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Adaptive trans-dimensional inversion of multimode dispersion curve based on slime mold algorithm

Wang Xin, Feng Xuan, Liu Qian, Bai Han, Dong Xuri, Wang TaiHan

Acta Geophysica

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2024

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Vol. 72, no. 1

233--245

EN

With the rise of low-cost and high-density observation system Distributed Acoustic Sensing (DAS), the effective utilization of high-mode surface wave becomes extremely important due to unique measuring method of DAS. To solve the interference of mode identification of dispersion curve and model dimension division on inversion results, we introduced the fitting degree of the dispersion curve, the model dimension, and the uncertainty estimation of the picked dispersion curve to construct a new objective function, and developed a strategy of adaptive trans-dimensional inversion of multimode dispersion curve based on slime mold algorithm (SMA). The research results show that our objective function can not only satisfy the fitting degree of dispersion curve, but also adaptively select the best model dimension, and does not depend on the mode identification of dispersion curve. Inversion strategy based on SMA algorithm has high flexibility, accuracy, stability, and practicality. Our method develops a new technology for dispersion curve inversion and provides a new idea for DAS system to realize low-cost and high-resolution city underground structure detection.

2

The generalized S- and σ-inverse – a comparative case study for right- and left-invertible plants

Majewski P., Hunek W. P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 6

1517--1523

EN

In this paper, an advanced study covering the comparison between two classes of generalized inverses is conducted. Two sets of instances, strictly derived from the recently introduced nonunique S- and σ-inverse, are analyzed, especially in terms of degrees of freedom-oriented interchangeable application in different engineering tasks. Henceforth, the respective collections of right and left inverses can be combined in order to achieve a complex tool for robustification of a plethora of real processes. The great potential of two S- and σ-inverse, in particular in robust control and signal recovery as well as complex optimal tasks, is confirmed in the manuscript and supported by the recently carried out research investigations.

3

Approximation properties of certain summation integral type operators

Patel P., Mishra V. N.

Demonstratio Mathematica

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2015

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Vol. 48, nr 1

77--90

EN

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

4

Approximation of vector-valued functions by polynomials with coefficients in normed spaces applications

Anastassiou G., Gal S.

Demonstratio Mathematica

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2006

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Vol. 39, nr 3

539-552

EN

In this paper we prove basic results in the approximation of vector-valued functions by polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain : estimates in terms of Ditzian-Totik Lp-moduli of smoothness for approximation by Bernstein-Kantorovich generalized polynomials and by other kinds of operators like the Szasz-Mirakian operators, Baskakov operators, Post-Widder operators and their Kantorovich analogues and inverse theorems for these operators. Applications to approximation of random functions and of fuzzy-number-valued functions are given.