Search

The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations — stochastic differential equations (SDEs) — and deterministic equations for the probability characteristics of processes determined by random perturbations. The resulting deterministic pseudodifferential equations are investigated by semigroup methods and Fourier transform methods. [ABSTRACT FROM AUTHOR]

In this paper, two special-shaped separated heat pipes with different condensation section structures are designed. The working medium is water, and the filling rate is 65%. The evaporation section is placed in the hot water tank, and the condensation section is equipped with a cold water jacket. The effects of different structures of condensing section on the thermal performance of separated heat pipes are experimentally studied, and the temperature changes of the two separated heat pipes during start-up and stable operation under different heating power are analyzed. The results show that the heat transfer characteristics of the two separated heat pipes are different due to the different structures of the condensation section, and the heat transfer capacity of sample 2 is higher. At the same time, the temperature fluctuation in the condensing section of sample 2 is also quite different from that in the condensing section of sample 1, and the temperature fluctuation in the condensing section of sample 2 is greater. The wall temperature fluctuates periodically in a steady-state, and a fast Fourier transform is used to analyze the temperature fluctuation. [ABSTRACT FROM AUTHOR]

The Lp$L_p$ Busemann–Petty problem for 00$\varepsilon >0$ small enough, if K is an Lp$L_p$ intersection body and L is a star body such that for any u∈Sn−1$u\in S^{n-1}$, the following inequality: ∥u∥IpK−p≤∥u∥IpL−p+ε$$\begin{equation*} \Vert u\Vert _{I_pK}^{-p}\le \Vert u\Vert _{I_pL}^{-p}+\varepsilon \end{equation*}$$implies V(K)n−pn≤V(L)n−pn+Cε,$$\begin{equation*} V(K)^{\frac{n-p}{n}}\le V(L)^{\frac{n-p}{n}}+C\varepsilon , \end{equation*}$$where ∥·∥IpK$\Vert \cdot \Vert _{I_pK}$ is the Minkowski functional of IpK$I_pK$, and C is a positive number depending only on p and n. Moreover, we also prove the linear stability and separation results for the negative answer of the Lp$L_p$ Busemann–Petty problem. [ABSTRACT FROM AUTHOR]

The state-space formulation for two-dimensional generalized thermoviscoelasticity has been formulated. In this formulation, the governing equations are transformed into a matrix equation whose solution enables us to write the solution of any two-dimensional problem in terms of the boundary conditions. The resulting formulation is applied to a 2 D problem of a half-space subjected to harmonically varying heating with constant angular frequency. [ABSTRACT FROM AUTHOR]

The utilization of handwritten electronic signatures has expanded in various application scenarios, leading to an increased demand for identification. Unlike handwriting signatures, handwritten electronic signatures offer the advantage of extracting dynamic feature data, including writing pressure, velocity, and acceleration. In this study, the Fourier transform was employed to extract 18 characteristics from the time domain and frequency domain of writing pressure, velocity, and acceleration. The experimental findings revealed distinguishable differences between genuine signatures and random forgeries in writing pressure. However, no statistically significant differences were observed in writing velocity and writing acceleration. Moreover, significant differences were detected in most characteristics when comparing genuine signatures with freehand imitation forgeries and tracing imitation forgeries. The canonical discriminant analysis was performed between the genuine and Non‐genuine signatures; the cross‐validation estimated the discriminating power of these characteristics with a satisfactory result. The study proposed a new approach to analyzing handwritten electronic signatures using time‐domain and frequency‐domain characteristics and demonstrated its effectiveness in the examination. [ABSTRACT FROM AUTHOR]

