Abstract ：

A fractional Fourier-transform digital holographic imaging method with resolution enhancement features is presented. In an optical configuration, an extended fractional Fourier-transform optical setup is set in the object arm of an off-axis digital holographic recording system to record a fractional Fourier-transform hologram via the optical interference of the fractional Fourier-transform wavefront of an object wave with a reference wave. For reconstruction imaging, the reconstruction approach for fractional Fourier-transform holograms is given. In the experiment, the fractional Fourier-transform digital holograms are recorded under the different recording parameters, and their amplitude images are effectively reconstructed. The imaging results demonstrate that the reconstruction-imaging resolution of fractional-order Fourier-transform holograms is obviously enhanced compared to that of conventional image-plane holograms. The presented fractional Fourier-transform digital holographic imaging with resolution enhancement and optical configuration flexibility provides, to our knowledge, a novel way for off-axis digital holographic imaging. (c) 2024 Optica Publishing Group

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Abstract ：

In order to achieve the protection of personal privacy, the author proposes research on sports data privacy protection and information security management. The author used the two-dimensional fractional Fourier transform (2D-FRFT) method to encrypt the detected human body parts, which can be decrypted when needed for viewing. Compared to traditional Fourier transform, Fractional Fourier Transform (FRFT) can better express the time-frequency characteristics of signals and is very sensitive to the order of the transform. It is widely used in image encryption systems. 2D-FRFT increases the range of keys, further enhancing the security of the system. The author achieved encryption by extracting the detected human body parts and then performing a certain order of FRFT in the x and y directions respectively; When decrypting, use the same order of encryption to perform inverse fractional Fourier transform. Finally, based on research on pedestrian detection and encryption technology, the author designed a human-machine interaction interface that integrates the functions of detection and encryption interfaces, making the entire operation more intuitive and concise. © 2024 SCPE.

Keyword ：

Sports Cryptography Sensitive data Information management Fourier transforms

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Abstract ：

An off-axis digital holographic reconstruction method with fractional Fourier transform domain filtering is proposed. The theoretical expression and analysis of the characteristics of fractional-transform-domain filtering are given. It is proven that the filtering in a lower fractional-order transform domain can utilize more high-frequency components than that in a conventional Fourier transform domain under the same size of filtering regions. In simulation and experiment, the results demonstrate that the reconstruction imaging resolution can be improved by filtering in the fractional Fourier transform domain. The presented fractional Fourier transform filtering reconstruction provides a novel (to our knowlede) optional way for off-axis holographic imaging.

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Background and objective: Recently, computational fluid dynamics enables the non-invasive calculation of fractional flow reserve (FFR) based on 3D coronary model, but it is time-consuming. Currently, machine learning technique has emerged as an efficient and reliable approach for prediction, which allows saving a lot of analysis time. This study aimed at developing a simplified FFR prediction model for rapid and accurate assessment of functional significance of stenosis.Methods: A reduced-order lumped parameter model (LPM) of coronary system and cardiovascular system was constructed for rapidly simulating coronary flow, in which a machine learning model was embedded for accurately predicting stenosis flow resistance at a given flow from anatomical features of stenosis. Importantly, the LPM was personalized in both structures and parameters according to coronary geometries from computed tomography angiography and physiological measurements such as blood pressure and cardiac output for personalized simulations of coronary pressure and flow. Coronary lesions with invasive FFR <= 0.80 were defined as hemodynamically significant.Results: A total of 91 patients (93 lesions) who underwent invasive FFR were involved in FFR derived from machine learning (FFRML) calculation. Of the 93 lesions, 27 lesions (29.0%) showed lesion-specific ischemia. The average time of FFRML simulation was about 10 min. On a per-vessel basis, the FFRML and FFR were significantly correlated (r = 0.86, p < 0.001). The diagnostic accuracy, sensitivity, specificity, positive predictive value and negative predictive value were 91.4%, 92.6%, 90.9%, 80.6% and 96.8%, respectively. The area under the receiver-operating characteristic curve of FFRML was 0.984.Conclusion: In this selected cohort of patients, the FFRML improves the computational efficiency and ensures the accuracy. The favorable performance of FFRML approach greatly facilitates its potential application in detecting hemodynamically significant coronary stenosis in future routine clinical practice.

Keyword ：

Fractional flow reserve Numerical simulation Reduced-order model Stenotic flow resistance Machine learning

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In this paper we consider the initial value problem to the fractional compressible isentropic generalized Navier-Stokes equations for viscous fluids with one Levy diffusion process in which the viscosity term appeared in the fluid equations is described by the nonlocal fractional Laplace operator. We give one detailed spectrum analysis on a linearized operator and the decay law in time of the solution semigroup for the linearized fractional compressible isentropic generalized Navier-Stokes equations around a constant state by the Fourier analysis technique, which is shown that the order of the fractional derivatives plays a key role in the analysis so that the spectrum structure involved here is more complex than that of the classical compressible Navier-Stokes system. Based on this and the elaborate energy method, the global-in-time existence and one optimal decay rate in time of the smooth solution are obtained under the assumption that the initial data are given in a small neighborhood of a constant state. (c) 2023 Elsevier Inc. All rights reserved.

