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...

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...

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...

( 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...

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

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 \|(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...

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

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...

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...

{\displaystyle f,g\in C(\sigma (a))} and scalars λ , μ ∈ C {\displaystyle \lambda ,\mu \in \mathbb {C} } : One can therefore imagine actually inserting the...

_{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...

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...

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

{d^{2}x^{\lambda }}{dt^{2}}}+\Gamma _{\mu \nu }^{\lambda }{\frac {dx^{\mu }}{dt}}{\frac {dx^{\nu }}{dt}}=0,} where Γ μ ν λ {\displaystyle \Gamma _{\mu \nu }^{\lambda...

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

v ν . {\displaystyle {\begin{aligned}x'^{\mu }&={\Lambda ^{\mu }}_{\nu }x^{\nu },\\v'^{\mu }&={\Lambda ^{\mu }}_{\nu }v^{\nu }.\end{aligned}}} This definition...

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

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...

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