相关论文: A Closed Form for the Pulsar Sequence

Broadband radio waves emitted from pulsars are distorted and delayed as they propagate toward the Earth due to interactions with the free electrons that compose the interstellar medium, with lower radio frequencies being more impacted than…

An almost square of type 2 is an integer $n$ that can be factored in two different ways as $n = a_1 b_1 = a_2 b_2$ with $a_1$, $a_2$, $b_1$, $b_2 \approx \sqrt{n}$. In this paper, we shall improve upon previous result on short intervals…

The Brocard porism is a known 1d family of triangles inscribed in a circle and circumscribed about an ellipse. Remarkably, the Brocard angle is invariant and the Brocard points are stationary at the foci of the ellipse. In this paper we…

Putinar and Vasilescu have given an algebraic characterization of Hamburger moment sequences in several variables. In this paper we give a characterization of sparse moment subsequences of Hamburger moment sequences and consider the problem…

We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a…

Any ultrafast optical spectroscopy experiment is usually accompanied by the necessary routine of ultrashort-pulse characterisation. The majority of pulse characterisation approaches solve either a one-dimensional (e.g. via interferometry)…

A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…

Euler had considered the problem of finding three integers whose sum, product, and also the sum of the products of the integers, taken two at a time, are all perfect squares. Euler's methods of solving the problem lead to parametric…

Pulsar timing is a powerful tool that, by accounting for every rotation of a pulsar, precisely measures the spin frequency, spin frequency derivatives, astrometric position, binary parameters when applicable, properties of the ISM, and…

The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…

Pulsars are famed for their rotational clock-like stability and their highly-repeatable pulse shapes. However, it has long been known that there are unexplained deviations (often termed "timing noise") from the rate at which we predict…

The intrinsic volumes are measures of the content of a convex body. This paper uses probabilistic and information-theoretic methods to study the sequence of intrinsic volumes of a convex body. The main result states that the intrinsic…

We study statistical properties of stochastic variations in pulse arrival times, timing noise, in radio pulsars using a new analysis method applied in the time domain. The method proceeds in two steps. First, we subtract low-frequency…

Characterizing the shape and evolution of pulsar radio emission beams is important for understanding the observed emission. The various attempts by earlier workers investigating beam shapes have resulted in widely different conclusions.…

We investigate the arithmetic nature of P-recursive sequences through the lens of their D-finite generating functions. Building on classical tools from differential algebra, we revisit the integrality criterion for Motzkin-type sequences…

Curve stitching is a classic educational activity where one constructs elegant curves from a family of straight lines. We perform curve stitching around a circle to make a modular stitch graph. Take $m$ points equally spaced around a…

Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the…

Pulsar timing, i.e. the analysis of the arrival times of pulses from a pulsar, is a powerful tool in modern astrophysics. It allows us to measure the time delays of an electromagnetic signal caused by a number of physical processes as the…

Searches for stochastic gravitational-wave backgrounds using pulsar timing arrays look for correlations in the timing residuals induced by the background across the pulsars in the array. The correlation signature of an isotropic,…

We present a physical interpretation for the generation of circular polarization resulting from the propagation of radiation through a magnetized plasma in terms of a rotation measure gradient, or `Faraday wedges'. Criteria for the…