Related papers: The Pulsar Sequence
This paper investigates a variant of the famous "happy numbers" sequence, given by A351327 on the oeis. First of all we'll define this integer sequence, and then we'll show some important results about it; in particular we conjectured that…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
We answer two questions of Kra, Moreira, Richter and Robertson regarding the existence of infinite sumsets of the form $B + C$ in dense and sparse sets of integers and the relation of sumsets to sets of recurrence. We then further…
We prove that a curious generating series identity implies Faber's intersection number conjecture (by showing that it implies a combinatorial identity already given in arXiv:1902.02742) and give a new proof of Faber's conjecture by directly…
In a previous article, we reduced the unsolved problem of the convergence of Collatz sequences, to convergence of Collatz sequences of odd numbers, that are divisible by 3. In this article, we further reduce this set to odd numbers that are…
A positive integer $n$ is said to be a Zumkeller number or an integer-perfect number if the set of its positive divisors can be partitioned into two subsets of equal sums. In this paper, we prove several results regarding Zumkeller numbers.…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
Pulsars are amongst the most stable rotators known in the Universe. Over many years some millisecond pulsars rival the stability of atomic clocks. Comparing observations of many such stable pulsars may allow the first direct detection of…
The authors discuss potential remarkable achievements for pulsar science with the FAST (pulsar monitoring, timing and searching, as well as others related), and expect a FAST era of pulsar science to come.
There is no convincing evidence that backpropagation is a biologically plausible mechanism, and further studies of alternative learning methods are needed. A novel online clustering algorithm is presented that can produce arbitrary shaped…
The phenomenal rotational stability of millisecond pulsars allows them to be used as precise celestial clocks. An array of these pulsars can be exploited to search for correlated perturbations in their pulse times of arrival due to…
We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
In this paper, we discuss the well known 3x+1 conjecture in form of the accelerated Collatz function T defined on the positive odd integers. We present a sequence of quotient spaces and an invertible map that are intrinsically related to…
This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A.Zelevinsky. Total positivity serves as the main motivation.
Ever since the first pulsar was discovered by Bell and Hewish over 40 years ago, we've known that not only are pulsars fascinating and truly exotic objects, but that we can use them as powerful tools for basic physics and astrophysics as…
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable systems on the other. Informally, integrable…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
Using a recent result of Salberger, we establish the paucity of non-trivial positive integer solutions to a certain system of diagonal Diophantine equations.
This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the…