Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems.

Examines the recent rise in the United States' use of preventive force More so than in the past, the US is now embracing the logic of preventive force: using military force to counter potential threats around the globe before they have fully materialized. While popular with individuals who seek to avoid too many "boots on the ground," preventive force is controversial because of its potential for unnecessary collateral damage. Who decides what threats are 'imminent'? Is there an international legal basis to kill or harm individuals who have a connection to that threat? Do the benefits of preventive force justify the costs? And, perhaps most importantly, is the US setting a dangerous international precedent? In Preventive Force, editors Kerstin Fisk and Jennifer Ramos bring together legal scholars, political scientists, international relations scholars, and prominent defense specialists to examine these questions, whether in the context of full-scale preventive war or preventive drone strikes. In particular, the volume highlights preventive drones strikes, as they mark a complete transformation of how the US understands international norms regarding the use of force, and could potentially lead to a 'slippery slope' for the US and other nations in terms of engaging in preventive warfare as a matter of course. A comprehensive resource that speaks to the contours of preventive force as a security strategy as well as to the practical, legal, and ethical considerations of its implementation, Preventive Force is a useful guide for political scientists, international relations scholars, and policymakers who seek a thorough and current overview of this essential topic.

This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed.

Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including:

* periodic solutions of systems with p-Laplacian type operators (J. Mawhin)

* bifurcation in variational inequalities (K. Schmitt)

* a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega)

* asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl)

* mechanics on Riemannian manifolds (W. Oliva)

* techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets)

A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles.

This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.

How do international norms evolve? This book examines the manner in which sovereignty, a bedrock norm of international relations since the seventeenth century, has evolved in response to changing conceptions of the responsibilities of government. Whereas most previous studies of international norms have examined how norms influence policy decisions, this book asks, instead, how state policies actively shape international norms. Changing Norms through Actions contends that the concept of sovereignty is moving towards one in which states that are unable or unwilling to fulfill their domestic and international obligations are forced to relinquish certain sovereign responsibilities to the international community. As issues such as genocide, weapons of mass destruction, and terrorism have forced states to reassess their understandings of sovereignty, Ramos is interested in how understandings of norms - particularly long-held norms such as absolute sovereignty - change. If action taken by states reinforces an existing norm or alters current understandings of the norm, states must consider how their actions may change the "rules of the game" for the future. Even when a major power acts primarily out of its own self-interest, without any concern to international norms, the action may have the unintended consequence of modifying the normative environment within which other minor powers act. Shifting understandings of sovereignty (and how states relate to one another) can also have profound implications for the workings of the international system. Ramos looks specifically at what happens to sovereignty when states choose to bypass traditional norms of non-intervention on behalf of other competing norms, such as those regarding counterterrorism, human rights, or weapons of mass destruction.

iPolitics provides a current analysis of new media's effect on politics. Politicians rely on Twitter, Facebook, and YouTube to exercise political power. Citizens around the world also use these tools to vent political frustrations, join political groups, and organize revolutions. Political activists blog to promote candidates, solicit and coordinate financial contributions, and provide opportunities for volunteers. iPolitics describes the ways in which new media innovations change how politicians and citizens engage the political arena. Most importantly, the volume emphasizes the implications of these changes for the promotion of democratic ideals. Among other things, contributors to this volume analyze whether the public's political knowledge has increased or decreased in the new media era, the role television still plays in the information universe, the effect bloggers have had on the debate and outcome of healthcare reform, and the manner in which political leaders should navigate the new media environment. While the majority of contributors examine new media and politics in the United States, the volume also provides a unique comparative perspective on this relationship using cases from abroad.

This book provides users, pump manufactures, engineers, researchers and students with extensive information about pump's behavior in reverse operation. It reports on cutting-edge methods for selecting the proper PAT and improving PAT's efficiency, discusses PAT's reliability, economic issues and environmental impact as well. The book describes in detail electromechanical equipment of PAT systems, their installation and operation, and gives important practical insight into the use of PAT in water transmission and distribution systems, as part of thermal power plants and cooling systems, in oil distribution systems and other systems as well. It reports on different types on PAT control modes as well as on numerical methods useful for PAT analysis and implementation. All in all, the book represents a comprehensive practice-oriented reference-guide to design engineers, as well as PAT general users and manufactures. It also provides researchers with extensive technical information on the use of PAT thus fostering new discussions and ideas to improve current methods and cope with future challenges.

