Philosophers have spilled much ink over the discovery of ideas in the classical “context of discovery.” However, there has been little engagement with the question of what constitutes a discovery of “things in the world.” A much-overlooked answer to this question is provided by T. S. Kuhn. In this article, I show that discoveries awarded the Nobel Prize in Physics over the past 53 years accord with a basic premise of Kuhn’s account and his distinction between two types of natural kind discoveries. I also draw normative conclusions for credit attribution in science.

We prove the central limit theorem (CLT), the first-order Edgeworth expansion and a mixing local central limit theorem (MLCLT) for Birkhoff sums of a class of unbounded heavily oscillating observables over a family of full-branch piecewise $C^2$ expanding maps of the interval. As a corollary, we obtain the corresponding results for Boolean-type transformations on $\mathbb {R}$. The class of observables in the CLT and the MLCLT on $\mathbb {R}$ include the real part, the imaginary part and the absolute value of the Riemann zeta function. Thus obtained CLT and MLCLT for the Riemann zeta function are in the spirit of the results of Lifschitz & Weber [Sampling the Lindelöf hypothesis with the Cauchy random walk. Proc. Lond. Math. Soc. (3) 98 (2009), 241–270] and Steuding [Sampling the Lindelöf hypothesis with an ergodic transformation. RIMS Kôkyûroku Bessatsu B34 (2012), 361–381] who have proven the strong law of large numbers for sampling the Lindelöf hypothesis.

We produce, relative to a $\textsf {ZFC}$ model with a supercompact cardinal, a $\textsf {ZFC}$ model of the Proper Forcing Axiom in which the nonstationary ideal on $\omega _1$ is $\Pi _1$-definable in a parameter from $H_{\aleph _2}$.

Data-based methods have gained increasing importance in engineering. Success stories are prevalent in areas such as data-driven modeling, control, and automation, as well as surrogate modeling for accelerated simulation. Beyond engineering, generative and large-language models are increasingly helping with tasks that, previously, were solely associated with creative human processes. Thus, it seems timely to seek artificial-intelligence-support for engineering design tasks to automate, help with, or accelerate purpose-built designs of engineering systems for instance in mechanics and dynamics, where design so far requires a lot of specialized knowledge. Compared with established, predominantly first-principles-based methods, the datasets used for training, validation, and test become an almost inherent part of the overall methodology. Thus, data publishing becomes just as important in (data-driven) engineering science as appropriate descriptions of conventional methodology in publications in the past. However, in mechanics and dynamics, quite widely, still traditional publishing practices are prevalent that largely do not yet take into account the rising role of data as much as that may already be the case in pure data-scientific research. This article analyzes the value and challenges of data publishing in mechanics and dynamics, in particular regarding engineering design tasks, showing that the latter raise also challenges and considerations not typical in fields where data-driven methods have been booming originally. Researchers currently find barely any guidance to overcome these challenges. Thus, ways to deal with these challenges are discussed and a set of examples from across different design problems shows how data publishing can be put into practice.

Time pressure is a central aspect of economic decision making nowadays. It is therefore natural to ask how time pressure affects decisions, and how to detect individual heterogeneity in the ability to successfully cope with time pressure. In the context of risky decisions, we ask whether a person’s performance under time pressure can be predicted by measurable behavior and traits, and whether such measurement itself may be affected by selection issues. We find that the ability to cope with time pressure varies significantly across decision makers, leading to selected subgroups that differ in terms of their observed behaviors and personal traits. Moreover, measures of cognitive ability and intellectual efficiency jointly predict individuals’ decision quality and ability to keep their decision strategy under time pressure.

It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set X of finitely many Cohen reals, by showing that, in the forcing extension, the transcendence degree of the reals over a combination of the reals in the extension given by each proper subset of X is also maximal. This answers a question of Kanovei and Schindler [2].

