Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to ......
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares ......
A little bucket, one-third full, is 8 inches deep, and its upper and lower diameters are 7 inches and 6 inches, respectively. How large is the frog which, jumping into the bucket, causes the water to rise 3 inches? Word problems not unlike this example are a staple on math tests and of abiding interest to students, teachers, and professional ......
Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi's introduction to wavelet theory explains this mathematical ......
Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi's introduction to wavelet theory explains this mathematical ......
Presents a technique for analyzing the effects of variables, groups, and treatments in both experimental and observational settings, considering not only the main effects of one variable upon another, but also the effects of group cases.
The widespread use of Geographical Information Systems (GIS) has significantly increased the demand for knowledge about spatial analytical techniques across a range of disciplines. As growing numbers of researchers realise they are dealing with spatial data, the demand for specialised statistical and mathematical methods designed to deal with spatial data is undergoing a rapid increase. Responding to this demand, The Handbook of Spatial Analysis is a comprehensive and authoritative discussion of issues and techniques in the field of Spatial Data Analysis. Its principal focus is on: * why the analysis of spatial data needs separate treatment * the main areas of spatial analysis * the key debates within spatial analysis * examples of the application of various spatial analytical techniques * problems in spatial analysis * areas for future research Aimed at an international audience of academics, The Handbook of Spatial Analysis will also prove essential to graduate level students and researchers in government agencies and the private sector.
Outlines a set of techniques that enable a researcher to discuss the 'hidden structure' of large data bases. These techniques use proximities, measures which indicate how similar or different objects are, to find a configuration of points which reflects the structure in the data.
This excellent introduction to stochastic parameter regression models is more advanced and technically difficult than other papers in this series. These models allow relationships to vary through time, rather than requiring them to be fixed, without forcing the analyst to specify and analyze the causes of the time-varying relationships. This volume will be most useful to those with a good working knowledge of standard regression models and who wish to understand methods which deal with relationships that vary slowly over time, but for which the exact causes of variation cannot be identified.
