Bounds for the perimeter of an ellipse

In this paper, we present several bounds for the perimeter of an ellipse, which improve some well-known results.     

The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems

The coexistence of quasi-periodic solutions and blow-up phenomena in a class of higher dimensional Duffing-type equations is proved in this paper. Moreover, we show that the initial point sets for both kinds of solutions are of infinite Lebesgue measure in the phase space. For the part of quasi-periodic solutions, the tool we used is the small twist theorem for higher dimensional cases.     

Symplectic flow for the square root of the negative Laplacian

The paper is concerned with symplectic flow for the square root of the negative Laplacian, which is motivated when studying a one-dimensional model about ferromagnetic thin film without Gilbert damping term (only Gyromagnetic term remained) derived from the stationary model of A. DeSimone, R.V. Kohn, S. Müller and F. Otto. Existence of weak solution to the model is proved by viscosity approximation and commutator estimate.     

Quantum wells micro-ring resonator laser emitting at 1746 nm for gas sensing

Gas sensing for measurement of gas components, concentrations, and other parameters plays an important role in many fields. In this Letter, a micro-ring resonator laser used for gas sensing is experimentally demonstrated. The multi-quantumwells micro-ring laser based on whispering-gallery modes with an annular resonator and an output waveguide was fabricated. A single-mode laser with a wavelength of 1746.4 nm was fabricated for the first time, to the best of our knowledge,experimentally. The output power of 1.65 m W under 40 m A injection current was obtained with a side-mode suppression ratio over 33 d B.     

Double-slit diffraction of terahertz wave generated by tilted-pulse-front pumping

We propose a spatial diffraction diagnostic method via inserting a millimeter-gap double slit into the collimated terahertz beam to monitor the minute variation of the terahertz beam in strong-field terahertz sources, which is difficult to be resolved in conventional terahertz imaging systems. To verify the method, we intentionally fabricate tiny variations of the terahertz beam through tuning the iris for the infrared pumping beam before the tilted-pulse-front pumping setups.The phenomena can be well explained by the theory based on the tilted-pulse-front technique and terahertz diffraction.     

All-silicon chiral metasurfaces and wavefront shaping assisted by interference

The usage of full-color imaging in digital pathology produces significant results. Compared with a grayscale image or a pseudocolor image containing contrast information, a full-color image can identify and detect the target object better with color texture information. Fourier ptychographic microscopy(FPM) is a high-throughput computational imaging technique that breaks the tradeoff between high resolution(HR) and a large field of view. It also eliminates the artifacts of scanning and stitching in digital pathology and improves its imaging efficiency. However, the conventional full-color digital pathology based on FPM is still time-consuming because of the repeated experiments with tri-wavelengths. A color transfer FPM approach termed "CFPM" was reported. The color texture information of a low-resolution full-color pathologic image is directly transferred to the HR grayscale FPM image captured by only a single wavelength. Both of the color space of FPM based on the standard CIE-XYZ color model and the display based on the standard RGB color space were established. Different FPM colorization schemes were analyzed and compared with 30 biological samples. Three types of evaluation approaches were provided, including the root-mean-square error(RMSE), the difference maps, and the image histogram cosine similarity. The average RMSE values of the conventional method and CFPM compared with the ground truth were 5.3% and 5.7%, respectively. Therefore, the reconstruction time is significantly reduced by 2/3 with the sacrifice of precision of only 0.4%. The CFPM method is also compatible with advanced fast FPM approaches to further reduce computation time.     

Speeding up generation of photon Fock state in a superconducting circuit via counterdiabatic driving

Optimal creation of photon Fock states is of importance for quantum information processing and state engineering.Here an efficient strategy is presented for speeding up generation of photon Fock state in a superconducting circuit via counterdiabatic driving.A transmon qubit is dispersively coupled to a quantized electrical field.We address a ∧-configuration interaction between the composite system and classical drivings.Based on two Gaussian-shaped drivings,a single-photon Fock state can be generated adiabatically.Instead of adding an auxiliary counterdiabatic driving,our concern is to modify these two Rabi drivings in the framework of shortcut to adiabaticity.Thus an accelerated operation with high efficiency can be realized in a much shorter time.Compared with the adiabatic counterpart,the shortcut-based operation is significantly insusceptible to decoherence effects.The scheme could offer a promising way to deterministically prepare photon Fock states with superconducting quantum circuits.     

X-ray absorption investigation of the site occupancies of the copper element in nominal Cu_3Zn(OH)_6FBr

With Zn substitution to the three-dimensional antiferromagnetically ordered barlowite Cu_4(OH)_6 FBr,Cu_3 Zn(OH)_6 FBr shows no magnetic phase transition down to 50 mK,and the system is suggested to be a two-dimensional kagome quantum spin liquid [Chin.Phys.Lett.34 077502(2017)].A key issue to identify such phase diagram is the exact chemical formula of the substituted compound.With Cu L-edge x-ray absorption spectrum(XAS) combined with the MultiX XAS calculations,we evaluate the Cu concentration in a nominal Cu_3 Zn(OH)_6 FBr sample.Our results show that although the Cu concentration is 2.80,close to the expected value,there is 34% residual Cu occupation in intersite layers between kagome layers.Thus the Zn substitution of the intersite layers is not complete,and likely it intrudes the kagome layers.     

Nonexistence of axially symmetric,stationary solution of Einstein Vacuum Equation with disconnected symmetric event horizon

In this short note, we prove that if an axially symmetric, asymptotically flat, stationary solution of the Einstein Vacuum Equation admits an involution interchanging the components of the event horizons, then the force between at least two of the event horizons must be positive. The proof is based on an observation that in this case the force can be expressed as a line integral with positive integrand.