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

Soft information matters in SME lending

Loan data from small and medium-sized enterprises (SMEs) has shown that such positive attributes as good management skills and character – so-called ‘soft’ facts – can improve a borrower’s bargaining power with their bank and thus loan terms

Bargaining power and information in SME lending

Small- and medium-sized enterprises (SMEs) are informationally opaque and bank dependent. In SME lending, banks largely rely on soft information, because the scale and scope of hard information are limited. We analyze whether and how hard and soft information affects the borrower's bargaining power vis-à-vis its bank. We use the fact that, for a given credit rating, certain borrowers obtain better loan terms than others to define measures of relative bargaining power. Using SME loan data from the USA and Germany, we find that more favorable soft information (management skills and character) increases borrower bargaining power. We also show that more favorable soft than hard information improves borrower bargaining power. The results are not driven by manipulation or statistical limitations of the credit ratings. Our study suggests that soft information represents an important and direct determinant of borrower bargaining power, affecting the outcomes of the loan contracting process

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

Chlorophyll Dynamics from Sentinel-3 Using an Optimized Algorithm for Enhanced Ecological Monitoring in Complex Urban Estuarine Waters

Urban estuaries are dynamic environments that hold high ecological and economic value. Yet, their optical complexity hinders accurate satellite retrievals of important biogeochemical variables, such as chlorophyll-a (Chl-a) biomass. Approaches based on a limited number of satellite spectral bands often fail to capture seasonal transitions and sharp spatial gradients in estuarine Chl-a concentrations, inhibiting integration of satellite data into water quality monitoring and conservation programs. We propose a novel approach that utilizes the wide range of spectral information captured by the Ocean and Land Color Instrument (OLCI) to retrieve estuarine Chl-a. To validate our approach, we used measurements in Long Island Sound (LIS), a highly urbanized estuary increasingly susceptible to anthropogenic stressors and climate change. Hyperspectral remote sensing reflectance (Rrs) and Chl-a data representing the spatiotemporal diversity of LIS were used to assess the ideal atmospheric correction approach for OLCI and develop a multi-spectral multiple linear regression (MS-MLR) Chl-a algorithm. POLYMER derived Rrs proved to be the preferred atmospheric correction approach. Evaluation of MS-MLR performance in retrieving Chl-a with in situ Rrs showed good agreement with field measurements. Application to OLCI-retrieved Rrs showed significant improvement (20%-30%) in common error metrics relative to other algorithms assessed. The MS-MLR approach successfully captured seasonal cycles and spatial gradients in Chl-a concentration. Application of this method to urban estuaries and coasts enables accurate, high resolution Chl-a observations at the ecosystem scale and across a range of conditions, as needed for conservation and ecosystem management efforts

Optical Classification of an Urbanized Estuary Using Hyperspectral Remote Sensing Reflectance

Optical water classification based on remote sensing reflectance (Rrs(.)) data can provide insight into water components driving optical variability and inform the development and application of bio-optical algorithms in complex aquatic systems. In this study, we use an in situ dataset consisting of hyperspectral Rrs(.) and other biogeochemical and optical parameters collected over nearly five years across a heavily urbanized estuary, the Long Island Sound (LIS), east of New York City, USA, to optically classify LIS waters based on Rrs(.) spectral shape. We investigate the similarities and differences of discrete groupings (k-means clustering) and continuous spectral indexing using the Apparent Visible Wavelength (AVW) in relation to system biogeochemistry and water properties. Our Rrs(.) dataset in LIS was best described by three spectral clusters, the first two accounting for the majority (89%) of Rrs(.) observations and primarily driven by phytoplankton dynamics, with the third confined to measurements in river and river plume waters. We found AVW effective at tracking subtle changes in Rrs(.) spectral shape and fine-scale water quality features along river-to-ocean gradients. The recently developed Quality Water Index Polynomial (QWIP) was applied to evaluate three different atmospheric correction approaches for satellite-derived Rrs(.) from the Sentinel-3 Ocean and Land Colour Instrument (OLCI) sensor in LIS, finding Polymer to be the preferred approach. Our results suggest that integrative, continuous indices such as AVW can be effective indicators to assess nearshore biogeochemical variability and evaluate the quality of both in situ and satellite bio-optical datasets, as needed for improved ecosystem and water resource management in LIS and similar regions

The Relation between Attitudes toward Functional Foods and Satisfaction with Food-Related Life

Purpose – To assess the effect of attitudes towards functional foods (FF) on university students’ satisfaction with food-related life and to distinguish student typologies, considering that the attitudes towards FF are not homogeneous among consumers. Design/methodology - A survey was applied to 372 university students (mean age=20.4 years, SD=2.4) in southern Chile. The questionnaire included the Attitudes towards Functional Foods (AFF) questionnaire and the Satisfaction with Food-related Life (SWFL) scale, questions about consumption and knowledge about FF and socio-demographic characteristics. Findings – Using Confirmatory Factor Analysis (CFA) and Structural Equation Modelling, it was found that attitudes toward functional foods directly and significantly influence students’ satisfaction with food-related life. A cluster analysis applied to the Z-scores from the factors obtained by the CFA classified three typologies: Positive towards FF (36.3%), moderately positive towards FF (43.0%) and negative towards FF (20.7%). The positive towards FF type had a significantly greater SWFL score than the negative towards FF type. The types differ according to consumption and knowledge about FF. Research limitations/implications – This study was conducted in the context of only one country in South America. Originality/value – This study is the first that assesses the effect of AFF on satisfaction with food-related life in a sample of university students. Fostering positive attitudes towards FF will allow for a growth in the degree of satisfaction with food-related life of university students with features similar to those of the study sample

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