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The Sigma-D relation, or Σ-D Relation, is the claimed relation between the radio surface brightness and diameter of a supernova remnant. It is generally
Sigma-D_relation
Concept in astronomy
The M–sigma (or M–σ) relation is an empirical correlation between the stellar velocity dispersion σ of a galaxy bulge and the mass M of the supermassive
M–sigma_relation
Succession of methods by which astronomers determine the distances to celestial objects
to a galaxy's distance. The Sigma-D relation (or Σ-D relation), used in elliptical galaxies, relates the angular diameter (D) of the galaxy to its velocity
Cosmic_distance_ladder
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
Binary relation in computer science
relation D = ( Σ × Σ ) ∖ I {\displaystyle D=(\Sigma \times \Sigma )\setminus I} is a dependency relation. The pair ( Σ , D ) {\displaystyle (\Sigma
Dependency_relation
Foundational principle in quantum physics
following uncertainty relation holds σ J x 2 + σ J y 2 + σ J z 2 ≥ j , {\displaystyle \sigma _{J_{x}}^{2}+\sigma _{J_{y}}^{2}+\sigma _{J_{z}}^{2}\geq j,}
Uncertainty_principle
Remnants of an exploded star
List of supernova remnants Local Bubble Nova remnant Planetary nebula Sigma-D relation Superbubble Discovery of most recent supernova in our galaxy May 14
Supernova_remnant
Theory of relational databases
{\displaystyle \sigma _{{\text{isFriend = true}}\,\lor \,{\text{isBusinessContact = true}}}({\text{addressBook}}).} The result would be a relation containing
Relational_algebra
Power law for galaxies
{\displaystyle \sigma } of elliptical galaxy, and was presented by the astronomers Sandra M. Faber and Robert Earl Jackson in 1976. Their relation can be expressed
Faber–Jackson_relation
Astronomical term for luminosity per area
Araucaria Project Low-surface-brightness galaxy Limiting magnitude Sigma-D relation Daintith, John; Gould, William (2006). The Facts on File dictionary
Surface_brightness
Subfield of astronomy
density profiles. M–sigma relation – Correlation between black hole mass and galaxy bulge velocity dispersion. Sigma-D relation – Links galaxy thickness
Outline_of_astrophysics
relation is (1) σ e ( ω ) σ a ( ω ) exp ( ℏ ω k B T ) = ( N 1 N 2 ) T = exp ( ℏ ω z k B T ) {\displaystyle {\frac {\sigma _{\rm {e}}(\omega )}{\sigma
McCumber_relation
Equation in stellar astrophysics
r^{2}D{\frac {\partial u}{\partial r}}\approx 4\pi \,R^{2}D{\frac {u}{R}}\\L&\approx {\frac {1}{15}}{\frac {64\pi ^{2}}{9}}{\frac {\sigma _{B}}{\sigma _{e\cdot
Mass–luminosity_relation
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
Hamiltonian used in quantum physics
}c_{k\sigma }+\sum _{\sigma }\epsilon _{\sigma }d_{\sigma }^{\dagger }d_{\sigma }+Ud_{\uparrow }^{\dagger }d_{\uparrow }d_{\downarrow }^{\dagger }d_{\downarrow
Anderson_impurity_model
Matrices important in quantum mechanics and the study of spin
sigma _{j},\sigma _{k}\right]+\{\sigma _{j},\sigma _{k}\}&=(\sigma _{j}\sigma _{k}-\sigma _{k}\sigma _{j})+(\sigma _{j}\sigma _{k}+\sigma _{k}\sigma
