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Twee Kanten van één Medaille
(2020)
Therefore Fermat is right
(2014)
It was Fernat's idea to investigate how many numbers would fulfill the equation according to the Pythagorean Theorem if the exponent were increased to random, e.g. to a3 + b3 = c3. His question became therefore: are there two whole numbers the cubes of which add up to the volume of the cube of a third whole number? He posed this same question, of course, for all kinds of higher exponents, so that the equation could be generalized: is there an integral solution for the equation an + bn = cn, if the exponent n is higher than 2? Although in 1993, the English mathematician Andrew Wiles was able to produce an arithmetical proof for Fermat's famous theorem, I will show that there is a simple logical explanation which is also pragmatic and plausible and what is the result of a fundamental alternative idea how our world seems to be constructed.
Purpose
The most commonly used mobility assessments for screening risk of falls among older adults are rating scales such as the Tinetti performance oriented mobility assessment (POMA). However, its correlation with falls is not always predictable and disadvantages of the scale include difficulty to assess many of the items on a 3-point scale and poor specificity. The purpose of this study was to describe the ability of the new Aachen Mobility and Balance Index (AMBI) to discriminate between subjects with a fall history and subjects without such events in comparison to the Tinetti POMA Scale.
Methods
For this prospective cohort study, 24 participants in the study group and 10 in the control group were selected from a population of patients in our hospital who had met the stringent inclusion criteria. Both groups completed the Tinetti POMA Scale (gait and balance component) and the AMBI (tandem stance, tandem walk, ten-meter-walk-test, sit-to-stand with five repetitions, 360° turns, timed-up-and-go-test and measurement of the dominant hand grip strength). A history of falls and hospitalization in the past year were evaluated retrospectively. The relationships among the mobility tests were examined with Bland–Altmananalysis. Receiver-operated characteristics curves, sensitivity and specificity were calculated.
Results
The study showed a strong negative correlation between the AMBI (17 points max., highest fall risk) and Tinetti POMA Scale (28 points max., lowest fall risk; r = −0.78, p < 0.001) with an excellent discrimination between community-dwelling older people and a younger control group. However, there were no differences in any of the mobility and balance measurements between participants with and without a fall history with equal characteristics in test comparison (AMBI vs. Tinetti POMA Scale: AUC 0.570 vs. 0.598; p = 0.762). The Tinetti POMA Scale (cut-off <20 points) showed a sensitivity of 0.45 and a specificity of 0.69, the AMBI a sensitivity of 0.64 and a specificity of 0.46 (cut-off >5 points).
Conclusion
The AMBI comprises mobility and balance tasks with increasing difficulty as well as a measurement of the dominant hand-grip strength. Its ability to identify fallers was comparable to the Tinetti POMA Scale. However, both measurement sets showed shortcomings in discrimination between fallers and non-fallers based on a self-reported retrospective falls-status.
Sterben und Tod aus wissenschaftlicher Sicht - dying and death from a scientific point of view
(2018)