Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle

Via a computer search, Altshuler and Steinberg found that there are 1296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold View the MathML source triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.

Low ML Decoding Complexity STBCs via Codes Over the Klein Group

In this paper, we give a new framework for constructing low ML decoding complexity space-time block codes (STBCs) using codes over the Klein group K. Almost all known low ML decoding complexity STBCs can be obtained via this approach. New full- diversity STBCs with low ML decoding complexity and cubic shaping property are constructed, via codes over K, for number of transmit antennas N = 2(m), m >= 1, and rates R > 1 complex symbols per channel use. When R = N, the new STBCs are information- lossless as well. The new class of STBCs have the least knownML decoding complexity among all the codes available in the literature for a large set of (N, R) pairs.

A Kaluza-Klein subtractor

We generalize the results of arXiv : 1212.1875 and arXiv : 1212.6919 on attraction basins and their boundaries to the case of a specific class of rotating black holes,namely the ergo-free branch of extremal black holes in Kaluza-Klein theory. We find that exact solutions that span the attraction basin can be found even in the rotating case by appealing to certain symmetries of the equations of motion. They are characterized by two asymptotic parameters that generalize those of the non-rotating case, and the boundaries of the basin are spinning versions of the (generalized) subtractor geometry. We also give examples to illustrate that the shape of the attraction basin can drastically change depending on the theory.

Revalidation of Natrix clerki Wall, 1925, an overlooked species in the genus Amphiesma Dumeril, Bibron & Dumeril, 1854 (Squamata: Natricidae)

Natrix clerki Wall, 1925, previously known from its sole holotype and considered a synonym of Amphiesma parallelum (Boulenger, 1890), is resurrected in the genus Amphiesma on the basis of the analysis of morphological variation in 28 specimens of ``Amphiesma parallelum'' auctorum, plus six living, unvouchered specimens discovered in Arunachal Pradesh and Nagaland, India, and one vouchered specimen from Talle Valley in Arunachal Pradesh. Specimens from northeast India (Nagaland), northern Myanmar, and China (Yunnan), previously identified as Amphiesma parallelum either in the literature or in museum's catalogues, are also here referred to A. clerki. The holotype of Amphiesma clerki is redescribed. As a consequence, the definition of Amphiesma parallelum is modified. A. parallelum inhabits the Khasi Hills and Naga Hills in Northeast India, whereas A. clerki has a wider range in the Eastern Himalayas, northern Myanmar and Yunnan (China). Amphiesma clerki differs from A. parallelum by its longer tail, dorsal scales more strongly keeled, scales of the first dorsal scale row strongly keeled vs. smooth, a postocular streak not interrupted at the level of the neck, and a much more vivid pattern on a darker background colour. Characters of species of the Amphiesma parallelum group, i.e. A. clerki, A. parallelum, A. bitaeniatum, A. platyceps and A. sieboldii are compared. A key to this group is provided.