$\mu$Cap is a software package (citeware) for economic experiments enabling experimenters to analyze emotional states of subjects using z-Tree and FaceReader™. $\mu$Cap is able to create videos of subjects on client computers based on stimuli shown on screen and restrict recording material to relevant time frames. Another feature of $\mu$Cap is the creation of time stamps in csv format at prespecified screens (or at prespecified points in time) during the experiment, measured on the client computer. The software makes it possible to import these markers into FaceReader™ easily. $\mu$Cap is the first program that significantly simplifies the process of connecting z-Tree and FaceReader™ with the additional benefit of extremely high precision. This paper describes the usage, underlying principles as well as advantages and limitations of $\mu$Cap. Furthermore, we give a brief outlook of how $\mu$Cap can be beneficial in other contexts.

In this article I issue a challenge to what I call the Independence Thesis of Theory Assessment (ITTA). According to ITTA, the evidence for (or against) a theory must be assessed independently from the theory explaining the evidence. I argue that ITTA is undermined by cases of evidential uncertainty, in which scientists have been guided by the explanatory power of their theories in the assessment of the evidence. Instead, I argue, these cases speak in favor of a model of theory assessment in which explanatory power may indeed contribute to the stabilization of the evidential basis.

In this experimental study, we explore the dynamics of the thermal boundary layer in liquid metal Rayleigh–Bénard convection, covering the parameter ranges of $0.026 \leq$ Prandtl numbers $(Pr) \leq 0.033$ and Rayleigh numbers ($Ra$) up to $2.9\times 10^9$. Our research focuses on characterising the thermal boundary layer near the top plate of a cylindrical convection cell with an aspect ratio of 0.5, distinguishing between two distinct regions: the shear-dominated region around the centre of the top plate and a location near the side wall where the boundary layer is expected to be affected by the impact or ejection of thermal plumes. The dependencies of the boundary layer thickness on $Ra$ at these positions reveal deviating scaling exponents with the difference diminishing as $Ra$ increases. We find stronger fluctuations in the boundary layer and increasing deviation from the Prandtl–Blasius–Pohlhausen profile with increasing $Ra$, as well as in the measurements outside the centre region. Our data illustrate the complex interplay between flow dynamics and thermal transport in low-$Pr$ convection.

We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields.

During photochemical dissolution of goethite in acid/oxalate solution, Fe3+, Fe2+, and CO2 were released and towards the end of the reaction ferrous oxalate precipitated. The dissolution process involved an initial slow stage followed by a much faster reaction. The slow stage was eliminated by addition of 20 ppm Fe2+ to the system at the start of the reaction. The presence of this Fe2+ did not accelerate the secondary dissolution process. Both protons and oxalate ions appear to have been involved in the dissolution process. Dissolution was accelerated by an increase in oxalate concentration (from 0.0025 to 0.025 M) in the system and also depended on pH, reaching a maximum rate at pH 2.6. Highly substituted (15.9 mole % Al) goethite dissolved more slowly per unit area than unsubstituted goethite. Lepidocrocite (γ-FeOOH) dissolved faster than goethite. The first stage of the dissolution process probably proceeded by slow release of Fe3+ through complexation with oxalate adsorbed on the goethite surface. The faster, secondary step appears to have been a reductive dissolution reaction involving adsorbed ferrous oxalate.

The transformation of ferrihydrite to goethite and/or hematite in alkaline media is strongly retarded by the presence of silicate species. These species probably stabilize ferrihydrite by adsorbing on the particles of ferrihydrite and linking them into an immobile network.

At concentrations low enough for the transformation to proceed, silicate species promote the formation of hematite and hinder the nucleation of goethite. The presence of silicate species modifies the morphology of both reaction products. Hematite forms ellipsoidal single crystals, commonly displaying outgrowths of goethite. Silicate species in solution appear to enhance the development of the (021) faces of goethite, probably by preferential adsorption on these faces; at high levels of silicate species, goethite crystals adopt a pseudohexagonal habit. This morphology has not been observed previously for goethite.

