The Pythagoras number and the uu-invariant of Laurent series fields in several variables

We show that every sum of squares in the three-variable Laurent series field $\mathbb{R}((x,y,z))$ is a sum of 4 squares, as was conjectured in a paper of Choi, Dai, Lam and Reznick in the 1980's. We obtain this result by proving that every sum of squares in a finite extension of $\mathbb{R}((x,y))$ is a sum of $3$ squares. It was already shown in Choi, Dai, Lam and Reznick's paper that every sum of squares in $\mathbb{R}((x,y))$ itself is a sum of two squares. We give a generalization of this result where $\mathbb{R}$ is replaced by an arbitrary real field. Our methods yield similar results about the $u$-invariant of fields of the same type.Comment: final version, major revisions in the style of writing (abstract and introduction rewritten) compared to v.

The tenth order mock theta functions revisited

In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan's lost notebook. These were originally proved by Choi. Here we give an alternative (much shorter) proof.Comment: 11 pages; preprint, submitted for publicatio

Evaluations of some terminating hypergeometric ₂F₁(2) series with applications

Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).</p

Can the rapid braking of the white dwarf in AE Aquarii be explained in terms of the gravitational wave emitter mechanism?

The spin-down power of the white dwarf in the close binary AE Aquarii significantly exceeds the bolometric luminosity of the system. The interpretation of this phenomenon in terms of the gravitational-wave emitter mechanism has been recently suggested by Choi & Yi. The basic assumption of their interpretation is that the spatially limited blobs or mounds of the mass \delta m ~ 10^{-3} M_sun, are present at the magnetic poles of the white dwarf. We show that the mounds of this mass can be confined by the magnetic field of the white dwarf only if the dipole magnetic moment of the star exceeds 4x10^{37} G cm^3. Under these conditions, however, the magnetodipole losses of the white dwarf would exceed the evaluated spin-down power 6 orders of magnitude. On this basis we discard a possibility that the observed rapid braking of the white dwarf in AE Aquarii can be explained in terms of the mechanism proposed by Choi & Yi.Comment: 6 pages, published in ApJ, 576, L5

Service denied : injured military contractors fight for compensation

textDuring the Iraq and Afghanistan wars the U.S. government has relied heavily on military contracting companies and their employees to carry out military missions in Middle East. Since 2001, high salaries and the call to serve the country have persuaded many people to take the risk of working in war zones. Yet the many individuals who have been injured while performing such duties now find themselves caught between their insurance companies and the U.S. Department of Labor, as they fight for the workers’ compensation and healthcare coverage they were promised.Journalis