Divisors of the Euler and Carmichael functions

We study the distribution of divisors of Euler's totient function and Carmichael's function. In particular, we estimate how often the values of these functions have "dense" divisors.Comment: v.3, 11 pages. To appear in Acta Arithmetica. Very small corrections and changes suggested by the referee. Added abstract, keywords, MS

Consumers’ Purchasing Intentions for Vegetable Oil in the Presence of Generic or Specific Information on Genetic Modification

In combination with the emergence of genetically modified (GM) food, there has been an urgent call for GM labeling to provide relevant information disclosure. Using data collected in Beijing, China, this study attempts to address the issue of whether different types of information may have distinct impacts on consumers’ stated purchasing decisions. Three types of information are used in this study: one is generic and the other two are linked with two important implications of GM technology—human health and the environment. Results verify that consumers’ purchasing decisions are affected by different types of information through their attitudes and personal characteristics. This finding has potential implications for establishing various GM marketing strategies and information campaigns.China, genetically modified (GM) food, labeling information, probit model, vegetable oil, Agribusiness, Food Consumption/Nutrition/Food Safety,

4Pi Single-molecule Switching Nanoscopy for Live-cell Imaging

plays a critical role in cell biology due to its ability tovisualize molecules of interest inside living cells with high specificity and contrast. However, diffraction of light limits spatial resolution to ~250 nm. Super-resolution microscopy bypasses this physical limit to achieve resolutions of ~10 nm, which is nearly the size of many biological macromolecules. Notably, 4Pi single-molecule switching nanoscopy achieves this resolution in all three spatial dimensions, finally making it possible to resolve specific proteins within convoluted structures like the Golgi. However, the current implementation is only compatible with dead or fixed cell samples, restricting experimental design. To explore the complexity of life in 3-D at near molecular resolution, I have developed a 4Pi single-molecule switching nanoscope for multi-color live-cell imaging and optimized 2-color live-cell labeling with spontaneously-blinking fluorophores

Quantum dot spectroscopy using cavity QED

Cavity quantum electrodynamics has attracted substantial interest, both due to its potential role in the field of quantum information processing and as a testbed for basic experiments in quantum mechanics. Here, we show how cavity quantum electrodynamics using a tunable photonic crystal nanocavity in the strong coupling regime can be used for single quantum dot spectroscopy. From the distinctive avoided crossings observed in the strongly coupled system we can identify the neutral and single positively charged exciton as well as the biexciton transitions. Moreover we are able to investigate the fine structure of those transitions and to identify a novel cavity mediated mixing of bright and dark exciton states, where the hyperfine interactions with lattice nuclei presumably play a key role. These results are enabled by a deterministic coupling scheme which allowed us to achieve unprecedented coupling strengths in excess of 0.15 meV.Comment: 5 pages, 3 figure

The Economics of Mortgage Terminations: Implications for Mortgage Lenders and Mortgage Terms

The paper begins with the development of models explaining the mortgage refinancing and assumption decisions of households Having identified the economic variables influencing these decisions, we then simulate the models for different values to determine under what conditions households will refinance or assume. Finally, we draw some implications of these results for: (1) the impact of a decline in mortgage rates on the asset portfolio yields of mortgage lending institutions and (2) the effect of the observed rise in interest rate volatility, including the optimal terminations response of mortgage borrowers, on the terms of the mortgage contract and the returns to mortgage lenders on recently issued mortgage loans.