Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.

https://www.springer.com/productFlyer_978-0-387-98463-6.pdf?SGWID=0-0-1297-1590487-0

One-Parameter Semigroups for Linear Evolution Equations

Conventional analyses of single spell duration models control for unobservables using a random effect estimator with the distribution of unobservables selected by ad hoc criteria. Both theoretical and empirical examples indicate that estimates of structural parameters obtained from conventional procedures are very sensitive to the choice of mixing distribution. Conventional procedures overparameterize duration models. We develop a consistent nonparametric maximum likelihood estimator for the distribution of unobservables and a computational strategy for implementing it. For a sample of unemployed workers our estimator produces estimates in concordance with standard search theory while conventional estimators do not. ECONOMIC THEORIES of search unemployment (Lippman and McCall [34]; Flinn and Heckman [14]), job turnover (Jovanovic [25]), mortality (Harris [17]), labor supply (Heckman and Willis [23]) and marital instability (Becker [3]) produce structural distributions for durations of occupancy of states. These theories generate qualitative predictions about the effects of changes in parameters on these structural distributions, and occasionally predict their functional forms.2 In order to test economic theories about durations and recover structural parameters, it is necessary to account for population variation in observed and unobserved variables unless it is assumed a priori that individuals are homogeneous.3 In every microeconomic study in which the hypothesis of heterogeneity is subject to test, it is not rejected. Temporally persistent unobserved components are an empirically important fact of life in microeconomic data (Heckman [19]). Since the appearance of papers by Silcock [39] and Blumen, Kogan, and McCarthy [5], social scientists have been aware that failure to adequately control for population heterogeneity can produce severe bias in structural estimates of duration models. Serious empirical analysts attempt to control for these unob

https://www.jstor.org/stable/pdfplus/1911491.pdf

A method for minimizing the impact of distributional assumptions in econometric models for duration data

A method is described which makes it possible to calculate rigorously the distribution of the adsorption energies of the sites of a catalyst surface when the adsorption isotherms are known, if the adsorption is localized and there are no interactions. This method is applied to a Freundlich isotherm, and also to a new theoretical isotherm which reduces to the Freundlich type for small pressures, but exhibits saturation for large pressures. It is shown that this isotherm corresponds to a distribution function which differs very little from a Gaussian one. The case of atomic adsorption of gases is also considered.

On the Structure of a Catalyst Surface

L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis and new methods of parameter estimation

https://www.jstor.org/stable/info/2345653

L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics

A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over ...

/pdf/scale-space-theory-in-computer-vision-1i931sm930.pdf

Scale-space theory in computer vision

The Laplace Transform

The heat equation

Introduction. The material I am reporting on here was prepared in collaboration with I. I. Hirschman. It will presently appear in book form in the Princeton Mathematical Series. I wish also to refer at once to the researches of I. J. Schoenberg and his students. Their work has been closely related to ours and has supplemented it in certain respects. Let me call attention especially to an article of Schoenberg [5, p. 199] in this Bulletin where the whole field is outlined and the historical development is traced. In view of the existence of this paper I shall t ry to avoid any parallel development here. Let me take rather a heuristic point of view and concentrate chiefly on trying to entertain you with what seems to me a fascinating subject.

https://projecteuclid.org/download/pdf_1/euclid.bams/1183519061

David Vernon Widder

Papers

The Laplace Transform

The Laplace Transform

The heat equation

The Convolution Transform

An introduction to transform theory