arXiv subjects

Piotr Szewczyk

Publications and source records attributed to Piotr Szewczyk.

4 recordsLinked to original sources

arXiv2025

Definable henselian valuations in positive residue characteristic

We study the question of $\mathcal{L}_{\mathrm{ring}}$-definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields.

math.LO↗

arXiv2025

Silica-coated admixtures of bismuth and gadolinium oxides for 3D printed concrete applications: Rheology, hydration, strength, microstructure, and radiation shielding perspective

This study examines the impact of replacing up to 5 vol% of Portland cement (PC) with both pristine Bi2O3/Gd2O3 (BG) and silica-coated BG particles. Two different types of silica coatings, each with varying synthesis methods, were applied to coat the BG structures, and their impact on the fresh, hardened, microstructure and radiation-shielding performances of the 3D printable cementitious composites (3DPC) was investigated. Isothermal calorimetry demonstrated that pristine BG incorporation delays hydration, whereas silica coatings mitigate this, with type A coating being more effective. Early compressive strength was reduced in BG-containing mixes but normalised after seven days. Rheological tests showed that BG additives enhanced thixotropy and yield shear stresses, with 2.5 vol% being optimal, especially with method B coating. Green strength properties improved significantly with method B coated particles, showing up to 62.4% and 57.7% increases in strength and modulus, respectively, after 30 minutes. Micro-CT and MIP analyses confirmed reduced porosity and refined pore structure with silica coatings. Radiation shielding tests indicated superior performance in uncoated BG mixes, with method B coating providing superior shielding performance compared to that of method A coatings due to their higher surface area. In general, silica-coated BG particles enhance the mechanical, rheological, and radiation shielding properties of 3DPC, with method B coatings offering the most significant benefits.

physics.app-ph↗

arXiv2022

Defect extensions and a characterization of tame fields

We study the relation between two important classes of valued fields: tame fields and defectless fields. We show that in the case of valued fields of equal characteristic or rank one valued fields of mixed characteristic, tame fields are exactly the valued fields for which all algebraic extensions are defectless fields. In general tame fields form a proper subclass of valued fields for which all algebraic extensions are defectless fields. We introduce a wider class of roughly tame fields and show that every algebraic extension of a given valued field is defectless if and only if its henselization is roughly tame. Proving the above results we also present constructions of Galois defect extensions in positive as well as mixed characteristic.

math.AC↗

arXiv2019

Caristi-Kirk and Oettli-Théra Ball Spaces and applications

Based on the theory of ball spaces introduced by Kuhlmann and Kuhlmann we introduce and study Caristi-Kirk and Oettli-Théra ball spaces. We show that if the underlying metric space is complete, then these have a very strong property: every ball contains a singleton ball. This fact provides quick proofs for several results which are equivalent to the Caristi-Kirk Fixed Point Theorem, namely Ekeland's Variational Principles, the Oettli-Théra Theorem, Takahashi's Theorem and the Flower Petal Theorem.

math.FA↗