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The Leray–Schauder Degree
Let X be a real Banach space. A compact perturbation of the identity in X is closed (i.e. maps closed sets into closed sets) and proper (i.e. inverse...
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Discrete and Continuous Versions of the Continuity Principle
The goal of this paper is to present a certain generalization of the classical Kontinuitätssatz of Behnke for holomorphic/meromorphic functions in...
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The Multi-sensitivity and Topological Sequence Entropy of Dynamical System with Group Action
In this paper, we study the relationship between the multi-sensitivity and the topological maximal sequence entropy of dynamical systems for general...
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On splittings and integration of almost periodic functions with and without geometry
Recently, the authors introduced the notion of weighted semigroups which apply to sun-dual semigroups and especially to the translation semigroup on...
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Banach Spaces Which are Isometric to Subspaces of c0(Γ)
In this paper, we give a number of characterizations for a Banach space X which is isometric to a subspace of c 0 , or, c 0 (Γ), successively, in terms...
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On Boundary Extension of Map**s in Metric Spaces in Terms of Prime Ends
In this chapter, we consider map**s that satisfy (direct) Poletsky inequality in a metric space. We study the boundary extension of such map**s...
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Multibranched Surfaces in 3-Manifolds
This article is a survey of recent works on embeddings of multibranched surfaces into 3-manifolds.
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The Convergence of Borel Probability Measures and Its Applications to Topological Dynamics
We give a topological characterization of the convergence of Borel probability measures on compact metric spaces and apply this result to topological...
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Dimension Theory
In this chapter, we present an introduction to dimension theory. We based our exposition on Chaps. II, III, IV, and VII of the monograph by Witold...
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Quickest Changepoint Detection in General Multistream Stochastic Models: Recent Results, Applications and Future Challenges
Modern information systems generate large volumes of data with anomalies that occur at unknown points in time and have to be detected quickly and...
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The Semilinear Wave Equation
In this chapter we study periodic solutions of the Dirichlet problem for the semilinear wave equation: $$\displaystyle \square u-\mu u:=...
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A Generalized Two-Component Camassa-Holm System with Complex Nonlinear Terms and Waltzing Peakons
In this paper, we deal with the Cauchy problem for a generalized two-component Camassa-Holm system with waltzing peakons and complex higher-order...
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Hardy Spaces on \( \mathbb {R}^n\)
We now study the \(\mathbb {R}^n\) theory. Let...
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Chapter V: Beyond Heights: Slopes and Distribution of Rational Points
The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin...
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Positive-instantaneous frequency and approximation
Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical...
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Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems
In this paper we extend the definitions of mean dimension and metric mean dimension for non-autonomous dynamical systems. We show some properties of...