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    25 July 2023, Volume 2023 Issue 4 Previous Issue   
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    Mathematics
    New types of solitons and multiwave solutions for two higher-dimensional nonlinear evolution equations with time-dependent coefficients
    Yuxin QIN, Yinping LIU, Guiqiong XU
    2023, 2023 (4):  1-10.  doi: 10.3969/j.issn.1000-5641.2023.04.001
    Abstract ( 172 )   HTML ( 17 )   PDF (3509KB) ( 89 )   Save

    Linear traveling-wave transformations are usually applied when constructing exact traveling-wave solutions for nonlinear evolution equations. Herein, for the first time, specific nonlinear traveling-wave transformations are introduced to extend the $N$ -soliton decomposition algorithm and an inheritance-solving strategy to a variable-coefficient nonlinear evolution equation. Two higher-dimensional nonlinear evolution equations with time-dependent coefficients, the Boiti-Leon-Manna-Pempinelli (BLMP) equation and the cylindrical Kadomtsev-Petviashvili (cKP) equation, are solved. The direct algebraic method and inheritance-solving strategy are used to construct several different types of multiwave-interaction solutions for the BLMP equation, specifically, the horseshoe-like solitons and their interaction with lump as well as different periodic waves. Using the $N$ -soliton decomposition algorithm, the higher-order interaction solutions between the horseshoe-like solitons, breathers, and lump waves of the cKP equation are established. These new multiwave-interaction solutions contribute to the existing solutions of nonlinear evolution equations with variable coefficients, enriching the repository of solutions to a certain extent.

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    LaSalle’s invariance principle for delay differential equations driven by α-stable processes
    Zhenzhong ZHANG, Xu CHEN, Jinying TONG
    2023, 2023 (4):  11-23.  doi: 10.3969/j.issn.1000-5641.2023.04.002
    Abstract ( 168 )   HTML ( 6 )   PDF (696KB) ( 214 )   Save

    LaSalle’s invariance principle is an important tool for studying the stability of stochastic systems. Considering the influence of time delay and pure-jump path on the stability of the system and using the convergence theorem for special semi-martingale, the LaSalle’s invariance principle for a class of stochastic delay differential equations driven by $\alpha$ -stable processes is established in this study. The sufficient conditions for the asymptotic stability of a class of delay equations are given by LaSalle’s invariance principle.

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    Blow-up of solutions to a class of weakly coupled semilinear double-wave systems with nonlinear terms of derivative type
    Baiping OUYANG
    2023, 2023 (4):  24-34.  doi: 10.3969/j.issn.1000-5641.2023.04.003
    Abstract ( 139 )   HTML ( 7 )   PDF (563KB) ( 62 )   Save

    In this paper, blow-up of solutions to a class of weakly coupled semilinear double-wave systems with nonlinear terms of derivative type is considered. By choosing suitable functionals and using an iteration technique, the weakly coupled phenomena are studied in-depth for the case when $ p\ne q $ . For the case when $ p=q $ , the solution is degenerated to a single semilinear double-wave equation with a nonlinear term of derivative type. Furthermore, the nonexistence of global solutions to the Cauchy problem in the subcritical case is proven. Meanwhile, the upper bound estimate of the lifespan of solutions is also derived.

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    Characterization and representation of weighted Drazin inverse of matrices based on weighted core-EP decomposition of the pair {A,W}
    Chunmei HU
    2023, 2023 (4):  35-42.  doi: 10.3969/j.issn.1000-5641.2023.04.004
    Abstract ( 137 )   HTML ( 5 )   PDF (507KB) ( 79 )   Save

    This paper presents an investigation of the weighted Drazin inverse $A^{d, W}$ of matrices based on the weighted core-EP decomposition of the pair $\{A, W\}$ . Some characterizations and representations of the weighted Drazin inverse are presented using the weighted core-EP decomposition of the pair $\{A, W\}$ . Further, the limit representations and the integral representations of the weighted Drazin inverse are discussed. Furthermore, an example is presented.