The utilization of broadband quantization data increases the possibility of practical applications for fish target recognition based on the acoustic scattering theory. However, the quantification of broadband data is more complex than that of narrowband systems, requiring consideration of the broadband characteristics of split-beam transducers, seawater absorption, and circuits. This paper elucidates the scatterer acoustic field equation, transducer power equation, and signal processing flow in split-beam broadband quantization technology for engineering applications. A broadband calculation model based on transducer parameters is proposed to enhance the generalization ability of broadband quantization technology to different types of sonar. The classical echo integration method is combined with Fourier transform to meet the requirements of target strength (TS) estimation under broadband signals. This paper includes a series of experiments to prove the rationality and effectiveness of the method. The results demonstrate that the provided calculation model can more accurately reflect the backscattering characteristics of the scatterer, but certain errors remain. This article analyzes the sources of errors and validates the effectiveness of the new TS calculation method. [ABSTRACT FROM AUTHOR]

In this paper we consider the Fourier transform of the convolution of a distribution and a function which is an element of the space S0(ℝ). Also, we give an application of the obtained result to the sequences that converge in the same space, and we give their analytic representation. [ABSTRACT FROM AUTHOR]

This paper introduces an encoder–decoder-based attentional decoder network to recognize small-size lesions in chest X-ray images. In the encoder-only network, small-size lesions disappear during the down-sampling steps or are indistinguishable in the low-resolution feature maps. To address these issues, the proposed network processes images in the encoder–decoder architecture similar to U-Net families and classifies lesions by globally pooling high-resolution feature maps. However, two challenging obstacles prohibit U-Net families from being extended to classification: (1) the up-sampling procedure consumes considerable resources, and (2) there needs to be an effective pooling approach for the high-resolution feature maps. Therefore, the proposed network employs a lightweight attentional decoder and harmonic magnitude transform. The attentional decoder up-samples the given features with the low-resolution features as the key and value while the high-resolution features as the query. Since multi-scaled features interact, up-sampled features embody global context at a high resolution, maintaining pathological locality. In addition, harmonic magnitude transform is devised for pooling high-resolution feature maps in the frequency domain. We borrow the shift theorem of the Fourier transform to preserve the translation invariant property and further reduce the parameters of the pooling layer by an efficient embedding strategy. The proposed network achieves state-of-the-art classification performance on the three public chest X-ray datasets, such as NIH, CheXpert, and MIMIC-CXR. In conclusion, the proposed efficient encoder–decoder network recognizes small-size lesions well in chest X-ray images by efficiently up-sampling feature maps through an attentional decoder and processing high-resolution feature maps with harmonic magnitude transform. We open-source our implementation at https://github.com/Lab-LVM/ADNet. • We propose the AD-Net that utilizes a new encoder–decoder classification architecture. • We provide a harmonic magnitude transform that efficiently combines feature maps in a translation invariant manner, using minimal additional resources. • We achieve state-of-the-art performance on three widely-used chest X-ray datasets. [ABSTRACT FROM AUTHOR]

