Given a fixed graph H that embeds in a surface $\Sigma$ , what is the maximum number of copies of H in an n-vertex graph G that embeds in $\Sigma$ ? We show that the answer is $\Theta(n^{f(H)})$ , where f(H) is a graph invariant called the ‘flap-number’ of H, which is independent of $\Sigma$ . This simultaneously answers two open problems posed by Eppstein ((1993) J. Graph Theory17(3) 409–416.). The same proof also answers the question for minor-closed classes. That is, if H is a $K_{3,t}$ minor-free graph, then the maximum number of copies of H in an n-vertex $K_{3,t}$ minor-free graph G is $\Theta(n^{f'(H)})$ , where f′(H) is a graph invariant closely related to the flap-number of H. Finally, when H is a complete graph we give more precise answers.

Glacier mass-balance observations at seasonal resolution have been performed since 1914 at two sites on Claridenfirn, Switzerland. The measurements are the longest uninterrupted records of glacier mass balance worldwide. Here, we provide a complete re-analysis of the 106-year series (1914–2020), focusing on both point and glacier-wide mass balance. The approaches to evaluate and homogenize the direct observations are described in detail. Based on conservative assumptions, average uncertainties of $\pm$0.25 m w.e. are estimated for glacier-wide mass balances at the annual scale. It is demonstrated that long-term variations in mass balance are clearly driven by melting, whereas decadal changes in accumulation are uncorrelated with mass balance and can only be relevant in short periods. Mass change of Claridenfirn is impacted by dry calving at a frontal ice cliff. Considerations of ice volume flux at a cross-profile reveal long-term variations in frontal ice loss accounting for $\sim$9% of total annual ablation on average. The effect of changes in frontal ablation mostly explains $\lt$10% of the mass-balance difference relative to the period 1960–1990, but accounts for $\sim$20% in 2010–2020. Glacier mass changes are discussed in the context of observations throughout the European Alps indicating that Claridenfirn is regionally representative.

We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that it has a normal projective compactification with trivial log canonical divisor. We connect this to a novel symmetry of generating series for counts of essential multicurves on the surface.

We derive the surface and basal radar reflectance and backscatter coefficients of the southern McMurdo Ice Shelf (SMIS) and part of the nearby Ross Ice Shelf (RIS), Antarctica, from radar statistical reconnaissance using a 60-MHZ airborne survey. The surface coefficients are further inverted in terms of snow density and roughness, providing a spatial distribution of the processes contributing to the surface boundary conditions. We disentangle the basal coefficients from surface transmission losses, and we provide the basal coherent content, an indicator of the boundary geometric disorder that is also self-corrected from englacial attenuation. The basal radar properties exhibit sharp gradients along specific iso-depths, suggesting an abrupt modification of the ice composition and geometric structure. We interpret this behavior as locations where the pressure-melting point is reached, outlining fields of freezing and melting ice. Basal steps are observed at both SMIS and RIS, suggesting a common geometric expression of widespread basal processes. This technique offers a simultaneous view of both the surface and basal boundary conditions to help investigate the ice-shelf stability, while its application to airborne data significantly improves coverage of the difficult-to-observe ice–ocean boundary. It also provides constraints on thermohaline circulation in ice shelves cavities, which are analogs for ice-covered ocean worlds.

The application of clay minerals in therapeutics is becoming important due to their structural and surface physicochemical properties. 5-aminosalicylic acid (5-ASA) is a very common pharmaceutical drug and is used worldwide. The interactions between the 5-ASA molecule and both the aluminol and siloxane surfaces of kaolinite are studied by means of atomistic calculations using force fields based on empirical interatomic potentials and quantum mechanics calculations based on density functional theory. A conformational analysis of 5-ASA has been performed and the anion of 5-ASA was also studied. The calculated adsorption energy values indicate that 5-ASA is likely to be adsorbed on the kaolinite surfaces with greater affinity to the aluminol surface. Hence, kaolinite may be considered as a promising pharmaceutical carrier of 5-ASA.

We prove that for every surface $\Sigma $ of Euler genus $g$, every edge-maximal embedding of a graph in $\Sigma $ is at most $O(g)$ edges short of a triangulation of $\Sigma $. This provides the first answer to an open problem of Kainen (1974).

The $\text{SL}\left( 2,\mathbb{C} \right)$-representation varieties of punctured surfaces form natural families parameterized by monodromies at the punctures. In this paper, we compute the loci where these varieties are singular for the cases of one-holed and two-holed tori and the four-holed sphere. We then compute the de Rham cohomologies of these varieties of the one-holed torus and the four-holed sphere when the varieties are smooth via the Grothendieck theorem. Furthermore, we produce the explicit Gauß-Manin connection on the natural family of the smooth $\text{SL}\left( 2,\mathbb{C} \right)$-representation varieties of the one-holed torus.

