Related papers: Twisting the Stern sequence
In a recent preprint on ArXiv, Bacher introduced a twisted version of the Stern sequence. His paper contains in particular three conjectures relating the generating series for the Stern sequence and for the twisted Stern sequence. Soon…
In a recent paper, Roland Bacher conjectured three identities concerning Stern's sequence and its twist. In this paper we prove Bacher's conjectures. Possibly of independent interest, we also give a way to compute the Stern value (or…
In this paper, we introduce the new class of twisted $B$-splines and study some properties of these B-splines. We also investigate the system of twisted translates and the wavelets corresponding to these twisted $B$-splines.
The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher dimensional analogues of continued…
The rotation rate of a star has important implications for the detectability, characterisation and stability of any planets that may be orbiting it. This chapter gives a brief overview of stellar rotation before describing the methods used…
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit representation of integers is an alternative representation of integers with much use in efficient…
We give a proof of an analogue of Connes' Hochschild character theorem for twisted spectral triples obtained from twisting a spectral triple by scaling automorphisms, under some suitable conditions. We also survey some of the properties of…
We generalize Stern's diatomic sequence in three ways.
We present a history and analysis of this experiment.
Rational twisted power series over a (commutative) field are studied. We give several characterizations of such series, which are similar to the classical results concerning rational power series over a commutative field. In particular, we…
We will construct twisted versions of the wild character varieties.
The possible spatial transformation properties of tetrons are discussed.
We study a special set of constellations of primes generated by twin primes.
Let w be a binary string and let a_w (n) be the number of occurrences of the word w in the binary expansion of n. As usual we let s(n) denote the Stern sequence; that is, s(0)=0, s(1)=1, and for n >= 1, s(2n)=s(n) and s(2n+1)=s(n)+s(n+1).…
In quantum mechanics, it is often thought that the spin of an object points in a fixed direction at any point in time. For example, after selecting the z-direction as the axis of quantization, a spin-1/2 object (such as an electron) may…
In this paper we review the basics of magneto-rotational properties of neutron stars focusing on spin-up/spin-down behavior at different evolutionary stages. The main goal is to provide equations for the spin frequency changes in various…
We prove that the Stern diatomic sequence is asymptotically distributed according to a normal law, on a logarithmic scale. This is obtained by studying complex moments, and the analytic properties of a transfer operator.
In this talk, after briefly reviewing some historical remarks concerning strange stars, the achievements in physics and dynamical behavior of strange stars are discussed. Especially, various observational effects in distinguishing strange…
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
For each element of certain families of integer sequences, we study the term-wise ratios of the Hankel transforms of three sequences related to that element by series reversion. In each case, the ratios define well-known sequences, and in…