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    Non-relativity of Cartan-Egg domains and complex Euclidean spaces
    Xiaoliang CHENG, Bo WANG, Yihong HAO
    2023, 2023 (4):  43-51.  doi: 10.3969/j.issn.1000-5641.2023.04.005
    Abstract ( 152 )   HTML ( 8 )   PDF (694KB) ( 44 )   Save

    In recent years, the relativity between domains with specific metrics and complex Euclidean spaces has been a topic of interest in the study of complex variables. Two Kähler manifolds are called relatives if they admit a common Kähler submanifold with their induced metrics. A Cartan-Egg domain is a type of bounded non-homogeneous domain. Its Bergman kernel function can be constructed as an explicit expression using the expansion principle. In this paper, the relativity between a Cartan-Egg domain with Bergman metrics and a complex Euclidean space with canonical metrics is explored. In relation research of complex Euclidean spaces, the working premise is that a Bergman kernel function is a Nash function. However, the Bergman kernel function of Cartan-Egg domains are not necessarily Nash functions. Therefore, existing methods cannot be used directly. By analyzing the algebraic properties of a Bergman kernel function’s partial derivative function of a Cartan-Egg domain, we show that a Cartan-Egg domain with Bergman metrics is not related to a complex Euclidean space with canonical metrics.

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    Computer Science
    Multimodal-based prediction model for acute kidney injury
    Wei DENG, Fang ZHOU
    2023, 2023 (4):  52-64.  doi: 10.3969/j.issn.1000-5641.2023.04.006
    Abstract ( 217 )   HTML ( 13 )   PDF (1179KB) ( 262 )   Save

    Acute kidney injury is a clinical disease with a high morbidity rate, and early identification of potential patients can facilitate medical interventions to reduce morbidity and mortality. In recent years, electronic health records have been widely used to predict an individual’s potential risk. Most of the existing acute kidney injury prediction models tackle the issue of sparsity and irregularity in the physiological variables data by aggregating data or imputing the missing value, but ignore the patient’s health status implied by the missing information. Moreover, they do not consider the characteristics of and correlation between the various modalities. To solve the above issues, we present a multi-modal disease prediction model for acute kidney injury. The proposed model considers a variety of modal data, including physiological variables, disease, and demographic data. A new mask and time span based long short term memory (LSTM) network is designed to learn the time span and missing information of individual Physiological variables, and furthermore, to capture their numerical changes and frequency changes. The multi-head self-attention mechanism is introduced to promote interaction learning of each modality representation. Experiments on the real-world application of acute kidney injury risk prediction and mortality risk prediction demonstrate the effectiveness and rationality of the proposed model.

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    Physics and Electronics
    Computational study on strain-induced transition of Fe2CrGe from an antiferromagnetic ground state to a ferromagnetic half-metal state
    Jin GUO, Xiao HU, Wenhui XIE
    2023, 2023 (4):  65-73.  doi: 10.3969/j.issn.1000-5641.2023.04.007
    Abstract ( 157 )   HTML ( 7 )   PDF (1097KB) ( 196 )   Save

    In this study, the electronic structure and magnetism of the Heusler alloy Fe2CrGe are investigated using first-principle calculations. Results show that the ground state of Fe2CrGe is antiferromagnetic metal in which Fe ion and Cr ion are in low- and high-spin states of $ S=0 $ and $ S=1 $ , respectively. The energy of the antiferromagnetic state is approximately 0.103 eV less than that of the ferromagnetic state. In addition, when a tetragonal strain is applied to Fe2CrGe, a transition from antiferromagnetic to ferromagnetic material occurs at +1.7% and –1.7% strains, and Fe2CrGe becomes a ferromagnetic half-metal. A half-metal energy gap of approximately 0.2 eV occurs when the strain reaches ±5%. The Curie temperature of Fe2CrGe is estimated to be 393 K, which is much higher than room temperature, indicating that Fe2CrGe may be a potential candidate for spintronic applications.