Next space missions will investigate the possibility of extinct or extant life on Mars. Studying the infrared spectral modifications, induced by thermal processing on different carbonate samples (recent shells and fossils of different ages), we developed a method able to discriminate biogenic carbonates from their abiogenic counterparts. The method has been successfully applied to microbialites, i.e. bio-induced carbonates deposits, and particularly to stromatolites, the laminated fabric of microbialites, some of which can be ascribed to among the oldest traces of biological activity known on Earth. These results are of valuable importance since such carbonates are linked to primitive living organisms that can be considered as good analogues for putative Martian life forms. Considering that the microstructures of biogenic carbonate are different from those of abiogenic origin, we investigated the micromorphology of shells, skeletal grains and microbialites at different scale with a scanning electron microscope. The results show that this line of research may provide an alternative and complementary approach to other techniques developed in the past by our group to distinguish biotic from abiotic carbonates. In this paper, we present some results that can be of valuable interest since they demonstrate the utility for a database of images concerning the structures and textures of relevant carbonate minerals. Such data may be useful for the analysis of Martian samples, coming from sample return missions or investigated by future in situ explorations, aimed to characterize the near-subsurface of Mars in search for past or present life.

Motivated by findings of new mineral related water sources for organisms under extremely dry conditions on Earth we studied in an interdisciplinary approach the water sorption behaviour of halite, soil component and terrestrial Nostoc commune biofilm under Mars relevant environmental conditions. Physicochemical methods served for the determination of water sorption equilibrium data and survival of heterotrophic bacteria in biofilm samples with different water contents was assured by recultivation. Deliquescence of halite provides liquid water at temperatures <273 K and may serve as water source on Mars during the morning stabilized by the CO2 atmosphere for a few hours. The protecting biofilm of N. commune is rather hygroscopic and tends to store water at lower humidity values. Survival tests showed that a large proportion of the Alphaproteobacteria dominated microbiota associated to N. commune is very desiccation tolerant and water uptake from saturated NaCl solutions (either by direct uptake of brine or adsorption of humidity) did not enhance recultivability in long-time desiccated samples. Still, a minor part can grow under highly saline conditions. However, the salinity level, although unfavourable for the host organism, might be for parts of the heterotrophic microbiota no serious hindrance for growing in salty Mars-like environments.

The role of the initial bacterial inoculates on the biocorrosion of API X52 pipeline steel coupons was evaluated by electrochemical noise technique. The experiments were performed under laboratory conditions using an aerobic bacteria identified as Achromobacter xylosoxidans. Inoculations in the interval strain of 1x104 – 1x108 CFU/ml were evaluated. Environmental scanning electron microscopy (ESEM) analysis was carried out to evaluate the corrosive effects induced on the API X52 electrodes. The results show that all corroded surfaces show sites of localized corrosion, however, the density of de sites of localized corrosion have different grades depending of the initial inoculation used during the experiments. The maximum density sites of localized corrosion were obtained in the experiments with 1x105 CFU/ml. From inoculates of 1x106 CFU/ml the density sites of localized corrosion diminished constantly. The results show that with inoculates over 1x106 CFU/ml, the oxygen demand for the bacterial strain limits the presence of oxygen available into the metallic surface to maintain the corrosion reactions. The results were supported by the EDX analysis of the corrosion products formed on the metallic surfaces where the oxygen peaks diminished as the bacterial inoculation increases.

We prove that if $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$ is a properly embedded $\pi _1$-injective surface in a compact 3-manifold $M$, then $\pi _1S$ is separable in $\pi _1M$.

To obtain a nanocrystalline surface layer, 316L stainless steel was treated by fast multiple rotation rolling (FMRR). The microstructure, after FMRR treatment and annealing treatment, was characterized by transmission electron microscopy and x-ray diffraction. Equiaxed nanocrystalline with the average grain size about 12 nm is obtained on the surface layer of FMRR sample. The investigation of thermal stability of the nanocrystalline layer indicates that the grains are still nanocrystalline and the average grain size is about 60 nm for annealing at 500 °C. In addition, the amount of α-martensite increases markedly as the annealing temperature increases from 300 to 500 °C. However, it begins to reduce at 600 °C due to the reversion transformation from martensite to austenite. After annealing at 400 °C, the microhardness of the annealed FMRR sample reaches a maximum value of about 660 HV, and it is four times higher than that of the original sample.

Today a wide range of instruments are available for the rapid roughness quantification of optical surfaces but especially for three dimensional measurement methods no standardized process is established. This leads to different results, even if the same specimen is tested with similar measurement devices. In order to solve this problem an exemplary process development is described in this paper. To do this firstly the term of roughness is defined as a surface deviation and then the functionality and importance of filters in roughness measurement as well as the used measurement devices are described. The following chapter defines the used materials and methods which were used during the measurement process. In the last part of this paper the results are discussed and a process assignment is suggested.

Let $C$ be a curve in a closed orientable surface $F$ of genus $g\geq 2$ that separates $F$ into subsurfaces $\widetilde {{F}_{i} } $ of genera ${g}_{i} $, for $i= 1, 2$. We study the set of roots in $\mathrm{Mod} (F)$ of the Dehn twist ${t}_{C} $ about $C$. All roots arise from pairs of ${C}_{{n}_{i} } $-actions on the $\widetilde {{F}_{i} } $, where $n= \mathrm{lcm} ({n}_{1} , {n}_{2} )$ is the degree of the root, that satisfy a certain compatibility condition. The ${C}_{{n}_{i} } $-actions are of a kind that we call nestled actions, and we classify them using tuples that we call data sets. The compatibility condition can be expressed by a simple formula, allowing a classification of all roots of ${t}_{C} $ by compatible pairs of data sets. We use these data set pairs to classify all roots for $g= 2$ and $g= 3$. We show that there is always a root of degree at least $2{g}^{2} + 2g$, while $n\leq 4{g}^{2} + 2g$. We also give some additional applications.