Arithmetics of homogeneous spaces over pp-adic function fields

Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $\mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak approximation problems for homogeneous spaces of $\textrm{SL}_{n,K}$ with geometric stabilizers extension of a group of multiplicative type by a unipotent group. The tools used are arithmetic (local and global) duality theorems in Galois cohomology, in combination with techniques similar to those used by Harari, Szamuely, Colliot-Th\'el\`ene, Sansuc, and Skorobogatov. As a consequence, we show that any finite abelian group is a Galois group over $K$, rediscovering the positive answer to the abelian case of the inverse Galois problem over $\mathbb{Q}_p(t)$. In the case where the curve is defined over a higher-dimensional local field instead of a finite extension of $\mathbb{Q}_p$, coarser results are also given.Comment: 55 pages, major improvements from the previous versio

Non-abelian descent types

We present the notion of non-abelian descent type, which classifies torsors up to twisting by a Galois cocycle. This relies on the previous construction of kernels and non-abelian Galois 2-cohomology due to Springer and Borovoi. The necessity of descent types arises in the context of the descent theory where no torsors are given a priori, for example, when we wish to study the arithmetic properties such as the Brauer--Manin obstruction to the Hasse principle on homogeneous spaces without rational points. This new definition also unifies the types by Colliot-Th\'el\`ene--Sansuc, the extended types by Harari--Skorobogatov, and the finite descent type by Harpaz--Wittenberg.Comment: 39 pages, separated from arXiv:2305.13228 with some improvement

On the descent conjecture for rational points and zero-cycles

The descent method is one of the strategies allowing one to study the Brauer--Manin obstruction to the local--global principle and to weak approximation on varieties over number fields, by reducing the problem to ``descent varieties''. Very recently, in his Park City lecture notes, Wittenberg formulated a ``descent conjecture'' for torsors under linear algebraic groups. The present article gives a proof of this conjecture in the case of connected groups, generalizing the toric case from the previous work of Harpaz--Wittenberg. As an application, we deduce directly from Sansuc's work the theorem of Borovoi for homogeneous spaces of connected linear algebraic groups with connected stabilizers. We are also able to reduce the general case to the case of finite (\'etale) torsors. When the set of rational points is replaced by the Chow group of zero-cycles, an analogue of the above conjecture for arbitrary linear algebraic groups is proved.Comment: 41 pages, fixed a gap in the proof of Proposition 2.7 on the abelianization map, added the section on the descent conjecture for zero-cycles, all the parts on non-abelian descent type have been separated into arXiv:2401.0034

The emerging business of science in Vietnam

Manh-Tung Ho, Khanh-Linh Hoang, Minh-Hoang Nguyen, Manh-Toan Ho (2019). Chapter 8. The emerging business of science in Vietnam. In Quan-Hoang Vuong, Trung Tran (Eds.), The Vietnamese Social Sciences at a Fork in the Road (pp. 163–177). Warsaw, Poland: De Gruyter. DOI:10.2478/9783110686081-013. Online ISBN: 9783110686081 © 2019 Sciendo / De Gruyte

Discrete-Time Control Design for Piezo-Actuated Positioning Systems

芝浦工業大学2018年

Nonlinear Control of an Active Magnetic Bearing with Output Constraint

In this paper, an appropriate control strategy is proposed to handle the nonlinear dynamics ofan active magnetic bearing (AMB). The goal of the control design is to drive the AMB rotor to the origin with improved transient response. In order to achieve this task, back stepping control technique with a barrier Lyapunov function are employed to keep the tracking error trajectory inside a predefined zone to avoid possible mechanical contact between rotor and stator. Besides, a speed observer is also used since information about rotor speed is not always available. The stability of the closed-loop system is proven. The effectiveness of the proposed control strategy is verified by numerical simulations

STEM education and outcomes in Vietnam: Views from the social gap and gender issues

United Nations’ Sustainable Development Goals 4 Quality Education has highlighted major challenges for all nations to ensure inclusive and equitable quality access to education, facilities for children, and young adults. The SDG4 is even more important for developing nations as receiving proper education or vocational training, especially in science and technology, means a foundational step in improving other aspects of their citizens’ lives. However, the extant scientific literature about STEM education still lacks focus on developing countries, even more so in the rural area. Using a dataset of 4967 observations of junior high school students from a rural area in a transition economy, the article employs the Bayesian approach to identify the interaction between gender, socioeconomic status, and students’ STEM academic achievements. The results report gender has little association with STEM academic achievements; however, female students (αa_Sex[2] = 2.83) appear to have achieved better results than their male counterparts (αa_Sex[1] = 2.68). Families with better economic status, parents with a high level of education (βb(EduMot) = 0.07), or non-manual jobs (αa_SexPJ[4] = 3.25) are found to be correlated with better study results. On the contrary, students with zero (βb(OnlyChi) = -0.14) or more than two siblings (βb(NumberofChi) = -0.01) are correlated with lower study results compared to those with only one sibling. These results imply the importance of providing women with opportunities for better education. Policymakers should also consider maintaining family size so the parents can provide their resources to each child equally

How Digital Natives Learn and Thrive in the Digital Age: Evidence from an Emerging Economy

As a generation of ‘digital natives,’ secondary students who were born from 2002 to 2010 have various approaches to acquiring digital knowledge. Digital literacy and resilience are crucial for them to navigate the digital world as much as the real world; however, these remain under-researched subjects, especially in developing countries. In Vietnam, the education system has put considerable effort into teaching students these skills to promote quality education as part of the United Nations-defined Sustainable Development Goal 4 (SDG4). This issue has proven especially salient amid the COVID−19 pandemic lockdowns, which had obliged most schools to switch to online forms of teaching. This study, which utilizes a dataset of 1061 Vietnamese students taken from the United Nations Educational, Scientific, and Cultural Organization (UNESCO)’s “Digital Kids Asia Pacific (DKAP)” project, employs Bayesian statistics to explore the relationship between the students’ background and their digital abilities. Results show that economic status and parents’ level of education are positively correlated with digital literacy. Students from urban schools have only a slightly higher level of digital literacy than their rural counterparts, suggesting that school location may not be a defining explanatory element in the variation of digital literacy and resilience among Vietnamese students. Students’ digital literacy and, especially resilience, also have associations with their gender. Moreover, as students are digitally literate, they are more likely to be digitally resilient. Following SDG4, i.e., Quality Education, it is advisable for schools, and especially parents, to seriously invest in creating a safe, educational environment to enhance digital literacy among students