Structural Properties of Algebras of S-probabilities

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73587182" target="_blank" >RIV/61989592:15310/18:73587182 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1515/ms-2017-0118" target="_blank" >http://dx.doi.org/10.1515/ms-2017-0118</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2017-0118" target="_blank" >10.1515/ms-2017-0118</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Structural Properties of Algebras of S-probabilities

Popis výsledku v původním jazyce

Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s in S define a function from S to [0; 1] called a numerical event or, more precisely, an S-probability. A set of S-probabilities comprising the constant functions 0 and 1 which is structured by means of the addition and order of real functions in such a way that an orthomodular partially ordered set arises is called an algebra of S-probabilities, a structure significant as a quantum-logic with a full set of states. The main goal of this paper is to describe algebraic properties of algebras of S-probabilities through operations with real functions. In particular, we describe lattice characteristics and characterize Boolean features. Moreover, representations by sets are considered and pertinent examples provided.

Název v anglickém jazyce

Structural Properties of Algebras of S-probabilities

Popis výsledku anglicky

Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s in S define a function from S to [0; 1] called a numerical event or, more precisely, an S-probability. A set of S-probabilities comprising the constant functions 0 and 1 which is structured by means of the addition and order of real functions in such a way that an orthomodular partially ordered set arises is called an algebra of S-probabilities, a structure significant as a quantum-logic with a full set of states. The main goal of this paper is to describe algebraic properties of algebras of S-probabilities through operations with real functions. In particular, we describe lattice characteristics and characterize Boolean features. Moreover, representations by sets are considered and pertinent examples provided.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Svazek periodika

68

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

6

Strana od-do

485-490

Kód UT WoS článku

000432900500002

EID výsledku v databázi Scopus

2-s2.0-85047849868