Musings on Multilinear Fitting

Fitting a Sum of Exponentials to Numerical Data

A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in the sum and the coefficients in the linear combination is highlighted. The fitting of exponential functions to a given dataset is therefore reduced to a multil...

Multilinear forms which are products of linear forms

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

Measuring Effectiveness: Musings on the What and the How

On Multilinear Singular Integrals of Calderón-zygmund Type

A variety of results regarding multilinear Calderón-Zygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur’s test, and a multilinear version of the T1 Theor...

A Fundamental Parameters Approach to X-ray Line-Profile Fitting

A convolution approach to X-ray powder line-profile fitting is developed in which the line shape is synthesized from the Cu Ks emission profile, the dimensions of the diffractometer and the physical variables of the specimen. In addition to the integrated intensities and 20 positions of the line profiles, the parameters that may be fitted include the receiving-slit width, the receiving-slit len...