Volume 51 , issue 1$-$2 ( 1999 ) | back |

Baire's space of permutations of $N$ and rearrangements of series | 1$-$8 |

**Abstract**

In the first part of the paper we investigate the structure of the space $(S,d)$ of all sequences of positive integers with Baire's metric. In the second part we study properties of the space $(E,d)$ of all permutations of $N$ in connection with rearrangements of non-absolutely convergent series.

**Keywords:** Rearrangements of series, Baire'sspace, set of first category,
residual set, $\sigma$-porosity, strong porosity.

**MSC:** 40A05

Some mean value theorems in terms of an infinitesimal function | 9$-$13 |

**Keywords:** Mean value theorem, infinitesimal function.

**MSC:** 26A24

Asymptotic linearity of mean values | 15$-$19 |

**Abstract**

The power and some other families of mean values, considered as the functions of parameter, have asymptotically linear distribution. This holds if either all the variables converge to the same value, or under the equal tending to infinity of additive increment of the variables. This limit linearity strengthens asymptotic property of Hoehn and Niven [10] which was investigated in several papers.

**Keywords:** Power mean values, asymptotic linearity.

**MSC:** 26B05

Classification of maps by their membership in maximal clones that contain minimum and complement | 21$-$28 |

**Abstract**

In this paper five-valued logic functions are classified according to their membership in the maximal clones which contain $\min(x,y)$ and $\bar x=4-x$.

**Keywords:** Multivalued logic, maximal clones.

**MSC:** 03B50

Extreme values of the sequences of independent random variables with mixed distributions | 29$-$37 |

**Abstract**

In this paper we consider some examples of the sequences of independent random variables with the same mixed distribution. In these cases we determine the type of extreme value distribution and the normalizing constants.

**Keywords:** Mixed distributions; extreme value distributions;
normal, Cauchy, uniform and truncated exponential distributions.

**MSC:** 60G70

Some fuzzy SP-topological properties | 39$-$51 |

**Abstract**

The concepts of fuzzy SP-irresolute continuous, fuzzy SP-irresolute open (closed) mappings, and a fuzzy SP-homeomorphism are being introduced and studied. Some of their characteristic properties are being considered. Finally, the claim that fuzzy semiregular properties are fuzzy SP-topological is being proved.

**Keywords:** Fuzzy topology, fuzzy strongly preopen set,
fuzyy SP-irresolute continuous mapping, fuzzy SP-irresolute open (closed)
mapping, fuzzy SP-homeomorphism.

**MSC:** 54A40

Segments of exponential series and regularly varying sequences | 53$-$59 |

**Abstract**

The task of this paper is to investigate asymptotic behavior of segments of exponential series defined as $$ T_{\lambda}(x):=\sum_{n<\lambda x}\dfrac{c_n}{n!}x^n,\qquad \lambda\in R^+,\quad x\to\infty, $$ where $(c_n)_{n\in N}$ belongs to the set of regularly varying sequences in Karamata sense of arbitrary index. Precise results are obtained.

**Keywords:** Segments of exponential series, regularly varying sequence.

**MSC:** 26A12