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

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

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

Hybrid Iterative Multiuser Detection for Channel Coded Space Division Multiple Access OFDM Systems

Space division multiple access (SDMA) aided orthogonal frequency division multiplexing (OFDM) systems assisted by efficient multiuser detection (MUD) techniques have recently attracted intensive research interests. The maximum likelihood detection (MLD) arrangement was found to attain the best performance, although this was achieved at the cost of a computational complexity, which increases exponentially both with the number of users and with the number of bits per symbol transmitted by higher order modulation schemes. By contrast, the minimum mean-square error (MMSE) SDMA-MUD exhibits a lower complexity at the cost of a performance loss. Forward error correction (FEC) schemes such as, for example, turbo trellis coded modulation (TTCM), may be efficiently combined with SDMA-OFDM systems for the sake of improving the achievable performance. Genetic algorithm (GA) based multiuser detection techniques have been shown to provide a good performance in MUD-aided code division multiple access (CDMA) systems. In this contribution, a GA-aided MMSE MUD is proposed for employment in a TTCM assisted SDMA-OFDM system, which is capable of achieving a similar performance to that attained by its optimum MLD-aided counterpart at a significantly lower complexity, especially at high user loads. Moreover, when the proposed biased Q-function based mutation (BQM) assisted iterative GA (IGA) MUD is employed, the GA-aided system’s performance can be further improved, for example, by reducing the bit error ratio (BER) measured at 3 dB by about five orders of magnitude in comparison to the TTCM assisted MMSE-SDMA-OFDM benchmarker system, while still maintaining modest complexity

Non-contact heat flux measurement using a transparent sensor

A working non-contact heat flux sensor was demonstrated using a transparent material (sapphire) and a multiwavelength pyrometer. The pyrometer is used to measure the temperatures of the two surfaces of the sensor from the spectrum of radiation originating from them. The heat conducted through the material is determined from the temperature difference of the two surfaces and the thermal conductivity of the material. The measured heat flux is equal to the incident heat flux within experimental error indicating that no calibration would be necessary. A steady state heat flux of 100 kW/sq m was easily achieved

Who are the net food importing countries ?

The purpose of this paper is to update the information on net food importing countries, using different definitions of food, separating countries by their level of income, whether they are in conflict and whether they are significant oil exporters. The study also estimates the changes in net food importing status of these countries over the last two and a half decades, and, most important, the study measures the relative importance of these net food imports in the import basket of the countries. Our results show that while many low-income countries are net food importers, the importance and potential impact of the net food importing status has been highly exaggerated. Many low-income countries that have larger food deficits are either oil exporters or countries in conflict. Food deficits of most low-income countries are not that significant as a percentage of their imports. Our results also show that only 6 low-income countries have food deficits that are more than 10 percent of their imports. Last two decades have seen a significant improvement in the food trade balances of low-income developing countries. SSA low-income countries are an exception to this trend. On the other hand, there are a group of countries which are experiencing civil conflicts which are large importers of food, and these countries can not meet their basic needs. They also need special assistance in the distribution of food within their boundaries. Therefore, one should modify the WTO Ministerial Declaration, and focus on these conflict countries rather than the broad net food importers.Food&Beverage Industry,Emerging Markets,Currencies and Exchange Rates,Economic Theory&Research,

Properties of a magnetic superconductor with weak magnetization - application to ErNi2B2CErNi_2B_2C

Using a Ginsburg-Landau free energy functional, we study the $H-T$ phase diagram of a weak magnetic superconductor, where the magnetization from the magnetic component is marginal in supporting a spontaneous vortex phase in absence of external magnetic field. In particular, the competition between the spiral state and spontaneous vortex phase is analysed. Our theory is applied to understand the magnetic properties of $ErNi_2B_2C$.Comment: 13 pages, 4 postscript figure