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Inclusion–exclusion principle. In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as. where A and B are two finite sets and | S | indicates the cardinality of a ...
Exchange interaction is the main physical effect responsible for ferromagnetism, and has no classical analogue. For bosons, the exchange symmetry makes them bunch together, and the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation.
In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements.
Bicarbonate buffer system. Carbon dioxide, a by-product of cellular respiration, is dissolved in the blood, where it is taken up by red blood cells and converted to carbonic acid by carbonic anhydrase. Most of the carbonic acid then dissociates to bicarbonate and hydrogen ions. The bicarbonate buffer system is an acid-base homeostatic mechanism ...
The Pauli exclusion principle prohibits any two electrons (e-) in a molecule from having the same set of quantum numbers. [4] Therefore each original atomic orbital of the isolated atoms (for example, the ground state energy level, 1 s ) splits into two molecular orbitals belonging to the pair, one lower in energy than the original atomic level ...
Probability theory. The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2]
Inclusion compounds are often molecules, whereas clathrates are typically polymeric. Intercalation compounds are not 3-dimensional, unlike clathrate compounds. [7] According to IUPAC, clathrates are "Inclusion compounds in which the guest molecule is in a cage formed by the host molecule or by a lattice of host molecules." [8]
In host–guest chemistry, an inclusion compound (also known as an inclusion complex) is a chemical complex in which one chemical compound (the "host") has a cavity into which a "guest" compound can be accommodated. The interaction between the host and guest involves purely van der Waals bonding. The definition of inclusion compounds is very ...