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in a sigma bond. Transition metal silane complexes are often especially stable sigma complexes. A particularly common subset of sigma complexes are those
Sigma_complex
Eighteenth letter of the Greek alphabet
Sigma (/ˈsɪɡmə/ SIG-mə; uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. When
Sigma
Forms during electrophilic substitution on benzene ring
this complex is also called a Wheland intermediate, after American chemist George Willard Wheland (1907–1976). They are also called sigma complexes. The
Arenium_ion
Formation of a 3-center 2-electron bond between a transition metal and C–H bond
is a special case of a C–H sigma complex. Historically, agostic complexes were the first examples of C–H sigma complexes to be observed spectroscopically
Agostic_interaction
Protein needed for initiation of transcription in prokaryotes
sigma factor with a molecular weight of 70 kDa. The sigma factor in the RNA polymerase holoenzyme complex is required for the initiation of transcription
Sigma_factor
Matrices important in quantum mechanics and the study of spin
complex matrices that are traceless, Hermitian, involutory and unitary. They are usually denoted by the Greek letter σ {\displaystyle \sigma } (sigma)
Pauli_matrices
Method for converting signals between digital and analog
Delta-sigma (ΔΣ; or sigma-delta, ΣΔ) modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency
Delta-sigma_modulation
Business process improvement technique
Six Sigma (6σ) is a set of techniques and tools for process improvement. It was introduced by American engineer Bill Smith while working at Motorola in
Six_Sigma
Non-tensorial representation of the spin group
{i} &=-\sigma _{2}\sigma _{3}=-i\sigma _{1}\\\mathbf {j} &=-\sigma _{3}\sigma _{1}=-i\sigma _{2}\\\mathbf {k} &=-\sigma _{1}\sigma _{2}=-i\sigma _{3}\end{aligned}}}
Spinor
Containing intact H2 as a ligand
Dihydrogen complexes are coordination complexes containing intact H2 as a ligand. They are a subset of sigma complexes. The prototypical complex is W(CO)3(PCy3)2(H2)
Dihydrogen_complex
Mathematics concept
field of complex numbers itself, considered as a complex vector space over itself and with the conjugation map σ : C → C {\displaystyle \sigma :{\mathbb
Real_structure
depending on the complex), a medium adaptin (mu), and a small adaptin (sigma): complex 1 AP1B1 AP1G1 AP1G2 AP1M1 AP1M2 AP1S1 AP1S2 AP1S3 complex 2 AP2A1 AP2A2
List_of_adaptins
Covalent chemical bond
In chemistry, sigma bonds (σ bonds) or sigma overlap are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic
Sigma_bond
Algebraic structure of set algebra
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In
Σ-algebra
Four-dimensional number system
2 complex matrix above can be written as a I + b i σ 3 + c i σ 2 + d i σ 1 , {\displaystyle a\,I+b\,i\,\sigma _{3}+c\,i\,\sigma _{2}+d\,i\,\sigma _{1}
Quaternion
Measure of covariance of components of a random vector
_{1})(X_{2}-\mu _{2})]}{\sigma (X_{1})\sigma (X_{2})}}&\cdots &{\frac {\operatorname {E} [(X_{1}-\mu _{1})(X_{n}-\mu _{n})]}{\sigma (X_{1})\sigma (X_{n})}}\\\\{\frac
Covariance_matrix
Business management method
Design for Six Sigma (DFSS) is a collection of best-practices for the development of new products and processes. It is sometimes deployed as an engineering
Design_for_Six_Sigma
Matrix decomposition
{U} \mathbf {\Sigma } \mathbf {V} ^{*}} , where U {\displaystyle \mathbf {U} } is an m × m {\displaystyle m\times m} complex unitary matrix
Singular_value_decomposition
silyl complexes describe coordination complexes in which a transition metal is bonded to an anionic silyl ligand, forming a metal-silicon sigma bond.
