相关论文: Legendre pair of length $77$ using complementary b…
We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from $\{0,1\}$ or $\{-1,1\}$. We describe efficient parallel algorithms for…
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
Modeling binary star populations is critical to linking the theories of star formation and stellar evolution with observations. In order to test these theories, we need accurate models of observable binary populations. The Kepler Eclipsing…
The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.
The first directly observed gravitational wave event, GW150914, featuring the merger of two massive black holes, highlighted the need to determine how these systems of compact remnant binaries are formed. We use the binary population…
Representing visual data using compact binary codes is attracting increasing attention as binary codes are used as direct indices into hash table(s) for fast non-exhaustive search. Recent methods show that ranking binary codes using…
Binary stars are common and it is necessary to model stellar populations using binary stars. We introduce a method to model binary-star stellar populations quickly. The method can also be used to model single-star stellar populations. The…
A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is…
In this paper, we enumerate the pairs of permutations that are long cycles and whose product has a given cycle-type. Our main result is a simple relation concerning the desired numbers for a few related cycle-types. The relation refines a…
Many interesting spaces --- including all positroid strata and wild character varieties --- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We show that the existence of cluster structures on these…
The statistical properties of planets in binaries were investigated. Any difference to planets orbiting single stars can shed light on the formation and evolution of planetary systems. As planets were found around components of binaries…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
Multi-epoch radial velocity measurements of stars can be used to identify stellar, sub-stellar, and planetary-mass companions. Even a small number of observation epochs can be informative about companions, though there can be multiple…
Masses of classical Cepheids of 3 to 11 M$\odot$ are predicted by theory but those measured, clump between 3.6 and 5 M$\odot$. As a result, their mass-luminosity relation is poorly constrained, impeding our understanding of basic stellar…
We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of $b$-adic integers, $\mathbb Z_{b}, b\in\mathbb N\setminus\{1\}$, by using such sequences as input for generating matrices. The…
Searches for planets in close binary systems explore the degree to which stellar multiplicity inhibits or promotes planet formation. There is a degeneracy between planet formation models when only systems with single stars are…
Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary…
We discuss an equivalence relation on the set of square binary matrices with the same number of 1's in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of…
Considering commutator monomials of the non-commutative associative variables $X_1,\ldots,X_n$; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by…