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Theory and applications of ordered fuzzy numbers

This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.

Theory of the Integral

The text is a self-contained account of integration theory on the real line. The usual curricula in real analysis courses do not allow for much time to be spent on the Henstock-Kurzweil integral. Instead extensive accounts of Riemann's integral and the Lebesgue integral are presented. Accordingly the version here would be mostly recommended for supplementary reading. Even so it would be a reasonable course design to teach this material prior to a course in abstract measure and integration. The student should end up as well-prepared as in more traditional courses. Certainly every professional mathematician should be aware of more than Lebesgue's theory; while nonabsolutely convergent integrals do not play an extensive role in applications, they are part of our history and of our culture.

Topology of Numbers

This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the classical topic of quadratic forms with integer coefficients, a central topic of the book. Quadratic forms of this type in two variables have a very rich theory, developed mostly by Euler, Lagrange, Legendre, and Gauss during the period 1750–1800. In this book their approach is modernized by using the splendid visualization tool introduced by John Conway in the 1990s called the topograph of a quadratic form. Besides the intrinsic interest of quadratic forms, this theory has also served as a stepping stone for many later developments in algebra and number theory. The book is accessible to students with a basic knowledge of linear algebra and arithmetic modulo $n$. Some exposure to mathematical proofs will also be helpful. The early chapters focus on examples rather than general theorems, but theorems and their proofs play a larger role as the book progresses.

Toposes, Triples and Theories

As its title suggests, this book is an introduction to three ideas and the connections between them. A topos is a special kind of category defined by axioms saying roughly that certain constructions one can make with sets can be done in the category. The concept of triple originated (under the name "standard constructions") in Godement's book on sheaf theory for the purpose of computing sheaf cohomology. Chapter 1 is an introduction to category theory which develops the basic constructions in categories needed for the rest of the book. Chapters 2, 3, 5, 6 and 7 form a fairly thorough introduction to the theory of toposes, covering topologies and the representation theorems but omitting the connections with algebraic geometry and logic. Adding chapters 4 and 8 provides an introduction to the concept of categorical theory, again without the connection to logic.

Illustrated anatomy of the head and neck

This textbook is coordinated with Illustrated Dental Embryology, Histology, and Anatomy by Margaret J. Fehrenbach and Tracy Popowics and can be considered a companion textbook to complete the curriculum in oral biology. Many of the figures in this text also appear as hand-drawn outlines in the Dental Anatomy Coloring Book, edited by Margaret J. Fehrenbac.

Основы теории электропривода

Книге предназначается в качестве учебного пособия по теории электропривода для студентов заочных и вечерних втузов специальности "Электропривод и автоматизация промышленных установок"

Tree Graphs and Orthogonal Spanning Tree Decompositions

Given a graph G, we construct T (G), called the tree graph of G. The vertices of T (G) are the spanning trees of G, with edges between vertices when their respective spanning trees differ only by a single edge. In this paper we detail many new results concerning tree graphs, involving topics such as clique decomposition, planarity, and automorphism groups. We also investigate and present a number of new results on orthogonal tree decompositions of complete graphs. While many papers about tree graphs have been published over the last half century, there is still much that remains to be considered, including many classic graph parameters, such as the clique number and independence number. Other standard graph theoretic concepts such as planarity, decomposition, and regularity, as well as more algebraic topics, like automorphism groups, vertex-transitivity, and integrality, are likewise ripe for exploration.

Электроразведочная аппаратура и оборудование.

В книге дан краткий исторический очерк развития электрораз-ведочного приборостроения. Описаны электроразведочная аппаратура и электроразведочные станции серийных выпусков отечественного производства, приведены краткие сведения о их конструкции, подробно рассмотрены электрические схемы и панели управления.

