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To satisfy the ion-optical requirement of a well-defined object spot-size, we opted for polypropylene foil targets instead of hydrogen gas.
His adaptation of the wave equation describes electrons, for example, not as a well-defined object in space but as quantum waves for which it is only possible to describe probabilities for position, momentum or other basic properties.
Then (mathsf{ev}^dagger (sigma )) with the collection ({chi (sigma (l))}) and isomorphisms (6.15) is a well-defined object in the category (F^{[n]}) for the free coalgebra functor (F:mathcal {C}_{[0]} rightarrow mathcal {C}'), so that we obtain a functor (B(mathcal {C})_{[n]} rightarrow F^{[n]}).
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Object: Radiosurgery utilizes stereotactic principles of localization and multiple cross-fired beams to deliver a large radiation dose to a well-defined target with little or no fractionation.
Tracking a bright well-defined object (nucleus) permits resolution of individual cells even if they are closely associated because the fluorescent nuclei are separated by a dark, non-fluorescent cytosol (Fig. 2).
We used photographs of different monkeys living in the same colony as the observers, taken while the individuals were sitting in the primate chair (head-fixed) with their head (and eyes) directed at a spatially well-defined object of attention.
These effects are most often detectible in simulation and phantom studies with well-defined object borders.
Under good conditions (i.e., with proper lighting, well-defined objects, and using a camera with a resolution of 640 × 480 pixels), objects can be tracked with a spatial precision of up to 0.3° (corresponding to about 2 mm in a regular setup; see Experiment 3).
Unlike general relativity, which dealt with well-defined objects existing in a smooth (albeit curved) space-time geometry, quantum mechanics described a random, choppy microworld where change happens in leaps, where particles act like waves (and vice versa), and where uncertainty reigns.
Brouwer considers Burali-Forti's contradiction not as a mathematical paradox, since it concerns a logical structure (the collection of all ordinals), which is not a well-defined mathematical object and has no proper mathematical content.
So the crucial problem becomes logical: to give a criterion for selecting those propositional functions which give rise to classes (understood as well-defined objects).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com