Controlling Internal Pore Sizes in Bicontinuous Polymeric Nanospheres

Complex polymeric nanospheres were formed in water from comb‐like amphiphilic block copolymers. Their internal morphology was determined by three‐dimensional cryo‐electron tomographic analysis. Varying the polymer molecular weight (MW) and the hydrophilic block weight content allowed for fine control over the internal structure. Construction of a partial phase diagram allowed us to determine the criteria for the formation of bicontinuous polymer nanosphere (BPN), namely for copolymers with MW of up to 17 kDa and hydrophilic weight fractions of ≤0.25; and varying the organic solvent to water ratio used in their preparation allowed for control over nanosphere diameters from 70 to 460 nm. Significantly, altering the block copolymer hydrophilic–hydrophobic balance enabled control of the internal pore diameter of the BPNs from 10 to 19 nm.     

Live encapsulation of a Keggin polyanion in NH2-MIL-101(Al) observed by in situ time resolved X-ray scattering

The templating effect of the Keggin polyanion derived from phosphotungstic acid (PTA) during the synthesis of NH(2)-MIL-101(Al) has been investigated by means of in situ SAXS/WAXS. Kinetic analysis and structural observations demonstrate that PTA acts as a nucleation site and that it stabilizes the precursor phase NH(2)-MOF-235(Al). Surprisingly kinetics of formation are little changed.     

Evaluation of Pt and Re oxidation state in a pressurized reactor: difference in reduction between gas and liquid phase

Determination of metal oxidation state under relevant working conditions is crucial to understand catalytic behaviour. The reduction behaviour of Pt and Re was evaluated simultaneously as a function of support and solvent in a pressurized reactor (autoclave). The bimetallic catalysts are used in selective hydrogenation of carboxylic acids and amides. Gas phase reduction reduced the metals more efficiently, in particular Pt.     

Study of the chemical mechanism involved in the formation of tungstite in benzyl alcohol by the advanced QEXAFS technique

Insight into the complex chemical mechanism for the formation of tungstite nanoparticles obtained by the reaction of tungsten hexachloride with benzyl alcohol is presented herein. The organic and inorganic species involved in the formation of the nanoparticles were studied by time-dependent gas chromatography and X-ray diffraction as well as by time-resolved in situ X-ray absorption near-edge structure and extended X-ray absorption fine structure spectroscopy. Principal component analysis revealed two intermediates, which were identified as WCl(4) and WOCl(4) by using linear combination analysis. Quick-scanning extended X-ray absorption fine structure spectroscopy enabled the time-dependent evolution of the starting compound, the intermediates and the product to be monitored over the full reaction period. The reaction starts with fast chlorine substitution and partial reduction during the dissolution of the tungsten hexachloride in benzyl alcohol followed by the generation of intermediates with W=O double bonds and finally the construction of the W-O-W network of the tungstite structure.     

Uniformly convex Banach spaces are reflexive—constructively

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman‐Pettis theorem that uniformly convex Banach spaces are reflexive.     

Detection of Wave Front Set Perturbations via Correlation: Foundation for Wave-equation Tomography

We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with respect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of wave field correlations. We investigate its theoretical foundation in simple mathematical case studies using the distribution theoretic definition of oscillatory integrals.     

Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension

For a polyhedron $P$ P let $B(P)$ B ( P ) denote the polytopal complex that is formed by all bounded faces of $P$ P . If $P$ P is the intersection of $n$ n halfspaces in $\mathbb R ^D$ R D , but the maximum dimension $d$ d of any face in $B(P)$ B ( P ) is much smaller, we show that the combinatorial complexity of $P$ P cannot be too high; in particular, that it is independent of $D$ D . We show that the number of vertices of $P$ P is $O(n^d)$ O ( n d ) and the total number of bounded faces of the polyhedron is $O(n^{d^2})$ O ( n d 2 ) . For inputs in general position the number of bounded faces is $O(n^d)$ O ( n d ) . We show that for certain specific values of $d$ d and $D$ D , our bounds are tight. For any fixed $d$ d , we show how to compute the set of all vertices, how to determine the maximum dimension of a bounded face of the polyhedron, and how to compute the set of bounded faces in polynomial time, by solving a number of linear programs that is polynomial in  $n$ n .     

Parabolically Induced Representations of Graded Hecke Algebras

We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained by induction from a discrete series representation of a parabolic subalgebra. We determine all intertwining operators between such parabolically induced representations, and use them to parametrize the irreducible representations. Finally we describe the spectrum of a graded Hecke algebra as a topological space.