Introduction to the Theory of Differential Inclusions

Introduction to the Theory of Differential Inclusions
Author: Georgi V. Smirnov
Publisher: American Mathematical Society
Total Pages: 226
Release: 2022-02-22
Genre: Mathematics
ISBN: 1470468549

A differential inclusion is a relation of the form $dot x in F(x)$, where $F$ is a set-valued map associating any point $x in R^n$ with a set $F(x) subset R^n$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form $dot x = f(x)$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of the set of solutions, selection of solutions with given properties, and many others. Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They also are very useful in proving existence theorems in control theory. This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level. Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Chapter 3 is devoted to the Mordukhovich version of nonsmooth analysis. Chapter 4 contains the main existence theorems and gives an idea of the approximation techniques used throughout the text. Chapter 5 is devoted to the viability problem, i.e., the problem of selection of a solution to a differential inclusion that is contained in a given set. Chapter 6 considers the controllability problem. Chapter 7 discusses extremal problems for differential inclusions. Chapter 8 presents stability theory, and Chapter 9 deals with the stabilization problem.

Theory of Fuzzy Differential Equations and Inclusions

Theory of Fuzzy Differential Equations and Inclusions
Author: V. Lakshmikantham
Publisher: CRC Press
Total Pages: 192
Release: 2004-11-23
Genre: Mathematics
ISBN: 9780203011386

Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. The chapters are presented in a clear and logical way and include the preliminary material for fuzzy set theory; a description of calculus for fuzzy functions, an investigation of the basic theory of fuzzy differential equations, and an introduction to fuzzy differential inclusions.

Impulsive Differential Inclusions

Impulsive Differential Inclusions
Author: John R. Graef
Publisher: Walter de Gruyter
Total Pages: 412
Release: 2013-07-31
Genre: Mathematics
ISBN: 3110295318

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Terms of Inclusion

Terms of Inclusion
Author: Paulina L. Alberto
Publisher: UNC Press Books
Total Pages: 413
Release: 2011-05-02
Genre: History
ISBN: 0807877719

In this history of black thought and racial activism in twentieth-century Brazil, Paulina Alberto demonstrates that black intellectuals, and not just elite white Brazilians, shaped discourses about race relations and the cultural and political terms of inclusion in their modern nation. Drawing on a wide range of sources, including the prolific black press of the era, and focusing on the influential urban centers of Sao Paulo, Rio de Janeiro, and Salvador da Bahia, Alberto traces the shifting terms that black thinkers used to negotiate their citizenship over the course of the century, offering fresh insight into the relationship between ideas of race and nation in modern Brazil. Alberto finds that black intellectuals' ways of engaging with official racial discourses changed as broader historical trends made the possibilities for true inclusion appear to flow and then recede. These distinct political strategies, Alberto argues, were nonetheless part of black thinkers' ongoing attempts to make dominant ideologies of racial harmony meaningful in light of evolving local, national, and international politics and discourse. Terms of Inclusion tells a new history of the role of people of color in shaping and contesting the racialized contours of citizenship in twentieth-century Brazil.

Diamond Inclusions

Diamond Inclusions
Author: A.I.D.C. Inc
Publisher:
Total Pages: 208
Release: 2011-01-01
Genre: Diamond cutting
ISBN: 9780966585476

This is the first book devoted entirely to diamond inclusions in all its known natural characteristics. The first half of the book defines external and internal inclusions, describing each variety with numerous full color examples. What makes this work outstanding is the section in which inclusions are tracked from the rough to the cut and how the integrity of the diamond can be compromised by depth and position of the remaining inclusions. Additionally, an entire section is devoted to the diamond manufacturing process and its relationship to inclusions. In this area inclusions are examined with regards to heat, pressure, rotation, and other mechanical influences. Inclusions trapped in diamonds are full of information that in many cases is still to be scientifically interpreted. This book take us into the fascinating would of micro-inclusions giving us fresh insight in one of natureżs most sought after gems.

