Line integral meaning

In the 9-s detector-reading matrix, the values tabulated are ln Io/I) as given in Eq. (2), which is the line integral of fj,. It has the property that higher values mean higher thicknesses and densities of material. 

Separation analysis at the outlet of the detector must respect three major conditions. The first is the cell integrity (i.e., the diagnosis of the particle). This can be operated on line, by means of classical photometric devices operated in the light-scattering mode (opacimetry) at 254 nm. Off-line methods, after fraction collection, are possible and recommended, by microscopy and granulometric analysis (Coulter counting). The second objective is to analyze cell viability. Off-line methods after fraction collection are equally possible. The blue trypan exclusion test, motility measurements, or specific enzymatic activities (esterase) can be performed on an aliquot of the collected fraction. 

This statement means two things. First, if the line integral / is independent of path, then dM/dy = dN/dx. Second, if dM/dy = dN/dx, then the line integral / is independent of path. The equality given by Eq. (14-3) is commonly called the Maxwell relationship. 

A differential equation contains one or more derivatives of an unknown function, and solving a differential equation means finding what that function is. One important class of differential equations consists of classical equations of motion, which come from Newton s second law of motion. We will discuss the solution of several kinds of differential equations, including linear differential equations, in which the unknown function and its derivatives enter only to the first power, and exact differential equations, which can be solved by a line integration. We will also introduce partial differential equations, in which partial derivatives occur and in which there are two or more independent variables. We will also discuss the solution of differential equations by use of Laplace transformations. Some differential equations can be solved either symbolically or numerically using Mathematica. 

As is well known, explicit expressions for the polarization fields can be given such that equation (3) has the requisite properties these expressions, involving multipole series or line integrals, are by no means tmique. That this must be so can be seen from at least two levels of theory. We noted earlier that the notion of an electric field (or a magnetic field) is not invariant with respect to Lorentz transformations under such transformations however V should be an invariant scalar and this implies a definite transformation law for (P(x), M(x) that mixes them, and mirrors that for E(x), B(x) classically both pairs can be shown to be components of skew-symmetric second-rank tensors [7]. Although... 

We have now seen that the requirement that the two integrals be exact differentials is exactly the requirement that the Cauchy-Riemann conditions be satisfied. This means of course that the line integral... 

Base lines complicate the process as a nonzero base line integrates as a linear increasing offset. This can be minimized by calculating the mean value of each spectra and subtract it from the original spectra. The absorbance vectors should also be normalized. 

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