Ill-posedness of the hydrostatic Euler and singular Vlasov equations

In this paper, we develop an abstract framework to establish ill-posedness in the sense of Hadamard for some nonlocal PDEs displaying unbounded unstable spectra. We apply it to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system

Instabilities in the mean field limit

Consider a system of $N$ particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a $\mathcal{C}^2$ smooth potential in any dimension. We prove that in the mean field limit $N \to + \infty$, the $N$ particles system displays instabilities in times of order $\log N$ for some configurations approximately distributed according to unstable homogeneous equilibria.Comment: minor typos corrected; Journal of Statistical Physics, accepte

Safe & sound banking, 20 years later: what was proposed and what has been adopted

Banks and banking ; Bank supervision

Hong Kong's Currency Board and Changing Monetary Regimes

The paper discusses the historical background and institutional details of Hong Kong's currency board. We argue that its experience provides a good opportunity to test the macroeconomic implications of the currency board regime. Using the method of Blanchard and Quah (1989), we show that the parameters of the structural equations and the characteristics of supply and demand shocks have significantly changed since adopting the regime. Variance decomposition and impulse response analyses indicate Hong Kong's currency board is less susceptible to supply shocks, but demand shocks can cause greater short-term volatility under the system. The decent performance of Hong Kong's currency board is due mainly to the stable fiscal policy of its government. Counter-factual exercises also show that three-fourths of the reduction in observed output volatility and two-thirds of that in observed inflation volatility are explained by the adoption of the currency board, while the remainder is explained by changes in the external environment. The improvement in stability does not rule out the possibility of monetary collapse, however.

Pre-teenage children's vernacular perception and experience of maps in Hong Kong

This paper reports a questionnaire study conducted with a group of 87 pre-teenage children (age 11-12 years) in Hong Kong to show their vernacular perception and experience of maps before they began formal mapwork learning in their first year of secondary education. This study reveals major findings that these pre-teenage children see the main purpose of using maps is to find unfamiliar places and to locate them in most everyday situations. As a result, they like to deal with practical, real maps such as street maps and the MTR (Mass Transit Railway) transport maps where the above-mentioned practical map purpose can be achieved. Most of these pre-teenage children are aware of maps available in their surroundings. However, they may not be observant enough to notice or pay attention to reading them carefully. It is rather a matter of map awareness that puts these pre-teenage children into the two broad groups of map and non-map-users. It also revealed that even those pre-teenage children who claimed to be non-map-users demonstrated some intuitive superficial understanding of simple map concepts and elements. Teachers are strongly encouraged to tap into the intuitions and experiences possessed by pre-teenage children in order to develop their map interest further in geography lessons and to make the understanding of maps a practical life skill for them to master.published_or_final_versio

Geography and citizenship education in Hong Kong

published_or_final_versio

Ontogenetic changes in cutaneous and branchial ionocytes and morphology in yellowfin tuna (Thunnus albacares) larvae.

The development of osmoregulatory and gas exchange organs was studied in larval yellowfin tuna (Thunnus albacares) from 2 to 25 days post-hatching (2.9-24.5 mm standard length, SL). Cutaneous and branchial ionocytes were identified using Na+/K+-ATPase immunostaining and scanning electron microscopy. Cutaneous ionocyte abundance significantly increased with SL, but a reduction in ionocyte size and density resulted in a significant decrease in relative ionocyte area. Cutaneous ionocytes in preflexion larvae had a wide apical opening with extended microvilli; however, microvilli retracted into an apical pit from flexion onward. Lamellae in the gill and pseudobranch were first detected ~ 3.3 mm SL. Ionocytes were always present on the gill arch, first appeared in the filaments and lamellae of the pseudobranch at 3.4 mm SL, and later in gill filaments at 4.2 mm SL, but were never observed in the gill lamellae. Unlike the cutaneous ionocytes, gill and pseudobranch ionocytes had a wide apical opening with extended microvilli throughout larval development. The interlamellar fusion, a specialized gill structure binding the lamellae of ram-ventilating fish, began forming by ~ 24.5 mm SL and contained ionocytes, a localization never before reported. Ionocytes were retained on the lamellar fusions and also found on the filament fusions of larger sub-adult yellowfin tuna; however, sub-adult gill ionocytes had apical pits. These results indicate a shift in gas exchange and NaCl secretion from the skin to branchial organs around the flexion stage, and reveal novel aspects of ionocyte localization and morphology in ram-ventilating fishes