Semigroup Structure of Sets of Solutions to Equation X^s = X^m
Porubský, Štefan
2017 - anglický 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. Klíčová slova: 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 Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. 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 - anglický 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. Klíčová slova: 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 Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. 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

Application and Misapplication of the Czechoslovak STP Cipher During WWII - Report on an Unpublished Manuscript
Porubský, Štefan
2017 - anglický Klíčová slova: STP cipher; Josef Růžek; Karol Cigáň; František Moravec; Czechoslovak military cryptography; Word War II Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. Application and Misapplication of the Czechoslovak STP Cipher During WWII - Report on an Unpublished Manuscript

Porubský, Štefan
Ústav informatiky, 2017

Real-valued Score Function, New Description of Continuous Random Variables and the Central Limit Theorem
Fabián, Zdeněk
2016 - anglický Klíčová slova: score function; transformation-based score; generalized moment method; new descriptive characteristic of the data Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. Real-valued Score Function, New Description of Continuous Random Variables and the Central Limit Theorem

Fabián, Zdeněk
Ústav informatiky, 2016

On Nominal Automata as Models of Java-like Object-Oriented Programs
Suzuki, Tomoyuki
2016 - anglický In this paper, we proposed a model of Java-like object-oriented programs as nominal automata and a simple method invocation checker. Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. On Nominal Automata as Models of Java-like Object-Oriented Programs

In this paper, we proposed a model of Java-like object-oriented programs as nominal automata and a simple method invocation checker.

Suzuki, Tomoyuki
Ústav informatiky, 2016

Prediction diagnostics for Uncertain Systems
Novák, M.; Votruba, Z.; Brandejský, T.; Faber, J.; Coufal, David; Pelikán, Emil
2014 - anglický Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR. Prediction diagnostics for Uncertain Systems

Novák, M.; Votruba, Z.; Brandejský, T.; Faber, J.; Coufal, David; Pelikán, Emil
Ústav informatiky, 2014

The use of Score Functions of Distribution for Description of Parametric Families
Fabián, Zdeněk
2014 - anglický Klíčová slova: systems of distributions; Johnson transformations; score function of distribution; parametric families Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. The use of Score Functions of Distribution for Description of Parametric Families

Fabián, Zdeněk
Ústav informatiky, 2014

Description of Continuous Distributions and Data Samples by Means of Score Functions of Distribution
Fabián, Zdeněk
2014 - anglický Klíčová slova: score function; score mean; score variance; generalized Fisher information; data characteristics Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. Description of Continuous Distributions and Data Samples by Means of Score Functions of Distribution

Fabián, Zdeněk
Ústav informatiky, 2014

Robust Template Matching
Kalina, Jan
2013 - anglický Klíčová slova: correlation coefficient; robust statistics; image analysis Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. Robust Template Matching

Kalina, Jan
Ústav informatiky, 2013

Representations of Highly-Varying Functions by One-Hidden-Layer Networks
Kůrková, Věra
2013 - anglický Klíčová slova: model complexity of neural networks; one-hidden-layer networks; highly-varying functions; tractability of representations of multivariable functions by neural networks Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd. Representations of Highly-Varying Functions by One-Hidden-Layer Networks

Kůrková, Věra
Ústav informatiky, 2013