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The rising occurrence of digitally driven public consumer complaints has made it necessary for enterprises to obtain consumer forgiveness. However, existing research has provided little understanding regarding how to obtain consumer forgiveness effectively. Thus, the present study examined how brand avatars can improve consumer forgiveness in the context of public apology.

This study tested the mechanism of a brand avatar on consumer forgiveness using three studies. Specifically, we explored the direct and mediating effect of empathy toward a brand (Study 1); we identified the moderating mediating effect of humorous responses (Study 2) and product type (Study 3). Data for these studies were collected on Credamo. We analyzed the data using SPSS (26.0) for the primary analysis and PROCESS (3.5) for the mediating and moderating mediating analysis.

The results indicate that brand avatars enhance consumer forgiveness. Moreover, empathy toward a brand plays a mediating role in the effect of brand avatars on consumer forgiveness. Additionally, when a humorous response is present, a brand avatar can enhance customer forgiveness through empathy toward that brand. Compared to utilitarian products, hedonic products can also increase the impact of a brand avatar on empathy toward the brand, thus enhancing consumers' forgiveness.

From the perspective of emotion, this study explored the impact of brand avatars on consumer forgiveness via empathy toward a brand. It augments the research on brand avatars and consumer forgiveness. The study also verified the moderating mediating effect of humor response and product type while expanding the brand avatar research boundary.

The performance of the measurement matrix directly affects the quality of reconstruction of compressive sensing signal, and it is also the key to solve practical problems. In order to solve data collection problem of wireless sensor network (WSN), the authors design a kind of optimization of sparse matrix. The paper aims to discuss these issues.

Based on the sparse random matrix, it optimizes the seed vector, which regards elements in the diagonal matrix of Hadamard matrix after passing singular value decomposition (SVD). Compared with the Toeplitz matrix, it requires less number of independent random variables and the matrix information is more concentrated.

The performance of reconstruction is better than that of Gaussian random matrix. The authors also apply this matrix to the data collection scheme in WSN. The result shows that it costs less energy and reduces the collection frequency of nodes compared with general method.

The authors design a kind of optimization of sparse matrix. Based on the sparse random matrix, it optimizes the seed vector, which regards elements in the diagonal matrix of Hadamard matrix after passing SVD. Compared with the Toeplitz matrix, it requires less number of independent random variables and the matrix information is more concentrated.

Micro-holes are drilled and plated in flexible printed circuit boards (FPCs) for connecting circuits from different layers. More holes, with diameters smaller than 0.3 mm, are required to be drilled in smaller areas with flexible circuits’ miniaturization. The micro-hole quality of micro-drilling is one of the biggest issues of the flexible circuit manufacturers’ production. However, it is not easy to control the quality of micro-holes. The purpose of this study was to conduct research on the tool wear characteristics of FPC drilling process and its influence on micro-hole quality to improve the micro-hole quality of FPC.

The tool-wear characteristics of micro-drills after FPC drilling were observed. The influence of spindle speed, feed rate, number of drilled holes and entry board materials on tool-wear was analyzed. The hole qualities of FPC micro-drilling were measured and observed. The relationship between tool-wear and hole quality was analyzed.

The result showed that the tool-wear characteristics of FPC micro-drilling was similar to the tool-wear characteristics of rigid printed circuit board (RPC) micro-drilling. Abrasive wear occurred on both the main cutting edges and the chisel edges of micro-drills, even though there was no glass fiber reinforcing the cloth inside FPC. Resin adhesion was observed on the chisel edge. The influence of feed and number of drilled holes on tool-wear was significant. Tool-wear significantly influences the hole quality of FPC. Tool-wear will largely decrease the hole position accuracy of FPC micro-holes. Tool-wear will increase the thickness of PI nail heads and the height of exit burrs. Fracture was the main difference between tool wear of FPC and RPC micro-drilling. Resin adhesion of RPC was much more severe than FPC micro-drilling. Increasing the spindle speed properly may improve tool life and hole quality.

The technology and manufacturing of FPC has been little investigated. Research on micro-drilling FPC and research data is lacking so far. The micro-hole quality directly affects the reliability of FPC. Thus, improving the micro-hole quality of FPC is very important.

