Mixed solutions of the sine-Gordon equation

The aim of this note is to present an explicit formula for the mixed solution of the sine-Gordon equation, i.e. the solution describing a multisoliton process on a background of multiphase quasi-periodic process.     

Direct synthesis of mixed methylethyllead alkyls

The reactions of lead oxide, sulphide, and chloride with a mixture of dimethyl- and diethyl-aluminium chloride in the presence of Lewis bases have been studied. Mixtures of methylethyllead compounds of the type Me_4-nPbEt_n (0 ? n ? 4) are formed.A reaction path is proposed.     

Evolutionary screening of biomimetic coatings for selective detection of explosives

Susceptibility of chemical sensors to false positive signals remains a common drawback due to insufficient sensor coating selectivity. By mimicking biology, we have demonstrated the use of sequence-specific biopolymers to generate highly selective receptors for trinitrotoluene and 2,4-dinitrotoluene. Using mutational analysis, we show that the identified binding peptides recognize the target substrate through multivalent binding with key side chain amino acid elements. Additionally, our peptide-based receptors embedded in a hydrogel show selective binding to target molecules in the gas phase. These experiments demonstrate the technique of receptor screening in liquid to be translated to selective gas-phase target binding, potentially impacting the design of a new class of sensor coatings.     

Fluorescent composite hydrogels of metal-organic frameworks and functionalized graphene oxide

GO MOFs! Azobenzoic acid functionalized graphene (A-GO) can act as a structure-directing template that influences hydrogel formation together with metal-organic frameworks (MOFs). Zn(2+) MOFs of pyridine derivatives work as framework linkers between the A-GO sheets (MOF-A-GO, see figure). MOF-A-GO exhibits a strong fluorescence enhancement upon gel formation. In addition, MOF-A-GO selectively recognizes trinitrotoluene.     

Organelle-specific zinc detection using zinpyr-labeled fusion proteins in live cells

A protein labeling approach is employed for the localization of a zinc-responsive fluorescent probe in the mitochondria and in the Golgi apparatus of living cells. ZP1, a zinc sensor of the Zinpyr family, was functionalized with a benzylguanine moiety and thus converted into a substrate (ZP1BG) for the human DNA repair enzyme alkylguaninetransferase (AGT or SNAP-Tag). The labeling reaction of purified glutathione S-transferase tagged AGT with ZP1BG and the zinc response of the resulting protein-bound sensor were confirmed in vitro. The new detection system, which combines a protein labeling methodology with a zinc fluorescent sensor, was tested in live HeLa cells expressing AGT in specific locations. The enzyme was genetically fused to site-directing proteins that anchor the probe onto targeted organelles. Localization of the zinc sensors in the Golgi apparatus and in the mitochondria was demonstrated by fluorescence microscopy. The protein-bound fluorescence detection system is zinc-responsive in living cells.     

Determination of adrenolytic drugs by SPME–LC–MS

Five adrenolytic drugs have been analyzed by liquid chromatography–mass spectrometry (LC–MS). Samples were prepared by solid-phase microextraction (SPME) using polypyrrole fibers coated on stainless steel support as an adsorbent for the drugs. Adsorption efficiencies were 95% and were close for all the drugs investigated. Relative standard deviations (RSD), calculated for samples prepared in standard solutions, were in the range 2.5–13%, however RSD values for the drugs in human plasma were 2.5–4.5%. Using LC–MS the limit of detection (LOD) and the limit of quantification (LOQ) were in the ranges 0.11–0.18 and 0.39–0.54 ng mL⁻¹, respectively, for the five drugs.     

Probability measures on [SIN] groups and some related ideals in group algebras

In 1921, Blichfeldt gave an upper bound on the number of integral points contained in a convex body in terms of the volume of the body. More precisely, he showed that , whenever is a convex body containing n + 1 affinely independent integral points. Here we prove an analogous inequality with respect to the surface area F(K), namely . The proof is based on a slight improvement of Blichfeldt’s bound in the case when K is a non-lattice translate of a lattice polytope, i.e., K = t + P, where and P is an n-dimensional polytope with integral vertices. Then we have . Moreover, in the 3-dimensional case we prove a stronger inequality, namely . Authors’ addresses: Martin Henk, Institut für Algebra und Geometrie, Universit?t Magdeburg, Universit?tsplatz 2, D-39106 Magdeburg, Germany; J?rg M. Wills, Mathematisches Institut, Universit?t Siegen, ENC, D-57068 Siegen, Germany     

Random walks on almost connected locally compact groups: Boundary and convergence

We prove that, given an arbitrary spread out probability measure μ on an almost connected locally compact second countable groupG, there exists a homogeneous spaceG/H, called the μ-boundary, such that the space of bounded μ-harmonic functions can be identified withL ^∞ (G/H). The μ-boundary is an amenable contractive homogeneous space. We also establish that the canonical projection onto the μ-boundary of the right random walk of law μ always converges in probability and, whenG is amenable, it converges almost surely. The μ-boundary can be characterised as the largest homogeneous space among those homogeneous spaces in which the canonical projection of the random walk converges in probability.