On the powerful values of polynomials over number fields

In this paper, assuming a conjecture of Vojta on the bounded degree algebraic numbers on a number field $k$, we determine explicit lower and upper bounds for the cardinal number of the set of polynomials $f\in k[x]$ with degree $r\geq 2$ whose irreducible factors have multiplicity strictly less than $s$ and the values $f(b_1),\cdots, f(b_M)$ are $s$-powerful elements in $k^*$ for a certain positive integer $M$, where $b_i$'s belong to an arbitrary sequence of the pairwise distinct element of $k$ that satisfy certain conditions

Neutrino flavor instabilities in a time-dependent supernova model

A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial) spherical symmetry about the center of the supernova and the (directional) axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this paper we analyze the neutrino flavor instabilities in a time-dependent supernova model. Our results show that collective neutrino oscillations start at approximately the same radius in both the stationary and time-dependent supernova models unless there exist very rapid variations in local physical conditions on timescales of a few microseconds or shorter. Our results also suggest that collective neutrino oscillations can vary rapidly with time in the regimes where they do occur which need to be studied in time-dependent supernova models.Comment: 5 pages, 2 figures, version to appear in PL

On Optimal Turbo Decoding of Wideband MIMO-OFDM Systems Under Imperfect Channel State Information

We consider the decoding of bit interleaved coded modulation (BICM) applied to both multiband and MIMO OFDM systems for typical scenarios where only a noisy (possibly very bad) estimate of the channel is provided by sending a limited number of pilot symbols. First, by using a Bayesian framework involving the channel a posteriori density, we adopt a practical decoding metric that is robust to the presence of channel estimation errors. Then this metric is used in the demapping part of BICM multiband and MIMO OFDM receivers. We also compare our results with the performance of a mismatched decoder that replaces the channel by its estimate in the decoding metric. Numerical results over both realistic UWB and theoretical Rayleigh fading channels show that the proposed method provides significant gain in terms of bit error rate compared to the classical mismatched detector, without introducing any additional complexity