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Collins reagent is the complex of chromium(VI) oxide with pyridine in dichloromethane. [2] This metal-pyridine complex , a red solid, is used to oxidize primary alcohols to the corresponding aldehydes and secondary alcohols to the corresponding ketones .
In Cartesian coordinates (x, y, z), let the region y < 0 have refractive index n 1, intrinsic admittance Y 1, etc., and let the region y > 0 have refractive index n 2, intrinsic admittance Y 2, etc. Then the xz plane is the interface, and the y axis is normal to the interface (see diagram).
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product .
The Collins oxidation is also very useful because it is cheap in comparison to its oxidizing counterparts, PCC and PDC. [5] However, it is more difficult experimentally because of its required anhydrous conditions. The Collins oxidation is a good option when using uncomplicated substrates because it produces good yields of aldehyde and ketone ...
A complex refractive index can therefore be defined in terms of the complex angular wavenumber defined above: _ = _. where n is the refractive index of the medium. In other words, the wave is required to satisfy E ( z , t ) = Re [ E 0 e i ω ( n _ z / c − t ) ] . {\displaystyle \mathbf {E} (z,t)=\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i ...
One approach to cross ratio interprets it as a homography that takes three designated points to 0, 1, and ∞. Under restrictions having to do with inverses, it is possible to generate such a mapping with ring operations in the projective line over a ring. The cross ratio of four points is the evaluation of this homography at the fourth point.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The fact that Moran's I is a summation of individual cross products is exploited by the "local indicators of spatial association" (LISA) to evaluate the clustering in those individual units by calculating Local Moran's I for each spatial unit and evaluating the statistical significance for each I i.