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    25 January 2021, Volume 2021 Issue 1 Previous Issue    Next Issue
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    Mathematics
    Asymptotic properties of a class of delay differential equations with a sub-linear neutral term
    Zhongyue HAN, Yuanhong YU
    2021, 2021 (1):  1-7.  doi: 10.3969/j.issn.1000-5641.201911020
    Abstract ( 128 )   HTML ( 217 )   PDF (652KB) ( 101 )   Save

    This paper studies the oscillation and asymptotic properties of delay differential equations with damping and sub-linear neutral terms using the generalized Riccati transformation technique and the mean value theorem. After analyzing the function of the cross-link between the condition $\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ and the relationship of parameters $\gamma$ and $\beta$ in the differential equations oscillation, the sufficient conditions for the existence of vibration solutions are provided to extend the existing results in the cited literature. Lastly, some applications are given to illustrate the significance of these results.

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    Images of multilinear polynomials on algebra of upper triangular 3 × 3 matrices
    Aihui SUN, Jie BAI, Kaihua BAO
    2021, 2021 (1):  8-15.  doi: 10.3969/j.issn.1000-5641.201911047
    Abstract ( 132 )   HTML ( 201 )   PDF (635KB) ( 42 )   Save

    This study builds on the method developed by Wang for images of multilinear polynomials on algebra of upper triangular $ 2\times2$ matrices. The main goal of the paper is to give a description of the images of multilinear polynomials on algebra of upper triangular $ 3\times 3$ matrices, thereby partly solving the Fagundes and Mello conjecture, a variation of the famous Lvov-Kaplansky conjecture.

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    Asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory
    Yuting LIANG, Xuan WANG
    2021, 2021 (1):  16-27.  doi: 10.3969/j.issn.1000-5641.201911046
    Abstract ( 82 )   HTML ( 44 )   PDF (856KB) ( 35 )   Save

    In this paper, we study the long-time dynamic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory, where the internal nonlinearity and boundary nonlinearity adheres to polynomial growth of arbitrary order as well as the balance condition. In addition, the forcing term is translation bounded, rather than translation compact, by use of contractive function method and process theory. The existence and the topological structure of uniform attractors in $L^{2}(\Omega)\times L_\mu^2(\mathbb R^+; H_{0}^1(\Omega))$ are proven. This result extends and improves existing research in the literature.

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    Zeros and uniqueness of a class of difference polynomials
    Yiping WANG, Zhigang HUANG
    2021, 2021 (1):  28-35.  doi: 10.3969/j.issn.1000-5641.201911044
    Abstract ( 98 )   HTML ( 45 )   PDF (683KB) ( 46 )   Save

    In this paper, we investigate the uniqueness and distribution of zeros of a class of difference polynomials by using Nevanlinna’s value distribution theory. We obtain results about the uniqueness of the difference polynomials $P(f)\sum_{i=1}^{k}t_{i}f(z+c_{i})$ and the distribution of zeros of the difference polynomials $P(f)(\sum_{i=1}^{k}b_{i}(z)f(z+c_{i}))^s-b_0(z)$ , where $f(z)$ is a transcendental entire function of finite order, $c_i, t_i\;(i=1, 2, \cdots,k)$ are non-zero constants, and $b_i(z)\;(i=0, 1, \cdots,k)$ are small functions with respect to $f(z)$ .

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    Physics and Electronics
    Review of deep learning in cognitive radio
    Bo LIU, Xiaodong BAI, Gengxin ZHANG, Jun SHEN, Jidong XIE, Laiding ZHAO, Tao HONG
    2021, 2021 (1):  36-52.  doi: 10.3969/j.issn.1000-5641.201922017
    Abstract ( 99 )   HTML ( 41 )   PDF (1163KB) ( 24 )   Save

    The development of wireless communication has made spectrum resources increasingly scarce. Existing spectrum resources, however, are not currently used in an efficient way. This contradiction can usually be attributed to the problem created by static spectrum allocation strategies. Cognitive radio (CR) is widely regarded as a feasible solution to solve the problem of static spectrum allocation. In recent years, deep learning, an emerging field of machine learning, has contributed to a number of notable research and application achievements. It has become one of the driving technologies behind artificial intelligence. In this paper, we investigated the application of deep learning to CR; this includes the development of cognitive radio and deep learning as well as the usage of deep learning models in key technologies for CR (such as spectrum prediction, spectrum environment sensing, signal analysis, etc.). Lastly, we summarize and discuss conclusions from this review.

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    Plane circular restricted three-body problem using modified Newtonian dynamics
    Yanfang BI, Tao WANG
    2021, 2021 (1):  53-59.  doi: 10.3969/j.issn.1000-5641.201922016
    Abstract ( 103 )   HTML ( 45 )   PDF (593KB) ( 143 )   Save

    Modified Newtonian dynamics is a major competitor of dark matter theory and contains not only a gravitational constant but also an acceleration constant. Based on a circular orbit solution for a two-body problem, this paper is devoted to studying a plane circular restricted three-body problem using modified Newtonian dynamics. We work out the Lagrangian points and the Hill curves akin to those observed in Newtonian dynamics. In contrast, however, the location and number of Lagrangian points, as well as the profile of the Hill region, are dependent on both the acceleration constant and the mass ratio of the main celestial bodies. These findings reveal a new avenue for testing modified Newtonian dynamics.

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    Study on sentence similarity based on quantum theory
    Bingqing MENG, Lei MA
    2021, 2021 (1):  60-66.  doi: 10.3969/j.issn.1000-5641.201922018
    Abstract ( 75 )   HTML ( 15 )   PDF (684KB) ( 22 )   Save

    Quantum theory has the characteristics of superposition, entanglement, incompatibility, and interference, which make it an excellent modeling framework. For the purpose of sentence matching, we explore the ability of quantum theory as a framework to capture sentence meaning and model semantic processes. We use quantum states to construct the semantic Hilbert space and calculate the fidelity of information during sentence transformation. The similarity of sentences is subsequently determined by using word embedding technology to represent words or concepts in semantic vector spaces. Simulation data showed that the proposed method achieved better results than traditional methods for sentence matching datasets constructed on real business scenarios. Hence, this paper provides a new idea for similarity research of multiple sentences and introduces a breakthrough in interdisciplinary research between computer science and quantum theory, in line with current research trends.

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    Spatial flatness and large-scale Lorentz violation
    Jing LI, Xun XUE
    2021, 2021 (1):  67-81.  doi: 10.3969/j.issn.1000-5641.202022004
    Abstract ( 75 )   HTML ( 17 )   PDF (1736KB) ( 15 )   Save

    There is an inconsistency between the Hubble parameter obtained from local measurements and model-based parameters obtained from cosmic microwave background (CMB) measurements. This inconsistency motivated us to consider new cosmological models based on $\Lambda {\rm{CDM}}$ (Lambda Cold Dark Matter Model), such as a large-scale Lorentz violation model with non-vanishing spatial curvature. The degeneracy among the spatial curvature, cosmological constant, and cosmological contortion distribution makes the model viable for interpretation of the observation data. By comparing the luminosity distance modulus and redshift with the model prediction and calculating the change in matter density as well as the cosmological constant over time, we limit the spatial curvature density to a certain range. Accordingly, we discuss the performance of the large-scale Lorentz violation model with non-vanishing spatial curvature under these constraints.

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    Low-energy effective field theory study of nuclear matter
    Tingwei PAN, Jifeng YANG
    2021, 2021 (1):  82-91.  doi: 10.3969/j.issn.1000-5641.202022007
    Abstract ( 75 )   HTML ( 20 )   PDF (1113KB) ( 26 )   Save

    In this study, the low-energy effective field theory approach is used to analyze nuclear matter and a zero-temperature Fermi system. By solving the Bethe-Goldstone equation (BGE) in the 1S0 channel, we obtain the closed-form Brückner G matrix and derive its renormalized non-perturbative form. Upon selecting values for relevant parameters, a number of physical issues are analyzed with the Brückner G matrix, such as pairing and single particle energy of a Fermi system in the density background. Lastly, the framework and results are compared with those published in the literature.

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    Electron spin coherence dynamics in CdS crystals
    Jiaxing GUO, Zhen WU, Pan LIANG, Meizhen JIANG, Rongrong HU, Yuanyuan ZHANG, Donghai FENG
    2021, 2021 (1):  92-102.  doi: 10.3969/j.issn.1000-5641.202022005
    Abstract ( 79 )   HTML ( 15 )   PDF (1237KB) ( 16 )   Save

    In this paper, we use time-resolved Kerr rotation(TRKR) spectroscopy to study the electron spin coherence dynamics of a wurtzite (0001) plane n-CdS single crystal at different temperatures and wavelengths. Two types of electronic spin signals are observed in this material at low temperatures. One is a long-lived spin signal at relatively long pump probe wavelengths, where the spin dephasing time exceeds 4.8 ns at 5 K and decreases with increasing temperature. The other is a short-lived spin signal at relatively short pump probe wavelengths, where the spin dephasing time is about 40 ps and persists up to room temperature; in this case, the spin signal is largely independent of temperature. Studies have shown that long-lived spin signals can be attributed to localized electrons, while short-lived spin signals can be attributed to conduction delocalized electrons.

