Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, ..., $100\}$ and $(q, a) = 1$.Comment: 12 pages, 6 table

Investigating people: a qualitative analysis of the search behaviours of open-source intelligence analysts

The Internet and the World Wide Web have become integral parts of the lives of many modern individuals, enabling almost instantaneous communication, sharing and broadcasting of thoughts, feelings and opinions. Much of this information is publicly facing, and as such, it can be utilised in a multitude of online investigations, ranging from employee vetting and credit checking to counter-terrorism and fraud prevention/detection. However, the search needs and behaviours of these investigators are not well documented in the literature. In order to address this gap, an in-depth qualitative study was carried out in cooperation with a leading investigation company. The research contribution is an initial identification of Open-Source Intelligence investigator search behaviours, the procedures and practices that they undertake, along with an overview of the difficulties and challenges that they encounter as part of their domain. This lays the foundation for future research in to the varied domain of Open-Source Intelligence gathering

More efficient Bell inequalities for Werner states

In this paper we study the nonlocal properties of two-qubit Werner states parameterized by the visibility parameter 0<p<1. New family of Bell inequalities are constructed which prove the two-qubit Werner states to be nonlocal for the parameter range 0.7056<p<1. This is slightly wider than the range 0.7071<p<1, corresponding to the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by Gisin in the positive, i.e., there exist Bell inequalities which are more efficient than the CHSH inequality in the sense that they are violated by a wider range of two-qubit Werner states.Comment: 7 pages, 1 figur

Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations

I construct a two-dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined. The primary lattice studied here, the ``martini lattice'', is a hexagonal lattice with every second site transformed into a triangle. The site threshold of this lattice is found to be $0.764826...$, while the others have $0.618034...$ and $1/\sqrt{2}$. This last solution suggests a possible approach to establishing the bound for the hexagonal site threshold, $p_c<1/\sqrt{2}$. To derive these results, I solve a correlated bond problem on the hexagonal lattice by use of the star-triangle transformation and then, by a particular choice of correlations, solve the site problem on the martini lattice.Comment: 12 pages, 10 figures. Submitted to Physical Review

Universal Baxterization for Z\mathbb{Z}-graded Hopf algebras

We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with $\mathbb{Z}$-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group $U_q[sl(2)]$.Comment: 8 page

The Solar Neighborhood XXV: Discovery of New Proper Motion Stars with 0.40 "/yr > mu > 0.18 "/yr between Declinations -47 degrees and 00 degrees

We present 2817 new southern proper motion systems with 0.40 "/yr > mu > 0.18 "/yr and declination between -47 degrees and 00 degrees. This is a continuation of the SuperCOSMOS-RECONS (SCR) proper motion searches of the southern sky. We use the same photometric relations as previous searches to provide distance estimates based on the assumption that the objects are single main sequence stars. We find 79 new red dwarf systems predicted to be within 25 pc, including a few new components of previously known systems. Two systems - SCR 1731-2452 at 9.5 pc and SCR 1746-3214 at 9.9 pc - are anticipated to be within 10 pc. We also find 23 new white dwarf candidates with distance estimates of 15-66 pc, as well as 360 new red subdwarf candidates. With this search, we complete the SCR sweep of the southern sky for stars with mu > 0.18 "/yr and R_59F < 16.5, resulting in a total of 5042 objects in 4724 previously unreported proper motion systems. Here we provide selected comprehensive lists from our SCR proper motion search to date, including 152 red dwarf systems estimated to be within 25 pc (nine within 10 pc), 46 white dwarfs (ten within 25 pc), and 598 subdwarf candidates. The results of this search suggest that there are more nearby systems to be found at fainter magnitudes and lower proper motion limits than those probed so far.Comment: 47 pages, 16 of text. 7 figure

Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved spacetime. In the framework of zeta function regularization, we find the one-loop effective action to all orders in the magnetic field up to linear terms in the Riemannian curvature. As a particular case, we also obtain the one-loop effective action for massless scalar and spinor fields. In this setting, we found that the vacuum energy of charged spinors with small mass becomes very large due entirely by the gravitational correction.Comment: LaTeX, 23 page

Sunspot observations from the SOUP instrument on Spacelab 2

A series of white light images obtained by the SOUP instrument on Spacelab 2 of active region 4682 on August 5, 1985 were analyzed in the area containing sunspots. Although the umbra of the spot is underexposed, the film is well exposed in the penumbral regions. These data were digitally processed to remove noise and to separate p-mode oscillations from low velocity material motions. The results of this preliminary investigation include: (1) proper motion measurements of a radial outflow in the photospheric granulation pattern just outside the penumbra; (2) discovery of occasional bright structures (streakers) that appear to be ejected outward from the penumbra; (3) broad dark clouds moving outward in the penumbra in addition to the well known bright penumbral grains moving inward; (4) apparent extensions and contractions of penumbral filaments over the photosphere; and (5) observation of a faint bubble or loop-like structure which seems to expand from two bright penumbral filaments into the photosphere

Collective states of interacting D(D3)D(D_3) non-Abelian anyons

We study the finite size spectrum of integrable quantum chains of interacting non-Abelian anyons constructed using the Drinfeld double of the dihedral group $D_3$. The gapless low energy modes are identified as the direct product of two conformal field theories which can be decomposed according to the residual symmetries of the chains subject to periodic boundary conditions.Comment: 11 page