Although the advent of microwave technologies has both improved and accelerated tissue processing for microscopy, there still remain many limitations in conventional chemical fixation, dehydration, embedding, and sectioning, particularly with regard to plant materials. The Proteaceae, a family of plants widely distributed in the Southern Hemisphere and well adapted to harsh climates and nutrient-poor soils, is a perfect example; the complexity of Proteaceae leaves means that almost no ultrastructural data are available as these are notoriously difficult to both infiltrate and section. Here, a step-by-step protocol is described that allows for the successful preparation of Banksia prionotes (Australian Proteaceae) leaves for both light and transmission electron microscopy. The method, which applies a novel combination of vibratome sectioning, microwave processing and vacuum steps, and the utilization of an ultra low viscosity resin, results in highly reproducible, well-preserved, sectionable material from which very high-quality light and electron micrographs can be obtained. With this, cellular ultrastructure from the level of a leaf through to organelle substructure can be studied. This approach will be widely applicable, both within and outside of the plant sciences, and can be readily adapted to meet specific sample requirements and imaging needs.

The taxonomic history of the genus Podocarpus (Podocarpaceae) is reviewed as the first part of a revision of the genus. The major taxonomic and other works relating to the genus published during nine time periods (before 1800, 1800–1850, 1851–1875, 1876–1900, 1901–1926, 1927–1947, 1948–1967, 1968–1987 and 1988–present) are briefly but critically discussed. Three landmark works are those by Pilger (1903), Buchholz and Gray (between 1948 and 1962) and de Laubenfels (1985). The paper ends with an outline plan of the revision of the genus to which the paper forms an introduction.

We review recent stability and separation results in volume comparison problems and usethem to prove several hyperplane inequalities for intersection and projection bodies.

The inner knowledge of volumes from imagesis an ancient problem. This question becomes complicated when itconcerns quantization, as the case of any measurement and inparticular the calculation of fractal dimensions. Trabecular bonetissues have, like many natural elements, an architecture whichshows a fractal aspect. Many studies have already been developedaccording to this approach. The question which arises however is toknow to which extent it is possible to get an exact determination ofthe fractal dimension of a given volume only from the fractalmeasurement made on the projections or slice images given by medicalimaging. This paper gives general results about the Minkowskidimensions and contents of projections and sections of a set. Wealso show with examples that they depend essentially on thedirections of the planes and so there is - in general case - norelation between 3D and 2D fractal dimensions. This consideration isthen illustrated with examples from synthetic models and from CTscan images of wrists. In conclusion, this study reveals that thequantitative characterization of an organic volume (in particularosseous) requires taking into account the whole volume, and not onlysome of its slices or projections.