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Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1] [2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.
These forces and their associated displacements are called conjugate variables. [1] For example, consider the p V {\displaystyle pV} conjugate pair. The pressure p {\displaystyle p} acts as a generalized force: Pressure differences force a change in volume d V {\displaystyle \mathrm {d} V} , and their product is the energy lost by the system ...
Cinnamaldehyde is a naturally-occurring compound that has a conjugated system penta-1,3-diene is a molecule with a conjugated system Diazomethane conjugated pi-system. In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability.
The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis ( minor semiaxis ) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic ...
According to the correspondence principle, in certain limits the quantum equations of states must approach Hamilton's equations of motion.The latter state the following relation between the generalized coordinate q (e.g. position) and the generalized momentum p: {˙ = = {,}; ˙ = = {,}.
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One use of conjugate acids and bases lies in buffering systems, which include a buffer solution. In a buffer, a weak acid and its conjugate base (in the form of a salt), or a weak base and its conjugate acid, are used in order to limit the pH change during a titration process. Buffers have both organic and non-organic chemical applications.
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...