^Hugo Touchette, Legendre-Fenchel transforms in a nutshell https://www.ise.ncsu.edu/fuzzy-neural/wp-content/uploads/sites/9/2019/01/or706-LF-transform-1.pdf ^D. Hilbert, R. Courant, Methods of Mathematical Physics, Vol. 2, Wiley, 1989. ^Herbert Goldstein, C. P. Poole, J. L. Safko...
1. Legendre Transform 要介绍其由来, 不得不介绍Legendre对于函数导数以及其原函数关系的研究. Legendre变换主要研究的是从一个可微的凸函数 f(x) 到s=∇xf(x) 的转换, 其中 s=∇xf(x) 是由一些切线构成的. 为了了解这样的变换是怎样实现的, 我们必须意识到, 对于一个凸且光滑的函数, 在每个 x 点...
transform as describ ed in [1 , 14-16]. 2. The T ransform. W e shall de�ne the Legendre transform. Let f : R n ! R b e a con v ex function, i.e. r 2 f > 0 where r f is the hessian. De�nition 2.1. The Legendre transform L(f )(p) = max x (p � x ...
Legendre Transformation (redirected fromLegendre transform) [lə′zhän·drə ‚tranz·fər′mā·shən] (fluid mechanics) The basis for a version of the hodograph method for compressible flow in which a replacement is made not only of the independent variables but also of the depende...
Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable from the system's internal energy to its conjugate variable鈥攖he...
(Redirected from Legendre transform)In mathematics, it is often desirable to express a functional relationship as a different function, whose argument is the derivative of f , rather than x . If we let p = df /dx be the argument of this new function, then this new function is ...
Keywords:constantelasticityofvariance;Hamilton2Jacobi2Bellmanequation;Legendretransform;duality;defined benefitpensionfuns 1引言 养老金制度是为社会成员提供养老金的社会化制度安排,分为两种基本类型:一种是待遇预定计划 (definedbenefitplan),即预先觃定退休后的养老金水平,缴费水平需经过精算估计;另一种是缴费预定计划...
4) Legendre transform Legendre变换 1. It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant s whole life in the pension plan. 针对以年金形式发放待遇的缴费预定制养老基金,在退休前和退休后的两个阶段,...
Die Funktion𝑔(𝑦)heißt dieLegendre-Transformierte von𝑓(𝑥). Sie ist in Abb. D.2adargestellt.Bezeichnen wir dieLegendre-Transformierte von𝑓(𝑥)mitℒ[𝑓(𝑥)], so können wirfür dieLegendre-Transformierte von𝑔(𝑦)schreiben:ℒ[𝑔(𝑦)]=ℒ...
LEGENDRE TRANSFORM TO INTRODUCE THE CHEMICAL POTENTIAL OF A SPECIES When chemical work is involved in a single-phase system, the fundamental equation for G becomes N dG = - SdT + VdP + zpidni (5) where N is the number of species. When there are no chemical reactions, the amounts of ...