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    25 July 2022, Volume 2022 Issue 4 Previous Issue   
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    Mathematics
    New form of the alternating direction iteration scheme for real positive definite linear systems
    Daosheng ZHENG
    2022, 2022 (4):  1-12.  doi: 10.3969/j.issn.1000-5641.2022.04.001
    Abstract ( 353 )   HTML ( 374 )   PDF (789KB) ( 130 )   Save

    Alternating direction iteration (ADI) scheme is an effective method for solving real positive definite linear systems; in many cases, however, the method requires that all the direction matrices involved are multiplication exchangeable, which severely limits the scope of application. In this paper, new revised alternating direction iteration (RADI) schemes are proposed, that do not stipulate the multiplication exchangeable requirement, thereby expanding the application scope. In parallel, measures to improve the efficiency of RADI schemes are also discussed.

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    Generalized number operators defined in the space of a discrete time normal martingale functional
    Yulan ZHOU, Huafang KONG, Xiuqiang CHENG, Rui XUE, Jia CHEN
    2022, 2022 (4):  13-25.  doi: 10.3969/j.issn.1000-5641.2022.04.002
    Abstract ( 320 )   HTML ( 380 )   PDF (826KB) ( 134 )   Save

    A family of linear operators $\{N_{h};h\in\mathcal{P_{+}}(\mathbb{N})\}$ in $L^{2}(M)$ are defined. Firstly, we prove that $N_{h}$ is a positive, densely defined, self-adjoint closed linear operator. In general, $N_{h}$ is not bounded, hence, we explore the sufficient and necessary conditions such that $N_{h}$ is bounded. Secondly, we consider the dependence of $N_{h}$ on $h$ : $N_{h}$ is strictly increasing with respect to $h$ , and the operator-valued mapping $N_{h}$ is an isometry from $l^{1}_{+}(\mathbb{N})$ to the subspace of bounded generalized number operators on $L^{2}(M)$ , where $l^{1}_{+}(\mathbb{N})$ is the space of the summable function on $\mathbb{N}$ . We consider the conditions such that $\{N_{h_{n}};n\geqslant1\}$ is strongly and uniformly convergent. If $\{h_{n};n\geqslant1\}$ is convergent monotonically to $h$ , the domain of $\{N_{h_{n}};n\geqslant1\}$ and $N_{h}$ have some interesting properties, we show, furthermore, that a convergent family of $\{N_{h_{n}};n\geqslant1\}$ can be obtained. We prove that $\{N_{h};h\in\mathcal{P_{+}}(\mathbb{N})\}$ is commutative observable on $\mathcal{S}_{0}(M)$ .

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    Gradient shrinking Kähler-Ricci solitons with vanishing conditions on a Bochner tensor
    Dong SHEN, Jiancheng LIU
    2022, 2022 (4):  26-30.  doi: 10.3969/j.issn.1000-5641.2022.04.003
    Abstract ( 283 )   HTML ( 363 )   PDF (462KB) ( 99 )   Save

    In this paper, we study complete gradient shrinking K?hler-Ricci solitons with a vanishing fourth-order Bochner tensor (i.e. $\text{div}^{4}(W)=\nabla_{\bar{k}}\nabla_{j}\nabla_{\bar{i}}\nabla_{l}W_{i\bar{j}k\bar{l}}=0$ ), and obtain the corresponding classification results.

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    Computer Science
    Neural architecture search algorithms based on a recursive structure
    Jizhou LI, Xin LIN
    2022, 2022 (4):  31-42.  doi: 10.3969/j.issn.1000-5641.2022.04.004
    Abstract ( 341 )   HTML ( 40 )   PDF (772KB) ( 180 )   Save

    Neural architecture search algorithms aim to find more efficient neural network structures in a huge neural network structure space using computer heuristic search instead of manual search. Previous studies have addressed the problem of inefficient and time-consuming search for early neural network structures by introducing various constraints on the search space. While constraints on the search space can improve and stabilize the performance of the model, they ignore potentially efficient model structures. Hence, in this study, we constructed a recursive model search space that focuses more on the macroscopic structure of neural networks. We proposed a neural architecture search algorithm that explores this search space through a step-by-step incremental search approach. Experiments showed that the algorithm can efficiently perform neural architecture search tasks in complex search spaces, but still fell slightly short of the latest constrained search space-based neural architecture search algorithms.