OB’YEKTGA YO‘NALTIRILGAN BOSHQARISH

Ushbu darslik o‘z ichiga turli metod va vositalardan, xususan, aqliy hujum, klaster, didaktik o‘yinlar, portfolia, keys - stadi, shuningdek, kompyuter dasturlaridan (Dev C++, Code Blocks, Visual C++, MS Visual Studio), internet kabi tizimlardan, foydalanish mumkin.

CK-12 Trigonometry

CK-12's Trigonometry-Second Edition is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities and Equations, Circular Functions, Polar Equations and Complex Numbers. Right triangles play an integral part in the study of trigonometry. It is from right triangles that the basic definitions of the trigonometric functions are formed. In this chapter we will explore right triangles and their properties. Through this, we will introduce the six basic trig functions and the unit circle.

Единые правила безопасности при геологоразведочных работах

Настоящие правила составлены Всесоюзным научно-исследовательским институтом методики и техники разведки Государственного геологического комитета СССР на основе «Единых правил безопасности при геологоразведочных работах:», утвержденных б. Госгортехнадзором СССР в 1958 г

BINO VA INSHOOTLARNI TEXNIK EKSPLUATATSIYASI

Bino va inshootlarning qurilish konstruksiyalariga ekspluatatsiya qilish jarayonida turli-tuman omillar ta’sir qiladi. Bulardan tashqari konstruksiyalardagi ekspluatatsiyaviy xususiyatlarning pasayishiga loyihalashdagi xatolar, konstruksiyalarni tayyorlash va montaj qilishdagi nuqsonlar, nomaqbul ekspluatatsiya sharoiti, metallarning zanglashi, biokimyoviy ta’sirlar qo‘shimcha vaziyat vujudga keltiradi. Binolarni texnik ekspluatatsiyasi xizmatining asosiy vazifasi, butun xizmat muddati davomida unsur va tizimlarning me’yoriy ekspluatatsiyaviy holatini ta’minlab beruvchi majmuiy tadbirlarni shakllantirish bo‘lib qoladi.

Комплексное применение геофизических методов для решения геологических задач

В книге описаны комплексное применение геофизических методов и основные геологические результаты, достигнутые с их помощью при изучении внутренних зон Земли, верхней мантии и земной коры, при тектоническом районировании территорий и акваторий. Изложено применение геофизических методов для поисков месторождений нефти и газа с учетом особенностей методики исследований в различных геологических регионах. Рассмотрено комплексное применение методов геофизики при поисках месторождений каменного угля, солей, при решении задач инженерной геологии и гидрогеологии.

Trigonometry

This college level trigonometry text may be different than most other trigonometry textbooks. In this book, the reader is expected to do more than read the book but is expected to study the material in the book by working out examples rather than just reading about them. So the book is not just about mathematical content (although it does contain important topics in trigonometry needed for further study in mathematics), but it is also about the process of learning and doing mathematics and is designed not to be just casually read but rather to be engaged. Recognizing that actively studying a mathematics book is often not easy, several features of the textbook have been designed to help students become more engaged as they study the material. Some of the features are: Beginning activities in each section that engage students with the material to be introduced, focus questions that help students stay focused on what is important in the section, progress checks that are short exercises or activities that replace the standard examples in most textbooks, a section summary, and appendices with answers for the progress checks and selected exercises.

Геохимические методы поисков месторождений полезных ископаемых

Всё возрастающая потребность развивающегося общества в увеличении минерально-сырьевой базы требует совершенствова-ния методов поисков месторождений полезных ископаемых. Именно это и послужило основной причиной быстрого развития геохимических методов, ставших к настоящему времени ведущими при выявлении месторождений. Широкое использование этих методов в поисковой практике сделало необходимым введение соответствующего курса в программу обучения геологов.

Рессорные подвешивание вагонов

Решение задачи повышения скоростей движения поездов должно осуществляться параллельно с исследованием вопроса о взаимодействии пути и подвижного состава. Система рессорного подвешивания должна обеспечивать как наилучшую плавность хода кузова вагона, так и наименьшее динамическое воздействие подвижного состава на путь при различных скоростях движения