Transition metal silyl complexes
Transition_metal_silyl_complexes
Algebraic structure associated with a topological space
{\displaystyle \sigma [0]<\sigma [1]<\cdots <\sigma [n]} in the complex's vertex ordering, where σ [ i ] {\displaystyle \sigma [i]} is the i {\displaystyle
Homology_(mathematics)
Probability distribution
{\textstyle \sigma ^{2}} is the variance. The standard deviation of the distribution is the positive value σ {\displaystyle \sigma } (sigma). A random
Normal_distribution
Complex in algebraic topology
}(X)} . Then, for each σ ⊂ X {\displaystyle \sigma \subset X} , let σ ∈ C ˇ ε ( X ) {\displaystyle \sigma \in {\check {C}}_{\varepsilon }(X)} if the set
Čech_complex
Addition of Si-H bonds across unsaturated bonds
complex that contains a hydride, a silyl ligand (R3Si), and the alkene substrate. Oxidative addition proceeds by the intermediacy of a sigma-complex,
Hydrosilylation
Type of reaction in organometallic chemistry
three-centered σ complex is invoked, followed by intramolecular ligand bond cleavage of the ligand (probably by donation of electron pair into the sigma* orbital
Oxidative_addition
chemistry, sigma-bond metathesis is a chemical reaction wherein a metal-ligand sigma bond undergoes metathesis (exchange of parts) with the sigma bond in
Sigma-bond_metathesis
Characteristic property of holomorphic functions
f=(\sigma _{1}\partial _{x}+\sigma _{2}\partial _{y})(u+\sigma _{1}\sigma _{2}v)\\[4pt]&=\sigma _{1}\partial _{x}u+\underbrace {\sigma _{1}\sigma _{1}\sigma
Cauchy–Riemann_equations
vertices. An abstract simplicial complex Δ is a set of finite sets of vertices, known as faces σ ⊆ V {\displaystyle \sigma \subseteq V} , such that ∀ ρ ∀
Poset_topology
Concept in algebraic topology
− P ( ∂ σ ) . {\displaystyle \partial P(\sigma )=f_{\sharp }(\sigma )-g_{\sharp }(\sigma )-P(\partial \sigma ).} So if α in Cn(X) is an n-cycle, then
Singular_homology
Sigma non-innocence is a special form of non-innocence, an oxidation characteristic in metal complexes. It is mainly discussed in coordination complexes
Sigma_non-innocence
Measure with complex values
is a complex number. Formally, a complex measure μ {\displaystyle \mu } on a measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} is a complex-valued
Complex_measure
Probability distribution
, {\displaystyle f(x;\sigma )={\frac {x}{\sigma ^{2}}}e^{-x^{2}/(2\sigma ^{2})},\quad x\geq 0,} where σ {\displaystyle \sigma } is the scale parameter
Rayleigh_distribution
Problem in applied mathematics
}={\frac {\int D\sigma A[\sigma ]\exp(i\theta [\sigma ])\,p[\sigma ]}{\int D\sigma \exp(i\theta [\sigma ])\,p[\sigma ]}}={\frac {\langle A[\sigma ]\exp(i\theta
Numerical_sign_problem
Chemical reaction in organic chemistry
coordination of the C–H bond with the metal to form a metal–hydrocarbon sigma complex. The computed transition state involves concerted partial formation
Concerted metalation deprotonation
Concerted_metalation_deprotonation
Math concept
{\displaystyle \sigma _{1},\sigma _{2}\in {\mathcal {K}}} is a face of both σ 1 {\displaystyle \sigma _{1}} and σ 2 {\displaystyle \sigma _{2}} . Note that
Polyhedral_complex
Relativistic wave description of fermions
{\displaystyle \sigma ^{\mu }={\begin{pmatrix}\sigma ^{0}&\sigma ^{1}&\sigma ^{2}&\sigma ^{3}\end{pmatrix}}={\begin{pmatrix}I_{2}&\sigma _{x}&\sigma _{y}&\sigma _{z}\end{pmatrix}}}
Majorana_equation
Neighbour-dependent grapheme positioning
