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Linking Sandwich Sets
The theory presented in Chap. 2 gives precise criteria for the existence of sandwich pairs, but it does not provide a list of such pairs. There is...
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Sandwich Systems
As we saw in Chap. 1 , an important requirement for a linking pair is that they must separate the functional, i.e., they must satisfy...
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The Thin-Sandwich Problem in General Relativity
This paper serves a review on the history and results on the reduced thin-sandwich equations of general relativity (GR). These equations arise within...
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Adaptive seeding for profit maximization in social networks
Social networks are becoming important dissemination platforms, and a large body of works have been performed on viral marketing, but most are to...
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Bisections of Mass Assignments Using Flags of Affine Spaces
We use recent extensions of the Borsuk–Ulam theorem for Stiefel manifolds to generalize the ham sandwich theorem to mass assignments. A k -dimensional...
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Geometric Topology and Further Applications of Algebraic Topology
Geometric topology primarily studies manifolds and their embeddings in other manifolds. A particularly active area is low-dimensional topology, which...
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Elliptic Systems
In this chapter we show how monotonicity methods combined with infinite dimensional sandwich pairs can be used to solve very general systems of...
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Flows and Critical Points
In this chapter we study equations of the form $$\displaystyle \begin{aligned} \left\{\begin{aligned} - {\Delta_{\mathit p}} u & = f(x,u)\;\quad...
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The Monotonicity Trick
The use of linking or sandwich pairs cannot produce critical points by themselves. The most they can produce are sequences satisfying...
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Topological Inference of the Conley Index
The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed...
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Functions of Several Variables, Limits and Continuity
A real valued function of n variableReal valued function of variable is a function $$f:\mathbb...
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Nonsubmodular Optimization
In the real world, there are many set function optimization problems with objective function and/or constraint which is neither submodular nor...
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A novel physics-informed framework for reconstruction of structural defects
The ultrasonic guided wave technology plays a significant role in the field of non-destructive testing as it employs acoustic waves with the...