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From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory
Four classical systems, the Kelvin gyrostat, the Maclaurin spheroids, the Brouwer rotating saddle, and the Ziegler pendulum have directly inspired...
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Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian...
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Applications
Is the subject of ordinary differential equations important? The ultimate answer to this question is certainly beyond the scope of this book.
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Compact Operators
Compactness of an operator goes one step beyond continuity. Its treatment is fundamental in many areas in Applied Analysis, particularly Differential...
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A priori estimates for solutions to equations of motion of an inextensible hanging string
We consider the initial boundary value problem to equations of motion of an inextensible hanging string of finite length under the action of the...
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Curvature Properties of Interior Black Hole Metric
A spacetime is a connected 4-dimensional semi-Riemannian manifold endowed with a metric tensor g with signature (− + ++). The geometry of a spacetime...
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Generalized Lyapunov Exponents and Aspects of the Theory of Deep Learning
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of...
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Completeness of the Classical Spaces
Is devoted to proving the completeness of the important spaces of multivariate calculus and basic functional analysis.
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Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs,...
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Moduli Spaces of Higgs Bundles – Old and New
We give an overview of the differential geometric and analytic aspects of Higgs bundles and their moduli spaces and highlight some of their...
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Completeness and Separability
A sequence may appear to converge but fails to do so because its limit is ‘missing’ from the metric space. Such sequences are called ‘Cauchy’; these,...
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Properties of Complete Spaces
Explores the consequences of completeness. Includes the Banach fixed point theorem, the Baire category theorem, and some of their applications.
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Regularity Theory of Quasilinear Elliptic and Parabolic Equations in the Heisenberg Group
This note provides a succinct survey of the existing literature concerning the Hölder regularity for the gradient of weak solutions of PDEs of the...
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Positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces
In this paper, we consider positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces with an additional property concerning...
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A Filippov approximation theorem for strengthened one-sided Lipschitz differential inclusions
We consider differential inclusions with strengthened one-sided Lipschitz (SOSL) right-hand sides. The class of SOSL multivalued maps is wider than...
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Fractional variable exponents Sobolev trace spaces and Dirichlet problem for the regional fractional p(.) -Laplacian
In this paper we give a finer analysis of fractional variable exponents Sobolev spaces. We use the relative capacity to characterize completely the...