Microlending programs for low-income microentrepreneurs have become a global priority since the development of the Grameen Bank in 1976 and the Sustainable Development Goals of the United Nations in 2015. Inspired to create their own microlending program, the deans of the schools of social welfare and business at the University at Albany were aided by the university's Small Business Development Center and the State Employees Federal Credit Union. This led to the creation of the Small Enterprise Economic Development (SEED) program. Following this, new faculty were hired in the School of Social Welfare and the School of Business to address social entrepreneurship and lead these initiatives. The impetus for this book emerged from these developments including three forums in which national and international contributors participated in workshops, panels, and chapters for this book. These forums were co-organized by the School of Social Welfare, the School of Business, and a new Center for the Advancement & Understanding of Social Enterprises (CAUSE) at UAlbany. Building on the example set by UAlbany, Social Entrepreneurship and Enterprises in Economic and Social Development explains how and why we should integrate social entrepreneurship and social enterprises with economic and social development. While this global movement varies in pace and scope, the volume features snapshots from countries and regions representing nearly all continents, including Albania, Argentina, Cuba, India, Kenya, Kyrgyzstan, Russian Federation, Taiwan, Tajikistan, and Tanzania. One of the lessons is that social policies are critical for supporting social entrepreneurs since environmental, economic, and social sustainability are core goals of these initiatives. The chapters in this volume offer different contextual frames ranging from social enterprise business plans and measured entrepreneurial orientation to displacement dynamics (and how to avoid them) and the pitfalls of non-market economies. The contributing authors examine a variety of ventures and social policies to showcase how nations are supporting social enterprises as they attempt to meet human needs and achieve financial sustainability. The resulting volume provides a rationale for, and snapshots of, social enterprises and entrepreneurship in transitioning nations.

Examines the recent rise in the United States' use of preventive force More so than in the past, the US is now embracing the logic of preventive force: using military force to counter potential threats around the globe before they have fully materialized. While popular with individuals who seek to avoid too many "boots on the ground," preventive force is controversial because of its potential for unnecessary collateral damage. Who decides what threats are 'imminent'? Is there an international legal basis to kill or harm individuals who have a connection to that threat? Do the benefits of preventive force justify the costs? And, perhaps most importantly, is the US setting a dangerous international precedent? In Preventive Force, editors Kerstin Fisk and Jennifer Ramos bring together legal scholars, political scientists, international relations scholars, and prominent defense specialists to examine these questions, whether in the context of full-scale preventive war or preventive drone strikes. In particular, the volume highlights preventive drones strikes, as they mark a complete transformation of how the US understands international norms regarding the use of force, and could potentially lead to a 'slippery slope' for the US and other nations in terms of engaging in preventive warfare as a matter of course. A comprehensive resource that speaks to the contours of preventive force as a security strategy as well as to the practical, legal, and ethical considerations of its implementation, Preventive Force is a useful guide for political scientists, international relations scholars, and policymakers who seek a thorough and current overview of this essential topic.

How do international norms evolve? This book examines the manner in which sovereignty, a bedrock norm of international relations since the seventeenth century, has evolved in response to changing conceptions of the responsibilities of government. Whereas most previous studies of international norms have examined how norms influence policy decisions, this book asks, instead, how state policies actively shape international norms. Changing Norms through Actions contends that the concept of sovereignty is moving towards one in which states that are unable or unwilling to fulfill their domestic and international obligations are forced to relinquish certain sovereign responsibilities to the international community. As issues such as genocide, weapons of mass destruction, and terrorism have forced states to reassess their understandings of sovereignty, Ramos is interested in how understandings of norms - particularly long-held norms such as absolute sovereignty - change. If action taken by states reinforces an existing norm or alters current understandings of the norm, states must consider how their actions may change the "rules of the game" for the future. Even when a major power acts primarily out of its own self-interest, without any concern to international norms, the action may have the unintended consequence of modifying the normative environment within which other minor powers act. Shifting understandings of sovereignty (and how states relate to one another) can also have profound implications for the workings of the international system. Ramos looks specifically at what happens to sovereignty when states choose to bypass traditional norms of non-intervention on behalf of other competing norms, such as those regarding counterterrorism, human rights, or weapons of mass destruction.

DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents Limit Relative Category and Critical Point Theory G. Fournier, D. Lupo, M. Ramos, M. Willem 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Relative Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. Relative Cupiength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4. Limit Relative Category . . . . . . . . . . . . . . . . . . . . . . . '" . . . . " . . . . . . . . . . . . . . . . 10 5. The Deformation Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6. Critical Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7. Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed. Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including: * periodic solutions of systems with p-Laplacian type operators (J. Mawhin) * bifurcation in variational inequalities (K. Schmitt) * a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega) * asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl) * mechanics on Riemannian manifolds (W. Oliva) * techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets) A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles. This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.

This book provides users, pump manufactures, engineers, researchers and students with extensive information about pump's behavior in reverse operation. It reports on cutting-edge methods for selecting the proper PAT and improving PAT's efficiency, discusses PAT's reliability, economic issues and environmental impact as well. The book describes in detail electromechanical equipment of PAT systems, their installation and operation, and gives important practical insight into the use of PAT in water transmission and distribution systems, as part of thermal power plants and cooling systems, in oil distribution systems and other systems as well. It reports on different types on PAT control modes as well as on numerical methods useful for PAT analysis and implementation. All in all, the book represents a comprehensive practice-oriented reference-guide to design engineers, as well as PAT general users and manufactures. It also provides researchers with extensive technical information on the use of PAT thus fostering new discussions and ideas to improve current methods and cope with future challenges.