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    Redundancy measurement and reduction of automated tests in financial technology
    Xin GONG, Lihua XU, Liang DOU, Ruixiang ZHAO
    2022, 2022 (4):  43-55.  doi: 10.3969/j.issn.1000-5641.2022.04.005
    Abstract ( 333 )   HTML ( 33 )   PDF (981KB) ( 83 )   Save

    With the development and iteration of financial technology(FinTech) software programs, the size of test suites will gradually increase, which may introduce inherent redundancy. In order to effectively quantify test redundancy, a test redundancy evaluation metric called MVI (Most Valuable Item) is proposed in this study. To verify the validity of the MVI metric, the MVIR (Most Valuable Item Reduction) test case reduction algorithm is proposed. Experimental results show that the MVIR can achieve a test case reduction ratio of more than 89.88% assuming the test performance loss is less than 9.20%, this demonstrates that the MVI metric is valid.

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    A graph convolutional neural network for garment pattern classification
    Xiaozhen ZHAO, Weiqing TONG, Yongmei LIU
    2022, 2022 (4):  56-66.  doi: 10.3969/j.issn.1000-5641.2022.04.006
    Abstract ( 325 )   HTML ( 31 )   PDF (1868KB) ( 124 )   Save

    The identification and classification of garment patterns are important technologies for intelligent clothing production and management. This paper proposes a method to convert garment patterns into graphic data and subsequently proposes a lightweight graph neural network GPC-GCN (Garment Pattern Classification Graph Convolutional Network) that can process this graphic data. The proposed graph data modeling method can not only maintain information on the shape of each component in the garment pattern but also deal with the arbitrariness of the position of components in garment patterns. Experiments show that the proposed graph neural network GPC-GCN achieves a better result for the classification of garment patterns compared to convolutional neural networks and graph convolutional networks.

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    Assembly optimization of an AES-128-CTR algorithm based on a Cortex-M4 core
    Dongxuan YANG, Ganggang ZHANG, Xinliang LIU
    2022, 2022 (4):  67-78.  doi: 10.3969/j.issn.1000-5641.2022.04.007
    Abstract ( 430 )   HTML ( 35 )   PDF (920KB) ( 182 )   Save

    With the rapid development of the Internet of Things, embedded hardware products face great challenges in data security. The AES (Advanced Encryption Standard) algorithm has the advantages of strong attack resistance, fast operation speed and flexible block length in the field of data encryption and decryption. The speed of this algorithm on microcontroller platforms is far inferior to general-purpose CPUs (Central Processing Units) which have an extended instruction set for AES encryption. To solve this problem, a speed optimized AES algorithm in CTR (Counter) mode based on the Cortex-M4 core instruction set is implemented using assembly language. The kernel’s unique barrel shifter and three-stage pipeline are used to optimize the round transformation of the algorithm, and the number of instruction cycles is reduced. Testing on an FRDM-K82F development board shows that the assembly optimization of the algorithm is substantially more efficient than the code implemented using the C language, and it offers more advantages in both cost and power consumption compared to hardware encryption based on the coprocessor.

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    Modeling and simulation technology of roads for a battlefield environment
    Shucheng LU, Yan GAO, Changbo WANG
    2022, 2022 (4):  79-94.  doi: 10.3969/j.issn.1000-5641.2022.04.008
    Abstract ( 454 )   PDF (3909KB) ( 167 )   Save

    Battlefield environments are combat spaces that contain geographic elements such as terrain and roads. Road modeling and simulation is an important part of battlefield simulation and plays a key role in complex combat decision-making. Traditional road modeling is unable to handle the complex terrain conditions present in the field; hence, this paper proposes road modeling and simulation method for field environments. In particular, in order to support road modeling and simulation of complex terrain environments, road construction designs oriented to typical battlefield environments are proposed. This method divides the road network into different sub-models according to their characteristics and models them separately, improving the demand for realism in battlefield simulation. Then, the proposed method uses OpenStreetMap geographic information data to drive road network construction. The model offers real-time, high accuracy road information content and complete classification that can meet the needs of military operations and modeling simulations for typical battlefield environments. Secondly, using terrain elevation data, road construction rules, and other auxiliary information, the road height is adjusted to adapt to the complex terrain conditions of the battlefield and possible multi-level road network structures. Lastly, the introduction of a $ {G}^{2} $ continuous Hermite interpolation spline can flexibly represent the center line of the road and improves the reusability of the road model through grid deformation. Experiments show that the proposed simulation method can more reliably restore the real details of a road network to effectively fit complex terrain and improve the reusability of road models. Finally, it provides a feasible analysis angle and modeling method for researching geographic elements in battlefield environments.

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    Physics and Electronics
    Foldy-Wouthuysen transformation of the (2 + 1)-dimensional Dirac oscillator
    Wei SUN, Keye ZHANG
    2022, 2022 (4):  95-102.  doi: 10.3969/j.issn.1000-5641.2022.04.009
    Abstract ( 336 )   HTML ( 26 )   PDF (791KB) ( 217 )   Save

    The (2 + 1)-dimensional Dirac oscillator is a fundamental model used to study the relativistic extensions of quantum effects and principles. Due to the influence of relativistic effects, including the non-equidistant and negative excitation spectrum and the spin-orbit coupling, the eigenstates are complicated dressed states composed of spin and angular momentum state vectors; in turn, this renders theoretical research difficult. In this work, we decouple the spin and angular momentum state vectors and separate the spin-up and -down components into positive- and negative-energy states, respectively, using the Foldy-Wouthuysen (F-W) transformation. The Hamiltonian and eigenstates of the Dirac oscillator are then largely simplified in the F-W representation; nevertheless, we find the forms of the operators for spin and angular momentum in the same representation with complex combinations of each other. The results are useful in advancing research in relativistic quantum mechanics and spin-orbit coupling.

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    SU(3) covariant chiral effective theory and corrections to the octet baryon masses
    Zhou LIU, Jifeng YANG
    2022, 2022 (4):  103-113.  doi: 10.3969/j.issn.1000-5641.2022.04.010
    Abstract ( 298 )   HTML ( 24 )   PDF (823KB) ( 135 )   Save

    In this paper, corrections to the octet baryon masses based on the strange quark contribution are calculated using the SU(3) covariant chiral effective theory. We find that the items violating chiral power counting rules are local and can be subtracted by local counterterms which leads to extended minimal subtraction ${(\text{E}}\overline {{\text{MS}}})$ scheme. In addition to the chiral contribution, relativistic correction items are also retained, which is meaningful for accurately calculating the corrections to baryon masses and analytical extrapolation.

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    Bandgap tuning of C3N: A first-principles study
    Wei ZHAO, Qinghong YUAN
    2022, 2022 (4):  114-119.  doi: 10.3969/j.issn.1000-5641.2022.04.011
    Abstract ( 263 )   HTML ( 26 )   PDF (1418KB) ( 98 )   Save

    In this paper, bandgap tuning of C3N through the stacking pattern, layer number, and external electric field were investigated by employing first-principles density functional theory (DFT) calculations. Four stacking structures—namely AA-1, AA-2, AB-1, and AB-2—were investigated in our study; the calculation results showed that the AB-2 structure was the most energetically favorable. Accurate calculations of the bandgap by the HSE06 hybrid functional revealed a large bandgap difference between the C3N bilayers with AA and AB stacking; specifically, structures with AA stacking had much smaller bandgap than those with AB stacking. Moreover, we found that the bandgap of C3N decreases from 1.21 eV for a single layer to 0.69 eV for the AB-2 bulk structure. By applying a vertical electric field, the bandgap of a C3N bilayer, tri-layer, and four-layer with AB-2 stacking can be tuned to a nearly metallic state.

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    Protecting quantum Fisher information of a qubit-qutrit system near the horizon of the Garfinkle-Horowitz-Strominger dilation space-time
    Yijun LIAN, Jinming LIU
    2022, 2022 (4):  120-130.  doi: 10.3969/j.issn.1000-5641.2022.04.012
    Abstract ( 205 )   HTML ( 26 )   PDF (1067KB) ( 132 )   Save

    In this study, we investigated the dynamic behavior of quantum Fisher information (QFI) for the qubit-qutrit system suffering from noisy environments by considering quantum memory; the qubit is located near the event horizon of the Garfinkle-Horowitz-Strominger (GHS) dilation black hole and the qutrit stays at the asymptotically flat region. We proposed an effective strategy to protect QFI under the influence of noise by employing weak measurement and reversal measurement. The results show that QFI decays as the amplitude damping strength increases; meanwhile, QFI is nearly constant with an increase in the phase damping strength. QFI can be improved with the selection of appropriate values for measurement strengths and reversal strengths.

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    Bell correlation of separated two-mode squeezed Bose-Einstein condensates
    Xin MENG, Valentin IVANNIKOV, Tim BYRNES
    2022, 2022 (4):  131-138.  doi: 10.3969/j.issn.1000-5641.2022.04.013
    Abstract ( 222 )   HTML ( 26 )   PDF (794KB) ( 69 )   Save

    In this paper, a method for testing the Bell correlation between two spatially separated two-mode squeezed Bose-Einstein condensates (BECs) is proposed. Using the referenced method, violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed. First, the method for producing the required physical states is introduced, and then the Bell correlation is tested by calculating the relevant factors using the normalized expected value of the particle number operator. It is shown that violation of the Bell inequality can be observed when $r \lesssim 0.49$ . One of biggest violations occurs, furthermore, when $r \to 0$ and $B = 2\sqrt 2 $ . The method is highly robust in the presence of noise.

