Felix Hausdorff - gesammelte Werke 5 by Josef Bemelmans, Christa Binder, Srishti D. Chatterji,

By Josef Bemelmans, Christa Binder, Srishti D. Chatterji, Stefan Hildebrandt, Walter Purkert, Felix Schmeidler, Erhard Scholz

Band five umfa?t die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enth?lt Hausdorffs Dissertation ?ber die Refraktion des Lichtes in der Atmosph?re, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift ?ber die Extinktion des Lichtes in der Atmosph?re. Es folgt eine Arbeit ?ber geometrische Optik, die unmittelbar an die ber?hmte Publikation von H. Bruns ?ber das Eikonal anschlie?t und in der Hausdorff die damals ganz neuen Lieschen Theorien f?r die Optik nutzbar zu machen suchte.

Auf dem Gebiet der Stochastik ver?ffentlichte Hausdorff zwei l?ngere Arbeiten, die in verschiedenen Bereichen der Versicherungsmathematik und der Wahrscheinlichkeitsrechnung ihre Spuren hinterlassen haben. Von besonderem historischen Interesse sind die im Band publizierten St?cke aus Hausdorffs Nachla?, etwa seine Vorlesung "Wahrscheinlichkeitsrechnung" vom Sommersemester 1923 oder seine Briefe an Richard von Mises aus dem Jahre 1919.

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Felix Hausdorff - gesammelte Werke 5

Band five umfa? t die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enth? lt Hausdorffs Dissertation ? ber die Refraktion des Lichtes in der Atmosph? re, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift ? ber die Extinktion des Lichtes in der Atmosph? re. Es folgt eine Arbeit ?

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1 Cross section (yz-plane) of phantom at y = 0 mm. 6 mm all boundaries other than the convective boundary at the surface incident to the laser from affecting the laser heat affected zone. This phantom design could be adapted for the experimental optimization of various thermal treatments. 2 Vascularized Tissue Phantom Preparation The vascularized tissue phantoms were constructed of materials mimicking soft tissues and contained discrete vessels with constant countercurrent blood flow. PID temperature controllers were used to maintain the phantom interior at 37 °C, representing core human body temperature.

Injection of gold nanoparticles enhances the contrast of the time-resolved optical image at the tumor margins. The contrast is higher at the center of the tumor and has a sharp transition to the surrounding healthy tissue. The pixel images illustrate that injection of gold nanoparticles enhances the contrast of the images and increases the precision of time-resolved images by clearly distinguishing the tumor margin from healthy tissue. 3c, d. ) 350 300 250 200 150 100 1000 40 800 30 600 400 Time 20 200 10 0 0 Detector Position Fig.

6 Conclusions The numerical models presented are well suited for parametric analysis of the effects of thermophysical and optical properties of tissues on temperature rises due to short pulse laser irradiation for any given set of laser parameters (repetition rate, pulse width, average power, and irradiation duration). 03 W without introducing effects from the boundary conditions at the outer boundaries of the phantoms. Numerical models also demonstrated that blood flow had a significant effect on both the surface and subsurface transient temperature rise at all times during 20 s of laser irradiation.

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