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An RD-space 푀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 푀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé's class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces. [ABSTRACT FROM AUTHOR]

The body–boundary correspondence refers to the relationship between the body and boundary states of topological insulators (TIs). In TIs, the presence of boundary states is connected to the bulk topological properties of the material. The topology can be identified by studying the energy of the topological modes within the bulk bandgap. However, not all topological materials exhibit boundary states within the insulating energy gap. In many cases, the presence of boundary states can be hidden or masked by the bulk energy bands, making it difficult to measure TIs. Recent experiments have shown that defects, which are commonly found in crystalline materials, can be used as probes to explore higher-order topologies that have been recently realized on various platforms. These defects can generate fractional charges and stable bound states in the dispersion region, allowing us to observe the clear body–disclination correspondence. We have performed simulations using a coupled acoustic cavity system with C3 and C5 symmetries to investigate the body–disclination correspondence in topological crystal insulators (TCIs) in the field of acoustics. Simulation and theoretical results have demonstrated that defects such as disclinations can be used to probe higher-order topologies that were previously unobservable in three-dimensional structures. This approach allows us to detect fractional mode charges and stable bound states, which are crucial for understanding the topological nature of TCIs. Our work demonstrates the potential of using disclination defects to study the intricate relationship between the body and boundary states in topological materials, particularly in the context of acoustics. [ABSTRACT FROM AUTHOR]

The measurement of topological insulators is usually achieved by measuring spectra, which is inadequate in higher-order topological insulators because the separation of bandgaps may be blurred, such as body boundaries and corner state hybridization, and the above measurement requires that the energy of the topological mode must be located in the bulk bandgap to be measured. Recent experiments have shown a strong relationship between the fractional mode charge and the location of the Wannier center in the crystal body. The fractional quantization of the corner charge originates from the filling anomaly, and the fractional mode charge can be calculated from experimental measurements of the local density of states to describe the topological state of the system, which has been demonstrated in optical systems. We have achieved a similar effect in acoustics by utilizing a coupled acoustic-cavity system featuring C3, C4, and C6 symmetries for simulation. Furthermore, we extended our study to 3D third-order topological crystalline insulators to validate the fractional-corner charge approach. The simulation and theoretical results demonstrate that the fractional mode charge can clearly identify the high-order topology, even without gap states. [ABSTRACT FROM AUTHOR]

Non-Hermitian factors play a key role in introducing changes to the topology of acoustic systems, by significantly expanding the classification of topological phases beyond traditional Hermitian theory and presenting challenges to the conventional bulk–boundary correspondence. Traditional Hermitian theory cannot fully describe the complicated behavior of systems interacting with their environment, thus non-Hermitian theory emerged. Currently, most non-Hermitian topological systems derive their phases from Hermitian components, which entails concurrently considering the gain and loss of the system. In the study of higher-order topological insulators, higher-order topological states are usually achieved by modulating coupling strengths. While traditionally it is viewed that dissipation in topological systems is detrimental to the topological states, recent research studies have challenged this perspective. The nontrivial topology can arise by introducing loss of a specific configuration in a trivial phase. In this study, through finite-element simulations of coupled acoustic cavity systems from one-dimensional to three-dimensional structure, it is illustrated how intentionally introducing non-Hermitian loss can induce the higher-order topology. More crucially, we have simulated the acoustic local density of states (LDOS) and calculated fractional charge modes and can directly observe and prove through LDOS that introducing loss can convert a trivial system into a topological one. Both theoretical and simulated results show that the LDOS can be used to calculate fractional charge modes, effectively characterizing higher-order topological states in non-Hermitian acoustic systems. This study carves out a research pathway for the future of non-Hermitian acoustic topology. [ABSTRACT FROM AUTHOR]

Identifying rice cultivation areas in a timely and accurate manner holds great significance in comprehending the overall distribution pattern of rice and formulating agricultural policies. The remote sensing observation technique provides a convenient means to monitor the distribution of rice cultivation areas on a large scale. Single-source or single-temporal remote sensing images are often used in many studies, which makes the information of rice in different types of images and different growth stages hard to be utilized, leading to unsatisfactory identification results. This paper presents a rice cultivation area identification method based on a deep learning model using multi-source and multi-temporal remote sensing images. Specifically, a U-Net based model is employed to identify the rice planting areas using both the Landsat-8 optical dataset and Sentinel-1 Polarimetric Synthetic Aperture Radar (PolSAR) dataset; to take full into account of the spectral reflectance traits and polarimetric scattering traits of rice in different periods, multiple image features from multi-temporal Landsat-8 and Sentinel-1 images are fed into the network to train the model. The experimental results on China's Sanjiang Plain demonstrate the high classification precisions of the proposed Multi-Source and Multi-Temporal Rice Identification U-Net (MSMTRIU-NET) and that inputting more information from multi-source and multi-temporal images into the network can indeed improve the classification performance; further, the classification map exhibits greater continuity, and the demarcations between rice cultivation regions and surrounding environments reflect reality more accurately. [ABSTRACT FROM AUTHOR]

An attractive avenue for a memory device is offered by thermally induced magnetization switching (TIMS), which is expected to increase the storage density. As an essential step in TIMS, the transient ferromagnetic-like state (TFLS) has attracted much attention. Here, our research analyzes the TFLS from the perspective of magnetization rate based on extensive atomic spin simulations in a parameter space necessary for the formation of TIMS. The results demonstrate that the evolution of the magnetization rate for both Fe and Gd sublattices has two peaks at different timescales, and the two peaks are driven by the Langevin field and the exchange field, respectively. By modulating the pulse fluence, the initial temperature, the pulse duration, the electron–phonon coupling factor, and the damping constant, we find that the first peak of the magnetization rate depends not only on the electron thermal bath and temperature of the phonon but also on the energy transfer rate between the electronic system and the spin system. Moreover, we elucidate the role played by the Langevin field and the exchange field in TFLS formation when modulating the pulse fluence, initial temperature, and pulse duration. The simulation results show that the enhancement of the Langevin field prolongs the duration of TFLS. The enhancement of the exchange field at a long pulse duration before the electron system cools down leads to the shortening of the TFLS duration. However, the time required for Gd demagnetization after the electron system cools down to the Curie temperature changes only slightly when modulating these simulated parameters. [ABSTRACT FROM AUTHOR]

The authors consider the multilinear Riesz potential operator defined by , where denotes the -tuple , the nonnegative integers with , , and is a nonnegative -dimensional Borel measure. In this paper, the boundedness for the operator on the product of homogeneous Morrey-Herz spaces in nonhomogeneous setting is found.

Suppose that (X, d, µ) is a metric measure space of homogeneous type in the sense of Coifman and Weiss with a reverse doubling condition. By establishing the Littlewood-Paley characterization of Lipschitz spaces, a density argument in the weak sense and almost orthogonality estimate we prove that a Caldeŕon-Zygmund operator T is bounded on Lipschitz space if and only if T 1 = 0. [ABSTRACT FROM AUTHOR]

In this paper, the authors establish the three‐parameter Triebel–Lizorkin spaces and characterize these spaces as the intersection of two flag Triebel–Lizorkin spaces by applying the discrete Littlewood–Paley–Stein analysis. Moreover, they obtain the boundedness of product singular integral operators on the three‐parameter Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]