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If Humboldt had a laptop
(2001)
The difficult publication history and expensive editions of Alexander von Humboldt’s volumes on the expedition to the Americas have resulted in incomplete library holdings which has limited scholarly access and sometimes caused unbalanced scholarship. A plan for a Humboldt Digital Library examines the structures and features of this representational system in print and proposes models for converting these materials to electronic form. Several issues posed by Humboldt’s works include: establishing authoritative standard editions in several languages, creating high-resolution access to the many visual innovations in the works, and using software to restore the grand concept that all of the separate disciplines of study can be seen as interrelated parts of the whole. Using techniques of geographic visualization, a prototype is planned which will connect this historical body of knowledge with modern scientific databases.
In the middle of the 19th century the question whether expanding civilization and industrialization had an effect on climate was discussed intensely worldwide. It was feared that increasing deforestation would lead to continuous decrease in rainfall. This first scientific discussion about climate change as the result of human intervention was strongly influenced by the research Alexander von Humboldt and Jean-Baptiste Boussingault had undertaken when they investigated the falling water levels of Lake Valencia in Venezuela. This essay aims to clarify the question whether Alexander von Humboldt can be counted among the leading figures of modern environmentalism on account of this research as is being claimed by Richard H. Grove in his influential book Green Imperialism. Colonial Expansion, Tropical Island Edens and Origins of Environmentalism, 1600-1860 (1995).
Function spaces with asymptotics is a usual tool in the analysis on manifolds with singularities. The asymptotics are singular ingredients of the kernels of pseudodifferential operators in the calculus. They correspond to potentials supported by the singularities of the manifold, and in this form asymptotics can be treated already on smooth configurations. This paper is aimed at describing refined asymptotics in the Dirichlet problem in a ball. The beauty of explicit formulas highlights the structure of asymptotic expansions in the calculi on singular varieties.
A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. It is shown here that each VMO function is the difference of two functions in VLO.
Contents: 1 Introduction 2 Statement of the problem and definitions 3 The main results 4 Proof of theorem 2 4.1 Reduction of problem (2) to functional - integral equations 4.2 The uniqueness of a solution of equation (2) 4.3 The existence of a solution of equation (2) 5 Proof of theorem 1 6 Proof of theorem 3 7 First boundary problem for hyperbolic differential equations 7.1 Statement of the problem 7.2 The formulation of the result and a sketch of the proof
The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities.