Название: Bornologies and Lipschitz Analysis
Автор: Gerald Beer
Издательство: CRC Press
Год: 2023
Страниц: 243
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members. The largest bornology is the power set of the space and the smallest is the bornology of its finite subsets. Between these lie (among others) the metrically bounded subsets, the relatively compact subsets, the totally bounded subsets, and the Bourbaki bounded subsets. Classes of functions are intimately connected to various bornologies; e.g., (1) a function is locally Lipschitz if and only if its restriction to each relatively compact subset is Lipschitz; (2) a subset is Bourbaki bounded if and only if each uniformly continuous function on the space is bounded when restricted to the subset. A great deal of attention is given to the variational notions of strong uniform continuity and strong uniform convergence with respect to the members of a bornology, leading to the bornology of UC-subsets and UC-spaces. Spaces on which its uniformly continuous real-valued functions are stable under pointwise product are characterized in terms of the coincidence of the Bourbaki bounded subsets with a usually larger bornology.

Название: Bayesian Scientific Computing
Автор: Daniela Calvetti, Erkki Somersalo
Издательство: Springer
Серия: Applied Mathematical Sciences
Год: 2023
Страниц: 295
Язык: английский
Формат: pdf (true), epub
Размер: 38.1 MB

The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider's view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.

Название: The Mathematical Representation of Physical Reality
Автор: Shahen Hacyan
Издательство: Springer
Год: 2023
Страниц: 157
Язык: английский
Формат: pdf (true), epub
Размер: 10.1 MB

This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics—despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist—and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer’s conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its “existence” in an independent platonic realm, as Godel believed. Mathematics has been impressively successful in describing a wide variety of phenomena in Nature.

Название: Эмпириометрия: учебное пособие
Автор: Денисенко В.И.
Издательство: Владимир: Изд-во ВлГУ
Год: 2017
Страниц: 124
Формат: djvu
Размер: 11,7 Мб
Язык: Русский

Необходимым дополнением к традиционным методам моделирования служит и носит актуальный практический характер решение задач при построении математических моделей. Методы моделирования детерминантных и стохастических процессов в экономике и управлении обобщены и усовершенствованы в этом учебном пособии.

Название: Mathematical Methods for Engineering and Science, 2nd Edition
Автор: Merle C. Potter, Brian F. Feeny
Издательство: Springer
Год: 2023
Страниц: 512
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This book introduces undergraduate students of engineering and science to applied mathematics essential to the study of many problems. Topics are differential equations, power series, Laplace transforms, matrices and determinants, vector analysis, partial differential equations, complex variables, and numerical methods. Approximately, 160 examples and 1000 homework problems aid students in their study. This book presents mathematical topics using derivations rather than theorems and proofs. This textbook is uniquely qualified to apply mathematics to physical applications (spring-mass systems, electrical circuits, conduction, diffusion, etc.), in a manner that is efficient and understandable. MATLAB, as a common and useful software tool, has been integrated into the text primarily in matrix computations and numerical solution of differential equations. An Introduction to MATLAB has been added as a section in the Appendix and should help students who lack experience with the package.

Название: Contemporary Algorithms: Theory and Applications Volume II
Автор: Christopher I. Argyros, Samundra Regmi
Издательство: Nova Science Publishers
Серия: Mathematics Research Developments
Год: 2023
Страниц: 424
Язык: английский
Формат: pdf (true)
Размер: 32.4 MB

The book is a continuation of Volume I with the same title. It provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms are presented in a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience are required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems. A new technique is developed to extend the convergence region and provide tighter error estimates of Newton’s Algorithm (NA) for solving generalized equations for Hilbert space- valued operators without additional conditions. The technique is very general, so it can be used to extend the applicability of other algorithms too.

Название: Квалиметрия: Измерение качества промышленной продукции
Автор: Федюкин В.К.
Издательство: КноРус
Год: 2013
Cтраниц: 320
Формат: pdf/djvu
Размер: 25 мб
Язык: русский

Изложены принципы и общая теория квалиметрии — науки об измерении и количественной оценке качества объектов. Рассмотрены методы и средства квалиметрии. Представлена типовая номенклатура показателей качествообразующих свойств технических изданий. Описаны процедуры процесса (технологии) квалиметрического оценивания качества промышленной продукции.

Название: Искусствометрия: Методы точных наук и семиотики
Автор: Лотман Ю.М., Петров В.М. (сост.)
Издательство: М.: Издательство ЛКИ
Год: 2007 - Изд. 2-е, дополненное
Cтраниц: 370
Формат: djvu
Размер: 46 мб
Язык: русский

Вниманию читателя предлагается книга, содержащая работы французских, американских, немецких, шведских, польских и чехословацких ученых и ставящая своей целью познакомить отечественного читателя с интересными направлениями в зарубежных исследованиях на стыке гуманитарных и точных наук.

Название: Структура и интерпретация классической механики
Автор: Джеральд Джей Сассман, Джек Уиздом
Издательство: ДМК Пресс
Год: 2023
Страниц: 490
Язык: русский
Формат: pdf
Размер: 19.2 MB

В настоящее время нам известно, что содержание классической механики гораздо богаче, чем представлялось раньше. Вывод уравнений движения – центральная тема традиционных изложений механики – всего лишь начало. В этой новаторской книге акцент сделан на разработке общих методов изучения поведения классических систем вне зависимости от того, имеют они аналитическое решение или нет. В фокусе внимания авторов сам феномен движений, а для его исследования применяется компьютерное моделирование. Недавние открытия в области нелинейной динамики органично вплетены в текст, а не добавлены по завершении работы. Изучение таких явлений, как переход к хаотическому движению и нелинейные резонансы, помогают читателю освоить аналитический инструментарий, необходимый для их понимания. В этой книге мы используем для написания программ Scheme – вариант языка программирования Lisp, который также применяется на вводном курсе информатики в Массачусетском технологическом институте. Существует много хороших описаний Scheme, здесь мы приводим только краткое введение в этот язык программирования в приложении.

Название: Mathematical Formulas and Scientific dаta: A Quick Reference Guide
Автор: C.P. Kothandaraman, PhD
Издательство: Mercury Learning and information
Год: 2023
Страниц: 245
Язык: английский
Формат: pdf (true)
Размер: 13.7 MB

Designed as a quick reference guide for engineers, mathematicians, scientists, and industry professionals, this book provides the essential formulas in all areas of mathematics and the key scientific data used in engineering and science. Part One covers the mathematical formulas from algebra, trigonometry, analytic geometry, differential and integral calculus, and vectors. Part Two covers MKS, CGS, and SI units, mechanical units, electrical and magnetic units, gases, elements, acoustics, materials, thermodynamics, radioactivity, geodetic data, astronomical data, optics, solids, organic and inorganic compounds, and more. Technical terms are defined, and theorems and applicable laws are stated and explained in detail. This data book is essential for every scientist, engineering student, and practicing professional.