We prove a decomposition formula of logarithmic Gromov–Witten invariants in a degeneration setting. A one-parameter log smooth family $X \longrightarrow B$ with singular fibre over $b_0\in B$ yields a family $\mathscr {M}(X/B,\beta ) \longrightarrow B$ of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over $b_0$ in terms of rigid tropical maps to the tropicalization of $X/B$. This generalizes one aspect of known results in the case that the fibre $X_{b_0}$ is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.

Sample geometry effects on mechanical strengths of gold micro-cantilevers are evaluated by a micro-bending test. Six micro-cantilevers with the same length of 50 μm are prepared, and the width and the thickness are varied to examine individual effects on the yield stress. The yield stress increases from 428 to 519 MPa when the thickness decreases from 11.1 to 6.0 μm. No obvious dependency is observed when varying the width. The results reveal that the thickness and the width each has a different influence on the yield stresses of micro-cantilevers evaluated by the bending test, which is the sample geometry effect.

In this article, we consider the possible application of the European General Data Protection Regulation (GDPR) to “citizen scientist”-led health research with mobile devices. We argue that the GDPR likely does cover this activity, depending on the specific context and the territorial scope. Remaining open questions that result from our analysis lead us to call for lex specialis that would provide greater clarity and certainty regarding the processing of health data by for research purposes, including these non-traditional researchers.

Let $p$ be a prime, $G$ a solvable group and $P$ a Sylow $p$ -subgroup of $G$ . We prove that $P$ is normal in $G$ if and only if $\unicode[STIX]{x1D711}(1)_{p}^{2}$ divides $|G:\ker (\unicode[STIX]{x1D711})|_{p}$ for all monomial monolithic irreducible $p$ -Brauer characters $\unicode[STIX]{x1D711}$ of  $G$ .

Let $G$ be a group, $p$ be a prime and $P\in \text{Syl}_{p}(G)$ . We say that a $p$ -Brauer character $\unicode[STIX]{x1D711}$ is monolithic if $G/\ker \unicode[STIX]{x1D711}$ is a monolith. We prove that $P$ is normal in $G$ if and only if $p\nmid \unicode[STIX]{x1D711}(1)$ for each monolithic Brauer character $\unicode[STIX]{x1D711}\in \text{IBr}(G)$ . When $G$ is $p$ -solvable, we also prove that $P$ is normal in $G$ and $G/P$ is nilpotent if and only if $\unicode[STIX]{x1D711}(1)^{2}$ divides $|G:\ker \unicode[STIX]{x1D711}|$ for all monolithic irreducible $p$ -Brauer characters $\unicode[STIX]{x1D711}$ of $G$ .

Let $G$ be a finite group and let $p$ be a prime factor of $|G|$ . Suppose that $G$ is solvable and $P$ is a Sylow $p$ -subgroup of $G$ . In this note, we prove that $P{\vartriangleleft}G$ and $G/P$ is nilpotent if and only if $\unicode[STIX]{x1D711}(1)^{2}$ divides $|G:\ker \unicode[STIX]{x1D711}|$ for all irreducible monomial $p$ -Brauer characters $\unicode[STIX]{x1D711}$ of $G$ .

Liquid water on Mars might be created by deliquescence of hygroscopic salts or by permafrost melts, both potentially forming saturated brines. Freezing point depression allows these heavy brines to remain liquid in the near-surface environment for extended periods, perhaps as eutectic solutions, at the lowest temperatures and highest salt concentrations where ices and precipitates do not form. Perchlorate and chlorate salts and iron sulphate form brines with low eutectic temperatures and may persist under Mars near-surface conditions, but are chemically harsh at high concentrations and were expected to be incompatible with life, while brines of common sulphate salts on Mars may be more suitable for microbial growth. Microbial growth in saturated brines also may be relevant beyond Mars, to the oceans of Ceres, Enceladus, Europa and Pluto. We have previously shown strong growth of salinotolerant bacteria in media containing 2M MgSO4 heptahydrate (~50% w/v) at 25°C. Here we extend those observations to bacterial isolates from Basque Lake, BC and Hot Lake, WA, that grow well in saturated MgSO4 medium (67%) at 25°C and in 50% MgSO4 medium at 4°C (56% would be saturated). Psychrotolerant, salinotolerant microbes isolated from Basque Lake soils included Halomonas and Marinococcus, which were identified by 16S rRNA gene sequencing and characterized phenetically. Eutectic liquid medium constituted by 43% MgSO4 at −4°C supported copious growth of these psychrotolerant Halomonas isolates, among others. Bacterial isolates also grew well at the eutectic for K chlorate (3% at −3°C). Survival and growth in eutectic solutions increases the possibility that microbes contaminating spacecraft pose a contamination risk to Mars. The cold brines of sulphate and (per)chlorate salts that may form at times on Mars through deliquescence or permafrost melt have now been demonstrated to be suitable microbial habitats, should appropriate nutrients be available and dormant cells become vegetative.

Analogy is a core cognition process used to produce inferences as well as new ideas using previous knowledge and experience. Ontology is a formal representation of a set of domain concepts and their relationships. The use of analogy and ontology in design activities to support design creativity have previously been explored. This paper explores an approach to construct ontologies with sufficient richness and coverage to support reasoning over real-world datasets for prompting creative idea generation. This approach has been implemented into a computational tool for assisting designers in generating creative ideas during the early stages of design. The tool, called “the Retriever”, has been developed based on ontology by embracing the aspects of analogical reasoning. A case study has indicated that the tool can be effective and useful for idea generation. The results have indicated that the tool, in its current formulation, can significantly improve the fluency and flexibility of idea generation and the usefulness of ideas, as well as slightly increase the originality of ideas, for the case study concerned.