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Given a finite set of probability density functions p 1 (x), ..., p n (x), or corresponding cumulative distribution functions P 1 (x), ..., P n (x) and weights w 1, ..., w n such that w i ≥ 0 and Σw i = 1, the mixture distribution can be represented by writing either the density, f, or the distribution function, F, as a sum (which in both ...
In chemistry, the mass concentration ρ i (or γ i) is defined as the mass of a constituent m i divided by the volume of the mixture V. [1]= For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture.
Olivine is described by the formula (Mg, Fe) 2 SiO 4, which is equivalent to (Mg 1−x Fe x) 2 SiO 4. The ratio of magnesium to iron varies between the two endmembers of the solid solution series: forsterite (Mg-endmember: Mg 2 SiO 4) and fayalite (Fe-endmember: Fe 2 SiO 4) [2] but the ratio in olivine is not normally defined. With increasingly ...
Mathematically, density is defined as mass divided by volume: [1] =, where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume , [ 2 ] although this is scientifically inaccurate – this quantity is more ...
In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble [1] of physical systems as quantum states (even if the ensemble contains only one system). It allows for the calculation of the probabilities of the outcomes of any measurements performed upon the systems of the ensemble using the Born rule .
In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material. [ 1 ] [ 2 ] [ 3 ] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus , ultimate tensile strength , thermal conductivity , and electrical conductivity . [ 3 ]
For a substance X with a specific volume of 0.657 cm 3 /g and a substance Y with a specific volume 0.374 cm 3 /g, the density of each substance can be found by taking the inverse of the specific volume; therefore, substance X has a density of 1.522 g/cm 3 and substance Y has a density of 2.673 g/cm 3. With this information, the specific ...
It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction (percentage by volume, vol%) are others. When the prevalences of interest are those of individual chemical elements , rather than of compounds or other substances, the term mass fraction can also refer ...
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