In the field of optics, there exist numerous chaotic processes like dissipative soliton dynamics, random laser generation, and laser scattering. It's very challenging to accurately capture the dynamics of these stochastic processes from the wavelength perspective with traditional spectrometers due to their slow signal integration speeds. Here, we propose a new approach, named time-delay Fourier transform spectrometer (TDFTS), to characterize the spectra of laser pulses with durations ranging from fs to ns with high speeds. Based on a fiber array with different lengths to impose frequency-dependent time delay, TDFTS efficiently maps the spectral distribution of light pulses to the temporal domain, and the spectrum can thus be detected with a photodiode and an oscilloscope. In experimental operation, the TDFTS provides spectral acquisition speeds up to 56 MHz frame rates and a bandwidth of tens of nanometers, while keeping comparable fidelity to traditional grating-scan spectrometers. While its spectral resolution of the current configuration is ∼0.1 nm, it can be further improved to 0.001 nm through optimizing the system. Based on its high speed, high spectral resolution, broad-bandwidth coverage, and compact configuration, TDFTS can be used to monitor nanosecond-scale spectral dynamics of non-repetitive optical processes. Numerous chaotic processes such as dissipative soliton dynamics, random laser generation and laser scattering contain rich and peculiar physical phenomena. Due to their fast occurrence and contingency, it is challenging to record their spectral changes with traditional spectrometers due to their slow signal integration speed. Therefore, developing a technology to capture the spectral dynamics of these stochastic processes has become a common concern for researchers. Existing real-time spectral measurement tools, e.g. dispersion Fourier transform (DFT), can hardly record ns-scale pulses due to too large amount of dispersion required. Other solution such as parametric spectro-temporal analyzer (PASTA) has the disadvantage of narrow measurement bandwidth. Here, we propose a new solution called Time-delay Fourier transform spectrometer (TDFTS), which makes use of specially designed fiber arrays (a bundle of fibers with different lengths) and a diffraction grating to achieve frequency-dependent time-delays. This method effectively maps the spectral distribution of light pulses to the temporal domain and the spectrum can be detected only with the combination of a detector and an oscilloscope. TDFTS has the advantages of high measurement speed (hundreds of MHz of frame rates), large operating bandwidth (can reach several hundreds of nanometers), simple configuration, and low cost. In particular, with the time-delay fiber array, it can measure the spectra of pluses with durations ranging from femtoseconds to nanoseconds. The TDFTS can not only be used for spectral measurement but is also expected to have wide applications in biomedical sensing, real-time continuous imaging and other fields. [ABSTRACT FROM AUTHOR]

We prove an operator-valued Laplace multiplier theorem for causal translation-invariant linear operators which provides a characterization of continuity from Hα(R,U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H^\alpha ({\mathbb {R}},U)$$\end{document} to Hβ(R,U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H^\beta ({\mathbb {R}},U)$$\end{document} (fractional U-valued Sobolev spaces, U a complex Hilbert space) in terms of a certain boundedness property of the transfer function (or symbol), an operator-valued holomorphic function on the right-half of the complex plane. We identify sufficient conditions under which this boundedness property is equivalent to a similar property of the boundary function of the transfer function. Under the assumption that U is separable, the Laplace multiplier theorem is used to derive a Fourier multiplier theorem. We provide an application to mathematical control theory, by developing a novel input-output stability framework for a large class of causal translation-invariant linear operators which refines existing input-output stability theories. Furthermore, we show how our work is linked to the theory of well-posed linear systems and to results on polynomial stability of operator semigroups. Several examples are discussed in some detail. [ABSTRACT FROM AUTHOR]

Long time series forecasting (LTSF), which involves modeling relationships within long time series to predict future values, has extensive applications in domains such as weather forecasting, financial analysis, and traffic prediction. Recently, numerous transformer-based models have been developed to address the challenges in LTSF. These models employ methods such as sparse attention to alleviate the inefficiencies associated with the attention mechanism and utilize decomposition architecture to enhance the predictability of the series. However, these complexity reduction methods necessitate additional calculations, and the series decomposition architecture overlooks the random components. To overcome these limitations, this paper proposes the Frequency Enhanced Decomposed Attention Free Transformer (FEDAF). FEDAF introduces two variants of the Frequency Enhanced Attention Free Mechanism (FEAFM), namely FEAFM-s and FEAFM-c, which seamlessly replace self-attention and cross-attention. Both variants perform calculations in the frequency domain without incurring additional costs, with the time and space complexity of FEAFM-s being O(LlogL)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {O}(L{\text {log}}L)$$\end{document}. Additionally, FEDAF incorporates a time series decomposition architecture that considers random components. Unlike other models that solely decompose the series into trend and seasonal components, FEDAF also eliminates random terms by applying Fourier denoising. Our study quantifies data drift and validates that the proposed decomposition structure can mitigate the adverse effects caused by data shift. Overall, FEDAF demonstrates superior forecasting performance compared to state-of-the-art models across various domains, achieving a remarkable improvement of 19.49% for Traffic in particular. Furthermore, an efficiency analysis reveals that FEAFM enhances space efficiency by 12.8% compared to the vanilla attention mechanism and improves time efficiency by 43.63% compared to other attention mechanism variants. [ABSTRACT FROM AUTHOR]

