This work delineates the impact of terrorism--and the American response--on the basic structure of international relations, the dimming prospects for global reform and the tendency to override the ...role of sovereign territorial states. Falk examines the changing role of the state, the relevance of institutions, the role of individuals and the importance of the worldwide religious resurgence, with its positive and negative implications. He also considers the post-modern geopolitics of the Bush presidency, with its emphasis on the militarization of space, the control of oil in the Middle East, and its reliance on military capabilities so superior to that of other states as to make any challenge impractical.
A classical technique to construct polynomial preserving extensions of scalar functions defined on the boundary of an
n
n
simplex to the interior is to use so-called rational blending functions. The ...purpose of this paper is to generalize the construction by blending to the de Rham complex. More precisely, we define polynomial preserving extensions which map traces of
k
k
-forms defined on the boundary of the simplex to
k
k
-forms defined in the interior. Furthermore, the extensions are cochain maps, i.e., they commute with the exterior derivative.
Local bounded cochain projections FALK, RICHARD S.; WINTHER, RAGNAR
Mathematics of computation,
11/2014, Letnik:
83, Številka:
290
Journal Article
Recenzirano
Odprti dostop
We construct projections from H \Lambda ^k(\Omega ) forms on \Omega L^2(\Omega ) L^2(\Omega ) H \Lambda ^k(\Omega ). Thus, their definition requires less smoothness than assumed for the definition of ...the canonical interpolants based on the degrees of freedom. Moreover, these projections have the properties that they commute with the exterior derivative and are bounded in the H \Lambda ^k(\Omega ). Unlike some other recent work in this direction, the projections are also locally defined in the sense that they are defined by local operators on overlapping macroelements, in the spirit of the Clément interpolant. A double complex structure is introduced as a key tool to carry out the construction.
The Global Governance Forum and the Global Challenges Foundation collaborate in this collection in their concern that the UN Charter and the contemporary infrastructure for international cooperation ...are no longer fit for purpose and lack the instruments, resources and legitimacy to address the catastrophic risks threatening our future.
Twenty-eight contributors offer thoughtful proposals for reforming existing international institutions and creating new ones to build a more peaceful, prosperous and just world, covering themes such as the management of weapons of mass destruction, collective security arrangements, justice and equity in economics, human rights, migration and refugees, climate mitigation, and food security, all bearing on the health of both people and planet.
The vital project of this century is building institutions that will underpin global governance in coming decades, requiring imagination, persistence, empathy, and confidence that we will find a path to enhanced mechanisms of binding international law and the resources to make that happen. The volume is essential reading for scholars and researchers on international politics and public policy and indispensable for diplomats and government agencies.
In this wide-ranging and multidisciplinary volume, leading scholars, activists, journalists, and public figures deliberate about the creative and critical potential of public imagination in an era ...paradoxically marked by intensifying globalization and resurgent nationalism. Divided into five sections, these essays explore the social, political, and cultural role of imagination and civic engagement, offering cogent, ingenious reflections that stand in stark contrast to the often grim rhetoric of our era. Short and succinct, the essays engage with an interconnected ensemble of themes and issues while also providing insights into the specific geographical and social dynamics of each author’s national or regional context. Part 1 introduces the reader to theoretical reflections on imagination and the public sphere;Part 2 illustrates dynamics of public imagination in a diverse set of cultural contexts;Part 3 reflects in various ways on the urgent need for a radically transformed public and civic imagination in the face of worldwide ecological crisis;Part 4 suggests new societal possibilities that are related to spiritual as well as politically revolutionary sources of inspiration;Part 5 explores characteristics of present and potentially emerging global society and the existing transnational framework that could provide resources for a more humane global order.Erudite and thought-provoking, On Public Imagination makes a vital contribution to political thought, and is accessible to activists, students, and scholars alike.
Two families of conforming finite elements for the two-dimensional Stokes problem are developed, guided by two discrete smoothed de Rham complexes, which we coin "Stokes complexes." We show that the ...finite element pairs are inf-sup stable and also provide pointwise mass conservation on very general triangular meshes.
Professor Falk gives special attention to the political setting that shapes international law and to the creation of those intellectual perspectives which would strengthen world order.
Originally ...published in 1970.
ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Basic principles of mixed Virtual Element Methods Brezzi, F.; Falk, Richard S.; Donatella Marini, L.
ESAIM. Mathematical modelling and numerical analysis,
07/2014, Letnik:
48, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n ...− 1) − Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim of making the basic philosophy clear. However, we consider an arbitrary degree of accuracy k (the Virtual Element analogue of dealing with polynomials of arbitrary order in the Finite Element Framework).
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in Falk and Winther (Found Comput Math 16(1):297–328, 2016) ...for scalar valued functions, or zero-forms, and represents a new tool for the understanding of finite element spaces of arbitrary polynomial degree. The present paper contains a similar study for differential forms. From a simplicial mesh
T
of the domain
Ω
, we build a map which decomposes piecewise smooth
k
-forms into a sum of local bubbles supported on appropriate macroelements. The key properties of the decomposition are that it commutes with the exterior derivative and preserves the piecewise polynomial structure of the standard finite element spaces of
k
-forms. Furthermore, the transform is bounded in
L
2
and also on the appropriate subspace consisting of
k
-forms with exterior derivatives in
L
2
.
This article suggests that Trump’s presidency threatens the United States with a fascist future, and this threat persist even if he fails to be reelected. The article also considers other ...deficiencies of U.S. democracy including antiquated vote counting, voter suppression aimed at poor and minorities, rejections of reason and science, excessive influence of money, and political disempowerment of the citizenry. Only a transformative progressive movement outside the party system can fix U.S. democracy.
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