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    Quantum entanglement of molecular dipole arrays trapped in an optical lattice
    Wenjing YUE, Qi WEI
    2023, 2023 (4):  74-85.  doi: 10.3969/j.issn.1000-5641.2023.04.008
    Abstract ( 124 )   HTML ( 5 )   PDF (3475KB) ( 62 )   Save

    For a polar molecule subjected to an external electric field, its molecular axis will oscillate around the direction of the electric field, forming pendular states. Taking the two lowest-lying pendular states with magnetic quantum number $M=0 $ as qubit states, we study quantum entanglement of polar molecular arrays trapped in a one-dimensional optical lattice. We evaluate pairwise concurrence and global entanglement as functions of three dimensionless variables related to external field intensity–permanent dipole moment, a rotation constant, dipole-dipole interaction, and temperature —thus revealing the properties of the entangled molecular dipole arrays.

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    Plasma grating generation based on interactions between intense lasers and solids
    Fengyi YUAN, Jiaxiang WANG, Yuanling HUANG, Xuzhong ZHU
    2023, 2023 (4):  86-93.  doi: 10.3969/j.issn.1000-5641.2023.04.009
    Abstract ( 103 )   HTML ( 5 )   PDF (2895KB) ( 68 )   Save

    Plasma gratings are important in physics because they do not break down in strong fields. Using particle-in-cell (PIC) simulations, a new mechanism to generate plasma grating was developed based on the interactions between picosecond intense laser pulses (the magnitude of $ I $ is ${10}^{15}\;\mathrm{W}/{\mathrm{c}\mathrm{m}}^{2}$ ) and overcritical solid-density plasma (particle number density $n \approx 10{n}_{\rm{c}}$ ). This plasma grating results from the interference of plasma waves excited by strong laser fields in solids. Hence, one laser beam is sufficient for generating the gratings. The method produced a nanometer spatial period, which is significantly different from the micrometer spatial period produced by traditional methods that use two counter-propagating lasers in gas-density plasma. This finding may be useful for manipulating strong x-band frequency laser fields.

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    Analysis of negative transmission in metagratings with different complex unit cells
    Haiqin GUO, Junjie DU
    2023, 2023 (4):  94-100.  doi: 10.3969/j.issn.1000-5641.2023.04.010
    Abstract ( 103 )   HTML ( 4 )   PDF (1145KB) ( 53 )   Save

    Based on multiple scattering theory, the effect of the configuration of complex unit cells on transmissivity in the negative first diffraction order is studied when negative transmission occurs in metagratings with a complex unit cell; that is, when transmitted beams lie on the same side of the normal as incident beams occurs in such metagratings. The complex unit cells are composed of two dielectric nanorods of different radii that constitute a metagrating when they are arranged in a line. Our calculations show that no stringent requirements on the radius of the smaller rods and their position in a complex unit cell are required in order for the negative transmission to be perfectly efficient. This implies that the configuration of complex unit cells is robust to the negative transmission, and hence, that it is easier to construct a high-efficiency dielectric metagrating with a complex unit cell.

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    Examination of the effect of decoherence evolution on Jaynes-Cummings model
    Yiman HUANG, Lei MA
    2023, 2023 (4):  101-108.  doi: 10.3969/j.issn.1000-5641.2023.04.011
    Abstract ( 102 )   HTML ( 5 )   PDF (985KB) ( 93 )   Save

    The Kraus operator-sum representation method for mixed-state evolution was used to analyze the change in the fidelity and von Neumann entropy of the final state after decoherent time evolution. The analysis was based on the Jaynes-Cummings model for the initial state set in the depolarization mode. The results show that the fidelity of the quantum state undergoing decoherent evolution exhibits decaying oscillations with time until it becomes stable, while the von Neumann entropy exhibits oscillations of decreasing amplitude with time.

