2013/1http://hdl.handle.net/11012/239912022-12-01T11:26:40Z2022-12-01T11:26:40ZSome applications of infinitary logical languages in universal algebraPinus, Aleksandr G.http://hdl.handle.net/11012/239982021-08-11T10:06:20Z2013-11-26T11:08:34ZSome applications of infinitary logical languages in universal algebra
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.
2013-11-26T11:08:34ZThe Baker-Campbell-Hausdorff formula and the Zassenhaus formula in synthetic differential geometryNishimura, Hirokazuhttp://hdl.handle.net/11012/239972021-08-11T10:06:22Z2013-11-26T11:07:27ZThe Baker-Campbell-Hausdorff formula and the Zassenhaus formula in synthetic differential geometry
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.
2013-11-26T11:07:27ZAxiomatic differential geometry II-2 - differential formsNishimura, Hirokazuhttp://hdl.handle.net/11012/239962021-08-11T10:06:21Z2013-11-26T11:06:19ZAxiomatic differential geometry II-2 - differential forms
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.
2013-11-26T11:06:19ZSome Wolstenholme type congruencesMeštrović, Romeohttp://hdl.handle.net/11012/239952021-08-11T10:06:20Z2013-11-26T11:04:50ZSome Wolstenholme type congruences
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; p1) S(fsgl; p1)
8>><
>>:
s(ls + 1)p2
2(ls + 2)
Bpls2 (mod p3) if 2 - ls
(1)l1 sp
ls + 1
Bpls1 (mod p2) if 2 j ls:
APs an application, for given prime p 5, we obtain explicit formulae for the sum
1 k1< <kl p1 1=(k1 kl) (mod p3) if k 2 f1; 3; : : : ; p 2g, and for the sum P
1 k1< <kl p1 1=(k1 kl) (mod p2) if k 2 f2; 4; : : : ; p 3g
2013-11-26T11:04:50ZTopology of the cyclic Čech-Hochschild bicomplexKubarski, Janhttp://hdl.handle.net/11012/239942021-08-11T10:06:21Z2013-11-26T10:56:08ZTopology of the cyclic Čech-Hochschild bicomplex
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.
2013-11-26T10:56:08ZHidden modalities in algebras with negation and implicationJärvinen, JouniKondo, MichiroMattila, Jorma K.Radeleczki, Sándorhttp://hdl.handle.net/11012/239932021-08-11T10:06:19Z2013-11-26T10:19:17ZHidden modalities in algebras with negation and implication
Järvinen, Jouni; Kondo, Michiro; Mattila, Jorma K.; Radeleczki, Sándor
Lukasiewicz 3-valued logic may be seen as a logic with hidden truthfunctional
modalities de ned by A := :A ! A and A := :(A ! :A). It is
known that axioms (K), (T), (B), (D), (S4), (S5) are provable for these modalities,
and rule (RN) is admissible. We show that, if analogously de ned modalities are
adopted in Lukasiewicz 4-valued logic, then (K), (T), (D), (B) are provable, and
(RN) is admissible. In addition, we show that in the canonical n-valued Lukasiewicz-
Moisil algebras Ln, identities corresponding to (K), (T), and (D) hold for all n
3 and 1 = 1. We de ne analogous operations in residuated lattices and show
that residuated lattices determine modal systems in which axioms (K) and (D) are
provable and 1 = 1 holds. Involutive residuated lattices satisfy also the identity
corresponding to (T). We also show that involutive residuated lattices do not satisfy
identities corresponding to (S4) nor (S5). Finally, we show that in Heyting algebras,
and thus in intuitionistic logic, and are equal, and they correspond to the double
negation
2013-11-26T10:19:17ZThe Kraft sum as a monotone function on the refinement-ordered set of uniquely decipherable codesFoldes, Stephanhttp://hdl.handle.net/11012/239922021-08-11T10:06:19Z2013-11-26T10:15:51ZThe Kraft sum as a monotone function on the refinement-ordered set of uniquely decipherable codes
Foldes, Stephan
The set of all uniquely decipherable (UD) codes is partially ordered by
re nement, meaning that all strings in the cruder code can be represented as con-
catenations of strings taken from the ner code. The Kraft sum is a monotone
(increasing) function on this poset. In the re nement order, chains of UD codes
having the same Kraft sum are necessarily of the simple descending type.
2013-11-26T10:15:51Z