Was Singapore extraordinary? A comparative view of Singapore's saving performance 1965-99

Although the mere observation of saving aggregates might have us believe differently, this article argues that Singapore's sustained high saving performance was far from extraordinary once the country's particular circumstances are econometrically controlled for. Singapore's saving performance should therefore not be regarded as a mere blip in economic history. As a matter of fact, not the high saving rates in the late 1980s and 1990s, which usually attract the most attention, but rather the speed of transformation of the country's saving behaviour in the first years of independence is shown to be indeed extraordinary. Singapore was able to overcome its low initial saving performance much faster and much more strongly than could have been expected given its circumstances. --Asia,Singapore,saving rate,economic growth

Characteristics of return stroke electric fields produced by lightning flashes at distances of 1 to 15 kilometers

Electric field derivative signals from single and multiple lightning strokes are presented. For about 25 pct. of all acquired waveforms, produced by return strokes, stepped leaders or intracloud discharges, type and distance of the signal source are known from the observations by an all sky video camera system. The analysis of the electric field derivative waveforms in the time domain shows a significant difference in the impulse width between return stroke signals and those of stepped leaders and intracloud discharges. In addition, the computed amplitude density spectrum of return stroke waveforms lies by a factor of 10 above that of stepped leaders and intracloud discharges in the frequency range from 50 to 500 kHz

The Danger of Stalled Flight and an Analysis of the Factors which Govern It

A definition of "stalled fight" is presented as well as a detailed discussion on the how and why it occurs. Some suggestions are made to prevent its occurrence such as carrying an air speed instrument in the airplane

Classical Motion in Random Potentials

We consider the motion of a classical particle under the influence of a random potential on R^d, in particular the distribution of asymptotic velocities and the question of ergodicity of time evolution.Comment: 45 pages, 3 figure

Orthospectra of Geodesic Laminations and Dilogarithm Identities on Moduli Space

Given a measured lamination on a finite area hyperbolic surface we consider a natural measure Mon the real line obtained by taking the push-forward of the volume measure of the unit tangent bundle of the surface under an intersection function associated with the lamination. We show that the measure M gives summation identities for the Rogers dilogarithm function on the moduli space of a surface.Comment: 21 pages, 2 figure

Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons

Kaniadakis and Quarati (1994) proposed a Fokker--Planck equation with quadratic drift as a PDE model for the dynamics of bosons in the spatially homogeneous setting. It is an open question whether this equation has solutions exhibiting condensates in finite time. The main analytical challenge lies in the continuation of exploding solutions beyond their first blow-up time while having a linear diffusion term. We present a thoroughly validated time-implicit numerical scheme capable of simulating solutions for arbitrarily large time, and thus enabling a numerical study of the condensation process in the Kaniadakis--Quarati model. We show strong numerical evidence that above the critical mass rotationally symmetric solutions of the Kaniadakis--Quarati model in 3D form a condensate in finite time and converge in entropy to the unique minimiser of the natural entropy functional at an exponential rate. Our simulations further indicate that the spatial blow-up profile near the origin follows a universal power law and that transient condensates can occur for sufficiently concentrated initial data.Comment: To appear in Kinet. Relat. Model

Switching dynamics of spatial solitary wave pixels

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the domain of transverse effects, of the pulse area theorem for the switching process and a logarithmic law for the transient dynamics. We also consider, for what is the first time to our knowledge, phase-encoded address of solitary pixels and find that a near-square-wave temporal switching pattern is permitted without (transverse) cross switching

Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results

The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic similarity regimes, where the shock wave propagates outwards according to two self-similar laws, initially accelerating and eventually decelerating and vanishing, leading to a static state. The numerical study allows one to investigate in detail this dynamical problem and its time evolution, verifying and complementing the analytic results on the initial solution, intermediate self-similar laws and static long-term solution.Comment: 19 pages, 10 PS figures (some large

Fractal: formas de reconocer el mundo a través de cálculos matemáticos totalmente nuevos y atractivos la aventura del saber

El Grupo de Matemáticas “Henry Hopf”, iniciado en 2011, pretende responder el cuestionamiento: ¿Es posible conocer y aplicar los conceptos de la teoría de los fractales a nivel elemental, de forma que puedan generarse nuevos conocimientos en el contexto de los estudiantes? En este artículo, compartimos diversas actividades que nos han permitido comprender algunas nociones y elementos que hacen parte de la mencionada teoría