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...

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

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...

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...

( 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...

}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...

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

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...

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...

{\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...

order). We have λ i ≥ μ i ≥ λ n − r + i , {\displaystyle \lambda _{i}\geq \mu _{i}\geq \lambda _{n-r+i},} An algebraic proof, based on the variational interpretation...

{\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...

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

} . {\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...

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...

the lambda calculus. Church encoding performs a similar function. The data and operators form a mathematical structure which is embedded in the lambda calculus...

g λ ν = g μ ν = δ μ ν , {\displaystyle g^{\mu \lambda }\,g_{\lambda \nu }=g^{\mu }{}_{\nu }=\delta ^{\mu }{}_{\nu },} so any mixed version of the metric...

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...

_{n=1}^{N}x_{n}\right)\mu +\left(\sum _{n=1}^{N}\mu ^{2}\right)+\lambda _{0}\mu ^{2}-2\lambda _{0}\mu _{0}\mu +\lambda _{0}\mu _{0}^{2}\right\}+C_{3}\\&=-{\frac...

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

In multivariable calculus, the directional derivative measures the rate at which a function changes in a particular direction at a given point.[citation...

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...

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

x^{\sigma }}{\partial x^{\bar {\nu }}}}g_{\rho \sigma }=\Lambda ^{\rho }{}_{\bar {\mu }}\,\Lambda ^{\sigma }{}_{\bar {\nu }}\,g_{\rho \sigma }.} The metric...

x α ) . {\displaystyle \int _{x}^{x+t}\mu (y)dy=\alpha \lambda ^{\alpha }\int _{x}^{x+t}y^{\alpha -1}dy=\lambda ^{\alpha }((x+t)^{\alpha }-x^{\alpha })...