Sigma (σ, σ) Määratlus

The lowercase (σ) & uppercase (Σ) sigma are used for:

• Language & Linguistics:

• In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative /s/. In Modern Greek, this sound is voiced to /z/ before /m/, /n/, /v/, /ð/ or /ɣ/.

• The uppercase form of sigma (Σ) was re-borrowed into the Latin alphabet—more precisely, the International African Alphabet—to serve as the uppercase of modern esh (lowercase: ʃ).

• In phonology, σ is used to represent syllables.

• In linguistics, Σ represents the set of symbols that form an alphabet (see also computer science).

• Science & Mathematics:

• In general mathematics, lowercase σ is commonly used to represent unknown angles, as well as serving as a shorthand for "countably", whereas Σ is regularly used as the operator for summation, e.g.:

• In statistics, σ represents standard deviation of population or probability distribution (as opposed to lowercase mu or μ, used for mean).

• In topology, σ-compact topological space is one that can be written as a countable union of compact subsets.

• In mathematical analysis and in probability theory, there is a type of algebra of sets known as σ-algebra (aka σ-field). Sigma algebra also includes terms such as:

• σ(A), denoting the generated sigma-algebra of a set A

• σ-finite measure (see measure theory)

• In number theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function.

• In applied mathematics, σ(T) denotes the spectrum of a linear map T.

• In complex analysis, σ is used in the Weierstrass sigma-function.

• In probability theory and statistics, Σ denotes the covariance matrix of a set of random variables, to distinguish it from the summation operator.

• In statistics (as mentioned above), σ represents the standard deviation of a population or probability distribution.

• Theoretical spectral analysis uses σ as standard deviation opposed to lowercase mu as the absolute mean value.

• Biology, Physiology, & Medicine:

• In biology, the sigma receptor (σ–receptors) is a type of cell surface receptor.

• In biochemistry, the σ factor (or specificity factor) is a protein found in RNA polymerase.

• In bone physiology, the bone remodeling period—i.e., the life span of a basic multicellular unit—has historically been referred to as the sigma period.

• In early 20th-century physiology literature, σ had been used to represent milliseconds.

• Business, Finance, & Economics:

• In finance, σ is the symbol used to represent volatility of stocks, usually measured by the standard deviation of logarithmic returns.

• In accounting, Σ indicates the balance of invoice classes and the overall amount of debts and demands.

• In macroeconomics, σ is used in equations to represent the elasticity of substitution between two inputs.

• In the machine industry, Six Sigma (6σ) is a quality model based on the standard deviation.

• Keemia:

• Sigma bonds (σ bonds) are the strongest type of covalent chemical bond.

• In organic chemistry, σ symbolizes the sigma constant of Hammett equation.

• Engineering & Computer Science:

• In computer science, Σ represents the set of symbols that form an alphabet (see also linguistics)

• Relational algebra uses the values σ_aθb(R) and σ_aθv(R) to denote selections, which are a type of unary operation.

• In machine learning, σ is used in the formula that derives the Sigmoid function.

• In radar jamming or electronic warfare, radar cross-sections (RCS) are commonly represented as σ when measuring the size of a target's image on radar.

• In signal processing, σ denotes the damping ratio of a system parameter.

• In theoretical computer science, Σ serves as the busy beaver function.

• Füüsika:

• In nuclear and particle physics, σ is used to denote cross sections in general(see also RCS), while Σ represents macroscopic cross sections [1/length].

• The symbol is to denote the Stefan–Boltzmann constant.

• In relation to fundamental properties of material, σ is often used to signify electrical conductivity.

• In electrostatics, σ represents surface charge density.

• In continuum mechanics, σ is used to signify stress.

• In condensed matter physics, Σ denotes self-energy.

• The symbol can be used to signify surface tension (alternatively, γ or T are also used instead).

• In quantum mechanics, σ is used to indicate Pauli matrices.

• In astronomy, σ represents velocity dispersion

• In particle physics, Σ represents a class of baryons.

• Organizations:

• During the 1930s, an uppercase Σ was in use as the symbol of the Ação Integralista Brasileira, a fascist political party in Brazil.

• Sigma Corporation uses the name of the letter but not the letter itself, but in many Internet forums, photographers refer to the company or its lenses using the letter.

• Sigma Aldrich incorporate both the name and the character in their logo.

Vana -Kreeka tähestiku tähed, mida sageli kasutatakse matemaatikas ja teaduses:

• Kreeka tähestik
• Kreeka numbrid

“Sigma.” Wikipedia, Wikimedia Foundation, 6 May 2020, en.wikipedia.org/wiki/Sigma.