Advances In Statistics Combinatorics And Related Areas Selected Papers From The Scra2001fim Viii Wollongong Conference University Of Woolongong Australia 1921 December 2001 Chandra Gulati Forum For Interdisciplinary Mathematics International Conference Et Al Eds by Chandra Gulati; Forum For Interdisciplinary Mathematics. International Conference; Et Al (eds.) 9789812776372, 9812776370 instant download after payment.

The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This work looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, and more Efficient Estimators of Different Types for Domains (M C Agrawal & C K Midha); Chisquared Components as Tests of Fit for Discrete Distributions (D J Best & J C W Rayner); Simulating Transects Through Two-Phase Particles (B M Bray); Long Memory Processes -- An Economist's Viewpoint (C W J Granger); An Indifference Zone Approach to Testing for a Two-Component Normal Mixture (M Haynes & K Mengersen); Semiparametric Density Estimation with Additive Adjustment (K Naito); Bioinformatics: Statistical Perspectives and Controversies (P K Sen); Monitoring Pavement Construction Processes (R Sparks & J Ollis); Hypothesis Testing of Multivariate Abundance Data (D Warton & M Hudson); Statistical Process Monitoring for Autocorrelated Date (N F Zhang); and other papers