Regularity of very weak solutions for elliptic equation of divergence form

AbstractIn this paper, we study the local regularity of very weak solution u∈Lloc1(Ω) of the elliptic equation Dj(aij(x)Diu)=0. Using the bootstrap argument and the difference quotient method, we obtain that if aij∈Cloc0,1(Ω), then u∈Wloc2,p(Ω) for any p<∞

The Developing Blueberry Industry in China

The present situation of blueberry industry in China was summarized. The six main blueberry cultivation areas in China were reviewed and practical suggestions were made. Reference and guidance for water management of rabbiteye blueberry in Yangtze river basin was provided, and water physiological characteristics and water requirement of blueberry were also clarified so as to provide scientific management of blueberry. Effects of vinegar residue on soil physical and chemical properties, enzymatic activities, growth of blueberry, nutrient uptake, and fruit quality were studied. The effect of vinegar residue on the growth of blueberry and the mechanism revealed from the perspective of soil amelioration were also discussed from the results

Effect of Al on the growth and nutrients uptake of blueberries (Vaccinium spp.)

Aluminum (Al) is the major factor limiting plant growth on acidic soils. Blueberry (Vaccinum spp.) is an acidophilic plant. Highbush blueberry and rabbiteye blueberry are the main commercially cultivated species, while the response of which to Al is still unclear. Therefore, hydroponic experiments were conducted to determine the effect of Al (0 and 100 μmol L−1) on the growth and nutrient uptake of highbush blueberry ‘Brigitta’ and rabbiteye blueberry ‘Brightwell’. The results showed that root biomass, root length per fresh weight, root activity and foliar nitrogen (N) concentration of ‘Brigitta’ were significantly decreased by Al, while root lipid peroxidation was increased by Al. In contrast, the biomass and root activity of ‘Brightwell’ were not affected by Al treatment, root lipid peroxidation was significantly decreased, root length and surface area per fresh weight were increased compared with the control, which was benefic for nutrients absorption. In fact, foliar N concentration of ‘Brightwell’ was increased in Al treatments. However, fewer Al was accumulated in leaves of ‘Brightwell’ compared to ‘Brigitta’. Therefore, it could be concluded that growth and nutrients uptake of ‘Brightwell’ was not negative affected by Al, which meant ‘Brightwell’ was resistant to Al, compared to ‘Brigitta’

Holographic MIMO Communications with Arbitrary Surface Placements: Near-Field LoS Channel Model and Capacity Limit

Envisioned as one of the most promising technologies, holographic multiple-input multiple-output (H-MIMO) recently attracts notable research interests for its great potential in expanding wireless possibilities and achieving fundamental wireless limits. Empowered by the nearly continuous, large and energy-efficient surfaces with powerful electromagnetic (EM) wave control capabilities, H-MIMO opens up the opportunity for signal processing in a more fundamental EM-domain, paving the way for realizing holographic imaging level communications in supporting the extremely high spectral efficiency and energy efficiency in future networks. In this article, we try to implement a generalized EM-domain near-field channel modeling and study its capacity limit of point-to-point H-MIMO systems that equips arbitrarily placed surfaces in a line-of-sight (LoS) environment. Two effective and computational-efficient channel models are established from their integral counterpart, where one is with a sophisticated formula but showcases more accurate, and another is concise with a slight precision sacrifice. Furthermore, we unveil the capacity limit using our channel model, and derive a tight upper bound based upon an elaborately built analytical framework. Our result reveals that the capacity limit grows logarithmically with the product of transmit element area, receive element area, and the combined effects of $1/{{d}_{mn}^2}$, $1/{{d}_{mn}^4}$, and $1/{{d}_{mn}^6}$ over all transmit and receive antenna elements, where $d_{mn}$ indicates the distance between each transmit and receive elements. Numerical evaluations validate the effectiveness of our channel models, and showcase the slight disparity between the upper bound and the exact capacity, which is beneficial for predicting practical system performance.Comment: 30 pages, 8 figure

Mean Field Game-based Waveform Precoding Design for Mobile Crowd Integrated Sensing, Communication, and Computation Systems