Pauli_matrices
Failure Theory in continuum mechanics
_{11})^{2}+6(\sigma _{12}^{2}+\sigma _{23}^{2}+\sigma _{31}^{2}\right)}{2}}}\\&={\sqrt {\frac {(\sigma _{1}-\sigma _{2})^{2}+(\sigma _{2}-\sigma _{3})^{2}+(\sigma _{3}-\sigma
Von_Mises_yield_criterion
Unexplained empirical equation in particle physics
permutation σ {\displaystyle \sigma } of { e , μ , τ } {\displaystyle \{{\text{e}},\mu ,\tau \}} . The Koide relation is scale invariant; that is, multiplying
Koide_formula
Concept in continuum mechanics
={\frac {\sigma _{m}}{\sigma _{eq}}}={\frac {{\frac {1}{3}}(\sigma _{1}+\sigma _{2}+\sigma _{3})}{\sqrt {\frac {(\sigma _{1}-\sigma _{2})^{2}+(\sigma _{2}-\sigma
Stress_triaxiality
Wave on the surface of a fluid, dominated by surface tension
gravity. The dispersion relation for capillary waves is ω 2 = σ ρ + ρ ′ | k | 3 , {\displaystyle \omega ^{2}={\frac {\sigma }{\rho +\rho '}}\,|k|^{3}
Capillary_wave
Language consisting of balanced strings of brackets
equivalence relation R {\displaystyle R} on Σ ∗ {\displaystyle \Sigma ^{*}} as follows: for elements a , b ∈ Σ ∗ {\displaystyle a,b\in \Sigma ^{*}} we have
Dyck_language
Probability distribution
D x f U ( u ; σ ) f V ( v ; σ ) d A , {\displaystyle F_{X}(x;\sigma )=\iint _{D_{x}}f_{U}(u;\sigma )f_{V}(v;\sigma )\,dA,} where D x {\displaystyle D_{x}}
Rayleigh_distribution
Clavin–Garcia dispersion relation is given by a ( k ) σ 2 + b ( k ) σ + c ( k ) = 0 {\displaystyle a(k)\sigma ^{2}+b(k)\sigma +c(k)=0} where a ( k ) =
Clavin–Garcia_equation
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
\sigma '\neq \sigma ,} for otherwise the loop would fail to terminate. Next consider the reflexive, transitive closure of the "successor" relation. Call
Loop_variant
Generalization of strings in computer science
relation on Σ ∗ {\displaystyle \Sigma ^{*}} and is denoted by ≡ D {\displaystyle \equiv _{D}} , where D {\displaystyle D} is the dependency relation corresponding
Trace_monoid
Theorem in physics
)} and since σ = ∫ | f ( n , n ″ ) | 2 d Ω ″ {\displaystyle \sigma =\int |f(\mathbf {n} ,\mathbf {n} '')|^{2}\,d\Omega ''} . For scattering in a centrally
Optical_theorem
Method in artificial intelligence
{\displaystyle S} in the figure above, E x t σ ( S ) = { { a , d } } {\displaystyle Ext_{\sigma }(S)=\{\{a,d\}\}} for every Dung's semantic—the system is well-founded
Argumentation_framework
Model parameters in mathematical finance
{1}{2}}\sigma ^{2}\tau }{\sigma {\sqrt {\tau }}}}\\d_{2}&={\frac {\ln(F/K)-{\frac {1}{2}}\sigma ^{2}\tau }{\sigma {\sqrt {\tau }}}}=d_{1}-\sigma {\sqrt
Greeks_(finance)
Continuous stochastic process
stochastic differential equation (SDE): d S t = μ S t d t + σ S t d W t {\displaystyle dS_{t}=\mu S_{t}\,dt+\sigma S_{t}\,dW_{t}} where W t {\displaystyle W_{t}}
Geometric_Brownian_motion
Operations in formal language theory
}(t)&{\mbox{if }}s=ta{\mbox{ and }}a\notin \Sigma \\\pi _{\Sigma }(t)a&{\mbox{if }}s=ta{\mbox{ and }}a\in \Sigma \end{cases}}} Here ε {\displaystyle \varepsilon
String_operations
