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Characterizing Inverse Sequences For Which Their Inverse Limits Are Homeomorphic
In [11], Mioduszewski characterized inverse sequences of polyhedra for which their inverse limits are homeomorphic. In this article, we obtain a more...
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Limits of Sequences
In the previous chapter, we defined the real numbers as formal limits of rational (Cauchy) sequences, and we then defined various operations on the...
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Limits of Jensen polynomials for partitions and other sequences
It was discovered recently by Griffin, Ono, Rolen and Zagier that the Jensen polynomials associated to many sequences have Hermite polynomial limits....
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Limits: From Sequences to Functions of a Real Variable
From a really abstract point of view, the whole theory of limits for functions of a real variable is an immediate consequence of the theory of limits...
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Functions and Limits
In Chap. 5 , we have seen how sequences of real numbers and their limits behave. Now we are going to look at how...
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Calculation of Limits of Sequences
Up to now, we have only ever asked questions about convergence or divergence and have not yet paid any attention to calculating the possibly existing...
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Blow-Up Sequences and Blow-Up Limits
Let D be an open set in \(\mathbb {R}^d\) and...
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Limits of Inductive Sequences of Toeplitz–Cuntz Algebras
AbstractWe consider inductive sequences of Toeplitz–Cuntz algebras. The connecting homomorphisms of such a sequence are defined by a finite set of...
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On the q-statistical convergence of double sequences
In this paper, we study q -statistical convergence for double sequences. The definitions of q -analog of statistical Cauchy and statistical pre-Cauchy...
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Some Applications of Real Sequences
Now that we have seen real sequences and saw some of their properties, let us look at where they come in handy. We have seen that they allow us to...
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Thermodynamic Limits of Electronic Systems
We review thermodynamic limits and scaling limits of electronic structure models for condensed matter. We discuss several mathematical ways to...
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Limits and Continuity
The notion of limit does not only play a role for sequences, also a function f : D → W can have limits in the points a ∈ D and in the boundary...
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Sequences of Uncountable Iterated Function Systems: The Convergence of the Sequences of Fractals and Fractal Measures Associated
In this paper, we consider a sequence of uncountable iterated function system (U.I.F.S.). Each term of this sequence is built using an uncountable...
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Sequences
Sequences of real or complex numbers are of fundamental importance for mathematics: With their help, the basic concepts of calculus such as...
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Map** Theorems for Inverse Limits with Set-Valued Bonding Functions
We revisit the results from two papers, Mioduszewski’s “Map**s of inverse limits” and Feuerbacher’s “Map**s of inverse limits revisited” to...
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Dynamical Systems on Graph Limits and Their Symmetries
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than...
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Almost Convergent 0-1-Sequences and Primes
We study 0-1-sequences and establish the connection between the values of the upper and lower Sucheston functional on such sequence and the set of...
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Cubic Extensions of the Lucas Sequences
This is the first of three chapters devoted to the question of how to generalize the Lucas sequences. We begin with a detailed discussion of Lucas’s...
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Inverse Limits with Markov-Type Functions
In the paper, we introduce a new concept of Markov-type functions on trees allowing the graphs to be 2-dimensional. Also, we prove that two inverse...
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LHS-spectral sequences for regular extensions of categories
In (Xu, J Pure Appl Algebra 212:2555–2569, 2008), a LHS-spectral sequence for target regular extensions of small categories is constructed. We extend...