Abstract: The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.

Abstract: The ability of metal-organic frameworks (MOFs) to gelate under specific synthetic conditions opens up new opportunities in the preparation and shaping of hierarchically porous MOF monoliths, which could be directly implemented for catalytic and adsorptive applications. In this work, we present the first examples of xero-or aerogel monoliths consisting solely of nanoparticles of several prototypical Zr4+-based MOFs: UiO-66-X (X – H, NH2, NO2, (OH)(2)), UiO-67, MOF-801, MOF-808 and NU-1000. High reactant and water concentrations during synthesis were observed to induce the formation of gels, which were converted to monolithic materials by drying in air or supercritical CO2. Electron microscopy, combined with N-2 physisorption experiments, was used to show that irregular nanoparticle packing leads to pure MOF monoliths with hierarchical pore systems, featuring both intraparticle micropores and interparticle mesopores. Finally, UiO-66 gels were shaped into monolithic spheres of 600 mm diameter using an oil-drop method, creating promising candidates for packed-bed catalytic or adsorptive applications, where hierarchical pore systems can greatly mitigate mass transfer limitations.

Abstract: The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization.

Abstract: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.