The inverse scattering problem is to reconstruct or recover some physical and/or geometric properties of an object from the measured scattered field in the process of illumination by an incident wave. The probing radiation can be an electromagnetic wave (e.g., microwave, optical wave, and X-ray), an acoustic wave, or some other waves. The inverse scattering problem is important when detailed information about the structure and composition of an object is required, but it cannot be obtained directly from the measurements. The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered as a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The Fourier diffraction theorem is obtained in a coordinate-free representation by the use of tensor (dyadic) analysis techniques. The method of inversion is based on the first Born approximation. [ABSTRACT FROM AUTHOR]

Let { S d } d = 0 2 N − 1 be an iterated function system defined by S d (x) = (− 1) d ρ (x + d) , x ∈ R , where 0 < ρ < 1 and N is a positive integer. Let μ ρ , D 2 N be a self-similar measure defined by μ ρ , D 2 N (⋅) = 1 2 N ∑ d = 0 2 N − 1 μ ρ , D 2 N (S d − 1 (⋅)). We show that μ ρ , D 2 N is a spectral measure if and only if ρ = p − 1 for some nature number p and 2 N divides p. Moreover, we introduce a useful way to determine the spectrality of the convolution of two infinitely supported measures. [ABSTRACT FROM AUTHOR]

We propose a method for frequency domain feature analysis of point clouds based on the multilayer perceptron paradigm (MLP), named PFFA-MLP. By leveraging the Fourier transform and the latest MLP as a replacement for the transformer mechanism, PFFA-MLP maps point clouds to the frequency domain using a three-dimensional (3D) discrete Fourier transform. PFFA-MLP employs lightweight stacked DGCNN modules for initial feature extraction on multi-scale point cloud signals. It also includes a frequency domain feature analysis module, based on the MLP, which analyzes and aggregates the extracted multi-scale point cloud features. Point cloud understanding experiments are conducted on the ModelNet40, ScanObjectNN, and ShapeNet Part benchmarks. On ModelNet40, PFFA-MLP achieves an accuracy of 98% compared to PointMLP, while improving the detection speed by 7.2 times. On ScanObjectNN, the accuracy reaches 94% of PointMLP, while the detection speed is improved by 3.2 times. On ShapeNet Part, it achieves 97% of PointMLP. The experimental results demonstrate that PFFA-MLP achieves a favorable trade-off between training and inference speed. This method is applicable in scenarios that require efficient point cloud analysis while maintaining remarkable detection precision. [ABSTRACT FROM AUTHOR]

Air pollution has become a growing problem owing to its harmful effects on human health, making accurate air quality prediction an important task to avoid serious environmental impacts. Recently, graph-neural-network-based methods have emerged as promising approaches to modeling the spatial dependencies between adjacent stations. However, they have limitations in capturing the hierarchical temporal features of the time series, which include trends, and periodic components. They also overlook dynamic correlations between stations and multiple types of connections, resulting in generated graphs that lack dynamics. In this paper, we proposed a spatiotemporal hierarchical transmit neural network for the prediction of air quality by extracting long-term periodic features and short-term spatiotemporal dependencies. It incorporates a periodic feature extraction component (PFEC), a scene dynamic graph module (SDGM), a spatiotemporal extraction component (STEC), and a transmit attention (TransATT) component. The PFEC applies discrete Fourier transform and trend decomposition techniques to extract long-term periodic features from the spatiotemporal graph. The SDGM generates dynamic graphs by combining node features of time series with predefined graphs to encode diverse station relationships. The STEC comprises of two convolutional operations and attention mechanisms, enabling the model to capture the short-term spatiotemporal dependencies. TransATT integrates the extracted short-term spatiotemporal dependencies and long-term periodic features, allowing the model to transmit with short- and long-term features. To demonstrate the effectiveness of the proposed model, we conducted experiments on three real-world datasets and found that our approach outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this note, we discuss the validity of formula (4.54) in Grabisch's book from 2016. This equation expresses the Choquet integral of nonnegative functions w.r.t. a game in the form of linear invertible transform of set functions. However, the formula (erroneously) excludes the empty set, which has consequences for deriving Choquet integral representations in the literature using this approach. We point out that results for several transforms (e.g. Möbius, or co-Möbius transform) are not affected, but it is not the case of others (e.g. Fourier transform). In this spirit, we also provide a new formula for the Choquet integral representation via the Shapley interaction transform. [ABSTRACT FROM AUTHOR]

