Bp􀀀ls􀀀1 (mod p2) if 2 j ls: APs an application, for given prime p 5, we obtain explicit formulae for the sum 1 k1<
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    Topology of the cyclic Čech-Hochschild bicomplex
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2013) Kubarski, Jan
    We de ne the cyclic Cech-Hochschild bicomplex for a good covering of a smooth manifold and calculate its homology using some nonstandard spectral sequences. The results show that its homology is very rich.