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Sequences of Real Numbers
This chapter collects problems on sequences of real numbers. The problems included are challenging and the topics covered vary in diversity: from...
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An anisotropic summability and mixed sequences
In this paper we define and study a vector-valued sequence space, called the space of anisotropic ( s , q , r )-summable sequences, that generalizes the...
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One Segregation Problem for the Sum of Two Quasiperiodic Sequences
The subject of the study is a noise-proof segregation problem for the sequence being the sum of two independent quasiperiodic sequences. The problem...
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Scaling Limits of Slim and Fat Trees
We consider Galton–Watson trees conditioned on both the total number of vertices n and the number of leaves k . The focus is on the case in which both k ...
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Random Sequences
This chapter investigates the foundations of stochastic topology. The main types of convergence of random sequences are defined and compared: almost...
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Convergence analysis of the largest and smallest H-eigenvalues for a class of tensor sequences
This paper considers the convergence analysis of the H-eigenvalues for a class of real symmetric and convergent tensor sequences. We first establish...
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Furstenberg systems of Hardy field sequences and applications
We study measure preserving systems, called Furstenberg systems, that model the statistical behavior of sequences defined by smooth functions with at...
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Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits
We construct a non-polynomial generalization of the q -Askey scheme. Whereas the elements of the q -Askey scheme are given by q -hypergeometric series,...
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Sequences and Series of Functions
In Chapter 3, we discussed the convergence (or non-convergence) of sequences and series over the linear space...
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Sequences of Numbers
This definition is usually extended to the case of a more general domain...
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Additive averages of multiplicative correlation sequences and applications
We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ >0 , ×). In particular, we show that...
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Lifts and Limits
Beginning in this chapter, we present a more unified treatment of flows on compact connected surfaces of genus at least one. Chapters...
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Geometric and Functional Inequalities for Log-Concave Probability Sequences
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for...
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Peeling Sequences
Given a set of n labeled points in general position in the plane, we remove all of its points one by one. At each step, one point from the convex...
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Hosvd-tmpe: an extrapolation method for multidimensional sequences
Accelerating slowly convergent sequences is one of the main purposes of extrapolation methods. In this paper, we present a new tensor polynomial...
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On the convergence of some spectral characteristics of the converging operator sequences
Convergence of the differences between operator norm and spectral radius, operator norm and numerical radius, numerical radius and spectral radius,...
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Infinite Volume Limits of Entangled States
AbstractWe study the structure of entangled states on infinite tensor products. We prove that the infinite volume limit of entangled states is, in...
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Exceptional sequences in the derived category of a gentle algebra
In this paper, using the correspondence of gentle algebras and dissections of marked surfaces, we study full exceptional sequences in the perfect...