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    Study on the properties of temporal modes in stimulated Raman scattering
    Chen LU, Zhifei YU, Gaofeng JIAO, Liqing CHEN, Chunhua YUAN
    2023, 2023 (4):  109-118.  doi: 10.3969/j.issn.1000-5641.2023.04.012
    Abstract ( 129 )   HTML ( 6 )   PDF (1899KB) ( 81 )   Save

    Temporal modes are a set of orthogonal wave-packet modes that can be used to characterize temporal multi-mode quantum light fields. They provide a complete alternate theoretical framework for the description of quantum systems. This study is based on light-induced seeding as an input to stimulated Raman scattering (SRS), whose output, the Stokes field, is the input seed field of the next SRS ; thus, the process of a continuous iterative SRS system is realized. The pump light field is then fixed in a Gaussian waveform and super-Gaussian waveform, and the temporal waveform evolution characteristics of the output Stokes light field under the input of Gaussian waveform seed light with various structures are studied. The seed light injection can obtain the same stable waveform output through iteration, and the FWHM (full-width at the half of the maximum) of the output light field waveform depends on the pump light field. Furthermore, Schmidt mode decomposition is applied to the final stable output waveform, and the eigenvalues of the final output Stokes field are all concentrated in the fundamental mode by numerical calculation. The research on the temporal mode properties of light presented in this paper provides theoretical guidance and experimental reference for the further development and utilization of the quantum resource of temporal modes.

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    Time-resolved second-order correlation function of ultrafast evolutionary light field
    Zhenyu WANG, Wei XIE
    2023, 2023 (4):  119-126.  doi: 10.3969/j.issn.1000-5641.2023.04.013
    Abstract ( 88 )   HTML ( 7 )   PDF (939KB) ( 77 )   Save

    Based on the Monte Carlo algorithm, photon detection during ultrafast evolutionary light emission was simulated and analyzed in this study. In addition, a method for calculating the time-resolved photon second-order correlation function was developed, and the effects of various errors on the photon second-order correlation function were investigated. The results show that the synchronous time jitter (initial time drift) significantly increases the time-resolved second-order correlation function when the light intensity sharply increases at the initial time, and the value of the time-integrated second-order correlation function is high at any delay. The existence of background photon counts causes the value of the zero-delay second-order correlation function of thermal light to approach unity. This study proposes a simplified simulation method for the theoretical study of photon second-order correlation functions in complicated light fields. Furthermore, this study provides theoretical support and numerical analysis methods for the subsequent experimental measurements of second-order correlation functions with ultrahigh time resolution.

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    Subwavelength lithium niobate film guided mode resonance structure design and second harmonic conversion efficiency optimization
    Chunyu CAO, Minni QU, Wei XIE
    2023, 2023 (4):  127-136.  doi: 10.3969/j.issn.1000-5641.2023.04.014
    Abstract ( 139 )   HTML ( 8 )   PDF (1874KB) ( 94 )   Save

    The optical response characteristics of a subwavelength lithium niobate film guided-mode resonance metasurface were investigated via simulations. The influences of parameters such as the period, filling factor and etching depth of the etched micro–nano structure on the transmission spectrum were examined, and the effects of light sources with different polarization states and incidence angles on the spectral linewidth were imvestigated. Because of the asymmetric grating structure design, the bound states in the continuum (BIC) decay into a quasi-BIC mode with a high Q value (>10 000), and the second harmonic conversion efficiency of the subwavelength lithium niobate film increases by five orders of magnitude as a result of the local field enhancement effect of the bound state. The simulation results show that a high-efficiency conversion of the second harmonic can be realized in the ultraviolet band when the peak power density of the incident fundamental wave is on the order of ~1 GW/cm2, that is, the ultraviolet second harmonic conversion efficiency emitted after a single pass through the subwavelength lithium niobate film is up to 10–3 orders of magnitude. This study affords ideas and design schemes for improving the nonlinear response characteristics of a micro–nano structure and optical table interface system.

