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Ranks for Families of Theories and Their Spectra
AbstractWe define ranks and degrees for families of theories, similar to Morley rank and degree, as well as Cantor–Bendixson rank and degree, and the...
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Asymptotic Analysis of Operator Families and Applications to Resonant Media
We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for...
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Class numbers of certain families of totally real biquadratic fields and a result of Mollin
In this article we study the lower bounds for the class numbers of certain families of totally real biquadratic fields. The bounds we have obtained...
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Extensions and approximations of Banach-valued Sobolev functions
In complete metric measure spaces Z equipped with a doubling measure and supporting a weak Poincaré inequality, we consider a measurable subset
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The Singularity Theorems of General Relativity and Their Low Regularity Extensions
On the occasion of Sir Roger Penrose’s 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent...
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Indecomposable Involutive Set-Theoretic Solutions of the Yang–Baxter Equation and Orthogonal Dynamical Extensions of Cycle Sets
Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive...
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Limits of Eventual Families of Sets with Application to Algorithms for the Common Fixed Point Problem
We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of...
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On ultrafilter extensions of first-order models and ultrafilter interpretations
There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them (Goranko in Filter and...
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Strongly Continuous Resolving Families of Operators for Equations with a Fractional Derivative
AbstractUnder Hille–Yosida type conditions for a closed operator in a linear homogeneous equation with the Gerasimov–Caputo derivative a strongly...
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Quasiperiodic Sets at Infinity and Meromorphic Extensions of Their Fractal Zeta Functions
We construct an interesting family of unbounded sets at infinity having a quasiperiodic structure in their geometry. We study these sets by analyzing...
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Uniformly Computably Separable Algebras with Effectively Splittable Families of Negative Congruences
We characterize uniformly computably separable algebras with effectively splittable families of negative congruences and study certain properties...
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Central Extensions and the Orbit Method
In this chapter we treat central extensions of groups, a particular case of the construction in Sect. 1.5 ,...
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Discrete-to-Continuous Extensions: Lovász Extension and Morse Theory
This is the first of a series of papers that develop a systematic bridge between constructions in discrete mathematics and the corresponding...
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Preservation of splitting families and cardinal characteristics of the continuum
We show how to construct, via forcing, splitting families that are preserved by a certain type of finite support iterations. As an application, we...
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Thick families of geodesics and differentiation
The differentiation theory of Lipschitz functions on metric spaces taking values in a Banach space with the Radon-Nikodým property (RNP), originally...