There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Introduction to lie algebras and representation theory

General Theory of Banach Algebra. By C.E. Rickart. Pp. 394. 79s. 1960. (Van Nostrand, London)

/pdf/infinite-abelian-groups-2dvcz0046a.pdf

Infinite Abelian Groups

What do you do to start reading automatic sequences theory applications generalizations? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this automatic sequences theory applications generalizations.

Automatic sequences. Theory, applications, generalizations.

Preface .- Introduction .- Hadamard Sets.- $\epsilon$-Kronecker sets.- Sidon sets: Introduction and decomposition properties.- Characterizations of $I_0$ sets.- Proportional characterizations of Sidon sets.- Decompositions of $I_0$ sets.- Sizes of thin sets.- Sets of zero discrete harmonic density.- Related results.-Open problems.- Appendices (Groups, Probability, Combinatoric results,...).- Bibliography.- Author index.- Subject index.- Index of notation.

Interpolation and Sidon Sets for Compact Groups

We find conditions on the ratios of dissection of a Cantor set so that the
 group it generates under addition has positive Lebesgue measure. In
 particular, we answer affirmatively a special case of a conjecture posed by
 J. Palis.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0143385797097678

Sums of Cantor sets

Funding: Leverhulme Trust Research Fellowship (RF-2016-500) and EPSRC Standard Grant (EP/R015104/1) (JMF). HY was financially supported by the University of St Andrews.

/pdf/the-assouad-spectrum-and-the-quasi-assouad-dimension-a-tale-45noxtfp08.pdf

The Assouad spectrum and the quasi-Assouad dimension : a tale of two spectra

It is known that Laplacian operators on many fractals have gaps in their spectra. This fact precludes the possibility that a Weyl-type ratio can have a limit and is also a key ingredient in proving that the Fourier series on such fractals can have better convergence results than in the classical setting. In this paper we prove that the existence of gaps is equivalent to the total disconnectedness of the Julia set of the spectral decimation function for the class of fully symmetric p.c.f. fractals, and for self-similar fully symmetric finitely ramified fractals with regular harmonic structure. We also formulate conjectures related to geometry of finitely ramified fractals with spectral gaps, to complex spectral dimensions, and to convergence of Fourier series on such fractals.

https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/2012/0019/0003/MRL-2012-0019-0003-a003.pdf

Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals

In this paper we prove that if a Cantor set has ratios of dissection bounded away from zero, then there is a natural number N, such that its N-fold sum is an interval. Moreover, for each element z of this interval, we explicitly construct the N elements of C whose sum yields z. We also extend a result of Mendes and Oliveria showing that when s is irrational is an interval if and only if a /(1−2a) as/(1−2as) ≥ 1.

/pdf/sums-of-cantor-sets-yielding-an-interval-3a2636l1mx.pdf

Kathryn E. Hare

Papers

Interpolation and Sidon Sets for Compact Groups

Sums of Cantor sets

The Assouad spectrum and the quasi-Assouad dimension : a tale of two spectra

Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals

Sums of Cantor sets yielding an interval