to simply equate the two sigma codes for operations which are concerned with word content, for example. Examples of complex rendering — SIL international's
Complex_text_layout
Type of mathematical set
{\displaystyle \sigma \in {\mathcal {K}}} of dimension exactly k. Informally, a pure 1-complex "looks" like it's made of a bunch of lines, a 2-complex "looks"
Simplicial_complex
Species of snake
Boa sigma, known commonly as the Mexican west coast boa constrictor or Bateman’s Boa, is a species of snake in the family Boidae. The species is endemic
Boa_sigma
\operatorname {Lk} (\sigma ,X):=\{\tau \in X:~\tau \cap \sigma =\emptyset ,~\tau \cup \sigma \in X\}} . Given a geometric simplicial complex X and any face
Link_(simplicial_complex)
Failure Theory in continuum mechanics
strength, σ y {\displaystyle \sigma _{\text{y}}} . The von Mises stress is used to predict yielding of materials under complex loading from the results of
Von_Mises_yield_criterion
Combinatorial approach of studying the topology of a manifold
{\displaystyle \sigma } , provided that X {\displaystyle {\mathcal {X}}} is a regular CW complex. In this case, each cell σ ∈ X {\displaystyle \sigma \in {\mathcal
Discrete_Morse_theory
Equation relating to oscillating systems
{\displaystyle \sigma =\sigma _{r}+i\sigma _{i}} is the complex growth rate, l = l r + i l i {\displaystyle l=l_{r}+il_{i}} is a complex number and l r
Stuart–Landau_equation
Function that is holomorphic on the whole complex plane
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane
Entire_function
Number, approximately 2.41421
{\begin{aligned}\sigma ^{n}&=2\sigma ^{n-1}+\sigma ^{n-2}\\&=\sigma ^{n-1}+3\sigma ^{n-2}+\sigma ^{n-3}\\&=2\sigma ^{n-1}+2\sigma ^{n-3}+\sigma ^{n-4}\end{aligned}}}
Silver_ratio
Linear filter used for texture analysis
gabor_fn(sigma, theta, lambda, psi, gamma) sigma_x = sigma; sigma_y = sigma / gamma; % Bounding box nstds = 3; xmax = max(abs(nstds * sigma_x * cos(theta))
Gabor_filter
Set of eigenvalues of a matrix
{\displaystyle \sigma (T)\cap \mathbb {R} =\sigma _{\mathbb {R} }(T)} . Note that the real spectrum may or may not coincide with the complex spectrum. In
Spectrum (functional analysis)
Spectrum_(functional_analysis)
K {\displaystyle K} be an abstract simplicial complex. Suppose that τ , σ {\displaystyle \tau ,\sigma } are two simplices of K {\displaystyle K} such
Collapse_(topology)
Integral transform useful in probability theory, physics, and engineering
(Eq. 1) where s {\displaystyle s} is a complex frequency-domain parameter s = σ + i ω {\textstyle s=\sigma +i\omega } with real numbers σ and ω. An
Laplace_transform
Gaussian-windowed wavelet
) {\displaystyle \Psi _{\sigma }(t)=c_{\sigma }\pi ^{-{\frac {1}{4}}}e^{-{\frac {1}{2}}t^{2}}(e^{i\sigma t}-\kappa _{\sigma })} where κ σ = e − 1 2 σ
Morlet_wavelet
Elementary particles with a spin of 1/2
\right|{\boldsymbol {\sigma }}\left|\psi \right\rangle } , where σ = ( σ x , σ y , σ z ) {\displaystyle {\boldsymbol {\sigma }}=(\sigma _{x},\sigma _{y},\sigma _{z})}
Spin_1/2
Linear transformation of spacetime coordinates
{\displaystyle q^{*}=a-b\,\mathbf {\sigma } _{x}-c\,\mathbf {\sigma } _{y}-d\,\mathbf {\sigma } _{z}} The analog of the complex conjugate is q ¯ = a ¯ − b ¯
Biquaternion Lorentz transformation
Biquaternion_Lorentz_transformation
American materials scientist
advancement of the Los Alamos Neutron Science Center (LANSCE) and the Sigma Complex. In 2024 and 2025, Cerreta led teams conducting forefront research in
Ellen_Cerreta
