Atomicity (other)
Atomicity may refer to: Chemistry * Atomicity (chemistry), the total number of atoms present in 1 molecule of a substance * Valence (chemistry), sometimes referred to as atomicity Computing * Atomicity (database systems), a property of database transactions which are guaranteed to either completely occur, or have no effects * Atomicity (programming), an operation appears to occur at a single instant between its invocation and its response * Atomicity, a property of an S-expression, in a symbolic language like Lisp Mathematics * Atomicity, an element of orthogonality in a component-based system * Atomicity, in order theory; see Atom (order theory) See also * Atom (other) An atom is a basic unit of matter consisting of a nucleus within a cloud of one or more electrons. Atom(s) may also refer to: Mathematics * Atom (time), a medieval unit of time * Atom (measure theory), a minimal measurable set * Atom (order theo ...

Atomicity (chemistry)
Atomicity is the total number of atoms present in a molecule. For example, each molecule of oxygen (O2) is composed of two oxygen atoms. Therefore, the atomicity of oxygen is 2. In older contexts, atomicity is sometimes equivalent to valency. Some authors also use the term to refer to the maximum number of valencies observed for an element. Classifications Based on atomicity, molecules can be classified as: *Monoatomic (composed of one atom). Examples include He ( helium), Ne (neon), Ar ( argon), and Kr ( krypton). All noble gases are monoatomic. * Diatomic (composed of two atoms). Examples include H2 ( hydrogen), N2 ( nitrogen), O2 ( oxygen), F2 (fluorine), and Cl2 ( chlorine). Halogens are usually diatomic. *Triatomic (composed of three atoms). Examples include O3 ( ozone). * Polyatomic (composed of three or more atoms). Examples include S8. Atomicity may vary in different allotropes of the same element. The exact atomicity of metals, as well as so ...
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Valence (chemistry)
In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with other atoms when it forms chemical compounds or molecules. Description The combining capacity, or affinity of an atom of a given element is determined by the number of hydrogen atoms that it combines with. In methane, carbon has a valence of 4; in ammonia, nitrogen has a valence of 3; in water, oxygen has a valence of 2; and in hydrogen chloride, chlorine has a valence of 1. Chlorine, as it has a valence of one, can be substituted for hydrogen. Phosphorus has a valence of 5 in phosphorus pentachloride, . Valence diagrams of a compound represent the connectivity of the elements, with lines drawn between two elements, sometimes called bonds, representing a saturated valency for each element. The two tables below show some examples of different compounds, their valence diagrams, and the valences for each element of the compound. Modern definitions ...
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Atomicity (database Systems)
In database systems, atomicity (; from grc, ἄτομος, átomos, undividable) is one of the ACID (''Atomicity, Consistency, Isolation, Durability'') transaction properties. An atomic transaction is an ''indivisible'' and ''irreducible'' series of database operations such that either ''all'' occurs, or ''nothing'' occurs. A guarantee of atomicity prevents updates to the database occurring only partially, which can cause greater problems than rejecting the whole series outright. As a consequence, the transaction cannot be observed to be in progress by another database client. At one moment in time, it has not yet happened, and at the next it has already occurred in whole (or nothing happened if the transaction was cancelled in progress). An example of an atomic transaction is a monetary transfer from bank account A to account B. It consists of two operations, withdrawing the money from account A and saving it to account B. Performing these operations in an atomic transaction ...
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Atomicity (programming)
Atomicity may refer to: Chemistry * Atomicity (chemistry), the total number of atoms present in 1 molecule of a substance * Valence (chemistry), sometimes referred to as atomicity Computing * Atomicity (database systems), a property of database transactions which are guaranteed to either completely occur, or have no effects * Atomicity (programming), an operation appears to occur at a single instant between its invocation and its response * Atomicity, a property of an S-expression, in a symbolic language like Lisp Mathematics * Atomicity, an element of orthogonality in a component-based system * Atomicity, in order theory; see Atom (order theory) In the mathematical field of order theory, an element ''a'' of a partially ordered set with least element 0 is an atom if 0 < ''a'' and there is no ''x'' such that 0 < ''x'' < ''a''. Equivalently, one may define an atom to be an element that is < ...

S-expression
In computer programming, an S-expression (or symbolic expression, abbreviated as sexpr or sexp) is an expression in a like-named notation for nested list (tree-structured) data. S-expressions were invented for and popularized by the programming language Lisp, which uses them for source code as well as data. In the usual parenthesized syntax of Lisp, an S-expression is classically definedJohn McCarthy (1960/2006)Recursive functions of symbolic expressions. Originally published in Communications of the ACM. as # an atom of the form ''x'', or # an expression of the form (''x'' . ''y'') where ''x'' and ''y'' are S-expressions. This definition reflects LISP's representation of a list as a series of "cells", each one an ordered pair. In plain lists, ''y'' points to the next cell (if any), thus forming a list. The recursive clause of the definition means that both this representation and the S-expression notation can represent any binary tree. However, the representation can in princi ...
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Orthogonality
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry. Etymology The word comes from the Ancient Greek ('), meaning "upright", and ('), meaning "angle". The Ancient Greek (') and Classical Latin ' originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word ''orthogonalis'' came to mean a right angle or something related to a right angle. Mathematics Physics * In optics, polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization. * In special relativity, a time axis determined by a rapidity of motion is hyperbolic-orthogonal to a space axis of simu ...
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Atom (order Theory)
In the mathematical field of order theory, an element ''a'' of a partially ordered set with least element 0 is an atom if 0 < ''a'' and there is no ''x'' such that 0 < ''x'' < ''a''. Equivalently, one may define an atom to be an element that is minimal among the non-zero elements, or alternatively an element that covers the least element 0.

Atomic orderings

Let <: denote the covering relation in a partially ordered set. A partially ordered set with a least element 0 is atomic if every element ''b'' > 0 has an atom ''a'' below it, that is, there is some ''a'' such that ''b'' ≥ ''a'' :> ''0''. Every finite partially ordered set with 0 ...
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