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The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle/ZF. The proof builds upon a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the…
We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a…
We review the concept of superfluidity and, based on real and thought experiments, we use the formalism of second quantization to derive expressions that allow the calculation of the superfluid density for general Hamiltonians with…
There is a widely-held belief amongst theoreticians that the Gilbert damping parameter {\alpha} in magnetization dynamics is infinite for a pure metal at T=0. The basic error leading to this belief is pointed out explicitly and the various…
In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing.…
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
We introduce two related notions of pattern enforcement in $(0,1)$-matrices: $Q$-forcing and strongly $Q$-forcing, which formalize distinct ways a fixed pattern $Q$ must appear within a larger matrix. A matrix is $Q$-forcing if every…
Transition metal oxide heterostructures often, but by far not always, exhibit strong electronic correlations. State-of-the-art calculations account for these by dynamical mean field theory (DMFT). We discuss the physical situations in which…
We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the…
Let $M_n(\mathbb{F})$ denote the algebra of $n \times n$ matrices over an algebraically closed field $\mathbb{F}$ of characteristic different from $2$. For $n \ge 2$, we classify all maps $\phi : M_n(\mathbb{F}) \to M_n(\mathbb{F})$…
We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on $\omega_2$ and its restrictions to certain cofinalities. Our main result shows that the strengthening $MM^{++}$ of Martin's Maximum does not…
Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H…
This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…
We establish strict upper limits for the Casimir interaction between multilayered structures of arbitrary dielectric or diamagnetic materials. We discuss the appearance of different power laws due to frequency-dependent material constants.…
We propose four different mechanisms responsible for paramagnetic or diamagnetic persistent currents in normal metal rings and determine the circumstances for change of the current from paramagnetic to diamagnetic ones and {\it vice versa}.…
The ability to control the magnetic state provides a powerful means to tune the underlying band topology, enabling transitions between distinct electronic phases and the emergence of novel quantum phenomena. In this work, we address the…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes…
Schubert varieties of hyperplane arrangements, also known as matroid Schubert varieties, play an essential role in the proof of the Dowling-Wilson conjecture and in Kazhdan-Lusztig theory for matroids. We study these varieties as…
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…