Group whose operation is a composition of braids
B_{n}=\left\langle \sigma _{1},\ldots ,\sigma _{n-1}\mid \sigma _{i}\sigma _{i+1}\sigma _{i}=\sigma _{i+1}\sigma _{i}\sigma _{i+1},\sigma _{i}\sigma _{j}=\sigma _{j}\sigma
Braid_group
American astrophysicist (born 1955)
model, the Leonard–Merritt mass estimator and the M–sigma relation. He received in 1982 his PhD in Astrophysical Sciences from Princeton University with
David_Merritt
Concept in physics and electrical engineering
physics and electrical engineering, a nonlinear dispersion relation (NDR) is a dispersion relation that assigns the correct phase velocity v 0 {\displaystyle
Nonlinear dispersion relation in Vlasov–Poisson plasmas
Nonlinear_dispersion_relation_in_Vlasov–Poisson_plasmas
Generators of the Clifford algebra for relativistic quantum mechanics
D U T = i γ 2 γ 0 = ( i σ 2 0 0 − i σ 2 ) {\displaystyle C_{W}=UC_{D}U^{\text{T}}=i\gamma ^{2}\gamma ^{0}={\begin{pmatrix}i\sigma ^{2}&0\\0&-i\sigma ^{2}\end{pmatrix}}}
Gamma_matrices
Physical law on the emissive power of black body
∘ = σ T 4 . {\displaystyle M^{\circ }=\sigma \,T^{4}.} The constant of proportionality, σ {\displaystyle \sigma } , is called the Stefan–Boltzmann constant
Stefan–Boltzmann_law
Physics theorem for symmetries of action
d_{I}\left(E_{\sigma }R_{a}^{\sigma ,I}\right).} Hence, we have an off-shell relation 0 = Q a λ a + d i S λ i , {\displaystyle 0=Q_{a}\lambda ^{a}+d_{i}S_{\lambda
Noether's_second_theorem
Calculation of strain energy release rate
[ ε ] [ σ ] : d [ ε ] ; [ ε ] = 1 2 [ ∇ u + ( ∇ u ) T ] . {\displaystyle W=\int _{0}^{[\varepsilon ]}[{\boldsymbol {\sigma }}]:d[{\boldsymbol {\varepsilon
J-integral
Geometric civil engineering calculation technique
{\boldsymbol {\sigma }}=\left[{\begin{matrix}\sigma _{11}&\sigma _{12}&\sigma _{13}\\\sigma _{21}&\sigma _{22}&\sigma _{23}\\\sigma _{31}&\sigma _{32}&\sigma
Mohr's_circle
Mathematical structure
{\displaystyle \sigma \in \Sigma } , and d ∈ D {\displaystyle d\in D} , the transition relation δ ( q , σ , d ) {\displaystyle \delta (q,\sigma ,d)} has exactly
Infinite-tree_automaton
String rewriting system
rewriting relation or reduction relation on Σ ∗ {\displaystyle \Sigma ^{*}} induced by R {\displaystyle R} . In general, the set Σ ∗ {\displaystyle \Sigma ^{*}}
Semi-Thue_system
Force needed to pull a spring grows linearly with distance
{\boldsymbol {\sigma }}\,=\,{\begin{bmatrix}\sigma _{11}&\sigma _{12}&\sigma _{13}\\\sigma _{21}&\sigma _{22}&\sigma _{23}\\\sigma _{31}&\sigma _{32}&\sigma _{33}\end{bmatrix}}}
Hooke's_law
However, d d t ( σ r ) = σ ˙ r = Q ˙ ⋅ σ ⋅ Q T + Q ⋅ σ ˙ ⋅ Q T + Q ⋅ σ ⋅ Q ˙ T ≠ Q ⋅ σ ˙ ⋅ Q T . {\displaystyle {\cfrac {d}{dt}}({\boldsymbol {\sigma }}_{r})={\dot
Objective_stress_rate
Kind of transfinite induction
membership relation restricted to Σ {\displaystyle \Sigma } is considered, i.e. a minimal element with respect to Σ {\displaystyle \Sigma } is one without
Epsilon-induction
Quantity in fracture mechanics; predicts stress intensity near a crack's tip
