In mathematics, a π-system (or pi-system) on a set Ω {\displaystyle \Omega } is a collection P {\displaystyle P} of certain subsets of Ω , {\displaystyle...

participation in π bonding and their presence necessarily terminates a π system or separates two π systems. A basis p orbital that takes part in a π system can contribute...

Cation–π interaction is a noncovalent molecular interaction between the face of an electron-rich π system (e.g. benzene, ethylene, acetylene) and an adjacent...

In chemistry, π-effects or π-interactions are a type of non-covalent interaction that involves π systems. Just like in an electrostatic interaction where...

applications in measure theory and probability. A major application of 𝜆-systems is the π-𝜆 theorem, see below. Let Ω {\displaystyle \Omega } be a nonempty...

polar-π interactions. In general, π-effects are associated with the interactions of molecules with the π-systems of arenes. π–π interactions are associated...

disjoint subsets. Dynkin's π-λ theorem says, if P {\displaystyle P} is a π-system and D {\displaystyle D} is a Dynkin system that contains P , {\displaystyle...

A_{3},\ldots \right\}} has the finite intersection property (and is even a π–system). If the inclusions A 1 ⊇ A 2 ⊇ A 3 ⋯ {\displaystyle A_{1}\supseteq A_{2}\supseteq...

covalently bound atoms with specific characteristics: A delocalized conjugated π system, most commonly an arrangement of alternating single and double bonds Coplanar...

The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal...

cyclic molecule with a π electron system that has higher energy, i.e., it is less stable due to the presence of 4n delocalised (π or lone pair) electrons...

pi meson, denoted with the Greek letter pi ( π ), is any of three subatomic particles: π0 , π+ , and π− . Each pion consists of a quark and an antiquark...

describing concurrent systems, the π-calculus has also been used to reason about business processes and molecular biology. The π-calculus belongs to the...

element from some index set λ-system (Dynkin system) – Family closed under complements and countable disjoint unions π-system – Family of sets closed under...

Pi (/ˈpaɪ/; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive ϖ; Greek: πι [pi]) is the sixteenth letter of the Greek alphabet, representing...

a substituent moves from one part of a π-system to another part with simultaneous rearrangement of the π-system. True sigmatropic reactions are usually...

on opposite faces of the system and this can only be achieved in a conrotatory process. In open systems containing (4n + 2) π electrons, terminal bonding...

conjugated π system via resonance (mesomerism) or inductive effects (or induction)—called +M or +I effects, respectively—thus making the π system more nucleophilic...

{\mathcal {B}}\right\}.} A π–system is a prefilter if and only if it is proper. Every filter is a proper π–system and every proper π–system is a prefilter but...

coordinate systems used in mathematics normally use radians rather than degrees; (note 90 degrees equals π/2 radians). And these systems of the mathematics...

{\mathcal {B}}\right\}.} A π-system is a prefilter if and only if it is proper. Every filter is a proper π-system and every proper π-system is a prefilter but...

and conditions may be chemically meaningful. Molecules with an extended π system such as linear polyenes and polyaromatic compounds are well described by...

symbol ω), a conjugated system (π) or even a sigma bond (σ). The relationship is antarafacial when opposite faces of the π system or isolated orbital are...

still unknown. The Buckingham π theorem indicates that validity of the laws of physics does not depend on a specific unit system. A statement of this theorem...

products and new materials. The underlying concept has also been applied to π-systems involving heteroatoms, such as carbonyls and imines, which furnish the...

Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning...

Polar coordinate system. Many modern programming languages provide a function that will compute the correct azimuth φ, in the range (−π, π), given x and...

descriptions as a fallbackPages displaying short descriptions with no spaces π-system – Family of sets closed under intersection Preordered field – Algebraic...

atoms, and a resonance donating group (+M), due to the ability of its π system to donate electron density when conjugation is possible. The phenyl group...

mathematical constant pi (π). For more detailed explanations for some of these calculations, see Approximations of π. As of July 2024, π has been calculated...