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.

     

A study of high-level managerial decision processes, with implications for MCDM research

We study six real-world major strategic decisions and discuss the role that analytic Multiple Criteria Decision Making (MCDM) models could play in helping decision makers structure and solve such problems. We have interviewed successful and well-educated managers who had access to quantitative decision models, but did not use them as part of their decision process. Our approach is a clinical one that takes a close look at the decision processes. We believe that the normative MCDM framework is oversimplified and does not always fit well with complex, real-world organizational decision processes. This may be one reason why decision tools are not used more widely for solving high-level decision problems. We believe that it would be worthwhile to revise some of the MCDM mainstream postulates and practices to make existing models and tools more suitable for practical purposes. The MCDM mainstream research has until today focused on the choice among alternatives. One should realize that MCDM models could also be used in creating alternatives, in assessing the importance of criteria, in providing the decision makers with “post-commitment support”, and as part of a devil's advocate approach.     

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     

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.     

Copper(I) Bromide: An Alternative Emitter for Blue‐Colored Flame Pyrotechnics

Copper(I) bromide was evaluated as an alternative emitter for blue flame pyrotechnic compositions. CuBr and CuCl emission spectra were recorded from a butane torch flame and compared. Cu(BrO₃)₂ was synthesized and used in pyrotechnic compositions as an oxidizer and the source for the generation of CuBr species. Pyrotechnic compositions, which contained copper and potassium bromates as oxidizers, were optimized for the generation of blue flames. The experimental data, including emission spectra of the flames, chromaticity coordinates, burning rates, luminous intensities, and sensitivity tests, were analyzed and compared.     

Degradation and Crystallization of Cellulose in Hydrogen Chloride Vapor for High‐Yield Isolation of Cellulose Nanocrystals

Despite the structural, load‐bearing role of cellulose in the plant kingdom, countless efforts have been devoted to degrading this recalcitrant polysaccharide, particularly in the context of biofuels and renewable nanomaterials. Herein, we show how the exposure of plant‐based fibers to HCl vapor results in rapid degradation with simultaneous crystallization. Because of the unchanged sample texture and the lack of mass transfer out of the substrate in the gas/solid system, the changes in the crystallinity could be reliably monitored. Furthermore, we describe the preparation of cellulose nanocrystals in high yields and with minimal water consumption. The study serves as a starting point for the solid‐state tuning of the supramolecular properties of morphologically heterogeneous biological materials.     

Adjoint Ideals and Gorenstein Blowups in Two-dimensional Regular Local Rings

In this article we investigate when a complete ideal in a two-dimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the Gorenstein property of the blowup along the ideal.Dedicated to Prof. Kei-ichi Watanabe on the occasion of his 60th birthday.