Keyword ：

Optimal decay rate diffusion process Global-in-time existence Fractional compressible generalized Navier-Stokes equation

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In order to describe the system as realistically as possible, the fractional-order mem-ristive multidirectional associative memory neural networks (FOMMAMNNs) with pa-rameter disturbances, time-varying and distributed delays are established. Further, the master-slave synchronization is explored. Firstly, in the Filippov's sense, some conditions are derived via the contraction mapping principle to guarantee the uniqueness of equilibrium point of the system. Secondly, from the perspective of reducing control costs, pinning controller and adaptive pinning controller are designed for the first time to induce synchronization of FOMMAMNNs. Moreover, some synchronization criteria are obtained by using the properties of fractional calculus, the appropriate Lyapunov candidate functions and fractional Barbalat's lemma. Thirdly, a communication scheme based on chaotic synchronization is proposed to achieve the safe transmission of important information. Finally, two numerical simulations are given to illustrate the feasibility of the theoretical results and the security of the designed communication scheme.(c) 2023 Elsevier B.V. All rights reserved.

Keyword ：

Fractional-order Mixed delays Pinning control Master-slave synchronization Memristive multidirectional associative Secure communication memory neural networks Parameter disturbances

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The unified displacement function (UDF) is presented to describe the deformation behaviours of the tunnel profile along with time under the surface slope condition. Based on the discrete Fourier method, the third-order UDF in the physical plane is expanded to the Laurent series in the complex variable plane. The complex variable method is employed to derive the elastic analytical solution of stra-tum displacement, when the third-order UDF is taken as the displacement boundary condition of tunnel cross-section (DBCTC). The proposed elastic solution agrees well with the results of the finite element method for the consistent model, which verifies the correctness of the proposed analytical solution. Combining the corresponding principle and fractional Generalized Kelvin viscoelastic constitutive model, the fractional viscoelastic solution under the surface slope condition is determined. The time effect of stratum displacement is presented in two aspects: time-dependent DBCTC and time-dependent material parameters. The parameter analysis is performed to investigate influences of deformation modes of the third-order UDF, slope angle, tunnel radius and fractional order on the time effect of stratum vertical and horizontal displacement.

Keyword ：

Surface slope condition Complex variable method Third-order unified displacement function Fractional viscoelastic solution Discrete Fourier method

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An objective of this paper is to investigate the boundary value problem of a high-order nonlinear fractional q-difference equation. It was to obtain a unique iterative solution for this problem by means of applying a novel fixed-point theorem of ? - (h, r)-concave operator, in which the operator is increasing and defined in ordered sets. Moreover, we construct a monotone explicit iterative scheme to approximate the unique solution. Finally, we give an example to illustrate the use of the main result.

Keyword ：

Fractional q-difference equations ? - (h,r)-concave operator Fixed-point theorem Boundary value problem Monotone iterative scheme

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Abstract ：

We propose a single-frame zero-order-eliminated reconstruction method by fractional Fourier transform filtering for an off-axis digital hologram. The filtering in the fractional Fourier transform domain of the hologram can effectively improve the reconstruction resolution, but it is required to remove its zero-order term. With the zero-order-term elimination of the Laplacian hologram, the higher reconstruction resolution of a single-frame hologram is achieved by zero-padding the hologram and choosing the optimal option of the fractional-order number. The results demonstrate that the resolutions of reconstructed amplitude and phase images are obviously improved. It will have a promising application in real-time imaging for biological cells and moving objects. © 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

Keyword ：

Fourier transforms Image enhancement Microscopic examination Lithography Holograms

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This study simulates the polarization effect during the process of battery charging and discharging, and investigates the characteristics of the process. A fractional-order model (FOM) is established and the parameters of the FOM are identified with the adaptive genetic algorithm. As Kalman filter estimation causes error accumulation over time, using the fractional-order multi-innovation unscented Kalman filter (FOMIUKF) is a better choice for state of charge (SOC) estimation. A comparative study shows that the FOMIUKF has higher accuracy. A multiple timescales-based joint estimation algorithm of SOC and state of health is established to improve SOC estimation precision and reduce the amount of computation. The FOMIUKF algorithm is used for SOC estimation, while the UKF algorithm is used for SOH estimation. The joint estimation algorithm is then compared and analyzed alongside other Kalman filter algorithms under different dynamic operating conditions. Experimental results show that the joint estimation algorithm possesses high estimation accuracy with a mean absolute error of under 1% and a root mean square error of 1.35%.

Keyword ：

joint estimation parameter identification state of charge multi-innovation fractional-order model

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