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B. M. Quine

Publications and source records attributed to B. M. Quine.

At least 19 recordsLinked to original sources
arXiv2021

Scintillation of PSR B1508+55 -- the view from a 10,000-km baseline

We report on the simultaneous Giant Metrewave Radio Telescope (GMRT) and Algonquin Radio Observatory (ARO) observations at 550-750 MHz of the scintillation of PSR B1508+55, resulting in a $\sim$10,000-km baseline. This regime of measurement lies between the shorter few 100-1000~km baselines of earlier multi-station observations and the much longer earth-space baselines. We measure a scintillation cross-correlation coefficient of $0.22$, offset from zero time lag due to a $\sim 45$~s traversal time of the scintillation pattern. The scintillation time of 135~s is $3\times$ longer, ruling out isotropic as well as strictly 1D scattering. Hence, the low cross-correlation coefficient is indicative of highly anisotropic but 2D scattering. The common scintillation detected on the baseline is confined to low delays of $\lesssim 1 μ$s, suggesting that this correlation may not be associated with the parabolic scintillation arc detected at the GMRT. Detection of pulsed echoes and their direct imaging with the Low Frequency Array (LOFAR) by a different group enable them to measure a distance of 125~pc to the screen causing these echoes. These previous measurements, alongside our observations, lead us to propose that there are at least two scattering screens: the closer 125 pc screen causing the scintillation arc detected at GMRT, and a screen further beyond causing the scintillation detected on the GMRT-ARO baseline. We advance the hypothesis that the 125-pc screen partially resolves the speckle images on the screen beyond leading to loss of coherence in the scintillation dynamic spectrum, to explain the low cross-correlation coefficient.

astro-ph.HE↗
arXiv2020

A bright millisecond-duration radio burst from a Galactic magnetar

Magnetars are highly magnetized young neutron stars that occasionally produce enormous bursts and flares of X-rays and gamma-rays. Of the approximately thirty magnetars currently known in our Galaxy and Magellanic Clouds, five have exhibited transient radio pulsations. Fast radio bursts (FRBs) are millisecond-duration bursts of radio waves arriving from cosmological distances. Some have been seen to repeat. A leading model for repeating FRBs is that they are extragalactic magnetars, powered by their intense magnetic fields. However, a challenge to this model has been that FRBs must have radio luminosities many orders of magnitude larger than those seen from known Galactic magnetars. Here we report the detection of an extremely intense radio burst from the Galactic magnetar SGR 1935+2154 using the Canadian Hydrogen Intensity Mapping Experiment (CHIME) FRB project. The fluence of this two-component bright radio burst and the estimated distance to SGR 1935+2154 together imply a 400-800 MHz burst energy of $\sim 3 \times 10^{34}$ erg, which is three orders of magnitude brighter than those of any radio-emitting magnetar detected thus far. Such a burst coming from a nearby galaxy would be indistinguishable from a typical FRB. This event thus bridges a large fraction of the radio energy gap between the population of Galactic magnetars and FRBs, strongly supporting the notion that magnetars are the origin of at least some FRBs.

astro-ph.HE↗
arXiv2019

A rational approximation of the sinc function based on sampling and the Fourier transforms

In our previous publications we have introduced the cosine product-to-sum identity [17] $$ \prod\limits_{m = 1}^M {\cos \left( {\frac{t}{2^m}} \right)} = \frac{1}{2^{M - 1}}\sum\limits_{m = 1}^{2^{M - 1}} {\cos \left( {\frac{2m - 1}{2^M}t} \right)} $$ and applied it for sampling [1, 2] as an incomplete cosine expansion of the sinc function in order to obtain a rational approximation of the Voigt/complex error function that with only $16$ summation terms can provide accuracy ${\sim 10^{ - 14}}$. In this work we generalize this approach and show as an example how a rational approximation of the sinc function can be derived. A MATLAB code validating these results is presented.

math.NA↗
arXiv2019

Carbon dioxide retrieval of Argus 1000 space data by using GENSPECT line-by-line radiative transfer model

The micro-spectrometer Argus 1000 being in space continuously monitors the sources and sinks of the trace gases. It is commonly believed that among other gases $\text{CO}_\text{2}$ is the major contributor causing the greenhouse effect. Argus 1000 along its orbit gathers the valuable spectral data that can be analyzed and retrieved. In this paper we present the retrieval of $\text{CO}_\text{2}$ gas in the near infrared window $1580$ to $1620$ nm by using line-by-line code GENSPECT. The retrieved Argus 1000 space data taken over British Columbia on May 31, 2010 indicates an enhancement of $\text{CO}_\text{2}$ by about $30\%$.

physics.ao-ph↗
arXiv2019

A single-domain implementation of the Voigt/complex error function by vectorized interpolation

In this work we show how to perform a rapid computation of the Voigt/complex error over a single domain by vectorized interpolation. This approach enables us to cover the entire set of the parameters $x,y \in \mathbb{R}$ required for the HITRAN-based spectroscopic applications. The computational test reveals that within domains $x\in\left[0,15\right]\cap y\in\left[10^{-8},15\right]$ and $x\in\left[0,50000\right]\cap y\geq 10^{-8}$ our algorithmic implementation is faster in computation by factors of about $8$ and $3$, respectively, as compared to the fastest known C/C++ code for the Voigt/complex error function. A rapid MATLAB code is presented.

