Phase diagramA phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium. Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.
Discrete mathematicsDiscrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.
AutocovarianceIn probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question. With the usual notation for the expectation operator, if the stochastic process has the mean function , then the autocovariance is given by where and are two instances in time.
Speckle imagingSpeckle imaging comprises a range of high-resolution astronomical imaging techniques based on the analysis of large numbers of short exposures that freeze the variation of atmospheric turbulence. They can be divided into the shift-and-add ("image stacking") method and the speckle interferometry methods. These techniques can dramatically increase the resolution of ground-based telescopes, but are limited to bright targets.
Bilinear time–frequency distributionBilinear time–frequency distributions, or quadratic time–frequency distributions, arise in a sub-field of signal analysis and signal processing called time–frequency signal processing, and, in the statistical analysis of time series data. Such methods are used where one needs to deal with a situation where the frequency composition of a signal may be changing over time; this sub-field used to be called time–frequency signal analysis, and is now more often called time–frequency signal processing due to the progress in using these methods to a wide range of signal-processing problems.
Lucky imagingLucky imaging (also called lucky exposures) is one form of speckle imaging used for astrophotography. Speckle imaging techniques use a high-speed camera with exposure times short enough (100 ms or less) so that the changes in the Earth's atmosphere during the exposure are minimal. With lucky imaging, those optimum exposures least affected by the atmosphere (typically around 10%) are chosen and combined into a single image by shifting and adding the short exposures, yielding much higher angular resolution than would be possible with a single, longer exposure, which includes all the frames.
