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of 42
pro vyhledávání: '"Peter Nickolas"'
Autor:
Peter Nickolas, Mikhail Tkachenko
Publikováno v:
Applied General Topology, Vol 6, Iss 1, Pp 43-56 (2005)
A systematic analysis is made of the character of the free and free abelian topological groups on metrizable spaces and compact spaces, and on certain other closely related spaces. In the first case, it is shown that the characters of the free and th
Externí odkaz:
https://doaj.org/article/0584598e318243c28b04a013e07030de
Publikováno v:
Bulletin of the Australian Mathematical Society. 103:11-21
For a positive real number $t$, define the harmonic continued fraction $$\begin{eqnarray}\text{HCF}(t)=\biggl[\frac{t}{1},\frac{t}{2},\frac{t}{3},\ldots \biggr].\end{eqnarray}$$ We prove that $$\begin{eqnarray}\text{HCF}(t)=\frac{1}{1-2t(\frac{1}{t+2
Publikováno v:
The Ramanujan Journal. 49:669-697
In this paper, we study the harmonic continued fractions. These form an infinite family of ordinary continued fractions with coefficients $$\frac{t}{1}, \frac{t}{2}, \frac{t}{3}, \ldots $$ for all $$t>0$$ . We derive explicit formulas for the numerat
Autor:
Ali Sayed Elfard, Peter Nickolas
Publikováno v:
Topology and its Applications. 160(1):220-229
Let $\FP(X)$ be the free paratopological group on a topological space $X$. For $n\in \N$, denote by $\FP_n(X)$ the subset of $\FP(X)$ consisting of all words of reduced length at most $n$, and by $i_n$ the natural mapping from $(X\oplus X^{-1}\oplus
Publikováno v:
Discrete Mathematics, Algorithms and Applications. :393-412
Traditional hash functions are designed to protect against even the slightest modification of a message. Thus, one bit changed in a message would result in a totally different message digest when a hash function is applied. This feature is not suitab
Autor:
Peter Nickolas, Reinhard Wolf
Publikováno v:
Mathematische Nachrichten. 284:747-760
Let (X, d) be a compact metric space and let denote the space of all finite signed Borel measures on X. Define by I(μ) = ∫X∫Xd(x, y) dμ(x)dμ(y), and set , where μ ranges over the collection of signed measures in of total mass 1. This paper, w
Autor:
Peter Nickolas, Reinhard Wolf
Publikováno v:
Mathematische Nachrichten. 284:332-341
Publikováno v:
Mathematische Zeitschrift. 268:887-896
Denote by B n the unit ball in the Euclidean space $${\mathbb{R}^n}$$ and define $$ M(B^n) = \sup \int_{B^n} \int_{B^n}\| x - y \| \, d\mu(x)d\mu(y),$$ where the supremum is taken over all finite signed Borel measures μ on B n of total mass 1. In th
Autor:
Peter Nickolas, Reinhard Wolf
Publikováno v:
Acta Mathematica Hungarica. 124:243-262
Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by $I(mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y)$, and set $M(X) = \sup I(mu)$, where
Publikováno v:
Topology and its Applications. 155:146-160
In 1957 Robert Ellis proved that a group with a locally compact Hausdorff topology T making all translations continuous also has jointly continuous multiplication and continuous inversion, and is thus a topological group. The theorem does not apply t