A Simple Proof of Farkas' Lemma

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

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The Farkas lemma of Shimizu, Aiyoshi and Katayama

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700009400 ◽

1985 ◽

Vol 31 (3) ◽

pp. 445-450 ◽

Cited By ~ 3

Author(s):

Charles Swartz

Keyword(s):

Convex Programming ◽

Infinite Dimensional ◽

Farkas Lemma ◽

Finite Dimensional

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.

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Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares

Mathematics of Operations Research ◽

10.1287/moor.20.4.818 ◽

1995 ◽

Vol 20 (4) ◽

pp. 818-837 ◽

Cited By ~ 15

Author(s):

V. Jeyakumar ◽

B. M. Glover

Keyword(s):

Global Optimization ◽

Least Squares ◽

Farkas Lemma ◽

Nonlinear Extensions

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Multiparameter Groups of Measure-Preserving Transformations: A Simple Proof of Wiener's Ergodic Theorem

The Annals of Probability ◽

10.1214/aop/1176994423 ◽

1981 ◽

Vol 9 (3) ◽

pp. 504-509 ◽

Cited By ~ 21

Author(s):

M. E. Becker

Keyword(s):

Ergodic Theorem ◽

Simple Proof ◽

Measure Preserving Transformations

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A representation theorem for the linear quasi-differential equation(py′)′+qy=0

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120000199x ◽

2000 ◽

Vol 23 (8) ◽

pp. 579-584

Author(s):

J. G. O'Hara

Keyword(s):

Differential Equation ◽

Comparison Theorem ◽

Simple Proof ◽

Representation Theorem ◽

Second Order ◽

Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

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