• A fast and highly accurate frequency estimation algorithm based on the union of amplitude-phase is proposed to redundant calculations and errors arising from the fast fourier transform process are reduced. • The size of the drive data is only 1 × 12 dimensions. • The neural network has simple structure, fast training and low calculation cost, which is conducive to the implementation in embedded system. • The model has strong universality and can be used to change of load power, cable length, load type, cable parameters and other working conditions. • According to the existing proposed low voltage AC series arc fault location methods, the method proposed in this paper has the highest positioning accuracy and the widest application range. In recent years, the safety of civil electricity has been seriously affected by low-voltage AC series arc faults. However, for indoor distribution lines (220 V/50 Hz), only a few researchers pay attention to the research of AC series arc fault location. Therefore, a fault location method of low-voltage AC series arc based on RBF neural network is proposed. Firstly, a fast and highly accurate frequency estimation algorithm based on the union of amplitude-phase is proposed to redundant calculations and errors arising from the Fast Fourier Transform (FFT) process are reduced. The proposed method extracts the voltage and current signals in the 0∼3 kHz frequency band. The current amplitude difference per meter of the line is calculated. However, influenced by the dynamic arc resistance, the minor differences no longer correspond to the actual fault point. The arc fault location model is trained by integrating the RBF neural network, and the deviation is eliminated. The performance of the model has also been verified in a variety of operating conditions with actual measurement data. The results show that the established localization model is generic and can be applied to complex indoor cable scenarios. [ABSTRACT FROM AUTHOR]

Although great success has been achieved in various computer vision tasks, deep neural networks (DNNs) suffer dramatic performance degradation when evaluated on out-of-distribution data. Domain generalization (DG) is proposed to handle this problem by learning domain-agnostic information from multiple source domains to generalize well on unseen target domains. Several methods resort to Fourier transform due to its simplicity and efficiency. They argue that amplitude spectra imply domain-specific information, which should be suppressed, while phase counterparts imply domain-agnostic information, which should be preserved. However, these methods only suppress the domain-specific information in source domains and neglect the relationship with target domains, leading to the persistence of the domain gap. Besides, these methods preserve domain-agnostic information by keeping phase components unchanged, causing them to be underutilized. In this paper, we propose Dual Branch Augmentation Module (DBAM) by leveraging Fourier transform and taking advantage of both amplitude and phase spectra. For the amplitude branch, we propose Inner-domain Amplitude Distribution Rectification (IADR) and Cross-domain Amplitude Dirichlet Mixup (CADM) to stabilize the training process and explore more feature space. In addition, we propose Test-time Amplitude Prototype Calibration (TAPC) to construct the connection between source and target domains during evaluation to further mitigate the domain gap. For the phase branch, we propose Random Symmetric Phase Perturbation (RSPP) to enhance the robustness for recognizing domain-agnostic information. With the combined contributions of the two branches, DBAM significantly surpasses other state-of-the-art (SOTA) methods. Extensive experiments on four benchmarks and further analysis demonstrate the effectiveness of DBAM. [ABSTRACT FROM AUTHOR]

The paper concerns problems of the recovery of operators from noisy information in weighted L q -spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the L p -metric. [ABSTRACT FROM AUTHOR]

The product q · q in Section 4 and Appendix should be replaced by qq. [ABSTRACT FROM AUTHOR]

