mathematical logic and computer science, the lambda-mu calculus is an extension of the lambda calculus introduced by Michel Parigot. It introduces two...

In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and...

in the variable Z {\displaystyle Z} , much like in lambda calculus λ Z . ϕ {\displaystyle \lambda Z.\phi } is a function with formula ϕ {\displaystyle...

ISBN 978-0-89791-343-0, S2CID 3005134. Parigot, Michel (1992), "Lambda-mu-calculus: An algorithmic interpretation of classical natural deduction", International...

This symbol satisfies the relations μ = λ κ = ι κ 2 . {\displaystyle \mu =\lambda \kappa =\iota \kappa ^{2}.} For example, the directed edge obtained by...

}{}_{\sigma \mu \nu }=\Gamma ^{\rho }{}_{\nu \sigma ,\mu }-\Gamma ^{\rho }{}_{\mu \sigma ,\nu }+\Gamma ^{\rho }{}_{\mu \lambda }\Gamma ^{\lambda }{}_{\nu...

Λ g μ ν = κ T μ ν . {\displaystyle R_{\mu \nu }-{\frac {1}{2}}Rg_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }.} In standard units, each term on...

the concepts of lambda calculus. λ indicates an eigenvalue in the mathematics of linear algebra. In the physics of particles, lambda indicates the thermal...

}H_{\lambda }\,d\mu (\lambda ).} The elements of this space are functions (or "sections") s ( λ ) , λ ∈ σ ( A ) , {\displaystyle s(\lambda ),\,\,\lambda \in \sigma...

{\displaystyle \mu (A)>0} implies λ ( A ) > 0 {\displaystyle \lambda (A)>0} . This condition is written as μ ≪ λ . {\displaystyle \mu \ll \lambda .} We say...

Lambda ^{1}}_{\mu }{\Lambda ^{2}}_{\nu }F^{\mu \nu }={\Lambda ^{1}}_{\mu }{\Lambda ^{2}}_{2}F^{\mu 2}={\Lambda ^{1}}_{0}{\Lambda ^{2}}_{2}F^{02}+{\Lambda...

f(x)\,dx-\lambda _{0}\left(1-\int _{-\infty }^{\infty }f(x)\,dx\right)-\lambda _{1}\left(\mu -\int _{-\infty }^{\infty }f(x)x\,dx\right)-\lambda _{2}\left(\sigma...

{\displaystyle \|(T_{h}-\lambda )f_{n}\|_{p}^{p}=\|(h-\lambda )f_{n}\|_{p}^{p}=\int _{S_{n}}|h-\lambda \;|^{p}d\mu \leq {\frac {1}{n^{p}}}\;\mu (S_{n})={\frac...

( t ) = 0 {\displaystyle \mu (t)=0} , f Δ = f ′ {\displaystyle f^{\Delta }=f'} ; is the derivative used in standard calculus. If T = Z {\displaystyle \mathbb...

} . {\displaystyle \lambda _{f}(t)=\mu \{x\in S:|f(x)|>t\}.} If f {\displaystyle f} is in L p ( S , μ ) {\displaystyle L^{p}(S,\mu )} for some p {\displaystyle...

In Itô calculus, the Euler–Maruyama method (also simply called the Euler method) is a method for the approximate numerical solution of a stochastic differential...

the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector fields can be resolved into the...

that s μ h r = ∑ λ s λ {\displaystyle \displaystyle s_{\mu }h_{r}=\sum _{\lambda }s_{\lambda }} where hr is a complete homogeneous symmetric polynomial...

g_{\lambda \nu ,\mu }{\dot {x}}^{\mu }{\dot {x}}^{\nu }+g_{\lambda \mu ,\nu }{\dot {x}}^{\mu }{\dot {x}}^{\nu }-g_{\mu \nu ,\lambda }{\dot {x}}^{\mu }{\dot...

diffused indefinitely in space. In 1821, Cauchy developed an operational calculus for the Laplace transform that could be used to study linear differential...

c_{\lambda }(x,c_{\mu }(y,z))=c_{\lambda \mu }\left(c_{\frac {\lambda (1-\mu )}{1-\lambda \mu }}(x,y),z\right)} (for λ μ ≠ 1 {\displaystyle \lambda \mu \neq...

including Isaac Newton. The formal calculus of finite differences can be viewed as an alternative to the calculus of infinitesimals. Three basic types...

\Lambda _{\nu }^{\mu }} , a real 4 × 4 matrix satisfying Λ ρ μ η μ ν Λ σ ν = η ρ σ . {\displaystyle \Lambda _{\rho }^{\mu }\eta _{\mu \nu }\Lambda _{\sigma...

) . {\displaystyle m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}=-\lambda \mathbf {v} +{\boldsymbol {\eta }}\left(t\right).} Here, v {\displaystyle...

{\displaystyle f(\lambda )=\pm (\lambda -\lambda _{1})^{\mu _{1}}(\lambda -\lambda _{2})^{\mu _{2}}\cdots (\lambda -\lambda _{r})^{\mu _{r}},} where λ 1...

}}}-\lambda \mathbf {\mathbb {I} } =-\left(\lambda +V\right)\mathbf {\mathbb {I} } +\epsilon _{0}\mathbf {E} \mathbf {E} ^{\textsf {T}}+{\frac {1}{\mu _{0}}}\mathbf...

{\displaystyle {\frac {d(\nu +\mu )}{d\lambda }}={\frac {d\nu }{d\lambda }}+{\frac {d\mu }{d\lambda }}\quad \lambda {\text{-almost everywhere}}.} If...

lexical scope was similar to the lambda calculus. Sussman and Steele decided to try to model Actors in the lambda calculus. They called their modeling system...

( λ ) < ∞ . {\displaystyle \int _{\mathbf {R} }|\lambda |^{2}\ \|\psi (\lambda )\|^{2}\,d\mu (\lambda )<\infty .} Non-negative countably additive measures...

{\displaystyle P(\mu +Z_{1}>Z_{2})={\begin{cases}e^{\mu }{\frac {(2-\mu )}{4}},&{\text{when }}\mu <0\\1-e^{-\mu }{\frac {(2+\mu )}{4}},&{\text{when }}\mu >0\\\end{cases}}}...