{\displaystyle \sigma _{ij}} goes to ∞ {\displaystyle \infty } resulting in a stress singularity. Practically however, this relation breaks down very
Stress_intensity_factor
mass density). ∇ ⋅ σ = D J D t − f {\displaystyle \nabla \cdot \sigma ={\frac {DJ}{Dt}}-\mathbf {f} } − p ∇ ⋅ v = D p D t − ρ D D t ( p ρ ) {\displaystyle
First law of thermodynamics (fluid mechanics)
First_law_of_thermodynamics_(fluid_mechanics)
Composite building material
elastically, the stress and strain relation is σ c = V f E f ε f + V m E m ε m = ε c ( V f E f + V m E m ) {\displaystyle \sigma _{c}=V_{f}E_{f}\varepsilon
Fiber-reinforced_composite
Physical field theory with no forces/interactions
{\displaystyle m^{2}A^{\rho }={\frac {1}{2}}\partial _{\sigma }(\partial ^{\sigma }A^{\rho }-\partial ^{\rho }A^{\sigma })} or 0 = 1 2 ∂ σ ( ∂ σ A ρ − ∂ ρ A σ ) {\displaystyle
Free_field
Intrinsic instability in flames
disturbance and σ {\displaystyle \sigma } is the temporal growth rate of the disturbance, then the dispersion relation is given by σ S L k = r r + 1 ( 1
Darrieus–Landau_instability
Tool in multivariate statistical analysis
separated by d distance units is given by C ν ( d ) = σ 2 2 1 − ν Γ ( ν ) ( 2 ν d ρ ) ν K ν ( 2 ν d ρ ) , {\displaystyle C_{\nu }(d)=\sigma ^{2}{\frac {2^{1-\nu
Matérn_covariance_function
Random change in the energy inside a volume
{p}}-m_{0}}}(-i\Sigma ){\frac {i}{{\cancel {p}}-m_{0}}}+{\frac {i}{{\cancel {p}}-m_{0}}}(-i\Sigma ){\frac {i}{{\cancel {p}}-m_{0}}}(-i\Sigma ){\frac {i}{{\cancel
Quantum_fluctuation
Type system used in computer programming and mathematics
_{S}\ e:\sigma } (Consistency) Γ ⊢ D e : σ ⇒ Γ ⊢ S e : σ {\displaystyle \Gamma \vdash _{D}\ e:\sigma \Rightarrow \Gamma \vdash _{S}\ e:\sigma } (Completeness)
Hindley–Milner_type_system
law defines the relation between stress σ {\displaystyle \sigma } and strain ϵ {\displaystyle \epsilon } as: σ = M ϵ {\displaystyle \sigma =M\epsilon } ϵ
Anelasticity
Set of bivariate correlations among galaxies
called the Faber–Jackson relation (Faber & Jackson 1976). Analytically this is: L e ∼ σ o 4 {\displaystyle L_{e}\sim \sigma _{o}^{4}} . This is analogous
Fundamental plane (elliptical galaxies)
Fundamental_plane_(elliptical_galaxies)
Probability theory and statistics concept
\sim \ {\mathcal {N}}\left(\mu _{Y}+{\frac {\sigma _{Y}}{\sigma _{X}}}\rho (70-\mu _{X}),\,(1-\rho ^{2})\sigma _{Y}^{2}\right).} Random variables X {\displaystyle
Conditional probability distribution
Conditional_probability_distribution
Statistical mechanics theorem relating non-equilibrium work to free energy differences
] = e σ [ x ( t ) ] . {\displaystyle {\frac {P[\sigma (x(t))]}{P[\sigma ({\tilde {x}}(t))]}}=e^{\sigma [x(t)]}.} The above quotient is well defined because
Crooks_fluctuation_theorem
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
Statistical measure of the magnitude of a phenomenon
{n_{1}n_{2}}{n_{1}+n_{2}}}}{\frac {\mu _{1}-\mu _{2}}{\sigma }}} and Cohen's d := M 1 − M 2 S D within {\displaystyle d:={\frac {M_{1}-M_{2}}{SD_{\text{within}}}}}
Effect_size
Gauge theory providing unifying formalism for integrable systems