An infinitely smooth symmetric convex body K ⊂ R d is called k -separably integrable, 1 ≤ k < d , if its k -dimensional isotropic volume function V K , H (t) = H d ({ x ∈ K : dist (x , H ⊥) ≤ t }) can be written as a finite sum of products in which the dependence on H ∈ Gr k (R d) and t ∈ R is separated. In this paper, we will obtain a complete classification of such bodies. Namely, we will prove that if d − k is even, then K is an ellipsoid, and if d − k is odd, then K is a Euclidean ball. This generalizes the recent classification of polynomially integrable convex bodies in the symmetric case. [ABSTRACT FROM AUTHOR]

This paper studies thermo-hydro-mechanical (T-H-M) coupled responses of layered transversely isotropic (TI) saturated media under moving thermal and mechanical loads. Firstly, governing equations including dynamic balance equations, T-H-M coupled constitutive equations, and generalized energy equations are established based on the thermodynamics and poroelastic mechanics. Next, the Fourier transform technology is utilized to transform complex coupled partial differential equations into ordinary ones in the wavenumber domain. With the help of a moving coordinate system, the key matrix equation of the moving load problem is derived. Then, combining with boundary, external load and interlayer continuity conditions, the extended precise integration method (PIM) is used to derive the solution in the wavenumber domain. After using the Gauss-Legendre numerical integration technique, the physical solution is obtained by programming on the MATLAB platform. Finally, numerical examples are designed to verify the proposed method, and further explore the influences of thermal loads, TI permeability and stratification on the T-H-M response. [ABSTRACT FROM AUTHOR]

Through optimization of terminal frequencies and effective sampling rates, we have developed nonlinear sawtooth-shaped frequency sweeps for efficient Fourier transform ion mobility mass spectrometry (FT-IM-MS) experiments. This is in contrast to conventional FT-IM-MS experiments where ion gates are modulated according to a linear frequency sweep. Linear frequency sweeps are effective but can be hindered by the amount of useful signal obtained using a single sweep over a large frequency range imposed by ion gating inefficiencies, particularly small ion packets, and gate depletion. These negative factors are direct consequences of the inherently low gate pulse widths of high-frequency ion gating events, placing an upper bound on FT-IM-MS performance. Here, we report alternative ion modulation strategies. Sawtooth frequency sweeps may be constructed for the purpose of either extending high-SNR transients or conducting efficient signal-averaging experiments for low-SNR transients. The data obtained using this approach show high-SNR signals for a set of low-mass tetraalkylammonium salts (<1000 m / z) where resolving powers in excess of 500 are achieved. Data for low-SNR obtained for multimeric protein complexes streptavidin (53 kDa) and GroEL (800 kDa) also reveal large increases in the signal-to-noise ratio for reconstructed arrival time distributions. [Display omitted] • Nonlinear frequency modulation increases efficiency and performance for atmospheric pressure ion mobility mass spectrometry. • Resolving power increases for low-mass analytes with high-SNR transients. • SNR increases for large multimeric proteins with low-SNR transients. [ABSTRACT FROM AUTHOR]

Let F q [ t ] be the polynomial ring over the finite field F q of q elements. For 1 ≤ j ≤ l , let a j , a j ′ ∈ F q [ t ] with a j ≠ 0. Let H (x) denote the product of l linear functions a j x + a j ′. Let X (H) be the set of all monic polynomials n in F q [ t ] such that H (n) is the product of l monic irreducible polynomials in F q [ t ]. The Hardy-Littlewood l -tuple conjecture provides an asymptotic formula for the cardinality of the set A N : = { n ∈ X (H) : deg ⁡ n = N } when N tends to ∞. In this paper an F q [ t ] -version of the enveloping sieve theory is established by following the constructing method of Green-Tao. It is applied to give an upper bound for the cardinality of ⋃ j < N A j. It is also applied to obtain Lebesgue space estimates for the exponential sum over X (H). These results are the best possible if the Hardy-Littlewood l -tuple conjecture is true. [ABSTRACT FROM AUTHOR]

