Tensor Multivariate Trace Inequalities and their Applications

We prove several trace inequalities that extend the Araki Lieb Thirring (ALT) inequality, Golden Thompson (GT) inequality and logarithmic trace inequality to arbitrary many tensors. Our approaches rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent mechanism to treat generic tensor multivariate trace inequalities. As an example application of our tensor extension of the Golden Thompson inequality, we give the tail bound for the independent sum of tensors. Such bound will play a fundamental role in high dimensional probability and statistical data analysis

Toward World Englishes Writing: Is It Idealism in the Introductory Composition Class?

The purpose of the present study is to discover how teaching college introductory composition for international students within the World Englishes paradigm looks like. The study was conducted through questionnaires, blog entries, and interviews across three semesters in a public university in Indiana, America. In total, three introductory composition classes consisting of 41 students participated the study. The students were introduced to World Englishes through a series of related readings and the designed World Englishes workshop while they were also prepared for writing for other university courses. The results of this mixed-method study show that by learning about World Englishes, international undergraduates were able to improve their writing process – particularly the idea forming stage. Furthermore, it gave the students confidence to write in English when they were no longer stuck in the beginning of the writing. Learning about World Englishes made the students more positive about their cultures playing a role in their writing which also brought them more confidence. Lastly, learning about World Englishes helped the students identify rhetorical situations. Based on the findings, the author suggests that it is applicable to introduce World Englishes to international undergraduate English writing learners

Algebraic Connectivity Characterization of Ensemble Random Hypergraphs

Random hypergraph is a broad concept used to describe probability distributions over hypergraphs, which are mathematical structures with applications in various fields, e.g., complex systems in physics, computer science, social sciences, and network science. Ensemble methods, on the other hand, are crucial both in physics and machine learning. In physics, ensemble theory helps bridge the gap between the microscopic and macroscopic worlds, providing a statistical framework for understanding systems with a vast number of particles. In machine learning, ensemble methods are valuable because they improve predictive accuracy, reduce overfitting, lower prediction variance, mitigate bias, and capture complex relationships in data. However, there is limited research on applying ensemble methods to a set of random hypergraphs. This work aims to study the connectivity behavior of an ensemble of random hypergraphs. Specifically, it focuses on quantifying the random behavior of the algebraic connectivity of these ensembles through tail bounds. We utilize Laplacian tensors to represent these ensemble random hypergraphs and establish mathematical theorems, such as Courant-Fischer and Lieb-Seiringer theorems for tensors, to derive tail bounds for the algebraic connectivity. We derive three different tail bounds, i.e., Chernoff, Bennett, and Bernstein bounds, for the algebraic connectivity of ensemble hypergraphs with respect to different random hypergraphs assumptions

Research on the Foreign Direct Investment Factors of Japanese Hotel Industry in Taiwan-Taking Okura Hotel as an Example

Due to the impact of COVID-19 in 2019, the global hotel industry has been severely impacted by the disconnection of the tourism industry. However, even with the impact of the epidemic, the Japanese hotel industry’s investment in Taiwan has not stopped. What are the factors that drive the Japanese hotel industry to defy the threat of the epidemic and choose Taiwan as its destination for foreign direct investment? This is the research goal of this article. This article intends to adopt Push-Pull-Mooring (PPM)migration theory to construct the possible factors of why the Japanese hotel industry chooses Taiwan as its foreign direct investment destination. These factors consist of three effects to describe Japan Okura hotel’s migration. First, the push effect refers to factors that induce people to leave their place of origin. Second, the pull effect refers to factors that attract people to a destination. Third, the mooring effect refers to intervention variables for push and pull effects that facilitate or inhibit the determination of movement. The finding is that push and pull factors still play an active role in promoting Okura Hotel’s investment in Taiwan, even if the influence of some factors is slightly reduced due to the shift in international conditions. With the development of globalization and high technology, mooring factors are no longer the reason that hinders Japanese Okura’s investment in Taiwan. Combined with push and pull factors, PPM migration model can fully explain why the Japanese hotel industry chooses to conduct foreign direct investment in Taiwan, even if it is affected by COVID-19.It’s just that COVID-19 has not stopped so far, and the unstable situation on both sides of the strait may impact the original PPM model and affect the results of the analysis. It is worth further observation and research by subsequent researchers