Search results
Results from the WOW.Com Content Network
A discrete measure is atomic but the inverse implication fails: take = [,], the -algebra of countable and co-countable subsets, = in countable subsets and = in co-countable subsets. Then there is a single atomic class, the one formed by the co-countable subsets.
In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a " random variable ". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.
The Dirac measure of any set containing 0 is 1, and the measure of any set not containing 0 is 0. In mathematics, more precisely in measure theory, a measure on the real line is called a discrete measure (in respect to the Lebesgue measure) if it is concentrated on an at most countable set. The support need not be a discrete set. Geometrically ...
Because a dalton, a unit commonly used to measure atomic mass, is exactly 1/12 of the mass of a carbon-12 atom, this definition of the mole entailed that the mass of one mole of a compound or element in grams was numerically equal to the average mass of one molecule or atom of the substance in daltons, and that the number of daltons in a gram ...
The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested and named by the physicist Douglas Hartree. [1]
The SI unit of molar absorption coefficient is the square metre per mole (m 2 /mol), but in practice, quantities are usually expressed in terms of M −1 ⋅cm −1 or L⋅mol −1 ⋅cm −1 (the latter two units are both equal to 0.1 m 2 /mol). In older literature, the cm 2 /mol is sometimes used; 1 M −1 ⋅cm −1 equals 1000 cm 2 /mol.
In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
This unit is commonly used in physics and chemistry to express the mass of atomic-scale objects, such as atoms, molecules, and elementary particles, both for discrete instances and multiple types of ensemble averages. For example, an atom of helium-4 has a mass of 4.0026 Da. This is an intrinsic property of the isotope and all helium-4 atoms ...