Related papers: A proof of Fatou's interpolation theorem
In this short note I restate and simplify the proof of the impossibility of probabilistic induction from Popper (1992). Other proofs are possible (cf. Popper (1985)).
We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
We prove an interpolation result for homogeneous polynomials over the integers, or more generally for PIDs with finite residue fields. Previous proofs of this result use the well-known but nontrivial fact that class groups of rings of…
The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
A generalization of an inequality from IMO is proven.
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We present a creative reimagining of Zolotarev's classical proof of the Law of Quadratic Reciprocity.
In this paper some proof theory for propositional Lax Logic is developed. A cut free terminating sequent calculus is introduced for the logic, and based on that calculus it is shown that the logic has uniform interpolation. Furthermore, a…
We present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.
In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…
Let $A$ be a square complex matrix, $z_1$, ..., $z_{n}\in\mathbb C$ be (possibly repetitive) points of interpolation, $f$ be analytic in a neighborhood of the convex hull of the union of the spectrum of $A$ and the points $z_1$, ...,…
We show some elementary facts about the semantical analogue of Parikh's Splitting, which we call Factorization.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error…
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.