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.     

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.     

Critical Mandelbrot Cascades

We study Mandelbrot’s multiplicative cascade measures at the critical temperature. As has been recently shown by Barral et al. (C R Acad Sci Paris Ser I 350:535–538, 2012), an appropriately normalized sequence of cascade measures converges weakly in probability to a nontrivial limit measure. We prove that these limit measures have no atoms and give bounds for the modulus of continuity of the cumulative distribution function of the measure. Using the earlier work of Barral and Seuret (Adv Math 214:437–468, 2007), we compute the multifractal spectrum of the measures. We also extend the result of Benjamini and Schramm (Commun Math Phys 289:653–662, 2009), in which the KPZ formula from quantum gravity is validated for the high temperature cascade measures, to the critical and low temperature cases.     

New bonding modes of gas-phase deposited gamma-aminopropyltriethoxysilane on silica studied by 29Si CP/MAS NMR

Besides the well-known reaction between the ethoxy groups of the silane end of the gamma-aminopropyltriethoxysilane (APTS) molecule and the silanols of silica, the amino ends of APTS molecules were observed to react in the gas phase with ethoxy groups of other APTS molecules and silanols of silica at elevated temperatures on the silica surface, dehydroxylated at 600 degrees C, forming Si-N linkages, as established by 29Si CP/MAS NMR.     

On local cohomology and Hilbert function of powers of ideals

Let I be a homogeneous ideal in a polynomial ring R=K[x₁,,x_m], where K is an infinite field. In this article we investigate the asymptotic behaviour of the a_i-invariants and the regularity index of the ring R/Iⁿ when n»0.Both authors were supported by the Academy of Finland, Project 48556. The first named author was also supported in part by the National Basic Research Program (Vietnam)Mathematics Subject Classification (2000):13D40, 13D45     

The diagonal subring and the Cohen-Macaulay property of a multigraded ring

Let be a multigraded ring defined over a local ring . This paper deals with the question how the Cohen-Macaulay property of is related to that of its diagonal subring . In the bigraded case we are able to give necessary and sufficient conditions for the Cohen-Macaulayness of . If are ideals of positive height, we can then compare the Cohen-Macaulay property of the multi-Rees algebra with the Cohen-Macaulay property of the usual Rees algebra . We also obtain a bound for the joint reduction numbers of two -primary ideals in the case the corresponding multi-Rees algebra is Cohen-Macaulay.

     

Structure of subspaces of the compact operators having the Dunford-Pettis property

The structure of the subspaces having the Dunford-Pettis property (DPP) is studied, where is the space of all compact operators on and . The following conditions are shown to be equivalent: (i) M has the DPP, (ii) M is isomorphic to a subspace of (iii) the sets and are relatively compact for all and . The equivalence between (i) and (iii) was recently proven in the case of arbitrary Hilbert spaces by Brown and ülger. It is also shown that (i) and (ii) are equivalent for subspaces . This result is optimal in the sense that for there is a DPP-subspace that fails to be isomorphic to a subspace of . Received January 9, 1998; in final form October 1, 1998     

Coefficient ideals and the Cohen-Macaulay property of Rees algebras

Let be a local ring and let be an ideal of positive height. If is a reduction of , then the coefficient ideal is by definition the largest ideal such that . In this article we study the ideal when the Rees algebra is Cohen-Macaulay.