Abstract: A method of synthesizing a reaction product of the formula R3-R4 by reacting a pnictogenium salt of the formula including a phosphonium salt of the formula with a Lewis acid in the presence of a nucleophile. The reaction products can then be isolated for use. R1 and R2 are individually selected from the group consisting of hydrogen, alkyl, heteroalkyl, aryl, heteroaryl, aralkyl, alkoxy, amino, and organosilyl. R3 and R4 are individually selected from the group consisting of optionally substituted monocyclic or polycyclic heteroaromatic moieties, optionally substituted monocyclic or polycyclic heteroaliphatic moieties, and optionally substituted linear or branched heteroaliphatic moieties. R1 or R2 optionally forms a covalent bond with R3 or R4. X is an anion.

Abstract: The invention is a method to predict the type of deformation of an object as elastic, plastic or fracture from a time series of specklegram patterns or fringe patterns (the difference of specklegrams). From the recorded patterns, a velocity vector field is calculated. The behavior of the velocity vector, as it evolves in time or space, is used to predict the deformation type. Fracture is predicted at a particular spatial location if the velocity vector file shows the dominate wavelength (or period) as increasing over time at that particular point. Plastic deformation is predicted at a particular spatial location if the maximum excursion of the velocity vector field at that particular location is decaying or distortion tensor parameters begin to depend on locations (they are different at different locations).

Abstract: The invention is a method of determining the phase difference between two interferometric images. The method includes the steps of measuring the intensities of the two beam arms, and measuring the intensities of the interfering beam arms at two different times (two frames). From the recorded data, the phase angle between the arms can be determined for each frame. These frame phase angles subtracted, and the sine of the difference is taken. The resulting data set is examined to determine a multiplicative factor that converts the minimum and maximum to the bounds of the sine function (?1, +1). This multiplicative factor is applied to a bounded trig function of the difference of the frame angles, and the inverse of the bounded trig function is taken, resulting in the phase difference between frames.