{\displaystyle \Sigma ,} which is fixed to be R 2 {\displaystyle \mathbb {R} ^{2}} for engineering integrable field theories. This defect D {\displaystyle D} is then
Four-dimensional Chern–Simons theory
Four-dimensional_Chern–Simons_theory
Hyperelastic material model
{\displaystyle \sigma _{11}} gives a relation for J {\displaystyle J} as a function of λ {\displaystyle \lambda } , i.e., 4 C 1 3 J 5 / 3 ( λ 2 − J λ ) + 2 D 1 (
Neo-Hookean_solid
Equation
x d x d y d z + ∂ σ y x ∂ y d y d x d z + ∂ σ z x ∂ z d z d x d y F p y = ∂ σ x y ∂ x d x d y d z + ∂ σ y y ∂ y d y d x d z + ∂ σ z y ∂ z d z d x d y
Cauchy_momentum_equation
Entropy production in Newtonian fluids
\cdot (\sigma \cdot {\bf {v}})-\sigma _{ij}{\partial v_{i} \over {\partial x_{j}}}\end{aligned}}} With the aid of the thermodynamic relation for enthalpy
General equation of heat transfer
General_equation_of_heat_transfer
Series representing modular forms
recurrence relation. Let d k = ( 2 k + 3 ) ! G 2 k + 4 {\displaystyle d_{k}=(2k+3)!G_{2k+4}} . Then the d k {\displaystyle d_{k}} satisfy the relation ∑ k =
Eisenstein_series
Theory in continuum mechanics
dashpot [ σ ( d ε / d t ) = σ = λ ( d ε / d t ) 1 / N ] {\displaystyle [\sigma (\mathrm {d} \varepsilon /\mathrm {d} t)=\sigma =\lambda (\mathrm {d} \varepsilon
Viscoplasticity
Concept in measure theory
∫ f ( x ) μ ( d x ) < ∞ . {\displaystyle \int f(x)\mu (\mathrm {d} x)<\infty .} If μ {\displaystyle \mu } is a σ {\displaystyle \sigma } -finite measure
Σ-finite_measure
Equation in materials science engineering
The Larson–Miller relation, also widely known as the Larson–Miller parameter and often abbreviated LMP, is a parametric relation used to extrapolate experimental
Larson–Miller_relation
Dipolar relaxation process of a system
different spin states changes in relation to the strength of the self-relaxation rate constant R and σ 12 {\displaystyle \sigma _{12}} , which accounts instead
Solomon_equations
Four-dimensional number system
-i\,\sigma _{1}=-\sigma _{2}\,\sigma _{3},\quad \mathbf {j} \mapsto -i\,\sigma _{2}=-\sigma _{3}\,\sigma _{1},\quad \mathbf {k} \mapsto -i\,\sigma _{3}=-\sigma
Quaternion
Partial differential equation
differential equation (SDE) d X t = μ ( X t , t ) d t + σ ( X t , t ) d W t {\displaystyle dX_{t}=\mu (X_{t},t)\,dt+\sigma (X_{t},t)\,dW_{t}} with drift μ (
Fokker–Planck_equation
Model in statistical mechanics
J^{*})=\sum _{\{\sigma \}}\exp \left(K\sum _{\langle ij\rangle _{H}}\sigma _{i}\sigma _{j}+L\sum _{\langle ij\rangle _{V}}\sigma _{i}\sigma _{j}\right).}
Square_lattice_Ising_model
Pair of equations describing black holes
equation. The equations read as ( d 2 d r ∗ 2 + σ 2 ) Z ± = V ± Z ± {\displaystyle \left({\frac {d^{2}}{dr_{*}^{2}}}+\sigma ^{2}\right)Z^{\pm }=V^{\pm }Z^{\pm
Regge–Wheeler–Zerilli equations
Regge–Wheeler–Zerilli_equations
Dimensionless number in fluid mechanics
{u} \ +{\frac {\sigma }{\zeta }}{Q}\ ({\mathbf {\nabla } }\wedge \mathbf {B} )\wedge \mathbf {B} ,} where σ {\displaystyle \ \sigma } is the Prandtl
