Related papers: Transseries: Composition, Recursion, and Convergen…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
We deduce several curious q-series expansions by applying inverse relations to certain identities for basic hypergeometric series. After rewriting some of these expansions in terms of q-integrals, we obtain, in the limit q -> 1, some…
In this work I look at the distribution of primes by calculation of an infinite number of intersections. For this I use the set of all numbers which are not elements of a certain times table in each case. I am able to show that it exists a…
We consider series of the form $$ \frac{p}{q} +\sum_{j=2}^\infty \frac{1}{x_j}, $$ where $x_1=q$ and the integer sequence $(x_n)$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for $n\geq 1$.…
Perturbation Theory to Large Scale Structure Cosmology proposes corrections to the linearly evolved density contrast and velocity in terms of a series development in which all terms are integrals of powers of the linear density contrast…
Transformers can generate predictions in two approaches: 1. auto-regressively by conditioning each sequence element on the previous ones, or 2. directly produce an output sequences in parallel. While research has mostly explored upon this…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
Considering the sets of subsums of series (or achievement sets) we show that for conditionally convergent series the multidimensional case is much more complicated than that of the real line. Although we are far from the full topological…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.
We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
First this report presents a restricted set of finite transducers used to synthesise structural time-series constraints described by means of a multi-layered function composition scheme. Second it provides the corresponding synthesised…