Effect of feedback on the control of a two-level dissipative quantum system

We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the function $\Delta_A(\vec{x})$ and $\Delta_B(\vec{x})$ that characterize the optimal trajectories, as well as the switching function $\Phi(t)$ and $\theta(t),$ which characterize the switching point in time for the time-optimal trajectory.Comment: 5 pages, 5 figure

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

A unique distant submillimeter galaxy with an X-ray-obscured radio-luminous active galactic nucleus

We present a multiwavelength study of an atypical submillimeter galaxy in the GOODS-North field, with the aim to understand its physical properties of stellar and dust emission, as well as the central AGN activity. Although it is shown that the source is likely an extremely dusty galaxy at high redshift, its exact position of submillimeter emission is unknown. With the new NOEMA interferometric imaging, we confirm that the source is a unique dusty galaxy. It has no obvious counterpart in the optical and even NIR images observed with HST at lambda~<1.4um. Photometric-redshift analyses from both stellar and dust SED suggest it to likely be at z~>4, though a lower redshift at z~>3.1 cannot be fully ruled out (at 90% confidence interval). Explaining its unusual optical-to-NIR properties requires an old stellar population (~0.67 Gyr), coexisting with a very dusty ongoing starburst component. The latter is contributing to the FIR emission, with its rest-frame UV and optical light being largely obscured along our line of sight. If the observed fluxes at the rest-frame optical/NIR wavelengths were mainly contributed by old stars, a total stellar mass of ~3.5x10^11Msun would be obtained. An X-ray spectral analysis suggests that this galaxy harbors a heavily obscured AGN with N_H=3.3x10^23 cm^-2 and an intrinsic 2-10 keV luminosity of L_X~2.6x10^44 erg/s, which places this object among distant type 2 quasars. The radio emission of the source is extremely bright, which is an order of magnitude higher than the star-formation-powered emission, making it one of the most distant radio-luminous dusty galaxies. The combined characteristics of the galaxy suggest that the source appears to have been caught in a rare but critical transition stage in the evolution of submillimeter galaxies, where we are witnessing the birth of a young AGN and possibly the earliest stage of its jet formation and feedback.Comment: 13 pages in printer format, 10 figures, 1 table, accepted for publication in the A&

Formal and finite order equivalences

We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent

Joint optimal relay location and power allocation for ultra-wideband-based wireless body area networks

© 2015, Ding et al.; licensee Springer. In this paper, we study the joint optimal relay location and power allocation problem for single-relay-assisted ultra-wideband (UWB)-based wireless body area networks (WBANs). Specifically, to optimize spectral efficiency (SE) for single-relay cooperative communication in UWB-based WBANs, we seek the relay with the optimal location together with the corresponding optimal power allocation. With proposed relay-location-based network models, the SE maximization problems are mathematically formulated by considering three practical scenarios, namely, along-torso scenario, around-torso scenario, and in-body scenario. Taking into account realistic power considerations for each scenario, the optimal relay location and power allocation are jointly derived and analyzed. Numerical results show the necessity of utilization of relay node for the spectral and energy-efficient transmission in UWB-based WBANs and demonstrate the effectiveness of the proposed scheme in particular for the around-torso and in-body scenarios. With the joint optimal relay location and power allocation, the proposed scheme is able to prolong the network lifetime and extend the transmission range in WBANs significantly compared to direct transmission

Optimal spectral efficiency for cooperative UWB based on-body area networks

© 2014 IEEE. In this paper, spectral efficiency (SE) is investigated for cooperative ultra-wideband (UWB) based on-body area networks (OBANs). To optimize SE for single-relay cooperation, an equivalent generic cooperative model in UWB based OBANs is established first. With the proposed model, joint optimal relay location and power allocation for cooperation is then derived to solve the SE maximization problem. Simulation results show that direct transmission is preferable for UWB based OBANs when the transmitter and receiver are located on the same side of the human body. However, the joint optimal cooperative transmission scheme can achieve a significant improvement on SE compared with direct transmission when the transmitter and receiver are located on the different sides of the human body, which indicates that cooperation is more feasible to be applied in this case due to its robustness to the significant path loss

Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

Trace doping of multiple elements enables stable battery cycling of LiCoO2 at 4.6 V

LiCoO2 is a dominant cathode material for lithium-ion (Li-ion) batteries due to its high volumetric energy density, which could potentially be further improved by charging to high voltages. However, practical adoption of high-voltage charging is hindered by LiCoO2’s structural instability at the deeply delithiated state and the associated safety concerns. Here, we achieve stable cycling of LiCoO2 at 4.6 V (versus Li/Li+) through trace Ti–Mg–Al co-doping. Using state-of-the-art synchrotron X-ray imaging and spectroscopic techniques, we report the incorporation of Mg and Al into the LiCoO2 lattice, which inhibits the undesired phase transition at voltages above 4.5 V. We also show that, even in trace amounts, Ti segregates significantly at grain boundaries and on the surface, modifying the microstructure of the particles while stabilizing the surface oxygen at high voltages. These dopants contribute through different mechanisms and synergistically promote the cycle stability of LiCoO2 at 4.6 V