Chandrasekhar_number
Formal language concept
a matching relation of length ℓ {\displaystyle \ell } . Nested words over the alphabet Σ = { a 1 , a 2 , … , a n } {\displaystyle \Sigma =\{a_{1},a_{2}
Nested_word
Matrix decomposition
{\Sigma } } equal to m × n {\displaystyle m\times n} . Then [ U 1 U 2 ] [ [ D 1 2 0 0 0 ] 0 ] [ V 1 V 2 ] ∗ = [ U 1 U 2 ] [ D 1 2 V 1 ∗ 0 ] = U 1 D 1
Singular_value_decomposition
Concept in applied statistics
transformation is y = ∫ x d μ σ 2 + s 2 μ 2 = 1 s asinh x σ / s ∝ asinh x λ . {\displaystyle y=\int ^{x}{\frac {d\mu }{\sqrt {\sigma ^{2}+s^{2}\mu ^{2}}}}={\frac
Variance-stabilizing transformation
Variance-stabilizing_transformation
Wave where gravity is the main restoring force
representation, this relation becomes c 2 ρ D Ψ = g Ψ ρ + σ k 2 Ψ . {\displaystyle \scriptstyle c^{2}\rho D\Psi =g\Psi \rho +\sigma k^{2}\Psi .} Using the
Gravity_wave
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
Measure of covariance of components of a random vector
combinations: d T Σ c = cov ( d T X , c T X ) {\displaystyle \mathbf {d} ^{\mathsf {T}}{\boldsymbol {\Sigma }}\mathbf {c} =\operatorname {cov} (\mathbf {d} ^{\mathsf
Covariance_matrix
Statistical measure of variability
)=P\left(\left|{\frac {X-\mu }{\sigma }}\right|\leq {\frac {\operatorname {MAD} }{\sigma }}\right)=P\left(|Z|\leq {\frac {\operatorname {MAD} }{\sigma }}\right).} Therefore
Median_absolute_deviation
Mathematical operation
of absolute convergence, σ 0 , f ∈ R {\displaystyle \sigma _{0,f}\in \mathbb {R} } . The relation of the Mellin transformation of the summatory function
Dirichlet_series_inversion
Simple potential between quarks
constant {\displaystyle V(r)=-{\frac {4}{3}}{\frac {\alpha _{s}}{\;r\;}}+\sigma \,r+{\text{constant}}} where r {\displaystyle r} is the effective radius
Cornell_potential
Ballistics measure of a weapon system's precision
F / 100 % ) 2 {\displaystyle Q(F,\sigma _{d})=\sigma _{d}{\frac {\sqrt {-2\ln(1-F/100\%)}}{\sqrt {2}}}} The relation between Q {\displaystyle Q} and F
Circular_error_probable
Model of viscoelastic material
σ t o t a l = σ D = σ S ε t o t a l = ε D + ε S {\displaystyle {\begin{aligned}\sigma _{\mathrm {total} }&=\sigma _{\rm {D}}=\sigma _{\rm {S}}\\[2pt]\varepsilon
Maxwell_model
Substance-specific relation between two physical quantities
physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities
Constitutive_equation
Physical law about electrical discharge in gases
{\displaystyle P} is the relation of the cross-sectional area of a collision between electron and ion σ {\displaystyle \sigma } in relation to the overall area
Paschen's_law
M'|_{\sigma }} , a satisfaction relation ⊨ Σ ⊆ | M o d ( Σ ) | × S e n ( Σ ) {\displaystyle {\models _{\Sigma }}\subseteq |{\mathbf {Mod} (\Sigma )|\times
Institution (computer science)
Institution_(computer_science)
Model for physics of semiconductors
\mathbf {s} =\sum _{k,k',\sigma ,\sigma '}c_{\mathbf {k} \sigma }^{\dagger }\mathbf {\sigma } _{\sigma ,\sigma '}c_{\mathbf {k'} \sigma '}} is the local spin-density
Kondo_model
