Results 291 to 300 of about 493,051 (329)

Some Lagrangians for systems without a Lagrangian

Physica Scripta, 2011
We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71–128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815–9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational ...
M.C. Nucci, P.G.L. Leach
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Lagrangian Subgradients

Management Science, 1970
There is a dual program linked with every nonlinear program. The dual objective function is called the Lagrangian; it is defined in terms of the original problem. This note presents a characterization of the Lagrangian subgradients under general conditions. The theorem follows from a result of Danskin [1] that can be used (see [2]) to characterize the
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Lagrangian-Perfect Hypergraphs

Annals of Combinatorics, 2023
For an \(r\)-graph \((r\ge2)\) \(G=(V,E)\) with \(V=[n]\), and \(\vec x=(x_1,\dots,x_n)\in[0,\infty)^n\), \(\lambda(G,\vec x)=\sum\limits_{e\in E}\prod\limits_{i\in e}x_i\); the Lagrangian is \(\lambda(G) =\max\{\lambda(G,\vec x):\vec x\in\Delta\}\), where \(\Delta=\{\vec x=(x_1,x_2,\dots,x_n)\in[0,1]^n:x_1+x_2+\dots+x_n=1\}\); the Lagrangian density \(
Yan, Zilong, Peng, Yuejian
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Gauging nonlocal Lagrangians

Physical Review D, 1991
We describe a method for introducing gauge fields into nonlocal Lagrangians, and for deriving the resulting Feynman rules. The method is applied in detail to the nonlocal chiral quark model. In particular we describe how to calculate coupling constants of the effective chiral Lagrangian that results when the quarks are integrated out of the theory.
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On Null Lagrangians

Mathematica Slovaca, 2015
Abstract We consider Lagrangians for parametric variational problems defined on velocity manifolds and show that a Lagrangian is null precisely when its shadow, a family of vector forms, is closed. We also show that a null Lagrangian can be recovered (to within a constant) from its shadow, and therefore that such a Lagrangian is (again ...
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