Vanishing theorems on complete Riemannian manifold with a parallel 11-form

In this article, we first consider the $L^{2}$ \textit{Morse-Novikov cohomology} on a complete Riemannian manifold $M$ equipped with a parallel $1$-form which includes Vaisman manifold. Based on a vanishing theorem of $L^{2}$ \textit{Morse-Novikov cohomology}, we prove that the $L^{2}$-harmonic forms on $M$ are identically zero.Comment: 13 pages; to appear in Mathematische Nachrichte

Phase-isometries on real normed spaces

We say that a mapping $f: X \rightarrow Y$ between two real normed spaces is a phase-isometry if it satisfies the functional equation \begin{eqnarray*} \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \quad (x,y\in X).\end{eqnarray*} A generalized Mazur-Ulam question is whether every surjective phase-isometry is a multiplication of a linear isometry and a map with range $\{-1, 1\}$. This assertion is also an extension of a fundamental statement in the mathematical description of quantum mechanics, Wigner's theorem to real normed spaces. In this paper, we show that for every space $Y$ the problem is solved in positive way if $X$ is a smooth normed space, an $\mathcal{L}^{\infty}(\Gamma)$-type space or an $\ell^1(\Gamma)$-space with $\Gamma$ being an index set.Comment: 16page

Analytical approach on linear and nonlinear pulse propagations in an open Lambda-type molecular system with Doppler broadening

We develop a systematic analytical approach on linear and nonlinear pulse propagations in an open Lambda-type molecular system with Doppler broadening. In linear case, by using residue theorem and a spectrum decomposition method, we prove that there exists a crossover from electromagnetically induced transparency (EIT) to Autler-Townes splitting (ATS) for co-propagating configuration of probe and control fields. However, there is no EIT and hence no EIT-ATS crossover for counter-propagating configuration. We give various explicit formulas, including probe-field spectrum decomposition, EIT condition, width of EIT transparency window, as well as a comparison with the result of cold molecules. Our analytical result agrees well with the experimental one reported recently by A. Lazoudis et al. [Phys. Rev.A82, 023812 (2010)]. In nonlinear case, by using the method of multiple-scales, we derive a nonlinear envelope equation for probe-field propagation. We show that stable ultraslow solitons can be realized in the open molecular system.Comment: 20 pages, 9 figure

Adaptive Power System Emergency Control using Deep Reinforcement Learning

Power system emergency control is generally regarded as the last safety net for grid security and resiliency. Existing emergency control schemes are usually designed off-line based on either the conceived "worst" case scenario or a few typical operation scenarios. These schemes are facing significant adaptiveness and robustness issues as increasing uncertainties and variations occur in modern electrical grids. To address these challenges, for the first time, this paper developed novel adaptive emergency control schemes using deep reinforcement learning (DRL), by leveraging the high-dimensional feature extraction and non-linear generalization capabilities of DRL for complex power systems. Furthermore, an open-source platform named RLGC has been designed for the first time to assist the development and benchmarking of DRL algorithms for power system control. Details of the platform and DRL-based emergency control schemes for generator dynamic braking and under-voltage load shedding are presented. Extensive case studies performed in both two-area four-machine system and IEEE 39-Bus system have demonstrated the excellent performance and robustness of the proposed schemes.Comment: 12 page

Translation-Invariant Representation for Cumulative Foot Pressure Images

Human can be distinguished by different limb movements and unique ground reaction force. Cumulative foot pressure image is a 2-D cumulative ground reaction force during one gait cycle. Although it contains pressure spatial distribution information and pressure temporal distribution information, it suffers from several problems including different shoes and noise, when putting it into practice as a new biometric for pedestrian identification. In this paper, we propose a hierarchical translation-invariant representation for cumulative foot pressure images, inspired by the success of Convolutional deep belief network for digital classification. Key contribution in our approach is discriminative hierarchical sparse coding scheme which helps to learn useful discriminative high-level visual features. Based on the feature representation of cumulative foot pressure images, we develop a pedestrian recognition system which is invariant to three different shoes and slight local shape change. Experiments are conducted on a proposed open dataset that contains more than 2800 cumulative foot pressure images from 118 subjects. Evaluations suggest the effectiveness of the proposed method and the potential of cumulative foot pressure images as a biometric.Comment: 6 page