math.GM↗
arXiv2018

A simple pseudo-Voigt/complex error function

In this work we present a simple approximation for the Voigt/comp-lex error function based on fitting with set of the exponential functions of form ${α_n}{\left| t \right|^n}{e^{ - {β_n}\left| t \right|}}$, where ${α_n}$ and ${β_n}$ are the expansion coefficients. The computational test reveals that the largest absolute differences for the real and imaginary parts of the complex error function are $0.037$ and $0.036$, respectively.

math.GM↗
arXiv2018

A formula for pi involving nested radicals

We present a new formula for pi involving nested radicals with rapid convergence. This formula is based on the arctangent function identity with argument $x=\sqrt{2-{{a}_{k-1}}}/{{a}_{k}}$, where \[ {{a}_{k}}=\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_{k\,\,\text{square}\,\,\text{roots}} \] is a nested radical consisting of $k$ square roots. The computational test we performed reveals that the proposed formula for pi provides a significant improvement in accuracy as the integer $k$ increases.

math.GM↗
arXiv2018

A sampling-based approximation of the complex error function and its implementation without poles

Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function $w\left(z \right) = e^{- {z^2}}\left(1 + \frac{2i}{\sqrt π}\int_0^z e^{t^2}dt\right),$ where $z = x + iy$. As a further development, in this work we show how this sampling-based rational approximation can be transformed into alternative form for efficient computation of the complex error function $w\left(z \right)$ at smaller values of the imaginary argument $y=\operatorname{Im}\left[z \right]$. Such an approach enables us to avoid poles in implementation and to cover the entire complex plain with high accuracy in a rapid algorithm. An optimized Matlab code utilizing only three rapid approximations is presented.

math.NA↗
arXiv2018

Efficient computation of pi by the Newton - Raphson iteration and a two-term Machin-like formula

In our recent publication we have proposed a new methodology for determination of the two-term Machin-like formula for pi with small arguments of the arctangent function of kind $$ \frac{π}{4} = {2^{k - 1}}\arctan \left( {\frac{1}{β_1}} \right) + \arctan \left( {\frac{1}{β_2}} \right), $$ where $k$ and ${β_1}$ are some integers and ${β_2}$ is a rational number, dependent upon ${β_1}$ and $k$. Although ${1/\left|β_2\right|}$ may be significantly smaller than ${1/β_1}$, the large numbers in the numerator and denominator of $β_2$ decelerate the computation. In this work we show how this problem can be effectively resolved by the Newton--Raphson iteration method.

math.GM↗
arXiv2017

A rational approximation of the Dawson's integral for efficient computation of the complex error function

In this work we show a rational approximation of the Dawson's integral that can be implemented for high-accuracy computation of the complex error function in a rapid algorithm. Specifically, this approach provides accuracy exceeding $\sim {10^{ - 14}}$ in the domain of practical importance $0 \le y < 0.1 \cap \left| {x + iy} \right| \le 8$. A Matlab code for computation of the complex error function with entire coverage of the complex plane is presented.

math.NA↗
arXiv2017

An iteration procedure for a two-term Machin-like formula for pi with small Lehmer's measure

In this paper we present a two-term Machin-like formula for pi \[\fracπ{4} = 2^{k - 1}\arctan\left(\frac{1}{u_1}\right) + \arctan\left(\frac{1}{u_2}\right)\] with small Lehmer's measure $e \approx 0.245319$ and describe iteration procedure for simplified determination of the required rational number $u_2$ at $k = 27$ and $u_1 = 85445659$. With these results we obtained a formula that has no irrational numbers involved in computation and provides $16$ digits of pi at each increment by one of the summation terms. This is the smallest Lehmer's measure ever reported for the Machin-like formulas for pi.

math.GM↗
arXiv2017

A set of the Viète-like recurrence relations for the unity constant

Using a simple Viète-like formula for $π$ based on the nested radicals $a_k = \sqrt{2 + a_{k-1}}$ and $a_1 = \sqrt{2}$, we derive a set of the recurrence relations for the constant $1$. Computational test shows that application of this set of the Viète-like recurrence relations results in a rapid convergence to unity.

math.GM↗
arXiv2016

The Fourier expansion approximation for high-accuracy computation of the Voigt/complex error function at small imaginary argument

It is known that the computation of the Voigt/complex error function is problematic for highly accurate and rapid computation at small imaginary argument $y << 1$, where $y = \operatorname{Im} \left[ z \right]$. In this paper we consider an approximation based on the Fourier expansion that can be used to resolve effectively such a problem when $y \to 0$.

math.NA↗
arXiv2016

A simple identity for derivatives of the arctangent function

We present an identity for the derivatives of the arctangent function as an alternative to the Adegoke - Layeni - Lampret formula. We show that algorithmic implementation of the proposed identity can significantly accelerate the computation since this approach requires no symbolic programming in determination of the derivatives for the arctangent function.

math.GM↗