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    Influence of the ground state wave function on the atomic high-order harmonic generation spectrum
    Zhongyuan LI, Yingchun GUO, bingbing WANG
    2021, 2021 (1):  103-111.  doi: 10.3969/j.issn.1000-5641.202022002
    Abstract ( 81 )   HTML ( 35 )   PDF (837KB) ( 18 )   Save

    High-order harmonic generation (HHG) may occur during the interaction between an intense laser field and an atom or molecule; HHG has become an important xtreme utility vehicle(XUV) light source which can be used to probe atomic and molecular structures. In this paper, we investigate the effect of the radial distribution of electric density on the HHG spectra by calculating the HHG spectrum of noble atomic gases in a polarized laser field using s and p orbital functions as ground state wave functions. The results show that the form of the wave function does not influence the cutoff value of the harmonic spectrum, which is determined by the ionization threshold energy and the laser intensity. However, different types of orbital wave functions do lead to different envelopes for the HHG spectrum. In particular, there is an additional dip in the plateau area for the p orbital case compared with the spectrum for the s orbital case. By analyzing the formula for the HHG spectrum, we attributed the dip position on the HHG spectrum to the density distribution of the ground state wave function in momentum space. This work may shed light on applications for using the HHG spectrum to visualize atomic orbitals.

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    Coupling behavior of WSe2 exciton and photon in an optical microcavity
    Shuang LIANG, Yichi ZHONG, Wei XIE
    2021, 2021 (1):  112-118.  doi: 10.3969/j.issn.1000-5641.202022003
    Abstract ( 95 )   HTML ( 43 )   PDF (894KB) ( 19 )   Save

    In this paper, we study the strong and weak coupling between excitons of a WSe2 monomolecular thin film and a light field in a self-made Fabry–Pérot semiconductor microcavity at 300 K. The optical properties of the sample were studied using a micro-fluorescence / white light reflection spectroscopy system with integrated angular resolution; the formation of exciton polaritons was observed in the strong coupling region, corresponding to a Rabi splitting energy of 46.7 meV. The theoretical fitting results agree with the experimental phenomena. This lays the foundation for further research on the coherent properties of exciton polaritons, and the study also provide ideas for the application of industrial optoelectronic devices in the future..

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    Whispering gallery mode in a two-dimensional electromagnetic Helmholtz cavity
    Qianjing WANG, Junjie DU
    2021, 2021 (1):  119-128.  doi: 10.3969/j.issn.1000-5641.202022006
    Abstract ( 84 )   HTML ( 24 )   PDF (1277KB) ( 16 )   Save

    In this paper, whispering gallery mode (WGM) excited in a two-dimensional electromagnetic Helmholtz cavity are studied using a rigorous, generalized dual series approach. The excitation wavelengths of several whispering gallery modes are given, and the dependence of electromagnetic whispering gallery modes on the angle of incidence and the angular width of opening cavities is investigated. It was found that WGM are very sensitive to slight changes in wavelength or the angular width of the opening; at the same time, WGM can be excited across a wide range of incident angles given a fixed orientation angle of the cavity. This shows that the angular width of the opening has a significant influence on the performance of Helmholtz cavities and hence is a key parameter in their design. On the other hand, given the lack of sensitivity to the incident angle, no particular specification is needed when designing an artificially structured electromagnetic material using these Helmholtz cavities; accordingly, the fabrication difficulty is relatively low.

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    Theoretical simulations of the square potential barrier with a super-Gaussian beam
    Jiaxin LI, Guangjiong DONG
    2021, 2021 (1):  129-136.  doi: 10.3969/j.issn.1000-5641.202022008
    Abstract ( 81 )   HTML ( 15 )   PDF (985KB) ( 11 )   Save

    The square potential barrier is an ideal model for investigation of quantum tunneling. We simulate the square potential barrier by using the dipole potential for the interaction between an atom and a blue-detuned far-off-resonant super-Gaussian beam, as well as the ponderomotive potential for the interaction between an electron and a super-Gaussian beam. A comparison between the numerical results for scattering by the super-Gaussian potential barrier and the analytical results for scattering by a square potential barrier shows that a super-Gaussian beam with an order exceeding 20 could simulate a square potential barrier accurately. We also show that two super-Gaussian beams could be used to study the resonant quantum tunneling effect. In summary, our results could be applied to an experimental investigation of quantum tunneling through a square potential barrier.

