Mathematical methods have been employed by a few geologists since the earliest days of the profession. For example, mining geologists and engineers have used samples to calculate tonnages and estimate ore tenor for centuries. As Fisher pointed out (1953, p. 3), Lyell’s subdivision of the Tertiary on the basis of the relative abundance of modern marine organisms is a statistical procedure. Sedimentary petrologists have regarded grain-size and shape measurements as important sources of sedimentological information since the beginning of the last century. The hybrid Earth sciences of geochemistry, geophysics, and geohydrology require a firm background in mathematics, although their procedures are primarily derived from the non-geological parent. Similarly, mineralogists and crystallographers utilize mathematical techniques derived from physical and analytical chemistry. <...>

Many contemporary problems faced by Earth sciences and society are complex, for example, climate change, disaster risk, energy and water security, and preservation of oceans. Studies of these challenges require an interdisciplinary approach and common knowledge. This book contributes to closing the gap between Earth science disciplines and assists in utilisation of the growing amount of data from observations and experiments using modern techniques on data assimilation and inversions developed within the same/another discipline or across the disciplines. <...>

This book is rather broad in that it covers many disciplines regarding both mathematical tools (algebra, calculus, statistics) and application areas (airborne, automotive, communication and standard signal processing and automatic control applications). The book covers all the theory an applied engineer or researcher can ask for: from algorithms with complete derivations, their properties to implementation aspects.

The technical world is changing very rapidly. In only 15 years, the power of personal computers has increased by a factor of nearly one-thousand. By all accounts, it will increase by another factor of one-thousand in the next 15 years. This tremendous power has changed the way science and engineering is done, and there is no better example of this than Digital Signal Processing. <...>

Рассмотрены математические методы, используемые для построения математических моделей информационных процессов и управления: теория множеств, теория графов, математическая логика и теория нечетких множеств. Приведено много примеров построения элементов математических моделей информационных процессов и управления.
Для студентов технических вузов, обучающихся по специальности “Автоматизированные системы обработки информации и управления”.

Digital Signal Processing (DSP) is concernedwith the theoretical and practical aspects of representing information bearing signals in digital form and with using computers or special purpose digital hardware either to extract that information or to transform the signals in useful ways. Areas where digital signal processing has made a significant impact include telecommunications, man-machine communications, computer engineering, multimedia applications, medical technology, radar and sonar, seismic data analysis, and remote sensing, to name just a few. <...>

Students learn in a number of ways and in a variety of settings. They learn through lectures, in informal study groups, or alone at their desks or in front of a computer terminal. Wherever the location, students learn most efficiently by solving problems, with frequent feedback from an instructor, following a worked-out problem as a model. Worked-out problems have a number of positive aspects. They can capture the essence of a key concept — often better than paragraphs of explanation. They provide methods for acquiring new knowledge and for evaluating its use. They provide a taste of real-life issues and demonstrate techniques for solving real problems. Most important, they encourage active participation in learning <...>

One of the by-products of the computer revolution has been the emergence of completely new fields of study. Each year, as integrated circuits have become faster, cheaper, and more compact, it has become possible to find feasible solutions to problems of ever-increasing complexity. Because it demands massive amounts of digital storage and comparable quantities of numerical computation, multidimensional digital signal processing is a problem area which has only recently begun to emerge.

Книга посвящена приложениям развитых в последнее время методов математической статистики временных рядов для решения практических задач, возникающих при анализе экспериментальных геофизических данных. Указанные методы связаны с параметрическими моделями многомерных временных рядов, представляющими собой более экономное описание этих рядов по сравнению с заданием их посредством корреляционных функций или энергетических спектров. В случае, когда функция правдоподобия (ФП) наблюдаемой реализации временного ряда зависит от конечного числа параметров, можно аппроксимировать ее ФП для некоторого экспоненциального семейства распределений, обладающего простой достаточной статистикой,и построить на этой основе практически реализуемые асимптотически оптимальные решающие правила для проверки гипотез и оценки параметров