Core versus graded core, and global sections of line bundles

We find formulas for the graded core of certain -primary ideals in a graded ring. In particular, if is the section ring of an ample line bundle on a Cohen-Macaulay complex projective variety, we show that under a suitable hypothesis, the core and graded core of the ideal of generated by all elements of degrees at least (for some, equivalently every, large ) are equal if and only if the line bundle admits a non-zero global section. We also prove a formula for the graded core of the powers of the unique homogeneous maximal ideal in a standard graded Cohen-Macaulay ring of arbitrary characteristic. Several open problems are posed whose solutions would lead to progress on a non-vanishing conjecture of Kawamata.

     

A non-singular spherically symmetric separable copy of the vacuum in SU(2) Landau gauge

We give a new non-singular spherically symmetric and separable copy of the vacuum in Landau gauge for SU(2) Yang-Mills theories. The solution can be considered as a generalization of Gribov's solution in Coulomb gauge and thus it demonstrates the similarity between vacua in Coulomb and Landau gauges.     

Influence of biological origin on the tensile properties of cellulose nanopapers

Cellulose - Cellulose nanopapers provide diverse, strong and lightweight templates prepared entirely from sustainable raw materials, cellulose nanofibers (CNFs). Yet the strength of CNFs has not...     

Rapid Cationization of Gold Nanoparticles by Two‐Step Phase Transfer

Cationic gold nanoparticles offer intriguing opportunities as drug carriers and building blocks for self‐assembled systems. Despite major progress on gold nanoparticle research in general, the synthesis of cationic gold particles larger than 5 nm remains a major challenge, although these species would give a significantly larger plasmonic response compared to smaller cationic gold nanoparticles. Herein we present the first reported synthesis of cationic gold nanoparticles with tunable sizes between 8–20 nm, prepared by a rapid two‐step phase‐transfer protocol starting from simple citrate‐capped particles. These cationic particles form ordered self‐assembled structures with negatively charged biological components through electrostatic interactions.     

Wounding-Induced VOC Emissions in Five Tropical Agricultural Species

Leaf mechanical wounding triggers a rapid release—within minutes—of a blend of volatile organic compounds. A wounding-induced VOC blend is mainly composed of oxygenated ubiquitous stress volatiles such as methanol and volatile products of lipoxygenase (LOX) pathway (mainly C5 and C6 alcohols and aldehydes and their derivatives), but also includes multiple minor VOCs that collectively act as infochemicals, inducing defences in non-damaged plant leaves and neighbouring plants and attracting herbivore enemies. At present, the interspecific variability of the rate of induction and magnitude of wounding-induced emissions and the extent to which plant structural traits and physiological activity alter these emissions are poorly known. Particularly scarce is information on the induced emissions in tropical agricultural plant species, despite their economic importance and large area of cultivation at regional and global scales. We chose five tropical crops with varying photosynthetic activity and leaf structural characteristics—Abelmoschus esculentus, Amaranthus cruentus, Amaranthus hybridus, Solanum aethiopicum, and Telfairia occidentalis—to characterize the kinetics and magnitude of wounding-induced emissions, hypothesizing that the induced emission response is greater and faster in physiologically more active species with greater photosynthetic activity than in less active species. Rapid highly repeatable leaf wounds (12 mm cuts) were generated by a within-leaf-chamber cutting knife. Wounding-induced VOC emissions were measured continuously with a proton-transfer reaction time-of-flight mass spectrometer and gas-chromatography mass spectrometry was used to separate isomers. Twenty-three ion VOCs and twelve terpenoid molecule structures were identified, whereas ubiquitous stress volatiles methanol (on average 40% of total emissions), hexenal (24%), and acetaldehyde (11%) were the main compounds across the species. Emissions of low-weight oxygenated compounds (LOC, 70% of total) and LOX products (29%) were positively correlated across species, but minor VOC components, monoterpenoids and benzenoids, were negatively correlated with LOC and LOX, indicating a reverse relationship between signal specificity and strength. There was a large interspecific variability in the rate of induction and emission magnitude, but the hypothesis of a stronger emission response in physiologically more active species was only partly supported. In addition, the overall emission levels were somewhat lower with different emission blend compared to the data reported for wild species, as well as different shares for the VOCs in the blend. The study demonstrates that wounding-dependent emissions from tropical agricultural crops can significantly contribute to atmospheric volatiles, and these emissions cannot be predicted based on current evidence of wild plant model systems.     

Optical energy storage properties of Sr<Subscript>2</Subscript>MgSi<Subscript>2</Subscript>O<Subscript>7</Subscript>:Eu<Superscript>2+</Superscript>,R<Superscript>3+</Superscript> persistent luminescence materials

The details of the mechanism of persistent luminescence were probed by investigating the trap level structure of Sr₂MgSi₂O₇:Eu²⁺,R³⁺ materials (R: Y, La-Lu, excluding Pm and Eu) with thermoluminescence (TL) measurements and Density Functional Theory (DFT) calculations. The TL results indicated that the shallowest traps for each Sr₂MgSi₂O₇:Eu²⁺,R³⁺ material above room temperature were always ca. 0.7 eV corresponding to a strong TL maximum at ca. 90 °C. This main trap energy was only slightly modified by the different co-dopants, which, in contrast, had a significant effect on the depths of the deeper traps. The combined results of the trap level energies obtained from the experimental data and DFT calculations suggest that the main trap responsible for the persistent luminescence of the Sr₂MgSi₂O₇:Eu²⁺,R³⁺ materials is created by charge compensation lattice defects, identified tentatively as oxygen vacancies, induced by the R³⁺ co-dopants.     

Random conformal weldings

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle. The homeomorphism is constructed using the exponential of βX, where X is the restriction of the 2-dimensional free field on the circle and the parameter β is in the “high temperature” regime \( \beta < \sqrt {2} \). The welding problem is solved by studying a non-uniformly elliptic Beltrami equation with a random complex dilatation. For the existence a method of Lehto is used. This requires sharp probabilistic estimates to control conformal moduli of annuli and they are proven by decomposing the free field as a sum of independent fixed scale fields and controlling the correlations of the complex dilatation restricted to dyadic cells of various scales. For the uniqueness we invoke a result by Jones and Smirnov on conformal removability of Hölder curves. Our curves are closely related to SLE(?) for ?<4.     

Jumping numbers and ordered tree structures on the dual graph

Let R be a two-dimensional regular local ring having an algebraically closed residue field and let ${\mathfrak{a}}$ be a complete ideal of finite colength in R. In this article we investigate the jumping numbers of ${\mathfrak{a}}$ by means of the dual graph of the minimal log resolution of the pair ${(X,\mathfrak{a})}$ . Our main result is a combinatorial criterium for a positive rational number ?? to be a jumping number. In particular, we associate to each jumping number certain ordered tree structures on the dual graph.     

Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node.We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set.We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.