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<jats:p>Doppler asymmetric spatial heterodyne spectroscopy (DASH) technique has developed rapidly in passive Doppler-shift measurements of atmospheric emission lines over the last decade. With the advantages of high phase shift sensitivity, compact, and rugged structure, DASH is proposed to be used for celestial autonomous navigation based on Doppler radial velocity measurement in this work. Unlike atmospheric emission lines, almost all targeted lines in the research field of deep-space exploration are the absorption lines of stars, so a mathematical model for the Doppler-shift measurements of absorption lines with a DASH interferometer is established. According to the analysis of the components of the interferogram received by the detector array, we find that the interferogram generated only by absorption lines in a passband can be extracted and processed by a method similar to the approach to studying the emission lines. In the end, numerical simulation experiments of Doppler-shift measurements of absorption lines are carried out. The simulation results show that the relative errors of the retrieved speeds are less than 0.7% under ideal conditions, proving the feasibility of measuring Doppler shifts of absorption lines by DASH instruments.</jats:p>

<jats:p>The measurement of the confocal volume of a confocal three-dimensional micro-x-ray fluorescence (3D-XRF) setup is a key step in the field of confocal 3D-XRF analysis. With the development of x-ray facilities and optical devices, 3D-XRF analysis with a micro confocal volume will create a great potential for 2D and 3D microstructural analysis and accurate quantitative analysis. However, the classic measurement method of scanning metal foils of a certain thickness leads to inaccuracy. A method for calibrating the confocal volume is proposed in this paper. The new method is based on the basic content of the textbook, and the theoretical results and the feasibility are given in detail for the 3D-XRF mono-chromatic x-ray condition and the poly-chromatic x-ray condition. We obtain a set of experimental confirmation using the poly-chromatic x-ray tube in the laboratory. It is proved that the sensitivity factor of the 3D-XRF can be directly and accurately obtained in a real calibration process.</jats:p>

<jats:p>This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order Cohen–Grossberg neural networks (FOCGNNs) with time delays. Based on Brouwer’s fixed point theorem, sufficient conditions are established to ensure the existence of <jats:inline-formula> <jats:tex-math> <?CDATA $\prod _{i=1}^{n}(2{K}_{i}+1)$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:munderover> <mml:mo>∏</mml:mo> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>n</mml:mi> </mml:munderover> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_020703_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> equilibrium points for FOCGNNs. Through the use of Hardy inequality, fractional Halanay inequality, and Lyapunov theory, some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of <jats:inline-formula> <jats:tex-math> <?CDATA $\prod _{i=1}^{n}({K}_{i}+1)$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:munderover> <mml:mo>∏</mml:mo> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>n</mml:mi> </mml:munderover> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_020703_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> equilibrium points for FOCGNNs. The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases. The activation functions are nonlinear and nonmonotonic. There could be many corner points in this general class of activation functions. The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points. Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained results.</jats:p>

<jats:p>The <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{3}{\Sigma }_{{\rm{g}}}^{-}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">X</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">g</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_023101_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, A′<jats:sup>3</jats:sup>Δ<jats:sub>u</jats:sub>, <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{A}}}^{3}{\Sigma }_{{\rm{u}}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">A</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">u</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_023101_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, 1<jats:sup>3</jats:sup>Π<jats:sub>g</jats:sub>, and <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{B}}}^{3}{\Sigma }_{{\rm{u}}}^{-}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">B</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">u</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_023101_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> electronic states of oxygen molecule (O<jats:sub>2</jats:sub>) are calculated by the multi-configuration self-consisted filed (MRCI) + Q method with the scalar relativistic correction and core–valence correlation correction. The obtained spectroscopic constants of the low-lying bound states are in excellent agreement with measurements. Based on the accurately calculated structure parameters, the opacities of the oxygen molecule at the temperatures of 1000 K, 2000 K, 2500 K, and 5000 K under a pressure of 100 atm (1 atm = 1.01325 × 10<jats:sup>5</jats:sup> Pa) and the partition functions between 10 K and 10<jats:sup>4</jats:sup> K are obtained. It is found that with the increase of temperature, the opacities for transitions in a long wavelength range are enlarged because of the larger population on excited electronic states at the higher temperatures.</jats:p>

