Jensen's functional equation on the symmetric group Sn\bold{S_n}

Two natural extensions of Jensen's functional equation on the real line are the equations $f(xy)+f(xy^{-1}) = 2f(x)$ and $f(xy)+f(y^{-1}x) = 2f(x)$, where $f$ is a map from a multiplicative group $G$ into an abelian additive group $H$. In a series of papers \cite{Ng1}, \cite{Ng2}, \cite{Ng3}, C. T. Ng has solved these functional equations for the case where $G$ is a free group and the linear group $GL_n(R)$, R=\z,\r, a quadratically closed field or a finite field. He has also mentioned, without detailed proof, in the above papers and in \cite{Ng4} that when $G$ is the symmetric group $S_n$ the group of all solutions of these functional equations coincides with the group of all homomorphisms from $(S_n,\cdot)$ to $(H,+)$. The aim of this paper is to give an elementary and direct proof of this fact.Comment: 8 pages, Abstract changed, the proof of Proposition 2.1 and Lemma 2.4 changed (minor), one reference added, final version, to be published in Aequationes Mathematicae (2011

Field #3 of the Palomar-Groningen Survey I. Variable stars at the edge of the Sagittarius dwarf galaxy

A catalogue is presented with variable (RR Lyrae, semiregular and Mira) stars located inside field #3 of the Palomar-Groningen Survey, at the outer edge of the Sagittarius dwarf galaxy. One of the semiregular variables is a carbon star, comparable with those found by Azzopardi et al. (1991). Serendipity provides the suggestion, that their carbon stars might not be located inside, but behind the bulge in the Sagittarius dwarf galaxy.Comment: 3 pages TeX with 3 postscript figures. Table 1 and the finding charts are available on request. Accepted for publication in A&A Supplement Serie

High Magnetic Field Rotation-powered Pulsars

Anomalous X-ray pulsars and soft gamma repeaters have recently emerged as a unified class of neutron stars, identified by dramatic X-ray and gamma-ray outbursts and via luminous X-ray pulsations, both thought to be powered by the decay of an enormous internal magnetic field. This "magnetar" hypothesis has raised the question of these objects' physical relationship with conventional rotation-powered pulsars (RPPs). The highest magnetic-field RPPs might therefore be expected to be transition objects between the two populations. The recently reported magnetar-like outburst of PSR J1846-0258, previously thought to be purely rotation-powered, clearly supports this suggestion. Here we review the observational properties of the highest magnetic-field RPPs known, and show some common characteristics that are notable among RPPs, which are plausibly related to their high fields. Using these objects, we consider the evidence for proposed "magneto-thermal evolution" in neutron stars, and argue that while some exists, it is not yet conclusive.Comment: 6 pages, 4 figures, Conference proceeding of "ASTROphysics of Neutron Stars 2010 -- a conference in honor of M. Ali Alpar", 2-6 August 2010, Cesme, Izmir, Turke

Slow subcarrier-hopped Space Division Multiple Access OFDM systems

Recently Space Division Multiple Access (SDMA) assisted Multi-Input-Multi-Output (MIMO) OFDM systems invoking Multi-User Detection (MUD) techniques have attracted substantial research interests, which are capable of exploiting both transmitter multiplexing gain and receiver diversity gain. Furthermore, the classic Frequency-Hopping (FH) technique can be effectively amalgamated with SDMA-OFDM systems, resulting in Frequency-Hopped (FH) SDMA-OFDM. In this paper we devise a Turbo Trellis Coded Modulation (TTCM) assisted subcarrier-based FH/SDMA-OFDM scheme, which may be able to fully exploit the attainable frequency diversity, while exhibiting a high Multi-User-Interference (MUI) resistance. In the high-throughput scenario investigated, the proposed Uniform Slow-SubCarrier-Hopped (USSCH) SDMA-OFDM system was capable of achieving 6dB Eb=N0 gain at the BER of 10¡4 over the conventional SDMA-OFDM system, while maintaining a similar complexity

The correspondence between augmentations and rulings for Legendrian knots

We strengthen the link between holomorphic and generating-function invariants of Legendrian knots by establishing a formula relating the number of augmentations of a knot's contact homology to the complete ruling invariant of Chekanov and Pushkar.Comment: v2: 10 pages, 3 figures; minor revisions, to appear in Pacific J. Mat

A note on the gaps between consecutive zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.Comment: 7 pages. Submitted for publicatio

TCM, TTCM, BICM and BICM-ID Assisted MMSE Multi-User Detected SDMA-OFDM Using Walsh-Hadamard Spreading

Space Division Multiple Access (SDMA) aided Orthogonal Frequency Division Multiplexing (OFDM) systems assisted by efficient Multi-User Detection (MUD) techniques have recently attracted intensive research interests. Forward Error Correction (FEC) schemes and frequency-domain spreading techniques can be efficiently amalgamated with SDMA-OFDM systems for the sake of improving the achievable performance. In this contribution a Coded Modulation (CM) assisted and Minimum Mean-Square Error (MMSE) multi-user detected SDMA-OFDM system combined with Walsh-Hadamard-Transform-Spreading (WHTS) across a number of subcarriers is proposed. The various CM schemes used are Trellis Coded Modulation (TCM), Turbo TCM (TTCM), Bit-Interleaved Coded Modulation (BICM) and Iteratively Decoded BICM (BICM-ID), which constitute bandwidth efficient schemes that combine the functions of coding and modulation. Invoking the WHTS technique is capable of further improving the average Bit Error Rate (BER) performance of the CM-SDMA-OFDM system, since the bursty error effects imposed by the frequency-domain fading encountered are spread over the entire WHT block length, therefore increasing the chances of correcting the transmission errors by the CM decoders