Periodic solutions for a porous medium equation

In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions

Dynamic Tagging for Enterprise Knowledge Sharing and Representation

The development of Web 2.0 technology provides an easy way for people to transfer and share knowledge. As a collaborative tagging tool, folksonomy is an efficient indexing method in Web 2.0 environments. After analyzing the pros and cons of current knowledge management systems, this research proposes a dynamic Tagging system that combines folksonomy technologies with other approaches including automatic schema enrichment and training. The proposed system improves access to a large, growing collection by supporting users collaboratively contribute to the building of tags. In addition, the proposed system provides an efficient way for firms to represent knowledge and share knowledge with customers and other firms

Image Denoising via Nonlinear Hybrid Diffusion

A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models

Electrochemical Sensors for Food Safety

Food safety poses an increasing threat to human health worldwide. The development of analytical methods and techniques to ensure food safety is therefore of great importance. Electrochemical sensors provide unique opportunity to realize sensitive, accurate, rapid, and portable detection for food safety. They have the potential to overcome the restrictions and limitations of traditional methods. In this chapter, we review the progress of electrochemical sensors for the detection of food contaminants including heavy metals, illegal additives, pesticide residues, veterinary drug residues, biological toxins, and foodborne pathogen. Future perspectives and challenges are also discussed

Capacity-based Spatial Modulation Constellation and Pre-scaling Design

Spatial Modulation (SM) can utilize the index of the transmit antenna (TA) to transmit additional information. In this paper, to improve the performance of SM, a non-uniform constellation (NUC) and pre-scaling coefficients optimization design scheme is proposed. The bit-interleaved coded modulation (BICM) capacity calculation formula of SM system is firstly derived. The constellation and pre-scaling coefficients are optimized by maximizing the BICM capacity without channel state information (CSI) feedback. Optimization results are given for the multiple-input-single-output (MISO) system with Rayleigh channel. Simulation result shows the proposed scheme provides a meaningful performance gain compared to conventional SM system without CSI feedback. The proposed optimization design scheme can be a promising technology for future 6G to achieve high-efficiency.Comment: 6 pages,conferenc

CDDM: Channel Denoising Diffusion Models for Wireless Semantic Communications

Diffusion models (DM) can gradually learn to remove noise, which have been widely used in artificial intelligence generated content (AIGC) in recent years. The property of DM for eliminating noise leads us to wonder whether DM can be applied to wireless communications to help the receiver mitigate the channel noise. To address this, we propose channel denoising diffusion models (CDDM) for semantic communications over wireless channels in this paper. CDDM can be applied as a new physical layer module after the channel equalization to learn the distribution of the channel input signal, and then utilizes this learned knowledge to remove the channel noise. We derive corresponding training and sampling algorithms of CDDM according to the forward diffusion process specially designed to adapt the channel models and theoretically prove that the well-trained CDDM can effectively reduce the conditional entropy of the received signal under small sampling steps. Moreover, we apply CDDM to a semantic communications system based on joint source-channel coding (JSCC) for image transmission. Extensive experimental results demonstrate that CDDM can further reduce the mean square error (MSE) after minimum mean square error (MMSE) equalizer, and the joint CDDM and JSCC system achieves better performance than the JSCC system and the traditional JPEG2000 with low-density parity-check (LDPC) code approach.Comment: submitted to IEEE Transactions on Wireless Communications. arXiv admin note: substantial text overlap with arXiv:2305.0916

Spectral Analysis of the Bounded Linear Operator in the Reproducing Kernel Space W

We first introduce some related definitions of the bounded linear operator L in the reproducing kernel space W2m(D). Then we show spectral analysis of L and derive several property theorems