Population genetics is that branch of genetics, whose object is the study of the genetical make-up of natural populations. By investigating the laws which govern the genetic structure of natural populations, we intend to clarify the mechanism of evolution.

Diffusion models in population genetics

The scientific community that includes meteorologists, physical scientists, engineers, medical doctors, biologists, and environmentalists has shown interest in a better understanding of fog for years because of its effects on, directly or indirectly, the daily life of human beings. The total economic losses associated with the impact of the presence of fog on aviation, marine and land transportation can be comparable to those of tornadoes or, in some cases, winter storms and hurricanes. The number of articles including the word ``fog'' in Journals of American Meteorological Society alone was found to be about 4700, indicating that there is substantial interest in this subject. In spite of this extensive body of work, our ability to accurately forecast/nowcast fog remains limited due to our incomplete understanding of the fog processes over various time and space scales. Fog processes involve droplet microphysics, aerosol chemistry, radiation, turbulence, large/small-scale dynamics, and surface conditions (e.g., partaining to the presence of ice, snow, liquid, plants, and various types of soil). This review paper summarizes past achievements related to the understanding of fog formation, development and decay, and in this respect, the analysis of observations and the development of forecasting models and remote sensing methods are discussed in detail. Finally, future perspectives for fog-related research are highlighted.

Fog Research: A Review of Past Achievements and Future Perspectives

Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods.

Integral Equation Methods for Electromagnetic and Elastic Waves

After a short survey I of the principles underlying the determination of the turbidity coefficient ?, earlier introduced by the author as a measure of the atmospheric turbidity, a condensed summary II is given of earlier and also of more recent determinations of ?. The variation of the turbidity with the time of the year, the airmass and with latitude is discussed. Finally a simple method of determining the wave length dependence of the extinction by atmospheric aerosol is outlined. The method is founded upon measurements of integral radiation values with aid of pyrheliometers and glass filters, III. Accuracy and probable error are considered, IV. DOI: 10.1111/j.2153-3490.1961.tb00078.x

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.2153-3490.1961.tb00078.x

Techniques of Determinig the Turbidity of the Atmosphere

The problem of error estimation in the numerical solution of integral equations that arise in electromagnetics is addressed. The direct method (Green's theorem or field approach) and the indirect method (layer ansatz or source approach) lead to well-known integral equations both of the first kind [electric field integral equations (EFIE)] and the second kind [magnetic field integral equations (MFIE)]. These equations are analyzed systematically in terms of the mapping properties of the integral operators. It is shown how the assumption that field quantities have finite energy leads naturally to describing the mapping properties in appropriate Sobolev spaces. These function spaces are demystified through simple examples which also are used to demonstrate the importance of knowing in which space the given data lives and in which space the solution should be sought. It is further shown how the method of moments (or Galerkin method) is formulated in these function spaces and how residual error can be used to estimate actual error in these spaces. The condition number of all of the impedance matrices that result from discretizing the integral equations, including first kind equations, is shown to be bounded when the elements are computed appropriately. Finally, the consequences of carrying out all computations in the space of square integrable functions, a particularly friendly Sobolev space, are explained.

Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics

It has been shown by Larmor, Kottler and others that the classical method of calculating diffraction from the Kirchhoff formula in terms of a scalar light function cannot be applied directly to the electromagnetic field since it takes into account neither the vector character of the field nor the effect of charges along the contour of the opening. The field equations are integrated directly by means of a vector analog of Green's theorem. The results are applied to the calculation of diffraction of electromagnetic waves from a rectangular slit in a screen of infinite conductivity. The results are compared with an exact solution obtained recently by Morse and Rubenstein.

Julius Adams Stratton

Papers

Diffraction Theory of Electromagnetic Waves

Spheroidal Wave Functions

A Theoretical Investigation of the Transmission of Light through Fog

Our Nation and the sea: a plan for national action:

Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients