Helical solitons in vector modified Korteweg–de Vries equations

We study existence of helical solitons in the vector modified Korteweg–de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations.     

Saint-Venant problem for solids with helical anisotropy

We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters.     

The investigation of the bitumen from ancient Greek amphora using FT ICR MS,H/D exchange and novel spectrum reduction approach.

Recently Russian archeologists have discovered on Taman peninsula an ancient (V B.C.) Greek amphora full of dense bitumen. This is the oldest amphora in the world that contains bitumen. We report the investigation of this bitumen using ultrahigh resolution Fourier transform mass spectrometry. Also we used recently developed in‐ESI source Hydrogen/Deuterium exchange approach for the structural characterization of the individual molecules and estimation of the biodegradation of the bitumen. The increase of number of the labile hydrogens compared to the non‐degraded oil can serve as an additional evidence of the degradation of bitumen via oxidation. For the facilitation of the spectrum processing we have developed the special iterative spectrum reduction approach. It was observed that molecules that have only oxygen heteroatoms possess two –OH groups what is unusual for the petroleum. Based on this we suggested that the bitumen degraded during its being in amphora for 2500 years. Copyright © 2016 John Wiley & Sons, Ltd.     

Explicit Semi-invariants and Integrals of the Full Symmetric {\mathfrak{sl}_n} Toda Lattice

We show how to construct semi-invariants and integrals of the full symmetric \({\mathfrak{sl}_n}\) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates in the corresponding projective spaces. Then we use these semi-invariants to construct the integrals. The existence of additional integrals which constitute a full set of independent non-involutive integrals was known but the chopping and Kostant procedures have crucial computational complexities already for low-rank Lax matrices and are practically not applicable for higher ranks. Our new approach solves this problem and results in simple explicit formulae for the full set of independent semi-invariants and integrals expressed in terms of the Lax matrix and its eigenvectors, and of eigenvalue matrices for the full symmetric \({\mathfrak{sl}_n}\) Toda lattice.     

Fragmentation methods on the balance: unambiguous top–down mass spectrometric characterization of oxaliplatin–ubiquitin binding sites

The interaction between oxaliplatin and the model protein ubiquitin (Ub) was investigated in a top–down approach by means of high-resolution electrospray ionization mass spectrometry (ESI-MS) using diverse tandem mass spectrometric (MS/MS) techniques, including collision-induced dissociation (CID), higher-energy C-trap dissociation (HCD), and electron transfer dissociation (ETD). To the best of our knowledge, this is the first time that metallodrug–protein adducts were analyzed for the metal-binding site by ETD-MS/MS, which outperformed both CID and HCD in terms of number of identified metallated peptide fragments in the mass spectra and the localization of the binding sites. Only ETD allowed the simultaneous and exact determination of Met1 and His68 residues as binding partners for oxaliplatin. CID-MS/MS experiments were carried out on orbitrap and ion cyclotron resonance (ICR)-FT mass spectrometers and both instruments yielded similar results with respect to number of metallated fragments and the localization of the binding sites. A comparison of the protein secondary structure with the intensities of peptide fragments generated by collisional activation of the [Ub + Pt-(chxn)] adduct [chxn = (1R,2R)-cyclohexanediamine] revealed a correlation with cleavages in solution phase random coil areas, indicating that the N-terminal β-hairpin and α-helix structures are retained in the gas phase.     

Nanoprobes for intracellular and single cell surface‐enhanced Raman spectroscopy (SERS)

Surface‐enhanced Raman spectroscopy (SERS) is a promising and powerful label free technique for high resolution analysis of single cells. For intracellular analysis, there is a need for SERS‐active nanoprobes that are minimally invasive to cells, do not affect cell viability, and provide reproducible signals. This work reviews the state‐of‐the‐art tools currently available for intracellular SERS. Various types of SERS probes are considered, including colloidal gold and silver nanoparticles, metallized optical fibers, and tip‐enhanced Raman probes. We also discuss recently developed SERS‐active nanopipettes implemented on the basis of pulled glass microcapillaries. Finally, the critical aspects of selecting an optimal SERS nanoprobe for single‐cell analysis depending on a particular application are summarized. Copyright © 2012 John Wiley & Sons, Ltd.     

