The number of removable edges in a 4-connected graph

AbstractLet G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G−e; second, for all the vertices x of degree 3 in G−e, delete x from G−e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G⊖e. If G⊖e is still 4-connected, then e is called a removable edge of G. In this paper we prove that every 4-connected graph of order at least six (excluding the 2-cyclic graph of order six) has at least (4|G|+16)/7 removable edges. We also give the structural characterization of 4-connected graphs for which the lower bound is sharp

Research Progress in Techniques for Postharvest Preservation of Green Sweet Peppers

Green sweat peppers are rich in nutrients and diverse in shape and color. Apart from being eaten as a vegetable, it is widely used as seasoning and side dishes. Due to respiration and infection by harmful microorganisms, postharvest green peppers are prone to water loss, wilting and even rot. Appropriate preservation technology can maximize the preservation of nutrients and extend the storage period of green peppers. This paper introduces the techniques used for postharvest preservation of green sweet peppers: physical preservation methods such as refrigeration and packaging, biological preservatives such as microbial, plant and animal extracts, and chemical preservatives such as calcium agents and 1-methylcyclopropene (1-MCP), and compares the advantages and disadvantages of these preservation techniques. It elaborates the effect of chitosan or konjac glucomannan-based composite coatings on preserving the quality of green sweet peppers. Our intention is to provide a reference and guidance for the storage and preservation of postharvest green peppers

Towards a molecular understanding of cellulose dissolution in ionic liquids: anion/cation effect, synergistic mechanism and physicochemical aspects

Cellulose is one of the most abundant bio-renewable materials on the earth and its conversion to biofueIs provides an appealing way to satisfy the increasing global energy demand. However, before carrying out the process of enzymolysis to glucose or polysaccharides, cellulose needs to be pretreated to overcome its recalcitrance. In recent years, a variety of ionic Liquids (ILs) have been found to be effective solvents for cellulose, providing a new, feasible pretreatment strategy. A Lot of experimental and computational studies have been carried out to investigate the dissolution mechanism. However, many details are not fully understood, which highlights the necessity to overview the current knowledge of cellulose dissolution and identify the research trend in the future. This perspective summarizes the mechanistic studies and microscopic insights of cellulose dissolution in ILs. Recent investigations of the synergistic effect of cations/anions and the distinctive structural changes of cellulose microfibril in ILs are also reviewed. Besides, understanding the factors controlling the dissolution process, such as the structure of anions/cations, viscosity of ILs, pretreatment temperature, heating rate, etc., has been discussed from a structural and physicochemical viewpoint. At the end, the existing problems are discussed and future prospects are given. We hope this article would be helpful for deeper understanding of the cellulose dissolution process in ILs and the rational design of more efficient and recyclable ILs.</p

Coherent Optical Field Manipulation and Optical Information Processing Based on Electromagnetically-Induced Transparency Effect in Pr3+:Y2SiO5 Crystal

We reviewed the recent progress in coherent manipulation on light fields based on the electromagnetically-induced transparency (EIT) effect in Pr3+-doped Y2SiO5 crystal. The results show that, on one hand, the atomic coherence grating, formed when the light pulse is stored in Pr3+:Y2SiO5 crystal under the EIT condition has similar properties to the traditional holographic grating. On the other hand, the atomic coherence grating has its own unique characteristics that are different from those of traditional holographic grating. The EIT-induced nonlinearity and atomic coherence gratings can be used to manipulate the amplitude, the phase and the polarization state of light fields; therefore, they are of important applications for optical signal processing, quantum information processing and imaging processing

Edge Caching for D2D Enabled Hierarchical Wireless Networks with Deep Reinforcement Learning

Edge caching is a promising method to deal with the traffic explosion problem towards future network. In order to satisfy the demands of user requests, the contents can be proactively cached locally at the proximity to users (e.g., base stations or user device). Recently, some learning-based edge caching optimizations are discussed. However, most of the previous studies explore the influence of dynamic and constant expanding action and caching space, leading to unpracticality and low efficiency. In this paper, we study the edge caching optimization problem by utilizing the Double Deep Q-network (Double DQN) learning framework to maximize the hit rate of user requests. Firstly, we obtain the Device-to-Device (D2D) sharing model by considering both online and offline factors and then we formulate the optimization problem, which is proved as NP-hard. Then the edge caching replacement problem is derived by Markov decision process (MDP). Finally, an edge caching strategy based on Double DQN is proposed. The experimental results based on large-scale actual traces show the effectiveness of the proposed framework