Data collection and processing timely is crucial for mobile crowd integrated sensing, communication, and computation~(ISCC) systems with various applications such as smart home and connected cars, which requires numerous integrated sensing and communication~(ISAC) devices to sense the targets and offload the data to the base station~(BS) for further processing. However, as the number of ISAC devices growing, there exists intensive interactions among ISAC devices in the processes of data collection and processing since they share the common network resources. In this paper, we consider the environment sensing problem in the large-scale mobile crowd ISCC systems and propose an efficient waveform precoding design algorithm based on the mean field game~(MFG). Specifically, to handle the complex interactions among large-scale ISAC devices, we first utilize the MFG method to transform the influence from other ISAC devices into the mean field term and derive the Fokker-Planck-Kolmogorov equation, which model the evolution of the system state. Then, we derive the cost function based on the mean field term and reformulate the waveform precoding design problem. Next, we utilize the G-prox primal-dual hybrid gradient algorithm to solve the reformulated problem and analyze the computational complexity of the proposed algorithm. Finally, simulation results demonstrate that the proposed algorithm can solve the interactions among large-scale ISAC devices effectively in the ISCC process. In addition, compared with other baselines, the proposed waveform precoding design algorithm has advantages in improving communication performance and reducing cost function.Comment: 13 pages,9 figure

Electromagnetic Hybrid Beamforming for Holographic Communications

It is well known that there is inherent radiation pattern distortion for the commercial base station antenna array, which usually needs three antenna sectors to cover the whole space. To eliminate pattern distortion and further enhance beamforming performance, we propose an electromagnetic hybrid beamforming (EHB) scheme based on a three-dimensional (3D) superdirective holographic antenna array. Specifically, EHB consists of antenna excitation current vectors (analog beamforming) and digital precoding matrices, where the implementation of analog beamforming involves the real-time adjustment of the radiation pattern to adapt it to the dynamic wireless environment. Meanwhile, the digital beamforming is optimized based on the channel characteristics of analog beamforming to further improve the achievable rate of communication systems. An electromagnetic channel model incorporating array radiation patterns and the mutual coupling effect is also developed to evaluate the benefits of our proposed scheme. Simulation results demonstrate that our proposed EHB scheme with a 3D holographic array achieves a relatively flat superdirective beamforming gain and allows for programmable focusing directions throughout the entire spatial domain. Furthermore, they also verify that the proposed scheme achieves a sum rate gain of over 150% compared to traditional beamforming algorithms.Comment: 13 page

Technological Evolution from RIS to Holographic MIMO

Multiple-input multiple-output (MIMO) techniques have been widely applied in current cellular networks. To meet the ever-increasing demands on spectral efficiency and network throughput, more and more antennas are equipped at the base station, forming the well-known concept of massive MIMO. However, traditional design with fully digital precoding architecture brings high power consumption and capital expenditure. Cost- and power-efficient solutions are being intensively investigated to address these issues. Among them, both reconfigurable intelligent surface (RIS) and holographic MIMO (HMIMO) stand out. In this chapter, we will focus on the ongoing paradigm shift from RIS to HMIMO, covering both topics in detail. A wide range of closely related topics, e.g., use cases, hardware architectures, channel modeling and estimation, RIS beamforming, HMIMO beamforming, performance analyses of spectral- and energy-efficiency, and challenges and outlook, will be covered to show their potential to be applied in the next-generation wireless networks as well as the rationales for the technological evolution from RIS to holographic MIMO

Enhancing the Carbon Monoxide Oxidation Performance through Surface Defect Enrichment of Ceria-Based Supports for Platinum Catalyst.

Effective synthesis and application of single-atom catalysts on supports lacking enough defects remain a significant challenge in environmental catalysis. Herein, we present a universal defect-enrichment strategy to increase the surface defects of CeO2-based supports through H2 reduction pretreatment. The Pt catalysts supported by defective CeO2-based supports, including CeO2, CeZrOx, and CeO2/Al2O3 (CA), exhibit much higher Pt dispersion and CO oxidation activity upon reduction activation compared to their counterpart catalysts without defect enrichment. Specifically, Pt is present as embedded single atoms on the CA support with enriched surface defects (CA-HD) based on which the highly active catalyst showing embedded Pt clusters (PtC) with the bottom layer of Pt atoms substituting the Ce cations in the CeO2 surface lattice can be obtained through reduction activation. Embedded PtC can better facilitate CO adsorption and promote O2 activation at PtC-CeO2 interfaces, thereby contributing to the superior low-temperature CO oxidation activity of the Pt/CA-HD catalyst after activation