Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.Comment: 16 page

An economic analysis of adaptation to climate change under uncertainty

Dit proefschrift presenteert een economische analyse van klimaatadaptatie onder onzekerheid. De economische evaluatiemethoden, multi-criteria analyse en kosten-batenanalyse worden toegepast. Een investeringsmodel gebaseerd op kosten-batenanalyse onder onzekerheid is ontwikkeld om de besluitvorming op het gebied van klimaatadaptatie te analyseren en te ondersteunen. De beleidsconclusie van dit proefschrift geeft een vijfstappenplan aan voor beleidsmakers die verantwoordelijk zijn voor het nemen van optimale investeringbeslissingen in klimaatadaptatie

Costs and benefits of adapting to climate change at six meters below sea level

Climate change increases the vulnerability of low-lying coastal areas. Careful spatial planning can reduce this vulnerability. An assessment framework aimed at reducing vulnerability to climate change enables decision-makers to make better informed decisions about investments in adaptation to climate change through spatial planning. This paper presents and evaluates an approach to assess adaptation options, with the use of cost-benefit analysis

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

Mindful awareness as a mechanism of change for natural childbirth in pregnant women with high fear of childbirth: a randomised controlled trial

BACKGROUND: Mindfulness-Based Childbirth and Parenting (MBCP) is effective in increasing natural childbirth in pregnant women with high fear of childbirth (FOC) as compared to enhanced care as usual (ECAU). We aimed to examine through which pathway of action MBCP reaches this effect, based on a model of approaching or avoiding the challenges related to childbirth. METHODS: One hundred eleven pregnant women with high FOC were measured pre- and post-intervention on FOC (emotion pathway), catastrophic beliefs about labour pain (cognition pathway) and mindful awareness (attention pathway). A multiple mediation model was used to examine through which pathway the mechanism of change operated in relation to approach (i.e., natural childbirth) versus avoidance (i.e., self-requested caesarean section). RESULTS: It was found that greater mindful awareness (18% R(2) = 0.18, F[1107] = 22.77, p < 0.0001) was the only significant mechanism of change operating through the attentional pathway leading to natural childbirth. More specifically, nonreactivity to inner experience (a facet of mindful awareness) showed to be the strongest mechanism of change. More extensive meditation practice was positively associated with natural childbirth; however, the number of completed MBCP sessions was not associated with the outcome. CONCLUSIONS: An increase in mindful awareness was the strongest mechanism of change for better adaptation to the challenges of childbirth. Decreases in neither FOC nor catastrophic beliefs about labour pain were identified as mechanisms of change. Additionally, the more one meditated, the more one was inclined towards a natural childbirth. MBCP enhances adaptation to the challenges of childbirth and less use of obstetric interventions in the presence of high FOC. TRIAL REGISTRATION: The Netherlands Trial Register (NTR; 4302). SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12884-022-04380-0

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

A modular agent-based environment for studying stock markets

Artificial stock markets are built with diffuse priors in mind regarding trading strategies and price formation mechanisms. Diffuse priors are a natural consequence of the unknown relation between the various elements that drive market dynamics and the large variety of market organizations, findings, however, might hold only within the specific market settings. In this paper we propose a framework for building agent-based artificial stock markets. We present the mechanism of the framework based on a previously identified list of organizational and behavioural aspects. Within the framework experiments with arbitrary many trading strategies, acting in various market organizations can be conducted in a flexible way, without changing its architecture. In this way experiments of other artificial stock markets, as well as theoretical models can be replicated and their findings compared. Comparisons of the different experimental results might indicate whether findings are due to traders’ behaviour or to the chosen market structure and could suggest how to improve market quality

Volatile aldehydes in libraries and archives

Volatile aldehydes are produced during degradation of paper-based materials. This may result in their accumulation in archival and library repositories. However, no systematic study has been performed so far. In the frame of this study, passive sampling was carried out at ten locations in four libraries and archives. Despite the very variable sampling locations, no major differences were found, although air-filtered repositories were found to have lower concentrations while a non-ventilated newspaper repository exhibited the highest concentrations of volatile aldehydes (formaldehyde, acetaldehyde, furfural and hexanal). Five employees in one institution were also provided with personal passive samplers to investigate employees’ exposure to volatile aldehydes. All values were lower than the presently valid exposure limits. The concentration of volatile aldehydes, acetic acid, and volatile organic compounds (VOCs) in general was also compared with that of outdoor-generated pollutants. It was evident that inside the repository and particularly inside archival boxes, the concentration of VOCs and acetic acid was much higher than the concentration of outdoor-generated pollutants, which are otherwise more routinely studied in connection with heritage materials. This indicates that further work on the pro-degradative effect of VOCs on heritage materials is necessary and that monitoring of VOCs in heritage institutions should become more widespread