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    Faddeev equation for three-boson system in low-energy short-distance effective field theory
    Kai WANG, Jifeng YANG
    2023, 2023 (4):  137-150.  doi: 10.3969/j.issn.1000-5641.2023.04.015
    Abstract ( 93 )   HTML ( 4 )   PDF (834KB) ( 44 )   Save

    Based on the closed-form t matrix of a two-body system in low-energy short-distance effective field theory, the approximate closed-form three-body T matrix for a zero-spin three-boson system is obtained using the Faddeev equation under two-body contact interactions. In momentum representation, the contact potentials are polynomials, and the Lippmann-Schwinger equation can be simplified to algebraic equations using a factorization trick, facilitating nonperturbative renormalization. However, it is impossible to apply such a factorization trick directly to the Faddeev equation. Therefore, the momenta dependence of the T matrix is “split” such that the factorization trick can still be applied. The closed-form T matrices are then obtained as nonperturbative approximate solutions of the Faddeev equation under the leading and next-to-leading order contact potentials with verified consistency. As in a two-body case, such a closed-form T matrix also facilitates the convenient implementation of the nonperturbative renormalization.

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    Electron vortices in the central field
    Yongxiang ZHOU, Xun XUE
    2023, 2023 (4):  151-163.  doi: 10.3969/j.issn.1000-5641.2023.04.016
    Abstract ( 100 )   HTML ( 6 )   PDF (1493KB) ( 67 )   Save

    Electron vortex beams were first discovered in systems that have a conservable orbital angular momentum; for systems where orbital angular momentum is not conserved, the existence of the electron vortices is uncertain. This article takes the electrons in the central field as examples and, in case of relativity, constructs a case where the orbital angular momentum is not conserved while the total angular momentum is conserved. When the electrons that carry a fixed total angular momentum propagate along the z-axis, the perturbation solution of the electron vortex beams corresponding to the system at this time is calculated and combined with the Foldy-Wouthuysen (F-W) transformation. Accordingly, we can prove, in the case of relativity central field, that the vortex solution does exist when the electrons with orbital angular momentum propagate along the z-axis. Consequently, the corresponding vortex wave solution and spiral isophase surface are shown in this article.

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    Effect of torsion on spin particles
    Peng HUI, Xun XUE
    2023, 2023 (4):  164-176.  doi: 10.3969/j.issn.1000-5641.2023.04.017
    Abstract ( 99 )   HTML ( 4 )   PDF (1496KB) ( 43 )   Save

    Theories of gravity with torsion indicate that spin-torsion coupling impacts the propagation of spin particles in a torsion field background. This paper encompasses the Dirac action in a curved spacetime with torsion, generalized geometrical hydrodynamics method from the flat Riemann spacetime to Robertson-Walker spacetime, and obtained semiclassical equations including the flow conservation equation, dynamic equation, and spin evolution equation, which describe the behavior of a spin 1/2 particle in arbitrary curved spacetime with torsion. These equations show that spin-torsion interaction usually causes the particles to deviate from the geodesic. Moreover, a solution for the cosmological background is found with definitive cosmological torsion; it concludes that the motion of the particle under the torsion field is a spiral motion along the propagation path, which the particle would take without torsion. This effect, subsequently, verifies the cosmological models established on theories of gravity with torsion.

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    Distinguishing fermionic types of neutrinos with rotating gravitational fields
    Jiaming GUO, Xun XUE
    2023, 2023 (4):  177-191.  doi: 10.3969/j.issn.1000-5641.2023.04.018
    Abstract ( 69 )   HTML ( 6 )   PDF (647KB) ( 42 )   Save

    Based on previous studies on the scattering of Majorana and Dirac fermions in Schwarzschild spacetime and the effects of the torsion on the scattering of the two fermions, under the weak field approximation of gravity and the lowest order approximation of the perturbation of the gravitational field scattering of fermions, this study decomposes the spin connection into a vector-like part under parity transformation and separately analyzes the effects of the two parts on the scattering matrix elements of the two fermions. A difference is found to exist between the general gravitational field on the quantum scattering matrix elements of the two fermions, where the difference derives from the vector-like part. These findings are then verified in the context of the Kerr gravitational field, where the difference between the scattering matrix elements of the two fermions is determined to be related to the mass and angular momentum of the gravitational source. The difference diminishes in the case of Schwarzschild spacetime when the angular momentum is zero.

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