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Consider the set X = {1, 2, ..., 9, 10} and let the sigma-algebra be the power set of X. Define the measure of a set to be its cardinality, that is, the number of elements in the set. Then, each of the singletons {i}, for i = 1, 2, ..., 9, 10 is an atom. Consider the Lebesgue measure on the real line. This measure has no atoms.
In type theory, an object of type 0 can be called an urelement; hence the name "atom". Adding urelements to the system New Foundations (NF) to produce NFU has surprising consequences. In particular, Jensen proved [ 5 ] the consistency of NFU relative to Peano arithmetic ; meanwhile, the consistency of NF relative to anything remains an open ...
Note: All measurements given are in picometers (pm). For more recent data on covalent radii see Covalent radius.Just as atomic units are given in terms of the atomic mass unit (approximately the proton mass), the physically appropriate unit of length here is the Bohr radius, which is the radius of a hydrogen atom.
In the mathematical field of order theory, an element a of a partially ordered set with least element 0 is an atom if 0 < a and there is no x such that 0 < x < a.. Equivalently, one may define an atom to be an element that is minimal among the non-zero elements, or alternatively an element that covers the least element 0.
1.2×10 9 J: Inflight 100-ton Boeing 757-200 at 300 knots (154 m/s) 1.4×10 9 J: Theoretical minimum amount of energy required to melt a tonne of steel (380 kWh) [132] [133] 2×10 9 J: Energy of an ordinary 61 liter gasoline tank of a car. [106] [134] [135] 2×10 9 J: Unit of energy in Planck units, [136] roughly the diesel tank energy of a mid ...
The atomic ratio is a measure of the ratio of atoms of one kind (i) to another kind (j). A closely related concept is the atomic percent (or at.%), which gives the percentage of one kind of atom relative to the total number of atoms. [1]
Two independent conditions that are both strictly stronger than the BFD condition are the half-factorial domain condition (HFD: any two factorizations of any given x have the same length) and the finite factorization domain condition (FFD: any x has but a finite number of non-associate divisors). Every unique factorization domain obviously ...
In quantum chemistry, the quantum theory of atoms in molecules (QTAIM), sometimes referred to as atoms in molecules (AIM), is a model of molecular and condensed matter electronic systems (such as crystals) in which the principal objects of molecular structure - atoms and bonds - are natural expressions of a system's observable electron density distribution function.