The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts.

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An experimental and theoretical study of the lifetimes of the 3s4p 3P levels in S V and C1 VI is reported. Using the beam-foil technique and extensive cascade corrections with the ANDC method we obtain the following lifetimes in ns: 0.72 f 0.07 ( 3Pz) and 0.37 i. 0.04 ( 3 P , ) in S V, whereas both levels have the same lifetime, 0.24 * 0.03 ns, in C1 VI. The theoretical analysis shows that the large lifetime difference in S V results from a mixing of the 3s4p IP, and 3P, levels, which is enhanced by interactions between the 3s4p and 3p 3d configurations. Calculated transition probabilities for the individual decay channels from the 3s4p 3P levels are also given. In addition, the theoretical analysis indicates an erroneous identification of the 3p 3d 'P and 'F levels in S V.

Background: Liver parenchymal injuries such as steatosis, steatohepatitis, fibrosis, and sinusoidal obstruction syndrome can lead to increased morbidity and liver failure after liver resection. Diffuse reflectance spectroscopy (DRS) is an optical measuring method that is fast, convenient, and established. DRS has previously been used on the liver with an invasive technique consisting of a needle that is inserted into the parenchyma. We developed a DRS system with a hand-held probe that is applied to the liver surface. In this study, we investigated the impact of the liver capsule on DRS measurements and whether liver surface measurements are representative of the whole liver. We also wanted to confirm that we could discriminate between tumor and liver parenchyma by DRS. Materials and Methods: The instrumentation setup consisted of a light source, a fiber-optic contact probe, and two spectrometers connected to a computer. Patients scheduled for liver resection due to hepatic malignancy were included, and DRS measurements were performed on the excised liver part with and without the liver capsule and alongside a newly cut surface. To estimate the scattering parameters and tissue chromophore volume fractions, including blood, bile, and fat, the measured diffuse reflectance spectra were applied to an analytical model. Results: In total, 960 DRS spectra from the excised liver tissue of 18 patients were analyzed. All factors analyzed regarding tumor versus liver tissue were significantly different. When measuring through the capsule, the blood volume fraction was found to be 8.4 ± 3.5%, the lipid volume fraction was 9.9 ± 4.7%, and the bile volume fraction was 8.2 ± 4.6%. No differences could be found between surface measurements and cross-sectional measurements. In measurements with/without the liver capsule, the differences in volume fraction were 1.63% (0.75-2.77), -0.54% (-2.97 to 0.32), and -0.15% (-1.06 to 1.24) for blood, lipid, and bile, respectively. Conclusion: This study shows that it is possible to manage DRS measurements through the liver capsule and that surface DRS measurements are representative of the whole liver. The results are consistent with data published earlier on the combination of liver chromophores. The results encourage us to proceed with in vivo measurements for further quantification of the liver's composition and assessment of parenchymal damage such as steatosis and fibrosis grade.

the inclusion of electron correlation could change the tran-Using the beam-foil excitation technique and the ANDC method for cascade corrections, we have determined lifetimes of the 2 . ~2 8 'S, 2?ns 'S (n = 3, 4, 5), 2s2pz *P, 22np zPO (n = 3, 4), and 2p' *Po terms in CII and the 2s2p 'Po level in C 111. The new experimental lifetimes are in very good agreement with the results of recent theoretical calculations.