A New Viewpoint to the Discrete Approximation: Discrete Yang-Fourier Transforms of Discrete-time Fractal Signal

It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.Comment: Key words: local fractional calculus, fractal, Yang Fourier transforms, discrete approximation, discrete Yang-Fourier transforms corrected sectio

Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative

This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.Comment: 10 page

The role of the diffusive protons in the gamma-ray emission of supernova remnant RX J1713.7−-3946 --- a two-zone model

RX~J1713.7$-$3946 is a prototype in the $\gamma$-ray-bright supernova remnants (SNRs) and is in continuing debates on its hadronic versus leptonic origin of the $\gamma$-ray emission. We explore the role played by the diffusive relativistic protons that escape from the SNR shock wave in the $\gamma$-ray emission, apart from the high-energy particles' emission from the inside of the SNR. In the scenario that the SNR shock propagates in a clumpy molecular cavity, we consider that the$\gamma$-ray emission from the inside of the SNR may arise either from the inverse Compton scattering or from the interaction between the trapped energetic protons and the shocked clumps. The dominant origin between them depends on the electron-to-proton number ratio. The diffusive protons that escaped from the shock wave during the expansion history can provide an outer hadronic $\gamma$-ray component by bombarding the surrounding dense matter. The broadband spectrum can be well explained by this two-zone model, in which the $\gamma$-ray emission from the inside governs the TeV band, while the outer emission component substantially contributes to the GeV $\gamma$-rays. The two-zone model can also explain the TeV $\gamma$-ray radial brightness profile that significantly stretches beyond the nonthermal X-ray-emitting region. In the calculation, we present a simplified algorithm for Li & Chen's (2010) "accumulative diffusion" model for escaping protons and apply the Markov Chain Monte Carlo method to constrain the physical parameters.Comment: 18 pages (including 3 figures and 2 tables), accepted for publication in Ap

Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole

We identify the quantum metric dipole as the geometric origin of the nonreciprocal directional dichroism which describes the change in the refractive index upon reversing the light propagation direction. Specifically, we find that the static limit of the nonreciprocal directional dichroism corresponds to a quadrupolar transport current from the quantum metric dipole, in response to a quadrupolar electric field. Moreover, at finite frequency, we demonstrate that the steepest slope of the averaged quantum metric dipole determines a peak. Finally, we illustrate both features in a low-energy model

m-Order Time Optimal Control Synthesis Function of Discrete System

In this paper, first of all, we introduce the basic concepts of generating function in combinatorics and some combinatorial identities. In order to facilitate the understanding of m-order time optimal control synthesis function of discrete system (referred as m-order synthesis function), secondly, we introduce the derivation process and control ideas of 2nd-order synthesis function, and then deduce in detail the m-order synthesis function by means of generating function. By use of the m-order tracking-form synthesis function with filter factor, the methods of signal extraction and its predictive compensation are presented in this paper, and their immunity and effectiveness are verified by numerical simulation.Comment: 22 pages,13 figures. arXiv admin note: substantial text overlap with arXiv:1806.0310

Effects of Pressure on the Electronic Structures of LaOFeP

We studied the electronic structures of LaOFeP under applied pressure using first-principles calculations. The electronic density of states at the Fermi level decreases continuously with increasing pressure. The electron branches of Fermi surfaces are rather robust to pressure, while the hole branches change significantly. Two hole surfaces shrink into small ellipsoid-like surfaces and disappear finally, at which the applied pressure is ~ 74.7 GPa. The pressure response can be understood by the band structures around the Fermi level. Comparative studies reveal that the disappearance of hole surfaces is mainly due to the compression of the FeP layer along the c-axis of unit cell.Comment: 26 pages, 9 figure

Singular perturbations with multiple poles of the simple polynomials

In this article, we study the dynamics of the following family of rational maps with one parameter: \begin{equation*} f_\lambda(z)= z^n+\frac{\lambda^2}{z^n-\lambda}, \end{equation*} where $n\geq 3$ and $\lambda\in\mathbb{C}^*$. This family of rational maps can be viewed as a singular perturbations of the simple polynomial $P_n(z)=z^n$. We give a characterization of the topological properties of the Julia sets of the family $f_\lambda$ according to the dynamical behaviors of the orbits of the free critical points.Comment: 15 pages, 5 figures, to appear in Qualitative Theory of Dynamical System

Electromagnetically Induced Entanglement

We present a novel quantum phenomenon named electromagnetically induced entanglement in the conventional Lambda-type three-level atomic system driven by a strong pump field and a relatively weak probe field. Nearly perfect entanglement between the pump and probe fields can be achieved with a low coherence decay rate between the two lower levels, high pump-field intensity, and large optical depth of the atomic ensemble. The physical origin is quantum coherence between the lower doublet produced by the pump and probe fields, similar to the well-known electromagnetically induced transparency. This method would greatly facilitate the generation of nondegenerate narrow-band continuous-variable entanglement between bright light beams by using only coherent laser fields, and may find potential and broad applications in realistic quantum information processing.Comment: 15pages, 4figure

Performance Analysis of Millimeter-Wave Relaying: Impacts of Beamwidth and Self-Interference

We study the maximum achievable rate of a two-hop amplified-and-forward (AF) relaying millimeter-wave (mm-wave) system, where two AF relaying schemes, i.e., half-duplex (HD) and full-duplex (FD) are discussed. By considering the two-ray mm-wave channel and the Gaussian-type directional antenna, jointly, the impacts of the beamwidth and the self-interference coefficient on maximum achievable rates are investigated. Results show that, under a sum-power constraint, the rate of FD-AF mm-wave relaying outperforms its HD counterpart only when antennas with narrower beamwidth and smaller self-interference coefficient are applied. However, when the sum-power budget is sufficiently high or the beamwidth of directional antenna is sufficiently small, direct transmission becomes the best strategy, rather than the AF relaying schemes. For both relaying schemes, we show that the rates of both AF relaying schemes scale as $\mathcal{O}\left(\min\left\lbrace\theta_m^{-1},\theta_m^{-2}\right\rbrace\right)$ with respect to beamwidth $\theta_ m$, and the rate of FD-AF relaying scales as $\mathcal{O}\left(\mu^{-\frac{1}{2}}\right)$ with respect to self-interference coefficient $\mu$. Besides, we show that, ground reflections may significantly affect the performance of mm-wave communications, constructively or destructively. Thus, the impact of ground reflections deserves careful considerations for analyzing or designing future mm-wave wireless networks.Comment: Accepted by IEEE Transactions on Communication

Note on the super inflation in loop quantum cosmology

Phenomenological effect of the super-inflation in loop quantum cosmology (LQC) is discussed. We investigate the case that the Universe is filled with the interacting field between massive scalar field and radiation. Considering the damping coefficient $\Gamma$ as a constant, the changes of the scale factor during super-inflation with four different initial conditions are discussed, and we find that the changes of the scale factor depends on the initial values of energy density of the scalar field and radiation at the bounce point. But no matter which initial condition is chosen, the radiation always dominated at the late time. Moreover, we investigate whether the super-inflation can provide enough e-folding number. For the super-inflation starts from the quantum bounce point, the initial value of Hubble parameter $H(t_i)\sim0$, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of \cite{Amoros-prd} to calculate particle horizon on the condition that the radiation dominated at bounce point, and we find that the Universe has had enough time to be homogeneous and isotopic.Comment: 9 pages, 4 figures. Physics Letters B, online publication complete: 13-NOV-201