Breather-like solution of the Korteweg-de Vries equation

A new real singular solution of the Korteweg-de Vries equation is briefly described. It is shown that the spectrum of the associated linear problem consists of a pair of complex conjugate eigenvalues. The existence of constants of motion and eigenfunction normalization integral is also discussed.     

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.     

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.     

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.     

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     

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.     

Fishbone-like instability in a looped-tube thermoacoustic engine

Quasi-periodic bursts of acoustic oscillations were observed during the start-up process in a looped-tube thermoacoustic engine. The acoustic oscillations have a constant frequency of 111 Hz, while the bursts have "quasi-periods" in the order of 14-25 s. The quasi-periodic bursts show a new mode of amplitude growth in this thermoacoustic engine. The envelope of the acoustic oscillations has a fishbone-like shape. The nature of the observed fishbone-like instabilities suggests a strong interaction between the acoustic and temperature field.     

Determination of loads applied perpendicularly to the outer boundary of a ring using coefficients of influence

A procedure is explained to determined the amount of several pairs of diametrical loads applied to the outside boundary of a ring when stresses at selected points of the inside or outside boundaries are known. Coefficients of influence are used, following an approach similar to the one presented in a previous paper. Examples of application are given and the possible increase in precision is shown when the number of points of measurements is larger than the number of loads to be determined.