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  1. Article ; Online: A study on the spectral properties of covariance type matrices with isotropic log-concave column vectors.

    Jin, Shaojia / Shi, Zhanwen

    PloS one

    2024  Volume 19, Issue 1, Page(s) e0297150

    Abstract: The limiting spectral distribution of matrix [Formula: see text] is considered in this paper. Existing results always focus on the condition of modifying Tn, but for Xn, it is usually assumed to be a matrix composed of n × N independent identically ... ...

    Abstract The limiting spectral distribution of matrix [Formula: see text] is considered in this paper. Existing results always focus on the condition of modifying Tn, but for Xn, it is usually assumed to be a matrix composed of n × N independent identically distributed elements. Here we specify the joint distribution of column vectors of Xn. In particular, entries on the same column of Xn are correlated, in contrast with more common independence assumptions. Assuming that the columns of Xn are random vectors following the isotropic log-concave distribution, and under some additional regularity conditions, we prove that the empirical spectral distribution [Formula: see text] of matrix Bn converges to a deterministic probability distribution F almost surely. Moreover, the Stieltjes transformation m = m(z) of F satisfies a deterministic form of equation, and for any [Formula: see text], it is the unique solution of the equation.
    Language English
    Publishing date 2024-01-26
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2267670-3
    ISSN 1932-6203 ; 1932-6203
    ISSN (online) 1932-6203
    ISSN 1932-6203
    DOI 10.1371/journal.pone.0297150
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article: Design and Fabrication of an Underwater Transducer Based on the Shear Vibration Mode and Trapezoid Transition Layer.

    Qiao, Yali / Jin, Shaojia / Zhong, Chao / Qin, Lei

    Micromachines

    2022  Volume 13, Issue 8

    Abstract: In this study, a new kind of underwater transducer was developed using the d15 shear vibration mode of piezoelectric ceramic and a trapezoid transition layer. A series of finite element simulations were conducted to investigate how the boundary ... ...

    Abstract In this study, a new kind of underwater transducer was developed using the d15 shear vibration mode of piezoelectric ceramic and a trapezoid transition layer. A series of finite element simulations were conducted to investigate how the boundary conditions of piezoelectric ceramic blocks affect the shear vibration. Finite element simulation was also used to investigate how the trapezoid transition layer transfers shear vibrations into longitudinal vibrations. A prototype of the proposed transducer was fabricated from piezoelectric vibrators working in the shear mode and a trapezoid transition layer. The underwater performance of this transducer was then tested. The results demonstrated that the transmitting voltage response, working frequency range, and bandwidth reached 163 dB (62 kHz), 37 kHz-68 kHz, and 31 kHz when the radiating area of the transducer was 120 mm × 240 mm. The transmitting voltage response caused by the d15 shear vibration mode reached 160.9 dB at 89 kHz.
    Language English
    Publishing date 2022-08-15
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2620864-7
    ISSN 2072-666X
    ISSN 2072-666X
    DOI 10.3390/mi13081320
    Database MEDical Literature Analysis and Retrieval System OnLINE

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