Constitutions are the most important legal foundation of politics. At the same time, the existence of a viable parliamentary opposition has been regarded one of the most distinctive characteristics of democracy. Bringing the two perspectives together, the principle of opposition can be constitutionalized to gain the highest status. Importantly, we refer to norms recognizing the opposition as such. Such counter-majoritarian rules are distinct because they empower opposition forces irrespective of their seat share and explicitly acknowledge that power should not be monopolized. While our subject has attracted little interest from comparative constitutionalists, it is too important to be overlooked. This is particularly true for autocratizing regimes where incumbents seek to use legislative lawfare to repress their opponents. Empirically, the study focuses on Africa, which proves revealing for various reasons. Among others, it addresses the critique that constitutional law studies often concentrate on usual suspect cases used to reveal purportedly universal insights. Our exercise in comparative constitutional law leads to two main conclusions that go beyond the continent. First, while we find a high number of opposition-related rules, the variation in design details and scope suggests that referring to the principle of opposition in an abstract manner is somewhat obscuring. And second, the obvious virtues of constitutionalizing dissent face noteworthy pitfalls since pertinent rules can lack legal clarity and even suppress dissent. Hence, the dividends of nominally democratic rules might be smaller than expected even if constitutional designers sincerely intend to fully uphold them in practice.

The effect of three organic ligands on the adsorption of Cu on Ca-montmorillonite was studied. The results indicate that these effects include three different processes:

1. 1) Enhanced uptake of positively charged Cu-ligand complexes by ion-exchange.

2. 2) Formation of ternary surface complexes involving surface aluminol groups.

3. 3) Inhibited uptake due to competition between the surface ligands and the dissolved ligands for dissolved copper.

Ethylenediamine promotes Cu uptake by ion-exchange at low pH but tends to suppress adsorption at aluminol groups by ligand competition at high pH. The same mechanisms are operative for β-alanine; however, the uptake of Cu(β-ala)+ by ion-exchange is not promoted by the attached ligand. The influence of malonate includes both ligand competition and formation of ternary complexes. A quantitative interpretation based on the surface complexation model using the least-square programs FITEQL (Westall, 1982) and GRFIT (Ludwig, 1992) is presented. The obtained equilibrium constants are listed in Tables 2b and 3.

The interaction of H+- and Cu2+-ions with Ca-montmorillonite was investigated in 0.1 mol/dm3 solutions of Ca(CIO4)2 at 298.2 K by Potentiometrie titrations using both glass electrodes (for H+) and ion specific electrodes (for Cu2+ ). The experimental data were interpreted on the basis of the surface complexation model. The calculations were performed with the least-squares program FITEQL (Westall, 1982) using the constant capacitance approximation. The best fit was obtained with a set of equilibria of the general form

$\begin{array}{c}p{H}^{+}+qC{u}^{2+}+\equiv SOH\iff \left(H^{+}{)}_p\right(C{u}^{2+}{)}_q(\equiv SOH{)}^{(p+2q)+}\\ {\beta }_{p,q\left(int\right)}^s=\frac{\text{[}{H}_{p}C{u}_q(\equiv SOH{)}^{(p+2q)}]}{\text{[}{H}^{+}{]}^p\left[C{u}^{2+}{]}^q\right[\equiv SOH]}\end{array}$

$\equiv TOH-H^{+}\iff \equiv {TO}^{-}log{\beta }_{-1,0\left(int\right)}^S=-5.77(\pm 0.07).$

The effects of three organic ligands on the adsorption of copper on Ca-montmorillonite were studied. The results indicate that these effects include three different processes:

1. 1) Enhanced uptake of positively charged copper-ligand complexes by ion-exchange.

2. 2) Formation of ternary surface complexes involving surface aluminol groups.

3. 3) Inhibited uptake due to competition between the surface ligands and the dissolved ligands for dissolved copper.

Ethylenediamine promotes copper uptake by ion-exchange at low pH but tends to suppress adsorption at aluminol groups by ligand competition at high pH. The same mechanisms are operative for β-alanine; however, the uptake of Cu(β-ala)+ by ion-exchange is not promoted by the attached ligand. The influence of malonate includes both ligand competition and formation of ternary complexes. A quantitative interpretation based on the surface complexation model using the least-squares programs FITEQL (Westall, 1982) and GRFIT (Ludwig, 1992) is presented. The obtained equilibrium constants are listed in Tables 2b and 3.