Inclusion on Purpose

Inclusion on Purpose
Author: Ruchika Tulshyan
Publisher: MIT Press
Total Pages: 305
Release: 2024-03-26
Genre: Business & Economics
ISBN: 0262548496

How organizations can foster diversity, equity, and inclusion: taking action to address and prevent workplace bias while centering women of color. Few would disagree that inclusion is both the right thing to do and good for business. Then why are we so terrible at it? If we believe in the morality and the profitability of including people of diverse and underestimated backgrounds in the workplace, why don't we do it? Because, explains Ruchika Tulshyan in this eye-opening book, we don't realize that inclusion takes awareness, intention, and regular practice. Inclusion doesn't just happen; we have to work at it. Tulshyan presents inclusion best practices, showing how leaders and organizations can meaningfully promote inclusion and diversity. Tulshyan centers the workplace experience of women of color, who are subject to both gender and racial bias. It is at the intersection of gender and race, she shows, that we discover the kind of inclusion policies that benefit all. Tulshyan debunks the idea of the “level playing field” and explains how leaders and organizations can use their privilege for good by identifying and exposing bias, knowing that they typically have less to lose in speaking up than a woman of color does. She explains why “leaning in” doesn't work—and dismantling structural bias does; warns against hiring for “culture fit,” arguing for “culture add” instead; and emphasizes the importance of psychological safety in the workplace—you need to know that your organization has your back. With this important book, Tulshyan shows us how we can make progress toward inclusion and diversity—and we must start now.

Mismatch

Mismatch
Author: Kat Holmes
Publisher: MIT Press
Total Pages: 173
Release: 2018-10-16
Genre: Technology & Engineering
ISBN: 0262038889

How inclusive methods can build elegant design solutions that work for all. Sometimes designed objects reject their users: a computer mouse that doesn't work for left-handed people, for example, or a touchscreen payment system that only works for people who read English phrases, have 20/20 vision, and use a credit card. Something as simple as color choices can render a product unusable for millions. These mismatches are the building blocks of exclusion. In Mismatch, Kat Holmes describes how design can lead to exclusion, and how design can also remedy exclusion. Inclusive design methods—designing objects with rather than for excluded users—can create elegant solutions that work well and benefit all. Holmes tells stories of pioneers of inclusive design, many of whom were drawn to work on inclusion because of their own experiences of exclusion. A gamer and designer who depends on voice recognition shows Holmes his “Wall of Exclusion,” which displays dozens of game controllers that require two hands to operate; an architect shares her firsthand knowledge of how design can fail communities, gleaned from growing up in Detroit's housing projects; an astronomer who began to lose her eyesight adapts a technique called “sonification” so she can “listen” to the stars. Designing for inclusion is not a feel-good sideline. Holmes shows how inclusion can be a source of innovation and growth, especially for digital technologies. It can be a catalyst for creativity and a boost for the bottom line as a customer base expands. And each time we remedy a mismatched interaction, we create an opportunity for more people to contribute to society in meaningful ways.

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces
Author: Mikhail Kamenskii
Publisher: Walter de Gruyter
Total Pages: 248
Release: 2001
Genre: Mathematics
ISBN: 9783110169898

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping. Of particular interest is the approach to the case when the linear part is a generator of a condensing, strongly continuous semigroup. In this context, the existence of solutions for the Cauchy and periodic problems are proved as well as the topological properties of the solution sets. Examples of applications to the control of transmission line and to hybrid systems are presented.

The Big Umbrella

The Big Umbrella
Author: Amy June Bates
Publisher: Simon and Schuster
Total Pages: 40
Release: 2018-02-06
Genre: Juvenile Fiction
ISBN: 153440659X

“A subtle, deceptively simple book about inclusion, hospitality, and welcoming the ‘other.’” —Kirkus Reviews “A boundlessly inclusive spirit...This open-ended picture book creates a natural springboard for discussion.” —Booklist “This sweet extended metaphor uses an umbrella to demonstrate how kindness and inclusion work...A lovely addition to any library collection, for classroom use or for sharing at home.” —School Library Journal In the tradition of Alison McGhee’s Someday, beloved illustrator Amy June Bates makes her authorial debut alongside her eleven-year-old daughter with this timely and timeless picture book about acceptance. By the door there is an umbrella. It is big. It is so big that when it starts to rain there is room for everyone underneath. It doesn’t matter if you are tall. Or plaid. Or hairy. It doesn’t matter how many legs you have. Don’t worry that there won’t be enough room under the umbrella. Because there will always be room. Lush illustrations and simple, lyrical text subtly address themes of inclusion and tolerance in this sweet story that accomplished illustrator Amy June Bates cowrote with her daughter, Juniper, while walking to school together in the rain.