Christina Taylor | Search arXiv

arXiv2026

Core Reactivity in Cs-Ba-O ternary system under pressure

High pressure can activate Cs $5p$ core electrons for covalent bonding. In this study, we investigate the Cs-Ba-O system at 150 and 250 GPa using first-principles structure searches. CsBa$_3$O$_8$ and CsBaO$_4$ both lie on the static-lattice convex hull at 250~GPa and exhibit mild Cs $5p$-O $2p$ bonding while retaining O$_2$ units with intermediate superoxide-peroxide character. Cs$_2$BaO$_3$ shows substantially stronger bonding but remains metastable with respect to CsO and BaO. A 1:1 Cs$_2$O-BaO$_2$ mixture provides a solid starting composition for investigating this chemistry, with core-reactive CsO among the predicted products at 250~GPa. Calculated Cs $L_3$-edge x-ray absorption near-edge spectra and powder diffraction patterns provide electronic and structural signatures to guide identification of the predicted phases in diamond anvil cell experiments.

cond-mat.mtrl-sci↗

arXiv2018

Faulhaber's Problem Revisited: Alternate Methods for Deriving the Bernoulli Numbers--Part I

This paper sets the groundwork for the consideration of families of recursively defined polynomials and rational functions capable of describing the Bernoulli numbers. These families of functions arise from various recursive definitions of the Bernoulli numbers. The derivation of these recursive definitions is shown here using the original application of the Bernoulli numbers: sums of powers of positive integers, i.e., Faulhaber's problem. Since two of the three recursive forms of the Bernoulli numbers shown here are readily available in literature and simple to derive, this paper focuses on the development of the third, non-linear recursive definition arising from a derivation of Faulhaber's formula. This definition is of particular interest as it shows an example of an equivalence between linear and non-linear recursive expressions. Part II of this paper will follow up with an in-depth look at this non-linear definition and the conversion of the linear definitions into polynomials and rational functions.

math.NT↗