Joseph Louis Lagrange(January 25, 1736–April 10, 1813) was an Italian mathematician/astronomer; who later lived in France and Prussia. Lagrange worked for Frederick II, in Berlin, for twenty years. It was Lagrange who developed the Mean Value Theorem and solved the isoperimetrical problem. Bio...
groupaction,momentum map,La- grange functionabout Lagrangesystem. Inthesecond part ofthis papeL weintroducevariational principle whichisthe foundationof Lagrangesystem reduction theory。On this basis,wegive outthetheo— remofLie-Poissonreduction,thetheoremofEuler-Poincarereductionand ...
In the advancement of almost every branch of pure mathematics Lagrange took a conspicuous part. The calculus of variations is indissolubly associated with his name. In the theory of numbers he furnished solutions of many of P. Fermat's theorems, and added some of his own. In algebra he dis...
where the functions Wαi and Wα are undetermined as yet. We can thus easily prove the following theorem. Theorem 10.3.2. The enlarged balance system ωαω¯α admits a variational principle if the additional functions Wαi and Wα are chosen as follows ...
Theorem 1.2 The coefficientaIJin the coproductΔgn=∑I,JaIJgI⊗gJis equal to the number of noncrossing partitions π of[n+1]of reduced ordered type I, and whose (right) Kreweras complementπ′has reduced ordered type J. This implies a quasi-symmetric refinement of Macdonald's realization...
One holds: Proposition 2.3 (Existence of canonical almost complex structures for Lagrange–Hamilton spaces) MDRs (1) deter- mining canonical N-connections N and N following con- ditions of Theorem 2.2 define respectively canonical almost complex structures J, on TV, and J, on T∗V. Proof ...
Hence, for any v1 and v2 belonging to Ox defin- ing a segment contained in Ox , we get by Taylor's theorem, Fc(x, v2) ≥ Fc(x, v1) + vFc(x, v1)[v2 − v1]. By continuity and the approximation by segments property in (a'), the above inequality holds on TM, hence ...
holonomic gerbes. We shall generalize the Lichnerowicz theorem and prove Atiyah–Singer type theorems for nonholonomic gerbes. For trivial holonomic manifolds, our results will transform into certain similar ones from Refs. [31, 32] but not completely if there are considered ’non-perturbative’ and...
A new speed enhancement technique for pulsed laser rangefinders based on Lagrange's theorem in group theory using an undersampling method has been developed. In the undersampling method, frequency conversion for high-resolution ranging and digitizing are conducted by sampling a reference frequency ...