The Nevo–Zimmer intermediate factor theorem over local fields

The Nevo–Zimmer theorem classifies the possible intermediate G-factors Y in Open image in new window , where G is a higher rank semisimple Lie group, P a minimal parabolic and X an irreducible G-space with an invariant probability measure. An important corollary is the Stuck–Zimmer theorem, which states that a faithful irreducible action of a higher rank Kazhdan semisimple Lie group with an invariant probability measure is either transitive or free, up to a null set. We present a different proof of the first theorem, that allows us to extend these two well-known theorems to linear groups over arbitrary local fields.     

A Voltage-Responsive Synthetic Cl−-Channel Regulated by pH

Transmembrane protein channels are an important inspiration for the design of artificial ion channels. Their dipolar structure helps overcome the high energy barrier to selectively translocate water and ions sharing one pathway, across the cell membrane. Herein, we report that the amino-imidazole (Imu) amphiphiles self-assemble via multiple H-bonding to form stable artificial Cl⁻-channels within lipid bilayers. The alignment of water/Cl⁻ wires influences the conduction of ions, envisioned to diffuse along the hydrophilic pathways; at acidic pH, Cl⁻/H⁺ symport conducts along a partly protonated channel, while at basic pH, higher Cl⁻/OH⁻ antiport translocate through a neutral channel configuration, which can be greatly activated by applying strong electric field. This voltage/pH regulated channel system represents an unexplored alternative for ion-pumping along artificial ion-channels, parallel to that of biology.     

Adiabatic frequency conversion of ultrafast pulses

A new method for efficient, broadband sum and difference frequency generation of ultrafast pulses is demonstrated. The principles of the method follow from an analogy between frequency conversion and coherent optical excitation of a two-level system. For conversion of ultrafast pulses, the concepts of adiabatic conversion are developed further in order to account for dispersion and group velocity mismatch. The scheme was implemented using aperiodically poled nonlinear crystals and a single step nonlinear mixing process, leading to conversion of near-IR (∼790 nm) ultrafast pulses into the blue (∼450 nm) and mid-IR (∼3.15 μm) spectral regions. Conversion bandwidths up to 15 THz FWHM and efficiencies up to 50% are reported.     

Surface modification and characterization of thermoplastic polyurethane

This work reports the modification of thermoplastic polyurethanes (TPUs) in order to enlarge their application range, for example, as biomaterials by increasing its hydrophilicity.A TPU was successfully modified by using three different strategies: ultra-violet irradiation (UV), gamma irradiation (GI) and interfacial modification (IM). The results suggested the possibility of modifying the polyurethane-based surface either with poly(ethylene glycol) (PEG) or hydroxylethyl methacrylate (HEMA) or hexamethylene diamine (HMD) or chitosan (CT) by using any of these methods. The properties of the grafted PU were evaluated by surface, structural and thermal analysis. The results suggest that, among the methods studied in this work, the modification by gamma irradiation (GI) seems to be the most promising, since this method gives high values of grafting yield and has the advantage of providing a clean modification, meaning that no initiator is needed.     

Optimal location with equitable loads

The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and for the special cases of the problem on a tree or on a path. The complexity of the problem is analyzed, O(n) algorithms and an O(pn ³) dynamic programming algorithm are proposed for the problem on a path respectively for p=2 and p>2 facilities. Heuristic algorithms (two types of a steepest descent approach and tabu search) are proposed for its solution. Extensive computational results are presented.     

A note on medieval microfabrication: the visualization of a prayer nut by synchrotron‐based computer X‐ray tomography

One of the most fascinating objects in the Rijksmuseum (Amsterdam, The Netherlands) is an early 16th century prayer nut. This spherical wooden object measures 4 cm in diameter and consists of two hemispheres connected with a small hinge so that it can be opened. The interior of the nut holds wood carvings with scenes from the life of Christ. These miniature reliefs show an incredible degree of finish with carving details well beyond the millimetre scale. In the present paper it is shown how synchrotron‐based computer X‐ray tomography revealed the structure and fabrication method of the bead. The central part of the relief was cut from a single piece of wood, rather than assembled from multiple components, underlining the extraordinary manual dexterity of its maker. In addition, a piece of fibrous material contained in the inner structure of the bead is revealed. This may have served as a carrier for an odorous compound, which would be in line with the religious function of the prayer nut.