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Abstract The soil mantle of the tropical karstic landscapes of Southern Mexico was shaped by specific processes of pedogenesis and long‐term human impacts of ancient Maya agriculture. To understand the interaction between natural and human‐induced soil‐forming processes in the calcareous mountains of Chiapas state, we studied soil toposequences around the Classic Maya site of Budsilhá and related them to the archaeological evidence of settlement and land‐use distribution. Soil chemical analysis, micromorphological observations, and clay mineral identification were carried out in key soil profiles at the main geoforms. Limestone hills are occupied by shallow Rendolls which are usually perceived as incipient soils. However, high content of silicate clay composed of kaolinite and vermiculite and ferruginous clayey soil material observed at macro‐ and microscale backed the hypothesis that these soils were formed from the residues of thick Terra Rossa after their erosion. Swampy lowlands are occupied by thick clayey gleyic soils with clay mineral assemblages similar to those in the upland Rendolls. We suppose that the mineral matrix of the lowland soils is largely derived from the pedosediments of eroded upland Terra Rossa, which lost original ferruginous pigmentation and aggregation due to redoximorphic processes. Some wetland soils contain neoformed gypsum that is atypical for humid tropics; sulfide‐sulfate transformation under fluctuating redox conditions could promote gypsum synthesis. Ancient Maya land use was closely related to soil‐geomorphic conditions: settlements with homegardens occupied calcareous hills, whereas the primary agricultural domain was developed on lowland soils after their drainage by artificial canals. 

Let { s j } j = 1 n \left \{ s_{j}\right \} _{j=1}^{n} be positive integers. We show that for any 1 ≤ L ≤ n , 1\leq L\leq n, ‖ ∏ j = 1 n ( 1 − z s j ) ‖ L ∞ ( | z | = 1 ) ≥ exp ⁡ ( 1 2 e L ( s 1 s 2 … s L ) 1 / L ) . \begin{equation*} \left \Vert \prod _{j=1}^{n}\left ( 1-z^{s_{j}}\right ) \right \Vert _{L_{\infty }\left ( \left \vert z\right \vert =1\right ) }\geq \exp \left ( \frac {1}{2e}\frac {L}{\left ( s_{1}s_{2}\ldots s_{L}\right ) ^{1/L}}\right ) . \end{equation*} In particular, this gives geometric growth if a positive proportion of the { s j } \left \{ s_{j}\right \} are bounded. We also show that when the { s j } \left \{ s_{j}\right \} grow regularly and faster than j ( log ⁡ j ) 2 + ε j\left ( \log j\right ) ^{2+\varepsilon } , some ε > 0 \varepsilon >0 , then the norms grow faster than exp ⁡ ( ( log ⁡ n ) 1 + δ ) \exp \left ( \left ( \log n\right ) ^{1+\delta }\right ) for some δ > 0 \delta >0 . 

Psychologists hypothesize that the effectiveness of normative messaging interventions increases when individuals have more personal attachment and similarity with reference groups. Using readily available energy consumption data, it is now possible to create highly personalized reference groups based on households’ daily energy use in a non-invasive matter. However, it still remains unclear to what degree individuals perceive behavioral reference groups as a cohesive entity. Therefore, this research investigates how individuals perceive energy profile-based groups relative to more standard geographic proximity-based groups. An online survey is conducted with 1,928 U.S. adults. Individuals do not perceive the profile-based groups as very entitative groups. Also, similarity between energy profile-based group members indirectly affects individuals’ identification with the groups via group entitativity. Lastly, this indirect effect is larger than the direct effect of similarity between group members on group identification. These results imply that a better understanding of what affects group entitativity would allow interveners to create more effective normative feedback messages.