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    Atom-light hybrid interference to achieve acceleration measurement
    Bo FANG, Zhifei YU, Liqing CHEN
    2022, 2022 (4):  139-146.  doi: 10.3969/j.issn.1000-5641.2022.04.014
    Abstract ( 266 )   HTML ( 23 )   PDF (997KB) ( 108 )   Save

    In this paper, we present a new type of atom-light accelerometer (ALA) based on use of an atom-light hybrid interferometer. At present, all-optical accelerometers are the most commonly used and most stable accelerometers on the market, owing to their small size and high accuracy. However, due to measurement bandwidth limitations, their practical application range is limited. Hence, we designed a new type of accelerometer to address this challenge. The atom-light hybrid interferometer is first constructed in the atomic system through the stimulated Raman scattering (SRS) process, and the elastic mass of the accelerometer is formed by a mirror. When the mass is subjected to acceleration on the experimental platform, it will perceive the change in external displacement, thereby introducing the phase into the interferometer. Through the change of the interference fringe, the change of the external phase and the displacement can be determined; hence, the magnitude of the acceleration can be obtained. The primary advantage of the atom-light accelerometer is that the Stokes field generated by the SRS process is phase related to the atomic spin-wave, which ensures the stability of the device phase. Secondly, the adjustable bandwidth of the device increases its scope of application. Finally, theoretical calculations show that its measurement accuracy exceeds the standard quantum limit (SQL) under ideal conditions.

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    Fluctuation behavior of the evolution of complex networks
    Qichen LIU, Jianghai QIAN, Hanyun CHANG
    2022, 2022 (4):  147-153.  doi: 10.3969/j.issn.1000-5641.2022.04.015
    Abstract ( 219 )   HTML ( 22 )   PDF (733KB) ( 234 )   Save

    Research on complex networks has given birth to models for understanding evolution dynamics and structure formation; their respective degree growth fluctuations, however, behave very differently. To test the validity of existing models, we carry out an empirical study on two real networks. The results show that both their fluctuation exponents decrease linearly with the observation interval, presenting an interval-dependent picture that has not been predicted by any of the existing models. By exploring the response of the fluctuation to shuffling data, we deduce the interval dependence from the reinforcement of the internal temporal correlation. These results reveal not only the limitations of the existing models, but the complex dynamics of the correlation itself, which is significant for further understanding the underlying mechanism of network evolution.

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    Quantum nondemolition measuremen generated spin-squeezed Bose-Einstein condensate confined in a double-well trap
    Yangxu JI, Ebubechukwu O. ILO-OKEKE, Tim BYRNES
    2022, 2022 (4):  154-162.  doi: 10.3969/j.issn.1000-5641.2022.04.016
    Abstract ( 212 )   HTML ( 23 )   PDF (1077KB) ( 170 )   Save

    This paper studies the use of quantum nondemolition (QND) measurement to produce a spin squeezed atomic Bose-Einstein condensate (BEC) in a double-well trap. The spin squeezed atomic Bose-Einstein condensate is performed by putting the BECs of a double well in the two arms of a Mach Zehnder interferometer and performing a QND measurement. The dynamics of the light-atom system are solved using an exact wave-function approach, in contrast to previous approaches where approximations were made using techniques like the Holstein-Primakoff approximation. The backaction of the measurement on atoms is minimized by monitoring the condensate at zero detection current and the identical coherent beams. At the weak atom-light interaction limit, we find that the average spin direction is relatively unaffected by observing the conditional probability distribution and the Q function distribution. The spin variance is squeezed along the axis of optical coupling.

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    Superfluorescence behavior of excitons in a quantum dot superlattice
    Jiqing TAN, Qiangqiang WANG, Wei XIE
    2022, 2022 (4):  163-168.  doi: 10.3969/j.issn.1000-5641.2022.04.017
    Abstract ( 310 )   HTML ( 32 )   PDF (838KB) ( 257 )   Save

    In this study, photoluminescence spectra are studied in perovskite quantum dot superlattices based on two-photon absorption processes at 10 K. The dynamics of excitons is obtained using a time-resolved photoluminescence detection system. The sample exhibits typical superfluorescence characteristics in the single-photon excitation case: When the pumping power increases, the transient peak intensity increases nonlinearly, and the radiation lifetime decreases rapidly. Meanwhile, the intensities of the two-photon absorption fluorescence spectra are proportional to the square of the excitation power, and the dynamics of excitons under the two-photon absorption case exhibits the same characteristics as those in the single-photon excitation case. Thus, when the excitation density reaches a certain intensity, two-photon absorption can also induce a superfluorescence process.

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