HYPERBOLICITY AND CERTAIN STATISTICAL PROPERTIES OF CHAOTIC BILLIARD SYSTEMS

In this thesis, we address some questions about certain chaotic dynamical systems. In particular, the objects of our studies are chaotic billiards. A billiard is a dynamical system that describe the motions of point particles in a table where the particles collide elastically with the boundary and with each other. Among the dynamical systems, billiards have a very important position. They are models for many problems in acoustics, optics, classical and quantum mechanics, etc.. Despite of the rather simple description, billiards of different shapes of tables exhibit a wide range of dynamical properties from being complete integrable to chaotic. A very important and also very interesting type of billiards is chaotic (or hyperbolic) billiards. In a hyperbolic billiard system, two nearby trajectories in the phase space can be separated exponentially fast in future. In the first two Chapters, we prove the Central Limit Theorem and the Almost Sure Invariance Principle for a class of billiard systems with flat points. They are two among the important statistical properties for chaotic systems. In the last chapter, we introduce a random perturbation to a wide class of billiards and prove that even if the original system is completely integrable, the perturbed system can be chaotic even under arbitrarily small random perturbation

QUANTITATIVE DETERMINATION AND PREPARATIVE ISOLATION OF TWO MAJOR ALKALOIDS FROM THE VIETNAMESE MEDICINAL HERB EVODIAE FRUCTUS

Objective: To develop a simple and accurate HPLC-DAD method for simultaneous determination, the content of major components: limonin, evodiamine, and rutaecarpine in Evodiae fructus and evaluation the quality of Evodiae fructus sold in markets. Methods: Open column chromatography was used to separate and purify rutaecarpine and evodiamine, the two major alkaloids from Evodiae fructus extract as a laboratory standard. Chromatographic separation was achieved using a Germini C18 column (150 mm × 4.6 mm I.D., 5 µm), detected at 210 nm. The mobile phase consisted of acetonitrile (A), methanol (B), and water (C). The validated method simultaneously determined alkaloid content in 40 batches of samples collected from markets in different regions of Vietnam. Results: In one-step purification, our method yielded 326 mg of rutaecarpine and 128 mg of evodiamine from 3.2 g of crude extract, with purities of 98.9 and 98.5%, respectively. The structures of these compounds were identified using 1H NMR and 13C NMR. There was a significant correlation between alkaloid content and fruit size, with a Spearman correlation coefficient of>0.5 (p<0.001), and there was a large difference in alkaloid contents between three maturity degrees of the fruit. Open-mouth fruits and fruits with average sizes of 4 to 6 mm had the highest alkaloid contents, whereas closed-mouth fruits had the lowest. Conclusion: This study provided information on the standardization and quality control of evodiamine and rutaecarpine in Evodiae fructus, as well as a foundation for further pharmacological and toxicological studies

‘The painting can be fake, but not the feeling’: an overview of the Vietnamese market through the lens of fake, forgery and copy paintings

A work of Vietnamese art crossed a million-dollar mark in the international art market in early 2017. The event was reluctantly seen as a sign of maturity from the Vietnamese art amidst the many existing problems. Even though the Vietnamese media has discussed the issues enthusiastically, there is a lack of literature from the Vietnamese academics examining the subject, and even rarer in from the market perspective. This paper aims to contribute an insightful perspective on the Vietnamese art market, and hesitantly the Vietnamese art as well, through the lens of fake, forgery and copy artworks. 35 cases of fake, forgery and copy paintings were found on the news and from the experts' wisdom. Through the examples, we argue that the Vietnamese art market is a temporary reaction to the immaturely rising of the Vietnamese art and the economy. Therefore, the art market is unable to function healthily unless the Vietnamese art and the economy developed

A Simple Linear Time Algorithm for Computing a 1-Median on Cactus Graphs

We address the problem of finding a 1-median on a cactus graph. The problem has already been solved in linear time by the algorithms of Burkard and Krarup (1998), and Lan and Wang (2000). These algorithms are complicated and need efforts. Hence, we develop in this paper a simpler algorithm. First, we construct a condition for a cycle that contains a 1-median or for a vertex that is indeed a 1-median of the cactus. Based on this condition, we localize the search for deriving a 1-median on the underlying cactus. Complexity analysis shows that the approach runs in linear time

Qualitative Evidence and Health Policy

Cáс tài liệu trướс đây сhо rằng sứс khỏе thời thơ ấu kém làm giảm kết quả sứс khỏе, giảm trình độ họс vấn và thu nhập tiềm năng khi trưởng thành. Hơn nữа, hậu quả tíсh lũy сủа tình trạng sứс khỏе kém trоng giаi đоạn đầu đời сó thể gây bất lợi và lâu dài hơn сhо trẻ еm ở сáс nướс đаng phát triển sо với сáс nướс phát triển. Dо đó, phát hiện сủа сhúng tôi nhấn mạnh tầm quаn trọng сủа giáо dụс bà mẹ trоng việс nâng сао điều kiện kinh tế và xã hội ở сáс nướс đаng phát triển

Health Policy and Outcomes

Cáс tài liệu trướс đây сhо rằng sứс khỏе thời thơ ấu kém làm giảm kết quả sứс khỏе, giảm trình độ họс vấn và thu nhập tiềm năng khi trưởng thành. Hơn nữа, hậu quả tíсh lũy сủа tình trạng sứс khỏе kém trоng giаi đоạn đầu đời сó thể gây bất lợi và lâu dài hơn сhо trẻ еm ở сáс nướс đаng phát triển sо với сáс nướс phát triển. Dо đó, phát hiện сủа сhúng tôi nhấn mạnh tầm quаn trọng сủа giáо dụс bà mẹ trоng việс nâng сао điều kiện kinh tế và xã hội ở сáс nướс đаng phát triển

Cultural evolution in Vietnam’s early 20th century: a Bayesian networks analysis of Franco-Chinese house designs

The study of cultural evolution has taken on an increasingly interdisciplinary and diverse approach in explicating phenomena of cultural transmission and adoptions. Inspired by this computational movement, this study uses Bayesian networks analysis, combining both the frequentist and the Hamiltonian Markov chain Monte Carlo (MCMC) approach, to investigate the highly representative elements in the cultural evolution of a Vietnamese city’s architecture in the early 20th century. With a focus on the façade design of 68 old houses in Hanoi’s Old Quarter (based on 78 data lines extracted from 248 photos), the study argues that it is plausible to look at the aesthetics, architecture, and designs of the house façade to find traces of cultural evolution in Vietnam, which went through more than six decades of French colonization and centuries of sociocultural influence from China. The in-depth technical analysis, though refuting the presumed model on the probabilistic dependency among the variables, yields several results, the most notable of which is the strong influence of Buddhism over the decorations of the house façade. Particularly, in the top 5 networks with the best Bayesian Information Criterion (BIC) scores and p\u3c0.05, the variable for decorations (DC) always has a direct probabilistic dependency on the variable B for Buddhism. The paper then checks the robustness of these models using Hamiltonian MCMC method and find the posterior distributions of the models’ coefficients all satisfy the technical requirement. Finally, this study suggests integrating Bayesian statistics in the social sciences in general and for the study of cultural evolution and architectural transformation in particular