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Start Over Subject completeness

1. Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

Creator:
Pérez Fernández, Francisco Javier , Benítez-Trujillo, F., and Aizpuru, Antonio
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
completeness, barrelledness, and weakly unconditionally Cauchy series
Language:
English
Description:
In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space $X$ can be characterized through the behaviour of its weakly-$\ast $ unconditionally Cauchy series in $X^\ast $.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Higher degrees of distributivity in $MV$-algebras

Creator:
Jakubík, Ján
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$MV$-algebra, archimedean $MV$-algebra, completeness, singular $MV$-algebra, and higher degrees of distributivity
Language:
English
Description:
In this paper we deal with the of an $MV$-algebra $\mathcal A$, where $\alpha $ and $\beta $ are nonzero cardinals. It is proved that if $\mathcal A$ is singular and $(\alpha,2)$-distributive, then it is . We show that if $\mathcal A$ is complete then it can be represented as a direct product of $MV$-algebras which are homogeneous with respect to higher degrees of distributivity.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On monotone permutations of $\ell$-cyclically ordered sets

Creator:
Jakubík, Ján
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$\ell $-cyclically ordered set;, completeness, monotone permutation, and half cyclically ordered group
Language:
English
Description:
For an $\ell $-cyclically ordered set $M$ with the $\ell $-cyclic order $C$ let $P(M)$ be the set of all monotone permutations on $M$. We define a ternary relation $\overline{C}$ on the set $P(M)$. Further, we define in a natural way a group operation (denoted by $\cdot $) on $P(M)$. We prove that if the $\ell $-cyclic order $C$ is complete and $\overline{C}\ne \emptyset $, then $(P(M), \cdot ,\overline{C})$ is a half cyclically ordered group.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. On the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$

Creator:
Xiangdong
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
completeness, Banach space, and complex Müntz theorem
Language:
English
Description:
Let $E=\bigcup _{n=1}^{\infty }I_{n}$ be the union of infinitely many disjoint closed intervals where $I_{n}=[a_{n}$, $b_{n}]$, $0<a_{1}<b_{1}<a_{2}<b_{2}<\dots <b_{n}<\dots $, $\lim _{n\rightarrow \infty }b_{n}=\infty .$ Let $\alpha (t)$ be a nonnegative function and $\{\lambda _{n}\}_{n=1}^{\infty }$ a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system $\{t^{\lambda _{n}}\log ^{m_{n}}t\}$ in $C_{0}(E)$ is obtained where $C_{0}(E)$ is the weighted Banach space consists of complex functions continuous on $E$ with $f(t){\rm e}^{-\alpha (t)}$ vanishing at infinity.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Rational Łukasiewicz logic and DMV-algebras

Creator:
Gerla, Brunella
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
many-valued logic, fuzzy logic, Rational Łukasiewicz logic, DMV-algebras, completeness, and computational complexity
Language:
English
Description:
In this paper we present some results concerning the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, the Rational Łukasiewicz logic is defined and its tautology problem is shown to be co-NP-complete.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public