<jats:p>Searching for two-dimensional (2D) stable materials with direct band gap and high carrier mobility has attracted great attention for their electronic device applications. Using the first principles calculations and particle swarm optimization (PSO) method, we predict a new 2D stable material (HfN<jats:sub>2</jats:sub> monolayer) with the global minimum of 2D space. The HfN<jats:sub>2</jats:sub> monolayer possesses direct band gap (∼ 1.46 eV) and it is predicted to have high carrier mobilities (∼10<jats:sup>3</jats:sup> cm<jats:sup>2</jats:sup>⋅V<jats:sup>−1</jats:sup>⋅s<jats:sup>−1</jats:sup>) from deformation potential theory. The direct band gap can be well maintained and flexibly modulated by applying an easily external strain under the strain conditions. In addition, the newly predicted HfN<jats:sub>2</jats:sub> monolayer possesses good thermal, dynamical, and mechanical stabilities, which are verified by <jats:italic>ab initio</jats:italic> molecular dynamics simulations, phonon dispersion and elastic constants. These results demonstrate that HfN<jats:sub>2</jats:sub> monolayer is a promising candidate in future microelectronic devices.</jats:p>

<jats:p>We present a theoretical investigation of the multiphoton resonance dynamics in the high-order-harmonic generation (HHG) process driven by a strong driving continuous wave (CW) field along with a weak control harmonic field. The Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the combined laser field. Multiple multiphoton-transition paths for the harmonic emission are coherently summed. The phase information about paths can be extracted via the Fourier transform analysis of the harmonic signals which oscillate as a function of the relative phase between driving and control fields. Phase jumps are observed when sweeping across the resonance by varying the frequency or intensity of the driving field. The phase variation as a function of driving frequency at a fixed intensity and as a function of the intensity at a fixed driving frequency allows us to determine the intensity dependence of the transition energy of quantum systems.</jats:p>

<jats:p>We report a detailed study of the enhanced optical molasses cooling of Cs atoms, whose large hyperfine structure allows to use the largely red-detuned cooling lasers. We find that the combination of a large frequency detuning of about −110 MHz for the cooling laser and a suitable control for the powers of the cooling and repumping lasers allows to reach a cold temperature of ∼ 5.5 μK. We obtain 5.1× 10<jats:sup>7</jats:sup> atoms with the number density around 1× 10<jats:sup>12</jats:sup> cm<jats:sup>−3</jats:sup>. Our result gains a lower temperature than that got in other experiments, in which the cold Cs atoms with the temperature of ∼ 10 μK have been achieved by the optical molasses cooling.</jats:p>

<jats:p>Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges. We show that for both the bicircular fields, ionization rates are enhanced when the two circularly polarized lights have comparable intensities. In addition, the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5 × 10<jats:sup>14</jats:sup> W/cm<jats:sup>2</jats:sup>, which agrees with the experimental observation. Moreover, the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity. With the help of the ADK theory, the above characteristics of the ionization rate curves can be well interpreted, which is related to the transition from the tunneling to multiphoton ionization mechanism.</jats:p>

<jats:p>The outer valence electron momentum distributions of benzene are reinvestigated with theoretical calculations involving the vibrational effects. The results are compared with recent experimental measurements [<jats:italic>Phys. Rev. A</jats:italic> <jats:bold>98</jats:bold> 042705 (2018)]. The significant discrepancies between theories and experiments in previous works have now been interpreted quantitatively, indicating that the vibrational motion in benzene molecule has noticeable influence on its electron momentum distributions.</jats:p>

<jats:p>The influence of oxidation aperture on the output characteristics of the circularly symmetric vertical-cavity-surface-emitting laser (VCSEL) structure is investigated. To do so, VCSELs with different oxide aperture sizes are simulated by the finite-difference time-domain (FDTD) method. The relationships among the field distribution of mode superposition, mode wavelength, output spectra, and far-field divergence with different oxide apertures are obtained. Further, VCSELs respectively with oxide aperture sizes of 2.7 μm, 4.4 μm, 5.9 μm, 7 μm, 8 μm, 9 μm, and 18.7 μm are fabricated and characterized. The maximum output power increases from 2.4 mW to 5.7 mW with oxide aperture increasing from 5.9 μm to 9 μm. Meanwhile, the wavelength tuning rate decreases from 0.93 nm/mA to 0.375 nm/mA when the oxide aperture increases from 2.7 μm to 9 μm. The thermal resistance decreases from 2.815 °C/mW to 1.015 °C/mW when the oxide aperture increases from 4.4 μm to 18.7 μm. It is demonstrated theoretically and experimentally that the wavelength spacing between adjacent modes increases with the augment of the injection current and the spacing becomes smaller with the oxide aperture increasing. Thus it can be reported that the aperture size can effectively reduce the mode overlaying but at the cost of the power decreasing and the wavelength tuning rate and thermal resistance increasing.</jats:p>