Generalized-Lush Spaces and the Mazur-Ulam Property

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable $C$-rich subspaces of $C(K)$), and even the two-dimensional space with hexagonal norm. We obtain that the space $C(K,E)$ of the vector-valued continuous functions is a GL-space whenever $E$ is, and show that the GL-space is stable under $c_0$-, $l_1$- and $l_\infty$-sums. As an application, we prove that the Mazur-Ulam property holds for a larger class of Banach spaces, called local-GL-spaces, including all lush spaces and GL-spaces. Furthermore, we generalize the stability properties of GL-spaces to local-GL-spaces. From this, we can obtain many examples of Banach spaces having the Mazur-Ulam property.Comment: 16 page

Lossless Airy Surface Polaritons in a Metamaterial via Active Raman Gain

We propose a scheme to realize a lossless propagation of linear and nonlinear Airy surface polaritons (SPs) via active Raman gain (ARG). The system we suggest is a planar interface superposed by a negative index metamaterial (NIMM) and a dielectric, where three-level quantum emitters are doped. By using the ARG from the quantum emitters and the destructive interference effect between the electric and magnetic responses from the NIMM, we show that not only the Ohmic loss of the NIMM but also the light absorption of the quantum emitters can be completely eliminated. As a result, non-diffractive Airy SPs may propagate for very long distance without attenuation. We also show that the Kerr nonlinearity of the system can be largely enhanced due to the introduction of the quantum emitters and hence lossless Airy surface polaritonic solitons with very low power can be generated in the system

Global existence and large time behavior for the system of compressible adiabatic flow through porous media in R3\mathbb{R}^{3}

The system of compressible adiabatic flow through porous media is considered in $\mathbb{R}^{3}$ in the present paper. The global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium. We also show that the pressure of the system converges to its equilibrium state at the same $L^2$-rate $(1+t)^{-3/4}$ as the Navier-Stokes equations without heat conductivity, but the velocity of the system decays at the $L^2$-rate $(1+t)^{-5/4}$, which is faster than the $L^2$-rate $(1+t)^{-3/4}$ for the Navier-Stokes equations without heat conductivity [3]

Crossover from Electromagnetically Induced Transparency to Autler-Townes Splitting in Open V-Type Molecular Systems

We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting(ATS) in an open V-type molecular system. Through detailed analytical calculations on the absorption spectrum of probe laser field by using residue theorem and spectrum decomposition, we find that EIT may occur and there exists a crossover from EIT to ATS (i.e. EIT-ATS crossover) for hot molecules. However, there is no EIT and hence no EIT-ATS crossover for cold molecules. Furthermore, we prove that for hot molecules EIT is allowed even for a counter-propagating configuration. We provide explicit formulas of EIT conditions and widths of EIT transparency windows of probe field when hot molecules work in co-propagating and counter-propagating configurations, respectively. Our theoretical result agrees well with the recent experimental one reported by Lazoudis et al. [Phys. Rev. A 83, 063419 (2011)].Comment: 26 pages, 8 figures. arXiv admin note: text overlap with arXiv:1212.565

Theoretical analysis on quantum interference effect in fast-light media

We make a systematic theoretical analysis on the quantum interference (QI) effects in various fast-light media (including gain-assisted $N$, gain-assisted ladder-I, and gain-assisted ladder-II atomic systems). We show that such fast-light media are capable of not only completely eliminating the absorption but also suppressing the gain of signal field, and hence provide the possibility to realize a stable propagation of the signal field with a superluminal velocity. We find that there is a destructive (constructive) QI effect in gain-assisted ladder-I (gain-assisted N) system, but no QI in the gain-assisted ladder-II system; furthermore, a crossover from destructive (constructive) QI to Autler-Townes splitting may occur for the gain-assisted ladder-I (gain-assisted N) system when the control field of the system is modulated. Our theoretical analysis can be applied to other multi-level systems, and the results obtained may have promising applications in optical and quantum information processing and transmission