Related papers: A recursive function coding number theoretic funct…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We show the equivalence between the existence of winning strategies for $G_{\delta \sigma}$ (also called $\Sigma^{0}_{3}$) games in Cantor or Baire space, and the existence of functions generalized-recursive in a higher type-2 functional.…
We study various proofs of the caracterization of constant functions, more precisely of the theorem: a derivable function, defined on a real interval, is constant if, and only if, its derivative is null. Our aim is to study the…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…
In this paper, we investigate recurrence relations for the Maclaurin coefficients of the products of a elementary function and the Bessel function of the first kind $\mathcal{J}(z) = h(z) J_\nu(z)$ and the modified Bessel function of the…
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
Convolution powers of $1/x$ are transformed into functions $f_n$, which satisfy a simple recurrence relation. Solutions are characterized and analyzed.
We extend the work of A. Ciaffaglione and P. Di Gianantonio on mechanical verification of algorithms for exact computation on real numbers, using infinite streams of digits implemented as co-inductive types. Four aspects are studied: the…
Given a linear recurrence of the form $c_n=a_1c_{n-1}+\cdots+a_j c_{n-j}$, it is well-known that $c_n=\sum_{r}p_r(n)r^n$, where the sum is taken over the set of characteristic roots and each $p_r(n)$ is some polynomial. We give a closed…
We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…
We provide a sound and relatively complete Hoare-like proof system for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism, and in which the correctness proofs…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
In this article we gave a recurrence to obtain the n-th prime number as function of the (n-1)-th prime number.
We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a…
We propose a recursive algorithm for the calculation of multi-baryon correlation functions that combines the advantages of a recursive approach with those of the recently proposed unified contraction algorithm. The independent components of…
Function-correcting codes were introduced in the work "Function-Correcting Codes" (FCC) by Lenz et al. 2023, which provides a graphical representation for the problem of constructing function-correcting codes. We use this function dependent…
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
Rouch\'e's Theorem is among the most useful results in complex analysis for counting zeros of analytic functions. Rouch\'e's Theorem also admits a harmonic analogue for counting zeros of complex harmonic functions. Previously, this analogue…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…