More than half of all main sequence stars, and an even larger fraction of pre-main sequence stars, reside in binary/multiple star systems [1, 2]. Numerical simulations of the collapse of molecular cloud cores to form binary stars suggest that disks form within binary star systems [3]. The presence of disk material has been indirectly observed around one or both components of some young binary s...

In the paper it is presented an algorithm for generating pseudo-random binary sequences. There are formulated theorems concerning properties of the sequence generated by the algorithm. The sequence is not periodic. Moreover, for any natural number n > 0, the initial fragment of the generated sequence of the length (2 · n) · 2(2·n) contains all (binary) series of the length n.

Binary sequences are the most fundamental random numbers and have been extensively used in several applications such as spread-spectrum CDMA communications and cryptosystems. M-sequences, Kasami sequences, and Gold sequences, all of which can be generated by linear feedback shift registers (LFSRs), are well known as conventional binary sequences [1]. It is also well known that chaos phenomena c...

Let X = (x1, . . . , xn) be a finite binary sequence of length n, i.e., xi = ±1 for all i. The derived sequence of X is the binary sequence ∂X = (x1x2, . . . , xn−1xn) of length n− 1, and the derived triangle of X is the collection ∆X of all derived sequences ∂X for 0 ≤ i ≤ n−1. We say that X is balanced if its derived triangle ∆X contains as many +1’s as −1’s. This concept was introduced by St...

Binary Golay sequence pairs exist for lengths 2, 10 and 26 and, by Turyn’s product construction, for all lengths of the form 21026 where a, b, c are non-negative integers. Computer search has shown that all inequivalent binary Golay sequence pairs of length less than 100 can be constructed from five “seed” pairs, of length 2, 10, 10, 20 and 26. We give the first complete explanation of the orig...

TIC 470710327, a massive compact hierarchical triple-star system, was recently identified by NASA's Transiting Exoplanet Survey Satellite (TESS). 470710327 is comprised of (1.10 d) circular eclipsing binary, with total mass $\approx 10.9-13.2\ \rm{M_{\odot}}$, and more ($\approx 14-17\ \rm{M_{\odot}}$) eccentric non-eclipsing tertiary in $52.04$ d orbit. Here we present progenitor scenario for ...

New binary and ternary sequences with low correlation and simple implementation are presented. The sequences are unfolded from arrays, whose columns are cyclic shifts of a short sequence or constant columns and whose shift sequence (sequence of column shifts) has the distinct difference property. It is known that a binary m-sequence/GMW sequence of length 2 − 1 can be folded row-by-row into an ...

A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the Horton-Strahler indices are calculated by using the sequence. By fitting the Gaussian distribution function to our numerical data, the values of variances are determined a...

A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic operations. The proposed model can serve as a deterministic alternative to existing probabilistic methods for checking balancedness in binary sequence generators. ...