The purpose of this study is to present the entry drilling process of flexible printed circuit board (FPCs) and its influence on hole quality, especially hole location accuracy. Compared with the traditional PCB drilling process, the technology of drilling FPCs is facing more problems, such as hole location accuracy, smear on the hole wall surface, burned hole wall surface, etc. Moreover, the materials of FPCs are quite different from the rigid printed circuit boards (RPCs). FPCs no longer contain glass fiber cloths to reinforce resin, resulting in flexibility. Micro-hole quality is the most important issue in FPC drilling. Suggestions were given to obtain higher hole qualities and higher FPC reliability.

The entry drilling process of FPC with different kind of entry boards was observed by a high-speed camera. The hole qualities of FPC micro-drilling, especially hole location accuracy and hole entrance quality, were measured. The relationship between entry boards and hole quality was analyzed.

Significant sliding occurred when drilling FPC with using no-entry board or pure aluminum plate entry board. On the contrary, no significant sliding occurred when using LC-110 or resin-coated aluminum foil (MVC) entry boards. The type, thickness and use-pattern of entry boards influenced hole location accuracy of FPCs seriously. In addition, entry board also influenced the micro-hole entrance quality and micro-hole diameter. The entrance quality of drilling FPC with LC-110 entry board was the best. The diameter variation of drilling FPC with MVC entry board was the smallest. The hole location accuracy decreased as the thickness of entry board increased. Thus, the best use-pattern of entry board was putting a LC-110 under MVC entry board, resulting in best entrance quality and hole location accuracy.

The technology and manufacturing of FPCs in China are obviously behind. Research of FPCs micro-drilling and research data are lacking so far. Thus, it is most necessary to improve the technology level of FPCs micro-drilling in China. Researches on hole quality, especially hole location accuracy of FPCs drilling, were performed in this paper. Suggestions were given to obtain higher hole quality of FPCs.

Compared with the traditional printed circuit board (PCB) drilling process, the technology of drilling IC substrate is facing more problems, such as much smaller hole diameter, more intensive hole space, thinner sheet and more complicated materials are drilled in process. Moreover, the base material of IC substrate is different from traditional PCB, more kinds of fillers added in IC substrate which make the drill worn seriously during drilling process. Micro-drills wear and micro holes quality are the most important questions when drilling IC substrate so far. Wear morphology of micro-drill, holes wall roughness and hole location accuracy are researched in this paper. The influence factors of micro-drills wear and micro holes quality are also studied in this drilling process. The paper aims to discuss these issues.

Two drills with same structure and different diameter are used to drill different stacks of IC substrate and drill different holes in this paper. There are four experiments made and the drilling parameters including spindle speed (n), feed rate (v_f) and retraction speed (v_r) are recommended by drill manufacturing company. Wear morphologies of drill are observed, holes wall roughness (R_max) and holes location accuracy (C_pk) are measured in this paper. Analyzing the main factors influence on drill wear, holes wall roughness and holes location accuracy through these experiments.

The micro-drills of IC substrate wear more severely compared with other material of PCB through the experimental results in this paper. Drill diameter has influence on micro-drill wear when drilling IC substrate, the smaller of drill is, the more severely of micro-drill wears. Drill diameter affect the holes wall roughness too, the holes wall roughness of larger holes is better than smaller one in a certain range. The drilled holes number also has influence on micro-drills wear, holes wall roughness and holes location accuracy. The more drilled holes, the seriously of micro-drills wear, and the worn drill would destroy the hole quality. Therefore, the more drilled holes lead the bad holes wall roughness and holes location accuracy in this paper. In addition, stacks of IC substrate affect much on the holes location accuracy, the more stacks, the worse holes location accuracy.

Chinese Mainland is obviously lagging behind in technology and manufacturer of IC substrate which is incompatible with the nation circumstances. There is few research of drilling IC substrate in China and research data are lacking so far. It is most necessary to improve the technology level of drilling IC substrate in China. In order to reduce the wear of micro-drills and improve the quality of micro-holes, many experimental tests about drilling IC substrate are researched in this paper.