Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.

Vulnerability of stream biota to climate change in mediterranean climate regions: a synthesis of ecological responses and conservation challenges

Freshwater species worldwide are experiencing dramatic declines partly attributable to ongoing climate change. It is expected that the future effects of climate change could be particularly severe in mediterranean climate (med-) regions, which host many endemic species already under great stress from the high level of human development. In this article, we review the climate and climate-induced changes in streams of med-regions and the responses of stream biota, focusing on both observed and anticipated ecological responses. We also discuss current knowledge gaps and conservation challenges. Expected climate alterations have already been observed in the last decades, and include: increased annual average air temperatures; decreased annual average precipitation; hydrologic alterations; and an increase in frequency, intensity and duration of extreme events, such as floods, droughts and fires. Recent observations, which are concordant with forecasts built, show stream biota of med-regions when facing climate changes tend to be displaced towards higher elevations and upper latitudes, communities tend to change their composition and homogenize, while some life-history traits seem to provide biota with resilience and resistance to adapt to the new conditions (as being short-lived, small, and resistant to low streamflow and desiccation). Nevertheless, such responses may be insufficient to cope with current and future environmental changes. Accurate forecasts of biotic changes and possible adaptations are difficult to obtain in med-regions mainly because of the difficulty of distinguishing disturbances due to natural variability from the effects of climate change, particularly regarding hydrology. Long-term studies are needed to disentangle such variability and improve knowledge regarding the ecological responses and the detection of early warning signals to climate change. Investments should focus on taxa beyond fish and macroinvertebrates, and in covering the less studied regions of Chile and South Africa. Scientists, policy makers and water managers must be involved in the climate change dialogue because the freshwater conservation concerns are huge.

Triggering the generation of an iron(IV)-oxo compound and its reactivity toward sulfides by RuII photocatalysis

The preparation of [FeIV(O)(MePy2tacn)]2+ (2, MePy2tacn = N-methyl-N,N-bis(2-picolyl)-1,4,7-triazacyclononane) by reaction of [FeII(MePy2tacn)(solvent)]2+ (1) and PhIO in CH3CN and its full characterization are described. This compound can also be prepared photochemically from its iron(II) precursor by irradiation at 447 nm in the presence of catalytic amounts of [Ru II(bpy)3]2+ as photosensitizer and a sacrificial electron acceptor (Na2S2O8). Remarkably, the rate of the reaction of the photochemically prepared compound 2 toward sulfides increases 150-fold under irradiation, and 2 is partially regenerated after the sulfide has been consumed; hence, the process can be repeated several times. The origin of this rate enhancement has been established by studying the reaction of chemically generated compound 2 with sulfides under different conditions, which demonstrated that both light and [Ru II(bpy)3]2+ are necessary for the observed increase in the reaction rate. A combination of nanosecond time-resolved absorption spectroscopy with laser pulse excitation and other mechanistic studies has led to the conclusion that an electron transfer mechanism is the most plausible explanation for the observed rate enhancement. According to this mechanism, the in-situ-generated [RuIII(bpy)3] 3+ oxidizes the sulfide to form the corresponding radical cation, which is eventually oxidized by 2 to the corresponding sulfoxide