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μ – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. R – rotation matrix. Consists of three axes (small [clarification needed] rotations around each of the three coordinate axes) r x, r y, r z. The rotation matrix is an orthogonal matrix. The angles are given in either degrees or radians.
In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V.The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
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In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [1]
Fluorescein aqueous solutions, diluted from 10,000 to 1 parts-per-million in intervals of 10 fold dilution. At 1 ppm the solution is a very pale yellow. At 1 ppm the solution is a very pale yellow. As the concentration increases the colour becomes a more vibrant yellow, then orange, with the final 10,000 ppm a deep red colour.
The Euler equations are the governing equations for inviscid flow. To implement shock-capturing methods, the conservation form of the Euler equations are used. For a flow without external heat transfer and work transfer (isoenergetic flow), the conservation form of the Euler equation in Cartesian coordinate system can be written as + + + = where the vectors U, F, G, and H are given by
The difference between the chemical shift of a given nucleus in a diamagnetic vs. a paramagnetic environment is called the hyperfine shift.In solution the isotropic hyperfine chemical shift for nickelocene is −255 ppm, which is the difference between the observed shift (ca. −260 ppm) and the shift observed for a diamagnetic analogue ferrocene (ca. 5 ppm).
For example, in a solution with a 1:5 dilution ratio, entails combining 1 unit volume of solute (the material to be diluted) with 5 unit volumes of the solvent to give 6 total units of total volume. In photographic development, dilutions are normally given in a '1+x' format.