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    Electric field modulated photoluminescence from WS2 monolayers
    Meng FEI, Wei XIE
    2021, 2021 (1):  137-143.  doi: 10.3969/j.issn.1000-5641.202022010
    Abstract ( 75 )   HTML ( 18 )   PDF (988KB) ( 11 )   Save

    Two-dimensional materials have been used in applications across a variety of fields; transition metal dichalcogenides(TMDCs), in particular, are a candidate for use in the field of optoelectronics due to the presence of a band gap. In this paper, WS2 monolayers prepared by micro-mechanical exfoliation are transferred to two micro-period electrode structures. We found that the photoluminescence of the material is modulated by external bias. We studied the effects of bias on the photoluminescence of the WS2 monolayer at room temperature and low temperature. The corresponding characteristics and physical mechanisms of the photoluminescence(PL) spectra, moreover, are analyzed and discussed. With the application of bias to modulate the optical properties of the WS2 monolayer, it is expected that the technology can be applied to many photoelectric products, including field effect transistors, photodetectors, flexible electronic devices, and heterojunction devices.

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    Second order mean field approach of non-Markovian susceptible-infected model for complex networks
    Ting QI, Zhaohua LIN, Mi FENG, Ming TANG
    2021, 2021 (1):  144-151.  doi: 10.3969/j.issn.1000-5641.20202s2001
    Abstract ( 80 )   HTML ( 16 )   PDF (929KB) ( 15 )   Save

    The objective of this paper is to propose a mathematical theory that can describe the non-Markovian characteristics of the network spreading process, thereby establishing theoretical support for controlling the propagation of diseases or rumors in the real world. According to the second-order mean-field approximation method and the concept of idle edges, a series of partial differential equations are presented that can be used to solve the non-Markovian spreading dynamics of a susceptible-infected (SI) model in complex networks. By comparing the simulation outputs with the theoretical results, this mathematical method can accurately predict the spreading process of the SI model on complex networks. The theory, moreover, can be used to predict the average time for a single node to be infected. The correctness and accuracy of the theory is verified by experimental simulation results.

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    Voice singing by function fitting
    Yibu WANG, Jianwen LI
    2021, 2021 (1):  152-164.  doi: 10.3969/j.issn.1000-5641.202022009
    Abstract ( 87 )   HTML ( 19 )   PDF (1182KB) ( 11 )   Save

    Intonation is the tone of speech, which is formed by variations in pitch and emphasis; it is one of the characteristics of human emotion transmission. By adjusting the intonation parameters to change the length and height of certain words in discourse, the controlled intonation can mimic the effect of singing; this approach, in turn, can be used to address the lack of research on voice synthesis in singing. The cepstrum method is used to extract the pitch frequency, the LPC (linear predictive coding) method is used to estimate the formant, and a high-order polynomial is used to fit the pitch of the voice; the fitting function is then adjusted in real time to form the tone required to achieve the objective of singing. Given two basic speech parameters, pitch frequency and formant, combined with the mathematical nature of pronunciation, this paper uses an intuitive mathematical method to synthesize the effect of singing; using this method, the original voice and the synthetic voice reach an overall recognition rate of 87.6%. The result of this synthesis shows that by adjusting the parameters of speech synthesis, we can achieve greater control over voice singing.

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    Chemistry and Chemical Engineering
    Study on the performance of I-doped TiO2 nanotube arrays for planar photocatalytic fuel cells
    Jun ZHOU, Qinghua XI, Yiqiang HUANG, Er NIE, Zhuo SUN
    2021, 2021 (1):  165-175.  doi: 10.3969/j.issn.1000-5641.201922019
    Abstract ( 69 )   HTML ( 22 )   PDF (1346KB) ( 24 )   Save

    The photoanode of I-doped TiO2 nanotube arrays (ITNA) prepared by anodization exhibited better degradation performance than TNA. The planar photocatalytic fuel cell (p-PFC) obtained by combining ITNA and Pt electrodes achieved a maximum decolorization rate of 93.1% when the concentration of methylene blue (MB) was 6 mg·L–1and the electrode plate spacing was 1.0 cm. The degradation of MB occurred on the surface of ITNA, which was a rate-limiting step. Compared to other structures, p-PFC had a higher photocatalytic performance and better production of h+ and ·OH, while degrading MB and other organics.

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