Related papers: On hereditarily rational functions

Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the…

Counting functions are constructed for sums of integers raised to a fixed positive rational power. That is, given values formed by $u_1^{j/k} + u_2^{j/k} + ... + u_l^{j/k}$, $u_i \in \mathbb{Z}^+$, the number of values less than or equal to…

Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of…

We modify the standard proof of Paley's theorem about lacunary coefficients of functions in $H^1$ to work without analytic factorization. This leads to the first direct proof of the extension of Paley's theorem that we applied to the former…

Let f(t,X) be an irreducible polynomial over the field of rational functions k(t), where k is a number field. Let O be the ring of integers of k. Hilbert's irreducibility theorem gives infinitely many integral specializations of t to values…

The main result shows a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighborhood consisting entirely of univalent functions. For the particular choice of a linear function in…

We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.

This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…

In this article we prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. Those results have already been proved by Alexander Vishik in the case of characteristic 0,…

In this article we prove modular and norm P\'olya-Szeg\"o inequalities in general fractional Orlicz-Sobolev spaces by using the polarization technique. We introduce a general framework which includes the different definitions of theses…

We evaluate the short-range asymptotic behavior of Green's function for a Hamiltonian when its potential energy part has an inverse power singularity at the origin. The analytically solvable case of sharply screened Coulomb potential is…

In this article we prove a result comparing rationality of integral algebraic cycles over the function field of a quadric and over the base field. This is an integral version of the result known for coefficients modulo 2. Those results have…

In (Borceux-Janelidze 2001) they prove a Categorical Galois Theorem for ordinary categories, and establish the main result of (Joyal-Tierney 1984), along with the classical Galois theory of Rings, as instances of this more general result.…

In this paper we present necessary and sufficient conditions (in terms of {\L}ojasiewicz inequalities) for the stability of local minimum points in smooth unconstrained optimization. In particular, we derive a sufficient condition for which…

We characterize normal families in the unit ball as those families of analytic functions whose restrictions to each complex line through the origin are normal. We then generalize this result to a characterization of normal functions…

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…

In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Carath\'eodory Theorem to the new setting.

A Jordan H\"older theorem is established for derived module categories of piecewise hereditary algebras. The resulting composition series of derived categories are shown to be independent of the choice of bounded or unbounded derived module…

Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These…

We discuss some problems posed by Ciesielski. For example we show that, consistently, d_c is a singular cardinal and e_c<d_c. Next we prove that the Martin Axiom for sigma --centered forcing notions implies that for every function f:R^2…