دانلود کتاب Advances in statistics, combinatorics and related areas : selected papers from the SCRA2001-FIM VIII, Wollo[n]gong conference, University of Woolongong, Australia, 19-21 December 2001

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