Zobrazeno 1 - 10
of 238
pro vyhledávání: '"A. F. Beardon"'
Autor:
A. F. Beardon
Publikováno v:
The Mathematical Gazette. 106:498-501
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3e7db315dfe571035a6f090d3d3cd884
https://doi.org/10.1017/mag.2022.125
https://doi.org/10.1017/mag.2022.125
Autor:
Alan F. Beardon
Publikováno v:
Archiv der Mathematik. 119:439-448
Some triangles in the hyperbolic plane have a circumscribed circle, and some do not. In this essay, we discuss hyperbolic polygons whose vertices lie on a circle, or a horocycle, or a hypercycle.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1a085a87ff75830dd03eaaedbaca821f
https://doi.org/10.1007/s00013-022-01761-x
https://doi.org/10.1007/s00013-022-01761-x
Autor:
A. F. Beardon
Publikováno v:
The Mathematical Gazette. 106:206-211
We denote the real logarithm of a positive number a by ln a, so that ax = exp (x ln a), and we shall discuss what is known about the real solutions x of the equation (1) $$x = {a^x},\;\,a > 0.$$ First, as exp t > 0 for all real t, each real solution
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5728079719e8be4797804c145e92fbdd
https://doi.org/10.1017/mag.2022.60
https://doi.org/10.1017/mag.2022.60
Autor:
A. F. Beardon, D. Minda
Publikováno v:
Computational Methods and Function Theory.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d559d69de83656c340dfc9bf65fb7217
https://doi.org/10.1007/s40315-022-00475-z
https://doi.org/10.1007/s40315-022-00475-z
Autor:
Alan F. Beardon
Publikováno v:
Computational Methods and Function Theory. 22:123-134
The positive solutions of the equation $$x^y = y^x$$ x y = y x have been discussed for over two centuries. Goldbach found a parametric form for the solutions, and later a connection was made with the classical Lambert function, which was also studied
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e09dbd01095a371655b16a143e937e1
https://doi.org/10.1007/s40315-021-00369-6
https://doi.org/10.1007/s40315-021-00369-6
Autor:
Alan F. Beardon, David Minda
Publikováno v:
Computational Methods and Function Theory. 21:557-564
In this note we present an alternative to Ford’s construction of the isometric circle of a Mobius map. This construction is based on the double coset decomposition of a group, together with the action of Mobius maps on spherical and hyperbolic spac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5365415cffdb75c7236f55deda0ae041
https://doi.org/10.1007/s40315-021-00375-8
https://doi.org/10.1007/s40315-021-00375-8
Autor:
D. Minda, A. F. Beardon
Publikováno v:
Canadian Mathematical Bulletin. 64:828-839
Many authors define an isometry of a metric space to be a distance-preserving map of the space onto itself. In this note, we discuss spaces for which surjectivity is a consequence of the distance-preserving property rather than an initial assumption.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5bc0cb1d82111a61a093b3d631b8b4af
https://doi.org/10.4153/s0008439520000867
https://doi.org/10.4153/s0008439520000867
Autor:
Alan F. Beardon, Nick Lord
Publikováno v:
The Mathematical Gazette. 104:460-468
In [1] the second author observed that it is possible to have a binary operation * on a set X with the property that two different arrangements of brackets in a given combination x1 * … * xn of elements of X yield the same outcome for all choices o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6eb0ea39959de23f24d2da54ae63318f
https://doi.org/10.1017/mag.2020.100
https://doi.org/10.1017/mag.2020.100
Publikováno v:
Computational Methods and Function Theory. 20:523-538
Several necessary and sufficient conditions for a family of Möbius maps to be a normal family in the extended complex plane $$\mathbb {C}_\infty $$ C ∞ are established. Each of these conditions involves collections of two or three points which may
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aeb8a0b2b7d477a647fad7fbf0dd6616
https://doi.org/10.1007/s40315-020-00328-7
https://doi.org/10.1007/s40315-020-00328-7
Autor:
Alan F. Beardon
Publikováno v:
Mathematics Magazine. 93:186-192
There is much confusion in the literature about the meaning of zw , where z and w are complex numbers with z≠0 . For example, we are often told that eiπ=−1 (a number), but that ii is an infinite se...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::26e26d94477cdcafa090dc05ae7d7862
https://doi.org/10.1080/0025570x.2020.1736876
https://doi.org/10.1080/0025570x.2020.1736876