On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system

The Camassa-Holm equation and its two-component Camassa-Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the original equation given in Eulerian coordinates, into a system of ordinary differential equations in Lagrangian coordinates. It is of considerable interest to study the stability of solutions and how this is manifested in Eulerian and Lagrangian variables. We identify criteria of convergence, such that convergence in Eulerian coordinates is equivalent to convergence in Lagrangian coordinates. In addition, we show how one can approximate global conservative solutions of the scalar Camassa-Holm equation by smooth solutions of the two-component Camassa-Holm system that do not experience wave breaking

Occasions, people and places for pork consumption in Europe. Empirical findings from the Q-Porkchains pan-European consumer survey

Objective: to describe the occasions when, the places where and people with whom respondents reported pork meat consumption. Design & Setting: Cross-sectional web based survey in Belgium, Denmark, Germany, Greece and Poland, January 2008, with quota samples on gender (male, female), age categories (20- 44y and 45-70y), and locality of residence (urban, rural with low pig production density and rural with high pig production density). Subjects: 2437 respondents (51% women, 49% men; mean age 41.4 y SD 13.1). Methods: Online computer based survey, including sociodemographic information, anthropometrics (weight, height), and further questions on frequency of pork consumption (30 common items, 17 country-specific items), the occasions (working day, any day, weekend, special occasions), the company (alone, with family, with friends, with others) and the place of actual consumption (at home, outside of home). Results are aggregated for the five European countries. Results: Tenderloin, mignonette, brochette together with pork shoulder ranked as the first choices for weekend and special occasions. The most out-of home consumed products are mixed gyros-pita meat, pork based brochette, pizza, small cuts, marinated meat, escalope, shoulder, tenderloin and mixed meat. The Greek country specific Sygglino, Tigania, and the Country-style sausage are amongst the main preferences for out of home consumption. At European level, most products are consumed at home and with the family. Meat products such as salami, ham, and similar products are amongst the first choices when eating alone. Semi-processed meat like brochettes, small cuts and marinated or ready to eat dishes as gyros-pitas and pizza are the main choice for eating in the company of friends. Conclusions: European respondents seem to make specific choices of food depending on to the occasions, the places and the company. This information highlights the potential orientation of consumers towards fresh meat for special occasions or weekends, and more processed and convenient products when alone or socializing. This information is also useful to address interventions aiming at the improvement of food related health in Europe.Occasions, Pork consumption, Europe, Q-Porkchains, Food Consumption/Nutrition/Food Safety,

Two-Photon Doppler cooling of alkaline-earth-metal and ytterbium atoms

A new possibility of laser cooling of alkaline-earth-metal and Ytterbium atoms using a two-photon transition is analyzed. We consider a $^{1}S_{0}$ - $^{1}S_{0}$ transition, with excitation in near resonance with the $^{1}P_{1}$ level. This greatly increases the two-photon transition rate, allowing an effective transfer of momentum. The experimental implementation of this technique is discussed and we show that for Calcium, for example, two-photon cooling can be used to achieve a Doppler limit of 123 microKelvin. The efficiency of this cooling scheme and the main loss mechanisms are analyzed.Comment: 7 pages, 5 figure

Magnetic trapping of metastable 3P2^3P_2 atomic strontium

We report the magnetic trapping of metastable $^3P_2$ atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole allowed $^1S_0-^1P_1$ transition at 461 nm. Decay via $^1P_1\to {^1D_2}\to {^3P_2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over $10^8$ atoms at a density of $8 \times 10^9$ cm$^{-3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energy of atoms as they are transferred from the MOT. This suggests that thermalization and evaporative cooling are occurring in the magnetic trap.Comment: This paper has been accepted by PR

Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of solutions of the Korteweg--de Vries equation which are decaying perturbations of a quasi-periodic finite-gap background solution. We compute a nonlinear dispersion relation and show that the $x/t$ plane splits into $g+1$ soliton regions which are interlaced by $g+1$ oscillatory regions, where $g+1$ is the number of spectral gaps. In the soliton regions the solution is asymptotically given by a number of solitons travelling on top of finite-gap solutions which are in the same isospectral class as the background solution. In the oscillatory region the solution can be described by a modulated finite-gap solution plus a decaying dispersive tail. The modulation is given by phase transition on the isospectral torus and is, together with the dispersive tail, explicitly characterized in terms of Abelian integrals on the underlying hyperelliptic curve.Comment: 45 pages. arXiv admin note: substantial text overlap with arXiv:0705.034

Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.Comment: 31 page

Application of stochastic programming to reduce uncertainties in quality-based supply planning of slaughterhouses

To match products of different quality with end market preferences under supply uncertainty, it is crucial to integrate product quality information in logistics decision making. We present a case of this integration in a meat processing company that faces uncertainty in delivered livestock quality. We develop a stochastic programming model that exploits historical product quality delivery data to produce slaughterhouse allocation plans with reduced levels of uncertainty in received livestock quality. The allocation plans generated by this model fulfil demand for multiple quality features at separate slaughterhouses under prescribed service levels while minimizing transportation costs. We test the model on real world problem instances generated from a data set provided by an industrial partner. Results show that historical farmer delivery data can be used to reduce uncertainty in quality of animals to be delivered to slaughterhouses

On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations

We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the respective spectral bands either coincide or are disjoint.Comment: 29 page

Die wirtschaftliche Lage Rußlands: Monetäre Orientierungslosigkeit und realwirtschaftlicher Aktionismus. Dritter Bericht

Die beteiligten Institute legen hiermit ihren dritten Bericht über die Wirtschaft Rußlands vor. Der Bericht ist in zwei Teile gegliedert. Im ersten Teil wird der aktuelle Stand der Wirtschaftsentwicklung und der Reformpolitik dargestellt. Seit der Fertigstellung des zweiten Berichts hat sich die politische und wirtschaftliche Lage in der Russischen Föderation nicht grundlegend geändert. Die politische Blockade zwischen Legislative und Exekutive lähmt weiterhin den Reformprozeß; eine Wende zum Besseren ist nicht zu erkennen. Der zweite Teil des Berichts beschäftigt sich schwerpunktmäßig mit der sozialen Lage der Bevölkerung. Gegenstand der Analyse sind die Entwicklung von Einkommen und Verbrauch, das System der sozialen Sicherung sowie das Angebotspotential für die Versorgung der Bevölkerung mit Gütern und Dienstleistungen. Nach wie vor werden die Analysen durch die unsichere politische Lage, den institutionellen Umbruch und das unzuverlässige Berichtssystem erheblich erschwert. Die statistische Berichterstattung hat sich im Zeitablauf sogar noch verschlechtert. Vor allem die Aktivitäten des sich neu entwickelnden privaten Sektors werden kaum erfaßt. Informationslücken konnten nur zu einem geringen Teil durch Befragung staatlicher Stellen und russischer Wissenschaftler vor Ort geschlossen werden, so daß erhebliche Unsicherheiten über den tatsächlichen Ablauf des Transformationsprozesses verbleiben

Die wirtschaftliche Lage Rußlands: Monetäre Orientierungslosigkeit und realwirtschaftlicher Aktionismus. Dritter Bericht

Die beteiligten Institute legen hiermit ihren dritten Bericht über die Wirtschaft Rußlands vor. Der Bericht ist in zwei Teile gegliedert. Im ersten Teil wird der aktuelle Stand der Wirtschaftsentwicklung und der Reformpolitik dargestellt. Seit der Fertigstellung des zweiten Berichts hat sich die politische und wirtschaftliche Lage in der Russischen Föderation nicht grundlegend geändert. Die politische Blockade zwischen Legislative und Exekutive lähmt weiterhin den Reformprozeß; eine Wende zum Besseren ist nicht zu erkennen. Der zweite Teil des Berichts beschäftigt sich schwerpunktmäßig mit der sozialen Lage der Bevölkerung. Gegenstand der Analyse sind die Entwicklung von Einkommen und Verbrauch, das System der sozialen Sicherung sowie das Angebotspotential für die Versorgung der Bevölkerung mit Gütern und Dienstleistungen. Nach wie vor werden die Analysen durch die unsichere politische Lage, den institutionellen Umbruch und das unzuverlässige Berichtssystem erheblich erschwert. Die statistische Berichterstattung hat sich im Zeitablauf sogar noch verschlechtert. Vor allem die Aktivitäten des sich neu entwickelnden privaten Sektors werden kaum erfaßt. Informationslücken konnten nur zu einem geringen Teil durch Befragung staatlicher Stellen und russischer Wissenschaftler vor Ort geschlossen werden, so daß erhebliche Unsicherheiten über den tatsächlichen Ablauf des Transformationsprozesses verbleiben. --