Dynamic simulation of thermal systems is crucial for their optimal control but facing the challenge of balancing calculation accuracy and efficiency, where numerically high-efficient and accurate heat exchanger (HX) modeling is a key. Herein, we propose a frequency domain model for HXs' dynamic simulation in the to meet this challenge. The governing equations of HXs are first converted to frequency domain through Fourier transform, and the analytical solution of the converted equations yields the frequency domain HX model in the form of transfer matrix that connects the inlet temperature variations and outlet temperature responses. Furthermore, integrating transfer matrices of HXs into the system's transfer matrix enables a high-efficiency thermal system simulation. Numerical cases of a single HX, a HX network, a district heating network, and a thermodynamic cycle are used to validate the developed method and demonstrate its efficacy by comparing it against finite difference/volume method. Results show that the proposed method could reduce the calculation time by 2–3 orders of magnitude, and the maximum deviation of node temperature is around 1 K. The proposed method can be a powerful tool for the analysis of thermal systems and potentially integrated energy systems. • Propose a dynamic frequency domain model for heat exchangers with Fourier transform. • Analytical solution of the dynamic model gives the outlet temperatures directly. • The proposed HX model can be directly integrated in thermal system simulation. • Calculation time is reduced by 2–3 orders of magnitude with the same accuracy. [ABSTRACT FROM AUTHOR]

• Semi-analytic methods are used to solve 3D DPL problems. • Compared with FEM, the semi-analytic method has higher computational efficiency. • The phase lag of heat flow and the phase lag of temperature gradient have influence on the temperature response speed and the formation of temperature field. With the development of picosecond laser technology, the dual-phase-lagging (DPL) model is more suitable to describe the heat transfer problem with micro-scale effect and micro-time effect. In this paper, a three-dimensional dual-phase-lagging heat transfer model for picosecond laser processing is established. Then Fourier transform (FT) and Laplace transform (LT) are used to derive the frequency response functions (FRFs) of the problem in the frequency domain, and the inverse Laplace transform (ILT) and discrete-convolution fast Fourier transform (DC-FFT) algorithm are used to solve the temperature field. The calculation accuracy of this method is verified and the effect of phase lag constants on temperature field is studied. The results show that the semi-analytical method has a high accuracy for solving the dual-phase-lagging heat conduction model, and the phase lag of heat flux will affect the heating rate in the heating stage, and the phase lag of temperature gradient will delay the formation of temperature field. The effect of phase lag constants on temperature-time history is investigated and the related phenomena are explained by using the two-step heat transfer theory. This semi-analytical method provides a new approach to solve the problem of three-dimensional dual-phase-lagging heat transfer. [ABSTRACT FROM AUTHOR]

• We introduce unified equations of multifield and quasicrystal materials. • We present a matrix approach for derivation of three-dimensional Green's functions. • We present a detailed study of the fundamental solution for all considered media. Present paper considers anisotropic elastic, magnetoelectroelastic and quasicrystal solids. It is shown that the equations of time-harmonic motion and constitutive relations for considered materials can be presented in the compact and unified form. The matrix approach is proposed for derivation of 3D time-harmonic Green's functions for considered materials. The cases of each material type are studied separately. Two models of phason field dynamics in quasicrystals are considered in details. It is shown that in the case of phason field models based on the use of hydrodynamic formulations, phonon oscillations have an elastic nature, while the phason field leads to their decay due to phonon-phason interaction. The strict proof is given to the statement that the eigenvalues of the time-harmonic magnetoelectroelaticity problem are all positive. The paper also shows the application of the obtained time-harmonic Green's functions in obtaining the boundary integral equations for the considered classes of problems. For this purpose, the novel approach is proposed, which utilizes only the symmetry of the unified material property tensor and the inertia matrix. Derived boundary integral equations can be used in the solution of boundary value problems for considered classes of materials. [ABSTRACT FROM AUTHOR]