Shortest distance between two points on the surface of a sphere
chord-length relation: Δ σ = archav ( hav Δ ϕ + ( 1 − hav Δ ϕ − hav ( ϕ 1 + ϕ 2 ) ) hav Δ λ ) . {\displaystyle {\begin{aligned}\Delta \sigma &={\operatorname
Great-circle_distance
Polarization in dielectric spectroscopy
by τ = ϵ 1 d 2 + ϵ 2 d 1 σ 1 d 2 + σ 2 d 1 {\displaystyle \tau ={\frac {\epsilon _{1}d_{2}+\epsilon _{2}d_{1}}{\sigma _{1}d_{2}+\sigma _{2}d_{1}}}} (Note
Maxwell–Wagner–Sillars polarization
Maxwell–Wagner–Sillars_polarization
Astronomical trend of star formation
n {\displaystyle \Sigma _{SFR}\propto (\Sigma _{gas})^{n}} . In general, the SFR surface density ( Σ S F R ) {\displaystyle (\Sigma _{SFR})} is in units
Kennicutt–Schmidt_law
Gröbner bases for non-commutative algebra
g_{\sigma }} such that its leading word w σ {\displaystyle w_{\sigma }} has coefficient 1. Thus we can write g σ = w σ − f σ {\displaystyle g_{\sigma }=w_{\sigma
Bergman's_diamond_lemma
Type of fluid
{\boldsymbol {\sigma }}'} ): σ = 1 3 tr ( σ ) I + σ ′ {\displaystyle {\boldsymbol {\sigma }}={\tfrac {1}{3}}\operatorname {tr} \left({\boldsymbol {\sigma }}\right)\
Newtonian_fluid
Families of matrices in mathematics, physics, and quantum information
{\displaystyle \Sigma _{1}^{d}=\Sigma _{3}^{d}=I} and the braiding relation, Σ 3 Σ 1 = ω Σ 1 Σ 3 = e 2 π i / d Σ 1 Σ 3 , {\displaystyle \Sigma _{3}\Sigma _{1}=\omega
Generalizations of Pauli matrices
Generalizations_of_Pauli_matrices
Elastostatics problem in linear elasticity
the contact set Σ {\displaystyle \Sigma } in the equilibrium configuration, since, according to the first relation, the displacement vector u {\displaystyle
Signorini_problem
Proportionality constant in some physical laws
written as D = D 0 T 1 / 2 n g ( σ ) Ω ( T ) {\displaystyle D=D_{0}{\frac {T^{1/2}}{ng(\sigma )\Omega (T)}}} where g ( σ ) {\displaystyle g(\sigma )} is the
Mass_diffusivity
Scientific law describing absorption of light
= 1 N σ i ∫ 0 ℓ n i ( z ) d z ) . {\displaystyle T=\exp \left(-\sum _{i=1}^{N}\sigma _{i}\int _{0}^{\ell }n_{i}(z)\mathrm {d} z\right).} One can also use
Beer–Lambert_law
Fluid dynamics theory on gravity waves
\mathrm {d} z}}-\int _{-h}^{0}{\tfrac {1}{2}}\rho \left|\mathbf {U} \right|^{2}\,\mathrm {d} z\\[6px]&={\tfrac {1}{4}}\rho {\frac {\sigma ^{2}}{k\tanh
Airy_wave_theory
Unstable behavior of two contacting fluids of different densities
\gamma } , then the dispersion relation becomes σ 2 = ρ 2 − ρ 1 ρ 2 + ρ 1 g k − γ k 3 ρ 2 + ρ 1 , {\displaystyle \sigma ^{2}={\frac {\rho _{2}-\rho _{1}}{\rho
Rayleigh–Taylor_instability
Probability distribution
{\ln x-\mu }{\sigma }}\right)}\\[6pt]&=\varphi {\left({\frac {\ln x-\mu }{\sigma }}\right)}{\frac {d}{dx}}\left({\frac {\ln x-\mu }{\sigma }}\right)\\[6pt]&=\varphi
Log-normal_distribution
Mathematical model in materials science
versus the applied normal stress. This relation is expressed as τ = σ tan ( ϕ ) + c {\displaystyle \tau =\sigma ~\tan(\phi )+c} where τ {\displaystyle
Mohr–Coulomb_theory
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