3,800 research outputs found

    Ground state sign-changing solutions for critical Choquard equations with steep well potential

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    In this paper, we study sign-changing solution of the Choquard type equation −∆u + (λV(x) + 1) u = Iα ∗ |u| 2 |u| 2 α−2u + µ|u| p−2u in R N, where N ≥ 3, α ∈ ((N − 4) +, N), Iα is a Riesz potential, p ∈ 2 2N N−2 , 2∗ := N+α N−2 is the upper critical exponent in terms of the Hardy–Littlewood–Sobolev inequality, µ > 0, λ > 0, V ∈ C(RN, R) is nonnegative and has a potential well. By combining the variational methods and sign-changing Nehari manifold, we prove the existence and some properties of ground state sign-changing solution for λ, µ large enough. Further, we verify the asymptotic behaviour of ground state sign-changing solutions as λ → +∞ and µ → +∞, respectivel

    Time Crystal in a Single-mode Nonlinear Cavity

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    Time crystal is a class of non-equilibrium phase with broken time-translational symmetry. Here we demonstrate the time crystal in a single-model nonlinear cavity. The time crystal originates from the self-oscillation induced by the linear gain and is stabilized by the nonlinear damping. We show this time crystal model exhibits four different characteristics: the emergence of classical limit cycle under the mean-field approximation, the dissipative gap closing in the thermodynamic limit, the quantum oscillation in the Husimi function, and the emergence of quantum limit cycle in the steady state. These properties provide a complete description of the time crystal and thus pave the way to investigate the time crystal in nonlinear systems

    Experimental Demonstration of an Indoor VLC Positioning System Based on OFDMA

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    We propose an indoor visible light communication (VLC) and positioning system using the orthogonal frequency division multiplexing access (OFDMA) scheme, which can provide both indoor positioning and communications. Three subcarriers with the maximum received signal intensity with respect to three light-emitting diodes (LEDs) are selected for indoor positioning based on the trilateration algorithm. The experiment results show that the proposed system with quadrature phase shift keying (QPSK) mapping offers a mean positioning error and an error vector magnitude of 1.68 cm and more than 15 dB, respectively

    Saliency Detection Gradient Preservation for Bayer Image Color Reconstruction

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    Image color reconstruction is a necessary process to recover high quality full color images from Bayer images. In view of the existence of image texture and edge blurring in color reconstruction algorithms, a four-direction joint gradient weighted residual interpolation algorithm is proposed, which uses four-direction weights obtained from RGB pixel gradients and residual gradients in Bayer images, linearly combined with the color difference estimation to effectively obtain the full G image. Aiming at the color cast phenomenon of the image after color interpolation, a saliency detection gradient-preserving color correction algorithm is proposed based on the RGB image captured under natural light. Firstly, the saliency detection method is used to segment the interpolated image and the RGB image into two regions, then carrying out the region correspondence for gradient-preserving color correction, and finally the weighted fusion method is used to obtain the final color reconstructed image. The experimental results show that the reconstructed image texture and edges are clearer and the colors are closer to RGB images
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