^{*}E_{0}{\stackrel {\sigma (P_{1})}{\longrightarrow }}\pi ^{*}E_{1}{\stackrel {\sigma (P_{2})}{\longrightarrow }}\ldots {\stackrel {\sigma (P_{k})}{\longrightarrow
Elliptic_complex
Mathematical representation
_{1}=\sigma _{3}^{-1}\sigma _{2}\sigma _{1}^{2}\sigma _{2}\sigma _{4}^{3}\sigma _{3}\sigma _{2},\quad \psi _{2}=\sigma _{4}^{-1}\sigma _{3}\sigma _{2}\sigma
Burau_representation
\mathbf {S} \sim {\mathcal {CW}}(\mathbf {\Sigma } ,\nu ,p)} with mean value Σ and ν {\displaystyle \mathbf {\Sigma } {\text{ and }}\nu } degrees of freedom
Complex inverse Wishart distribution
Complex_inverse_Wishart_distribution
Foundational principle in quantum physics
that year and by Hermann Weyl in 1928: σ x σ p ≥ ℏ 2 {\displaystyle \sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}} where ℏ = h 2 π {\displaystyle \hbar
Uncertainty_principle
Topological data
dimension of the simplicial complex, D σ {\displaystyle D_{\sigma }} is the maximal number of operations to access σ {\displaystyle \sigma } in a dictionary (if
Simplex_tree
Intermolecular forces between oppositely-charged sites on molecules
In chemistry, sigma hole interactions (or σ-hole interactions) are a family of intermolecular forces that can occur between several classes of molecules
Sigma_hole_interactions
Mathematical transform that expresses a function of time as a function of frequency
Still with ξ = σ + i τ {\displaystyle \xi =\sigma +i\tau } , if f ^ {\displaystyle {\widehat {f}}} is complex analytic for a ≤ τ ≤ b and has sufficient
Fourier_transform
Mode of convergence of an infinite series
\sigma \left(I_{\sigma ,\varepsilon }\right)=\min \left\{\sigma (k)\ :\ k\in I_{\sigma ,\varepsilon }\right\}\\L_{\sigma ,\varepsilon }&=\max \sigma \left(I_{\sigma
Absolute_convergence
Mathematical object
of CW complexes together with inclusions Σ E n → E n + 1 {\displaystyle \Sigma E_{n}\to E_{n+1}} of the suspension Σ E n {\displaystyle \Sigma E_{n}}
Spectrum_(topology)
Malaysia), and the United States (topographic survey). Sigma 30 can also be integrated in more complex systems (Positioning and Azimuth Determination System)
SAGEM_Sigma_30
Probability distribution
{\ln x-\mu }{\sigma }}\right)}{\frac {1}{\sigma x}}\\[6pt]&={\frac {1}{x\sigma {\sqrt {2\pi }}}}\exp \left(-{\frac {(\ln x-\mu )^{2}}{2\sigma ^{2}}}\right)~
Log-normal_distribution
Antagonists of a youth's slang
a sigma factor, an anti-sigma factor, an anti-anti-sigma factor, and an input phosphatase complex. A cell that is not under stress has an anti-sigma factor
Anti-sigma_factors
Result about when a matrix can be diagonalized
{\displaystyle \Sigma \in \mathbb {R} ^{m\times n}} is a diagonal matrix with nonnegative entries. The diagonal entries of Σ {\displaystyle \Sigma } are uniquely
Spectral_theorem
Scottish film production company
Sigma Films is a film production company based in Glasgow, Scotland. The company was formed in 1996 by Gillian Berrie, David Mackenzie and Alastair Mackenzie
Sigma_Films
Class of protein transcription factors
transcription initiation requires an RNA polymerase and a single GTF: sigma factor. In archaea and eukaryotes, transcription initiation requires an
General_transcription_factor
Effect of variables' uncertainties on the uncertainty of a function based on them
_{1}^{2}&\sigma _{12}&\sigma _{13}&\cdots \\\sigma _{21}&\sigma _{2}^{2}&\sigma _{23}&\cdots \\\sigma _{31}&\sigma _{32}&\sigma _{3}^{2}&\cdots
Propagation_of_uncertainty
Mathematical functions related to Weierstrass's elliptic function
