Pi (letter)

Pi (/ˈpaɪ/; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive π; πι pi) is the sixteenth letter of the Greek alphabet, meaning units united, and representing the voiceless bilabial plosive p. In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter Pe (). Letters that arose from pi include Latin P, Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀). The uppercase letter Π is used as a symbol for: In textual criticism, Codex Petropolitanus, a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia. In legal shorthand, it represents a plaintiff. In science and engineering: The product operator in mathematics, indicated with capital pi notation Π (in analogy to the use of the capital Sigma Σ as summation symbol). The osmotic pressure in chemistry. The viscous stress tensor in continuum mechanics and fluid dynamics. The lowercase letter pi is used as a symbol for: The mathematical real transcendental (and thus irrational) constant π ≈ 3.14159..., the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter "pi" is the first letter of the Greek words περιφέρεια 'periphery' and περίμετρος 'perimeter', i.e. the circumference. The prime-counting function in mathematics. Homotopy groups in algebraic topology. Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis. The hadron called the pion (pi meson). Often inflation rate in macroeconomics. Sometimes profit in microeconomics. A type of chemical bond in which the p orbitals overlap, called a pi bond. The natural projection on the tangent bundle on a manifold. The unary operation of projection in relational algebra. Policy in reinforcement learning. Polyamory (in the earliest polyamory pride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory). An early form of pi was , appearing almost like a gamma with a hook. Variant pi or "pomega" ( or π) is a glyph variant of lowercase pi sometimes used in technical contexts.

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Toyomu Matsuda

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024

Light-Controlled Multiconfigurational Conductance Switching in a Single 1D Metal-Organic Wire

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Learning the Exciton Properties of Azo-dyes

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Light-Controlled Multiconfigurational Conductance Switching in a Single 1D Metal-Organic Wire

Learning the Exciton Properties of Azo-dyes