This book is intended to be an introduction to the fundamentals and methods of spectral analysis and filter theory and their appli­ cations in geophysics. The principles and theoretical basis of the various methods are described, their efficiency and effectiveness eval­ uated, and instructions provided for their practical application. Be­ sides the conventional methods, newer methods arediscussed, such as the spectral analysis ofrandom processes by fitting models to the ob­ served data, maximum-entropy spectral analysis and maximum-like­ lihood spectral analysis, the Wiener and Kalman filtering methods, homomorphic deconvolution, and adaptive methods for nonstation­ ary processes. Multidimensional spectral analysis and filtering, as well as multichannel filters, are given extensive treatment. The book provides a survey of the state-of-the-art of spectral analysis and fil­ ter theory. The importance and possibilities ofspectral analysis and filter theory in geophysics for data acquisition, processing and eval­ uation are illustrated with practical examples from various fields of applied geophysics.

A boundary-breaking astrophysicist reimagines the universe—and our place within it—in this audacious journey through the Nine Realms of the cosmos.

Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H-functions are examined here. Discussion is confined to basic properties and selected applications. Introduction to statistical distribution theory is provided. Some recent extensions of Dirichlet integrals and Dirichlet densities are discussed. A glimpse into multivariable special functions such as Appell's functions and Lauricella functions is part of Chapter 1. Special functions as solutions of differential equations are examined. Chapter 2 is devoted to fractional calculus. Fractional integrals and fractional derivatives are discussed. Their applications to reaction-diffusion problems in physics, input-output analysis, and Mittag-Leffler stochastic processes are developed. Chapter 3 deals with q-hyper-geometric or basic hypergeometric functions. Chapter 4 covers basic hypergeometric functions and Ramanujan's work on elliptic and theta functions. Chapter 5 examines the topic of special functions and Lie groups. Chapters 6 to 9 are devoted to applications of special functions. Applications to stochastic processes, geometric infinite divisibility of random variables, Mittag-Leffler processes, alpha-Laplace processes, density estimation, order statistics and astrophysics problems, are dealt with in Chapters 6 to 9. Chapter 10 is devoted to wavelet analysis. An introduction to wavelet analysis is given. Chapter 11 deals with the Jacobians of matrix transformations. Various types of matrix transformations and the associated Jacobians are provided. Chapter 12 is devoted to the discussion of functions of matrix argument in the real case. Functions of matrix argument and the pathway models along with their applications are discussed.

This multidisciplinary work celebrates Wayne Orchiston's career and accomplishments in historical and cultural astronomy on the occasion of his 80th birthday. Over thirty of the world’s leading scholars in astronomy, astrophysics, astronomical history, and cultural astronomy have come together to honor Wayne across a wide range of research topics.

NASA's first successful mission to another planet, Mariner 2 to Venus in 1962, marked the beginning of what NASA Chief Scientist Jim Green describes in this volume as "a spectacular era" of solar system exploration. In its first 50 years of planetary exploration, NASA sent spacecraft to fly by, orbit, land on, or rove on every planet in our solar system, as well as Earth's Moon and several moons of other planets. Pluto, reclassified as a dwarf planet in 2006, was visited by the New Horizons spacecraft in 2015. In this volume, a diverse array of scholars addresses the science, technology, policy, and politics of planetary exploration. This volume offers a collection of in-depth studies of important projects, decisions, and milestones of this era. It is not possible to foresee what the next 50 years of NASA's planetary exploration program will reveal. However, the 2020s are already looking promising. Planetary missions in recent years have focused more and more on exploring potentially habitable environments in our solar system and developing a more in-depth understanding of the evolution of planetary environments. It is safe to say that by 2062, our understanding of our solar system will be radically different than it is today. And we will look forward to it.

In 2016, NASA took on a new responsibility: defending our planet from devastating impacts by asteroids and comets that approach the Earth, or near-Earth objects. That event, which followed the prominent Chelyabinsk meteor explosion in 2013, reflected a growing interest in, and concern about, the threat of celestial impacts. In ancient times, the solar system’s small bodies—asteroids and comets—were sometimes seen as ill omens and warnings from the gods. In modern times, they have come to be seen as the solar system’s rubble, leftovers from its formation, but were still largely ignored until the late 20th century. Increasingly, they have been seen by scientists as objects worthy of study, by the general public and the U.S. government as potential threats to be mitigated, and by space advocates as future resources. This book tells the fascinating story of these reinterpretations and NASA’s role in them.