of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta
Weierstrass_functions
Particular kind of algebraic structure
{\displaystyle x\in A,} denoted by σ ( x ) {\displaystyle \sigma (x)} , consists of all those complex scalars λ {\displaystyle \lambda } such that x − λ 1 {\displaystyle
Banach_algebra
notable alumni and honorary members of Alpha Chi Sigma professional chemistry fraternity. Carolyn Bertozzi, Sigma 2001 (2022), "for the development of click
List of Alpha Chi Sigma members
List_of_Alpha_Chi_Sigma_members
n_{1}\sigma _{1}+\cdots +n_{k}\sigma _{k}\in C_{0}} , then ε ( n 1 σ 1 + ⋯ + n k σ k ) = n 1 + ⋯ + n k ∈ Z {\displaystyle \varepsilon (n_{1}\sigma _{1}+\cdots
Poincaré_complex
Statistical measure of variability
{MAD} =\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(1/2)\approx 0.67449\sigma .} This form is used in, e.g., the probable error. In the case of complex values
Median_absolute_deviation
Fundamental operation on complex numbers
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in
Complex_conjugate
Measure of a substance's ability to resist or conduct electric current
sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{yx}&\sigma _{yy}&\sigma _{yz}\\\sigma _{zx}&\sigma _{zy}&\sigma
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
U.S. project to build a nuclear thermal rocket
Pajarito Site. Fuel and internal engine components were fabricated in the Sigma complex at Los Alamos. Testing of fuel elements and other materials science
Project_Rover
Chemical compounds
hydrogenations. Hydrosilanes form sigma complexes with unsaturated metals. The bonding is similar to that in dihydrogen complexes but stronger. One example is
Hydrosilanes
Relativistic wave equation describing massless fermions
{\displaystyle \sigma ^{\mu }={\begin{pmatrix}\sigma ^{0}&\sigma ^{1}&\sigma ^{2}&\sigma ^{3}\end{pmatrix}}={\begin{pmatrix}I_{2}&\sigma _{x}&\sigma _{y}&\sigma _{z}\end{pmatrix}}}
Weyl_equation
Generalization of the one-dimensional normal distribution to higher dimensions
_{Y}\end{pmatrix}},\quad {\boldsymbol {\Sigma }}={\begin{pmatrix}\sigma _{X}^{2}&\rho \sigma _{X}\sigma _{Y}\\\rho \sigma _{X}\sigma _{Y}&\sigma _{Y}^{2}\end{pmatrix}}
Multivariate normal distribution
Multivariate_normal_distribution
The Elitar Sigma or Elitar (Samara VVV-Avia) Sigma is a single engine light aircraft of wing and boom layout, seating two in side-by-side configuration
Elitar_Sigma
Law of electrical current and voltage
electromagnetics and material science: J = σ E , {\displaystyle \mathbf {J} =\sigma \mathbf {E} ,} where J is the current density at a given location in a resistive
Ohm's_law
Mathematical problems related to differential equations
{\displaystyle \Sigma } is a smooth, simple, closed contour in the complex plane. Divide the plane into two parts denoted by Σ + {\displaystyle \Sigma _{+}} (the
Riemann–Hilbert_problem
Type of spline curve
{\displaystyle \sigma (t)} satisfying the equation of the Pythagorean theorem: σ ( t ) 2 = x ′ ( t ) 2 + y ′ ( t ) 2 . {\displaystyle \sigma (t)^{2}=x'(t)^{2}+y'(t)^{2}
Pythagorean_hodograph_curve
Data-driven improvement cycle used for improving and optimizing business processes
improvement cycle is the core tool used to drive Six Sigma projects. However, DMAIC is not exclusive to Six Sigma and can be used as the framework for other improvement
DMAIC
Kind of mathematical function
{\displaystyle \sigma } -algebra of Lebesgue measurable sets, and B C {\displaystyle {\mathcal {B}}_{\mathbb {C} }} is the Borel algebra on the complex numbers
Measurable_function
Name of the protein necessary for prokaryotic regulation
necessary for the prokaryotic regulation transcription factor sigma N (sigma 54) to form an open complex with RNA polymerase in order to activate glnA transcription
NtrC
Interstellar cloud
Sh2-9 has Sigma Scorpii at its center, and Antares is just outside the picture at the bottom. The large multicoloured Rho Ophiuchi cloud complex with the
Rho_Ophiuchi_cloud_complex
Generalization of mass, length, area and volume
pair ( X , Σ ) {\displaystyle (X,\Sigma )} is called a measurable space, and the members of Σ {\displaystyle \Sigma } are called measurable sets. A triple
Measure_(mathematics)
Mathematical inequality
X ) + 3 σ ( X ) {\displaystyle c_{1}^{2}(X)=2e(X)+3\sigma (X)} where σ ( X ) {\displaystyle \sigma (X)} is the signature of the intersection form on the
Bogomolov–Miyaoka–Yau inequality
Bogomolov–Miyaoka–Yau_inequality
Mathematical series
{\displaystyle \sigma >0} : | f ( σ + i t ) | < C + ε | σ + i t | 1 σ . {\displaystyle |f(\sigma +it)|<C+\varepsilon |\sigma +it|{\frac {1}{\sigma }}.} A formal
Dirichlet_series
Technique used to study & characterize materials
following equations hold: Stress: σ = σ 0 sin ( t ω + δ ) {\displaystyle \sigma =\sigma _{0}\sin(t\omega +\delta )\,} Strain: ε = ε 0 sin ( t ω ) {\displaystyle
Dynamic_mechanical_analysis
Protein-coding gene in the species Homo sapiens
AP-3 complex subunit sigma-1 is a protein that in humans is encoded by the AP3S1 gene. GRCh38: Ensembl release 89: ENSG00000177879 – Ensembl, May 2017
AP3S1
Method to estimate the components of a signal
( ω i t + ϕ i ) {\displaystyle {\hat {f}}(t)=\sum _{i=1}^{N}A_{i}e^{\sigma _{i}t}\cos(\omega _{i}t+\phi _{i})} to the observed f ( t ) {\displaystyle
Prony's_method
Method in algebraic topology
) σ | [ v q , … , v p ] . {\displaystyle \sigma \frown \psi =\psi (\sigma |_{[v_{0},\ldots ,v_{q}]})\sigma |_{[v_{q},\ldots ,v_{p}]}.} Here, the notation
Cap_product
Links the homology groups of a product space with those of the individual spaces
C_{*}(Y)}(\sigma \otimes \tau )=\partial _{X}\sigma \otimes \tau +(-1)^{p}\sigma \otimes \partial _{Y}\tau } for σ ∈ C p ( X ) {\displaystyle \sigma \in C_{p}(X)}
Eilenberg–Zilber_theorem
Complex matrix whose conjugate transpose equals its inverse
}&0\\0&e^{i\zeta }\end{bmatrix}}{\begin{bmatrix}\;\cos \sigma &\sin \sigma \\-\sin \sigma &\cos \sigma \\\end{bmatrix}}~.} Many other factorizations of a unitary
Unitary_matrix
Distribution of singular values of large rectangular random matrices
s(z)={\frac {\sigma ^{2}(1-\lambda )-z-{\sqrt {(z-\sigma ^{2}(\lambda +1))^{2}-4\lambda \sigma ^{4}}}}{2\lambda z\sigma ^{2}}}} for complex numbers z of
Marchenko–Pastur_distribution
Chemical compound
1021/ja902046m. PMC 2746668. PMID 19441851. CPhos at Sigma Aldrich CPhos Pd G2 (precatalyst) at Sigma Aldrich CPhos Pd G3 (precatalyst) at Sigma Aldrich
CPhos
Discrete (i.e., incremental) version of infinitesimal calculus
S} be a simplicial complex. A simplicial k-chain is a finite formal sum ∑ i = 1 N c i σ i , {\displaystyle \sum _{i=1}^{N}c_{i}\sigma _{i},\,} where each
Discrete_calculus
Infinite series in mathematical analysis
converges everywhere on the complex plane. The abscissa of convergence of a Dirichlet series can be defined as σ c {\displaystyle \sigma _{c}} above. Another
General_Dirichlet_series
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