Logarithmic Gromov-Witten invariants

The goal of this paper is to give a general theory of logarithmic Gromov-Witten invariants. This gives a vast generalization of the theory of relative Gromov-Witten invariants introduced by Li-Ruan, Ionel-Parker, and Jun Li, and completes a program first proposed by the second named author in 2002. One considers target spaces X carrying a log structure. Domains of stable log curves are log smooth curves. Algebraicity of the stack of such stable log maps is proven, subject only to the hypothesis that the log structure on X is fine, saturated, and Zariski. A notion of basic stable log map is introduced; all stable log maps are pull-backs of basic stable log maps via base-change. With certain additional hypotheses, the stack of basic stable log maps is proven to be proper. Under these hypotheses and the additional hypothesis that X is log smooth, one obtains a theory of log Gromov-Witten invariants.Comment: 58 pages, 5 figure

Open Photoacoustic Cell for Blood Sugar Measurement: Numerical Calculation of Frequency Response

A new approach for continuous and non-invasive monitoring of the glucose concentration in human epidermis has been suggested recently. This method is based on photoacoustic (PA) analysis of human interstitial fluid. The measurement can be performed in vitro and in vivo and, therefore, may form the basis for a non-invasive monitoring of the blood sugar level for diabetes patients. It requires a windowless PA cell with an additional opening that is pressed onto the human skin. Since signals are weak, advantage is taken of acoustic resonances of the cell. Recently, a numerical approach based on the Finite Element (FE) Method has been successfully used for the calculation of the frequency response function of closed PA cells. This method has now been adapted to obtain the frequency response of the open cell. Despite the fact that loss due to sound radiation at the opening is not included, fairly good accordance with measurement is achieved