On the CR transversality of holomorphic maps into hyperquadrics

Let $M_\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\ell$ in $\mathbf C^n$ with $n\ge 3$, and write $H_\ell^N$ for the standard hyperquadric of the same signature in $\mathbf C^N$ with $N-n< \frac{n-1}{2}$. Let $F$ be a holomorphic map sending $M_\ell$ into $H_\ell^N$. Assume $F$ does not send a neighborhood of $M_\ell$ in $\mathbf C^n$ into $H_\ell^N$. We show that $F$ is necessarily CR transversal to $M_\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\ell$ into $H_\ell^N$.Comment: To appear in Abel Symposia, dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthda

A Two-Component Explosion Model for the Giant Flare and Radio Afterglow from SGR1806-20

The brightest giant flare from the soft $\gamma$-ray repeater (SGR) 1806-20 was detected on 2004 December 27. The isotropic-equivalent energy release of this burst is at least one order of magnitude more energetic than those of the two other SGR giant flares. Starting from about one week after the burst, a very bright ($\sim 80$ mJy), fading radio afterglow was detected. Follow-up observations revealed the multi-frequency light curves of the afterglow and the temporal evolution of the source size. Here we show that these observations can be understood in a two-component explosion model. In this model, one component is a relativistic collimated outflow responsible for the initial giant flare and the early afterglow, and another component is a subrelativistic wider outflow responsible for the late afterglow. We also discuss triggering mechanisms of these two components within the framework of the magnetar model.Comment: 7 pages including 3 figures, emulateapj5.sty, accepted for publication in ApJ Letter

Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE

Optical Flashes and Very Early Afterglows in Wind Environments

The interaction of a relativistic fireball with its ambient medium is described through two shocks: a reverse shock that propagates into the fireball, and a forward shock that propagates into the medium. The observed optical flash of GRB 990123 has been considered to be the emission from such a reverse shock. The observational properties of afterglows suggest that the progenitors of some GRBs may be massive stars and their surrounding media may be stellar winds. We here study very early afterglows from the reverse and forward shocks in winds. An optical flash mainly arises from the relativistic reverse shock while a radio flare is produced by the forward shock. The peak flux densities of optical flashes are larger than 1 Jy for typical parameters, if we do not take into account some appropriate dust obscuration along the line of sight. The radio flare always has a long lasting constant flux, which will not be covered up by interstellar scintillation. The non-detections of optical flashes brighter than about 9th magnitude may constrain the GRBs isotropic energies to be no more than a few $10^{52}$ ergs and wind intensities to be relatively weak.Comment: 21 pages, 6 figures, accepted by MNRAS on March 7, 200

A low-bandgap dimeric porphyrin molecule for 10% efficiency solar cells with small photon energy loss

Dimeric porphyrin molecules have great potential as donor materials for high performance bulk heterojunction organic solar cells (OSCs). Recently reported dimeric porphyrins bridged by ethynylenes showed power conversion efficiencies (PCEs) of more than 8%. In this study, we design and synthesize a new conjugated dimeric D-A porphyrin ZnP2BT-RH, in which the two porphyrin units are linked by an electron accepting benzothiadiazole (BT) unit. The introduction of the BT unit enhances the electron delocalization, resulting in a lower highest occupied molecular orbital (HOMO) energy level and an increased molar extinction coefficient in the near-infrared (NIR) region. The bulk heterojunction solar cells with ZnP2BT-RH as the donor material exhibit a high PCE of up to 10% with a low energy loss (Eloss) of only 0.56 eV. The 10% PCE is the highest for porphyrin-based OSCs with a conventional structure, and this Eloss is also the smallest among those reported for small molecule-based OSCs with a PCE higher than 10% to date

Signature of a spin-up magnetar from multi-band afterglow rebrightening of GRB 100814A

In recent years, more and more gamma-ray bursts with late rebrightenings in multi-band afterglows unveil the late-time activities of the central engines. GRB 100814A is a special one among the well-sampled events, with complex temporal and spectral evolution. The single power-law shallow decay index of the optical light curve observed by GROND between 640 s and 10 ks is $\alpha_{\rm opt} = 0.57 \pm 0.02$, which apparently conflicts with the simple external shock model expectation. Especially, there is a remarkable rebrightening in the optical to near infrared bands at late time, challenging the external shock model with synchrotron emission coming from the interaction of the blast wave with the surrounding interstellar medium. In this paper, we invoke a magnetar with spin evolution to explain the complex multi-band afterglow emission of GRB 100814A. The initial shallow decay phase in optical bands and the plateau in X-ray can be explained as due to energy injection from a spin-down magnetar. At late time, with the falling of materials from the fall-back disk onto the central object of the burster, angular momentum of the accreted materials is transferred to the magnetar, which leads to a spin-up process. As a result, the magnetic dipole radiation luminosity will increase, resulting in the significant rebrightening of the optical afterglow. It is shown that the observed multi-band afterglow emission can be well reproduced by the model.Comment: 14 pages, 2 figures, accepted by The Astrophysical Journa

CRLBs for Pilot-Aided Channel Estimation in OFDM System under Gaussian and Non-Gaussian Mixed Noise

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of channel estimation in wireless communication is a very important issue. Several CRLBs on channel estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic and stochastic CRLBs for Gaussian and non-Gaussian mixed noise. Due to the use of the non-parametric kernel method to build the PDF of non-Gaussian noise, the proposed CRLBs are suitable for practical channel environments with various noise distributions