Highly functionalized bridged silsesquioxanes

The objective of this work was to synthesize functionalized mesoporous silsesquioxanes with high concentrations of amine groups. During typical sol–gel syntheses, these materials are obtained by co-condensation of organic precursors with suitable linkers, such as tetraethoxysilane, necessary to prevent the mesoporous structure from collapsing. Thus, concentrations of amine groups in organosilicas usually do not exceed 2.7–3.4 mmol g⁻¹. The use of bridged bis-trimethoxysilanes, however, allowed formation of mesoporous materials with no linker. Polycondensation of bis-trimethoxysilanes containing amine groups was conducted in acidic, neutral and basic media, resulting in high yields of solid bridged silsesquioxanes. Gelation occurred quickly if no acid or base was added to the reaction mixture. The hybrid organic/inorganic nature of obtained materials was confirmed by FT-IR and MAS CP NMR spectroscopy. Elemental analysis showed that amino group concentration in the products was 3.3–4.1 mmol g⁻¹. Measurement of particle size distribution confirmed that choice of reaction media significantly affects particle sizes and agglomeration degrees, with the largest agglomerates (up to 50 μm) formed in basic media. A morphology study, using small-angle X-Ray scattering, displayed two-level fractal structures composed of aggregated 6.5–10.5 nm particles. Reactions in the presence of a surfactant resulted in formation of mesoporous structures. Furthermore, the obtained bridged silsesquioxanes were thermally stable down to 260 °C, but could reversibly absorb water and CO₂ at temperatures below 120 °C. Thus, condensation of the bridged precursor without a linker resulted in formation of a highly functionalized mesoporous material.     

Dynamically Harmonized FT-ICR Cell with Specially Shaped Electrodes for Compensation of Inhomogeneity of the Magnetic Field. Computer Simulations of the Electric Field and Ion Motion Dynamics

The recently introduced ion trap for FT-ICR mass spectrometers with dynamic harmonization showed the highest resolving power ever achieved both for ions with moderate masses 500?C1000?Da (peptides) as well as ions with very high masses of up to 200?kDa (proteins). Such results were obtained for superconducting magnets of very high homogeneity of the magnetic field. For magnets with lower homogeneity, the time of transient duration would be smaller. In superconducting magnets used in FT-ICR mass spectrometry the inhomogeneity of the magnetic field in its axial direction prevails over the inhomogeneity in other directions and should be considered as the main factor influencing the synchronic motion of the ion cloud. The inhomogeneity leads to a dependence of the cyclotron frequency from the amplitude of axial oscillation in the potential well of the ion trap. As a consequence, ions in an ion cloud become dephased, which leads to signal attenuation and decrease in the resolving power. Ion cyclotron frequency is also affected by the radial component of the electric field. Hence, by appropriately adjusting the electric field one can compensate the inhomogeneity of the magnetic field and align the cyclotron frequency in the whole range of amplitudes of z-oscillations. A method of magnetic field inhomogeneity compensation in a dynamically harmonized FT-ICR cell is presented, based on adding of extra electrodes into the cell shaped in such a way that the averaged electric field created by these electrodes produces a counter force to the forces caused by the inhomogeneous magnetic field.     

On parameter estimation of threshold autoregressive models

This paper studies the threshold estimation of a TAR model when the underlying threshold parameter is a random variable. It is shown that the Bayesian estimator is consistent and its limit distribution is expressed in terms of a limit likelihood ratio. Furthermore, convergence of moments of the estimators is also established. The limit distribution can be computed via explicit simulations from which testing and inference for the threshold parameter can be conducted. The obtained results are illustrated with numerical simulations.     

Polariton-assisted manipulation of energy relaxation pathways: donor–acceptor role reversal in a tuneable microcavity

Resonant interaction between excitonic transitions of molecules and localized electromagnetic field allows the formation of hybrid light–matter polaritonic states. This hybridization of the light and the matter states has been shown to significantly alter the intrinsic properties of molecular ensembles placed inside the optical cavity. Here, we have observed strong coupling of excitonic transition in a pair of closely located organic dye molecules demonstrating an efficient donor-to-acceptor resonance energy transfer with the mode of a tuneable open-access cavity. Analysing the dependence of the relaxation pathways between energy states in this system on the cavity detuning, we have demonstrated that predominant strong coupling of the cavity photon to the exciton transition in the donor dye molecule can lead not only to an increase in the donor–acceptor energy transfer, but also to an energy shift large enough to cause inversion between the energy states of the acceptor and the mainly donor lower polariton energy state. Furthermore, we have shown that the polariton-assisted donor–acceptor chromophores'' role reversal or “carnival effect” not only changes the relative energy levels of the donor–acceptor pair, but also makes it possible to manipulate the energy flow in the systems with resonant dipole–dipole interaction and direct energy transfer from the acceptor to the mainly donor lower polariton state. Our experimental data are the first confirmation of the theoretically predicted possibility of polariton-assisted energy transfer reversal in FRET systems, thus paving the way to new avenues in FRET-imaging, remote-controlled chemistry, and all-optical switching.

Polariton-assisted donor–acceptor role reversal in resonant energy transfer between organic dyes tagged with the terminus of the closed oligonucleotide-based molecular beacon strongly coupled to electromagnetic modes of a tuneable microcavity.