Number of found documents: 766
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Semigroup Structure of Sets of Solutions to Equation X^s = X^m
Porubský, Štefan
2017 - English
Using an idempotent semigroup approach we describe the semigroup and group structure of the set of solutions to equation X^m = X^s in successive steps over a periodic commutative semigroup, over multiplicative semigroups of factor rings of residually finite commutative rings and finally over multiplicative semigroups of factor rings of residually finite commutative principal ideal domains. The analysis is done through the use of the maximal subsemigroups and groups corresponding to an idempotent of the corresponding semigroup and in the case of residually finite PID’s employing the available analysis of the Euler-Fermat Theorem as given in [11]. In particular the case when this set of solutions is a union of groups is handled. As a simple application we show a not yet noticed group structure of the set of solutions to x^n = x connected with the message space of RSA cryptosystems and Fermat pseudoprimes. Keywords: set of solutions; idempotent; maximal semigroup corresponding to an idempotent; maximal group corresponding to an idempotent; equation X^s = X^m; finite commutative ring with identity element; residually finite commutative principal ideal domains Available at various institutes of the ASCR
Semigroup Structure of Sets of Solutions to Equation X^s = X^m

Using an idempotent semigroup approach we describe the semigroup and group structure of the set of solutions to equation X^m = X^s in successive steps over a periodic commutative semigroup, over ...

Porubský, Štefan
Ústav informatiky, 2017

Idempotents, Group Membership and their Applications
Porubský, Štefan
2017 - English
S.Schwarz in his paper [165] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought [167] into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups. Later in his papers he showed that a proper description of these structural elements can be used to (re)prove many useful and important results in algebra and number theory. The present paper gives a survey of selected results scattered throughout the literature where an semigroup approach based on tools like idempotent, maximal subgroup or maximal subsemigroup either led to a new insight into the substance of the known results or helped to discover new approach to solve problems. Special attention will be given to some disregarded historical connections between semigroup and ring theory. Keywords: multiplicative semigroup; finite semigroups; power semigroups; idempotent elements; finite commutative rings; principal ideal domain; Euler-Fermat theorem; Wilson theorem; matrices over fields; maximal groups contained in a semigroup; periodic sequence; multiplicative semigroup of Zm; semigroup of circulant Boolean matrices Available at various institutes of the ASCR
Idempotents, Group Membership and their Applications

S.Schwarz in his paper [165] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought [167] into play the maximal subsemigroups and thus he embodied the ...

Porubský, Štefan
Ústav informatiky, 2017

Stav předaných dat a úprava rozdělení vybraných měření 2017
Novák, Jakub; Jiřina jr., M.; Benešová, Michaela
2017 - Czech
Keywords: typový diagram dodávky; TDD; spotřeba plynu; měřící místa; kritéria; filtrace; náhrady Available on request at various institutes of the ASCR
Stav předaných dat a úprava rozdělení vybraných měření 2017

Novák, Jakub; Jiřina jr., M.; Benešová, Michaela
Ústav informatiky, 2017

Popis TDD modelu verze 3.8.
Novák, Jakub; Jiřina jr., M.; Benešová, Michaela
2017 - Czech
Keywords: typový diagram dodávky; TDD; spotřeba plynu; popis modelu Available at various institutes of the ASCR
Popis TDD modelu verze 3.8.

Novák, Jakub; Jiřina jr., M.; Benešová, Michaela
Ústav informatiky, 2017

Application and Misapplication of the Czechoslovak STP Cipher During WWII - Report on an Unpublished Manuscript
Porubský, Štefan
2017 - English
Keywords: STP cipher; Josef Růžek; Karol Cigáň; František Moravec; Czechoslovak military cryptography; Word War II Available on request at various institutes of the ASCR
Application and Misapplication of the Czechoslovak STP Cipher During WWII - Report on an Unpublished Manuscript

Porubský, Štefan
Ústav informatiky, 2017

UFO 2017. Interactive System for Universal Functional Optimization
Lukšan, Ladislav; Tůma, Miroslav; Matonoha, Ctirad; Vlček, Jan; Ramešová, Nina; Šiška, M.; Hartman, J.
2017 - English
This report contains a description of the interactive system for universal functional optimization UFO, version 2017. This version contains interfaces to the MATLAB and SCILAB graphics environments. Keywords: numerical optimization; nonlinear programming; nonlinear approximation; algorithms; software systems Available in digital repository of the ASCR
UFO 2017. Interactive System for Universal Functional Optimization

This report contains a description of the interactive system for universal functional optimization UFO, version 2017. This version contains interfaces to the MATLAB and SCILAB graphics environments.

Lukšan, Ladislav; Tůma, Miroslav; Matonoha, Ctirad; Vlček, Jan; Ramešová, Nina; Šiška, M.; Hartman, J.
Ústav informatiky, 2017

The IINC System under the ROOT Environment
Jiřina, Marcel
2017 - English
Keywords: IINC; data separation; classification; multivariate data; distance; metric Available in digital repository of the ASCR
The IINC System under the ROOT Environment

Jiřina, Marcel
Ústav informatiky, 2017

Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization
Vlček, Jan; Lukšan, Ladislav
2017 - English
Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in a digital repository NRGL
Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2017

Real-valued Score Function, New Description of Continuous Random Variables and the Central Limit Theorem
Fabián, Zdeněk
2016 - English
Keywords: score function; transformation-based score; generalized moment method; new descriptive characteristic of the data Available on request at various institutes of the ASCR
Real-valued Score Function, New Description of Continuous Random Variables and the Central Limit Theorem

Fabián, Zdeněk
Ústav informatiky, 2016

Nondeterministic Computations for Which Space is More Powerful than Time
Wiedermann, Jiří
2016 - English
Keywords: nondeterministic computation; crossing sequences; complexity Available in a digital repository NRGL
Nondeterministic Computations for Which Space is More Powerful than Time

Wiedermann, Jiří
Ústav informatiky, 2016

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