The largest singletons of set partitions

Recently, Deutsch and Elizalde studied the largest and the smallest fixed points of permutations. Motivated by their work, we consider the analogous problems in set partitions. Let $A_{n,k}$ denote the number of partitions of $\{1,2,\dots, n+1\}$ with the largest singleton $\{k+1\}$ for $0\leq k\leq n$. In this paper, several explicit formulas for $A_{n,k}$, involving a Dobinski-type analog, are obtained by algebraic and combinatorial methods, many combinatorial identities involving $A_{n,k}$ and Bell numbers are presented by operator methods, and congruence properties of $A_{n,k}$ are also investigated. It will been showed that the sequences $(A_{n+k,k})_{n\geq 0}$ and $(A_{n+k,k})_{k\geq 0}$ (mod $p$) are periodic for any prime $p$, and contain a string of $p-1$ consecutive zeroes. Moreover their minimum periods are conjectured to be $N_p=\frac{p^p-1}{p-1}$ for any prime $p$.Comment: 14page

Silica sulfuric acid: a versatile and reusable heterogeneous catalyst for the synthesis of N-acyl carbamates and oxazolidinones under solvent-free conditions

Silica sulfuric acid catalyzes efficiently the reaction of carbamates and oxazolidinones with anhydrides under solvent-free conditions. All the reactions were done at room temperature and the N-acyl carbamates and oxazolidinones were obtained with high yields and purity via an easy work-up procedure. This method is attractive and is in a close agreement with green chemistry.KEY WORDS: N-Acyl carbamates, N-Acyl oxazolidinones, Silica sulfuric acid, Solvent-free Bull. Chem. Soc. Ethiop. 2011, 25(1), 151-155

Failure prediction of ultra capacitor stack using fuzzy inference system

The failure of the ultracapacitor was significantly accelerated by elevated temperature or increased voltage. Because of the capacitance difference between the capacitor cells, after a number of deep charging/discharging cycles, the voltage difference between cells will be enlarged. This will accelerate the aging of the weak ultracapacitors and affect the output power. So, to improve stack reliability, a correct and timely failure prediction is essential. Based on diverse faults, a fuzzy rule-based inference system, which could approximate human reasoning, was considered. With this method we can reduce uncertainty, inconvenience and inefficiency resulting from the inherent factors. The simulate results under industrial application conditions are given to verify the method

End-to-End Learning for Simultaneously Generating Decision Map and Multi-Focus Image Fusion Result

The general aim of multi-focus image fusion is to gather focused regions of different images to generate a unique all-in-focus fused image. Deep learning based methods become the mainstream of image fusion by virtue of its powerful feature representation ability. However, most of the existing deep learning structures failed to balance fusion quality and end-to-end implementation convenience. End-to-end decoder design often leads to unrealistic result because of its non-linear mapping mechanism. On the other hand, generating an intermediate decision map achieves better quality for the fused image, but relies on the rectification with empirical post-processing parameter choices. In this work, to handle the requirements of both output image quality and comprehensive simplicity of structure implementation, we propose a cascade network to simultaneously generate decision map and fused result with an end-to-end training procedure. It avoids the dependence on empirical post-processing methods in the inference stage. To improve the fusion quality, we introduce a gradient aware loss function to preserve gradient information in output fused image. In addition, we design a decision calibration strategy to decrease the time consumption in the application of multiple images fusion. Extensive experiments are conducted to compare with 19 different state-of-the-art multi-focus image fusion structures with 6 assessment metrics. The results prove that our designed structure can generally ameliorate the output fused image quality, while implementation efficiency increases over 30\% for multiple images fusion.Comment: repor

In-situ Model Downloading to Realize Versatile Edge AI in 6G Mobile Networks

The sixth-generation (6G) mobile networks are expected to feature the ubiquitous deployment of machine learning and AI algorithms at the network edge. With rapid advancements in edge AI, the time has come to realize intelligence downloading onto edge devices (e.g., smartphones and sensors). To materialize this version, we propose a novel technology in this article, called in-situ model downloading, that aims to achieve transparent and real-time replacement of on-device AI models by downloading from an AI library in the network. Its distinctive feature is the adaptation of downloading to time-varying situations (e.g., application, location, and time), devices' heterogeneous storage-and-computing capacities, and channel states. A key component of the presented framework is a set of techniques that dynamically compress a downloaded model at the depth-level, parameter-level, or bit-level to support adaptive model downloading. We further propose a virtualized 6G network architecture customized for deploying in-situ model downloading with the key feature of a three-tier (edge, local, and central) AI library. Furthermore, experiments are conducted to quantify 6G connectivity requirements and research opportunities pertaining to the proposed technology are discussed.Comment: The paper has been submitted to IEEE for possible publicatio

Trends in corporate social responsibility reporting. The case of Chinese listed companies

Compared with Western developed countries, corporate social responsibility (CSR) implementation in China started relatively late, but so far, its development has been going on for more than ten years. Therefore, the development process of CSR reporting as a vital tool to reflect the CSR related information of Chinese listed companies is worth studying. It has been asserted in a large amount of literature that the government of a country has an important influence on the development of CSR reporting. Thus, in this paper, we aim to study the trends in CSR reporting practices of Chinese listed companies through statistical analysis methods and then consider the role of the government in it. The results show that the number of CSR reports issued by Chinese listed companies has increased year by year; notably, the number of voluntary CSR disclosure and environmental information disclosure has increased significantly. However, the overall disclosure rate of CSR reports is low and shows no upward trend, the published CSR reports lack third-party certification, and the information disclosure level of most CSR reports is concentrated at a relatively low level. The findings provide some useful references for the future development of Chinese CSR related laws, regulations, and guidelines.Web of Science1315art. no. 864