Related papers: The Pulsar Sequence
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
An increasing sequence $(a_n)$ of positive integers which satisfies $\frac{a_{n+1}}{a_n}>1+\eta$ for some positive $\eta$ is called a lacunary sequence. It has been known for over twenty years that every lacunary sequence is strong sweeping…
Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered visual fragments, is fundamental to numerous applications, and yet most of the literature of the last two decades has focused thus…
Pulsar timing is a promising technique for detecting low frequency sources of gravitational waves. Historically the focus has been on the detection of diffuse stochastic backgrounds, such as those formed from the superposition of weak…
We have found maximum possible runs of consecutive positive integers each having exactly $k$ divisors for some fixed values of $k$. In addition, we exhibit the run of 10 consecutive positive integers each having exactly 12 divisors and two…
We prove the existence of a ternary sequence of factor complexity $2n+1$ for any given vector of rationally independent letter frequencies. Such sequences are constructed from an infinite product of two substitutions according to a…
This is a structured compilation of some of my favourite open problems.
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word…
Radio-loud neutron stars known as pulsars allow a wide range of experimental tests for fundamental physics, ranging from the study of super-dense matter to tests of general relativity and its alternatives. As a result, pulsars provide…
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
We give a more detailed description of the new system of Pl\"ucker-like equations from [4], discuss how it relates to the usual Pl\"ucker equations, and correct a mistake in that article.
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15…
Pairs of consecutive integers have the same height in the Collatz problem with surprising frequency. Garner gave a conjectural family of conditions for exactly when this occurs. Our main result is an infinite family of counterexamples to…
The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…
We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra…
A sequence of positive integers is complete if every positive integer is a sum of distinct terms. A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneous linear recurrence relation with nonnegative coefficients…
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…
Pulsar timing arrays will be a window into the gravitational wave background