On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.Comment: 41 page

An acoustic metamaterial lens for acoustic point-to-point communication in air

Acoustic metamaterials have become a novel and effective way to control sound waves and design acoustic devices. In this study, we design a 3D acoustic metamaterial lens (AML) to achieve point-to-point acoustic communication in air: any acoustic source (i.e. a speaker) in air enclosed by such an AML can produce an acoustic image where the acoustic wave is focused (i.e. the field intensity is at a maximum, and the listener can receive the information), while the acoustic field at other spatial positions is low enough that listeners can hear almost nothing. Unlike a conventional elliptical reflective mirror, the acoustic source can be moved around inside our proposed AML. Numerical simulations are given to verify the performance of the proposed AML

China and European Union Countries: Do Chinese Partnerships Boost Cooperation Results?

The People’s Republic of China and countries of the European Union (EU) have signed multiple diplomatic documents for cooperation under different types of conception. France was the first EU country to start a comprehensive partnership with China in 1997, and, by 2021, among the 27 EU member countries, 19 had already established partnerships with China (the exceptions were Estonia, Latvia, Lithuania, Luxembourg, Malta, Slovakia, Slovenia, and Sweden). Since the Belt and Road Initiative (BRI) was announced in 2013, 18 EU member states (except Belgium, Denmark, Finland, France, Germany, Ireland, Netherlands, Spain, and Sweden) have signed MoUs with China. What this study investigates, however, is why some of the countries have opted to sign a BRI MoU but not establish partnerships with China. On the other hand, some countries that have long had partnerships with China have deepened or strengthened those partnerships, yet have not signed a BRI MoU. The current study is therefore motivated to pose this main research question: To what extent does the Chinese partnership framework facilitate practical cooperation between EU countries and China? The study also poses these secondary questions: What are the main differences between these cooperation documents? Do such differences in documentation result in discrepancies in the nature of cooperation? From a bilateral state-to-state perspective, the study compares joint statements pertaining to Chinese partnerships with different EU countries, analyzing how closely they are tailored to each European country’s specificity. Through reviewing the literature, the authors gather data concerning the outcomes of cooperations on trade and investment between China and EU member states, and analyze any official diplomatic documents availabl