Optimal lower bounds for cubature error on the sphere

We show that the worst-case cubature error E(Q_m;H^s) of an m-point cubature rule Q_m for functions in the unit ball of the Sobolev space H^s=H^s(S²),s>1, has the lower bound , where the constant c_s is independent of Q_m and m. This lower bound result is optimal, since we have established in previous work that there exist sequences of cubature rules for which with a constant independent of n. The method of proof is constructive: given the cubature rule Q_m, we construct explicitly a ‘bad’ function f_mH^s, which is a function for which Q_mf_m=0 and . The construction uses results about packings of spherical caps on the sphere.     

Convenient synthetic route of versatile 21-monothiatetraphenylporphyrins of the A4 and AB3 type

A novel convenient synthetic route for poly-functional 21-monothiatetraphenylporphyrins of the type A₄ und AB₃ having base labile substituents in meso position was developed. Using this method a series of symmetric and asymmetric 21-thiaporphyrins containing different functional groups at the meso position is reported. The new products were characterized by NMR, UV-Vis and mass spectroscopy.     

Heterotrimeric liquid crystalline thiadiazole derivatives

Various trimeric co-oligomers combining 2-phenyl-1,3,4-thiadiazole mesogenic moieties with a biphenyl mesogenic moiety were synthesized and their mesomorphic behaviour investigated by polarizing microscopy, calorimetry and X-ray scattering. Such co-oligomeric structures provide an opportunity to combine different mesogenic units. Thus readily accessible homochiral biphenyl mesogenic units were connected with thiadiazole mesogenic units leading to an oligomeric liquid crystal material with ferroelectric properties.     

Detection of laser induced dielectric breakdown in water using a laser doppler vibrometer

This study is focused on exploring the feasibility of an all-optic surface scanning method in determining the size and position of a submerged, laser generated, optoacoustic (OA) source. The optoacoustic effect in this case was generated when the absorption of a short electromagnetic pulse in matter caused a dielectric breakdown, a plasma emission flash and a subsequent acoustic wave. In the experiment, a laser pulse with λ = 1064 nm and 12 ns pulse length was aimed at a volume of deionized water. When the laser beam was focused by a f = 16 mm lens, a single dielectric breakdown spot occurred. When a f = 40 mm was used several breakdowns in a row were induced. The breakdowns were photographed using a double shutter camera. The acoustic wave generated by the dielectric breakdowns were detected at a point on the water surface using a laser Doppler vibrometer (LDV). First, the LDV signal was used to calculate the speed of sound with an accuracy of 10 m/s. Secondly, the location and length of the dielectric breakdown was calculated with an accuracy of 1 mm. The calculated position matched the breakdown location recorded by a camera. The results show that it is possible to use LDV surface measurements from a single spot to determine both the position and length of the OA source as well as the speed of sound in the medium. Furthermore, the LDV measurements also show a secondary peak that originates from the OA source. To unravel the origin and properties of this interesting feature, further investigations are necessary     

Antiviral activity of Engystol<Superscript>®</Superscript> and Gripp-Heel<Superscript>®</Superscript>: an in-vitro assessment

Background  

Infections with respiratory viruses can activate the innate immune response - an important host defence mechanism in the early stage of viral infection. Interferon (IFN) release, triggered by virus infection, is an important factor in establishing an antiviral state, where IFN activation occurs prior to the onset of the adaptive immune response.     

Monitoring of fluid motion in a micromixer by dynamic NMR microscopy

The velocity distribution of liquid flowing in a commercial micromixer has been determined directly by using pulsed-field gradient NMR. Velocity maps with a spatial resolution of 29 microm x 43 microm were obtained by combining standard imaging gradient units with a homebuilt rectangular surface coil matching the mixer geometry. The technique provides access to mixers and reactors of arbitrary shape regardless of optical transparency. Local heterogeneities in the signal intensity and the velocity pattern were found and serve to investigate the quality and functionality of a micromixer, revealing clogging and inhomogeneous flow distributions.