Numerical solution of vector Sturm–Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter

A numerical-analytical iterative method is proposed for solving generalized self-adjoint regular vector Sturm–Liouville problems with Dirichlet boundary conditions. The method is based on eigenvalue (spectral) correction. The matrix coefficients of the equations are assumed to be nonlinear functions of the spectral parameter. For a relatively close initial approximation, the method is shown to have second-order convergence with respect to a small parameter. Test examples are considered, and the model problem of transverse vibrations of a hinged rod with a variable cross section is solved taking into account its rotational inertia.     

Coordination polymers of rare-earth elements with 2-aminoterephthalic acid

Coordination polymers of REEs with 2-aminoterephthalic acid [Ln₂(C₈H₅NO₄)₃(H₂O)₅] _n · 2nH₂O (Ln = Eu, Gd, or Tb) and [Y₂(C₈H₅NO₄)₃(H₂O)₄] _n · 4nH₂O were prepared by hydrothermal synthesis. Studies of the thermal behavior of these coordination polymers have shown that the removal of the solvate and the coordinated water molecules occurs at heating to 250°C and dehydratation products are stable up to 400°C. Detailed studies of the magnetic behavior of Eu, Gd, and Tb polymers were performed.     

Equilibrium of a system of superconducting rings in a uniform gravitational field

To construct a plasma trap with levitating magnetic coils in the thin ring approximation, we derive the expression for the potential energy of a system of several superconducting rings (one of which is fixed) capturing the preset flows in the uniform gravitational field as a function of the coordinates of the free ring (or rings). Calculations performed in the Mathcad system show that the potential energy of such a system has a local minimum for certain values of parameters. Stable levitation of a superconducting ring in the position corresponding to calculations is realized in the field of another superconducting ring, and this leads to the conclusion that a magnetic Galatea trap can be prepared on the basis of a levitating quadrupole.     

Mononuclear Transition Metal Cymantrenecarboxylates as Precursors for Spinel-Type Manganites

Novel mononuclear cymantrenecarboxylate complexes of transition metals, [Co(H₂O)₆](CymCO₂)₂·4H₂O (Cym = (η⁵-C₅H₄)Mn(CO)₃) (1), [Ni(H₂O)₆](CymCO₂)₂·4H₂O (2), [Zn(H₂O)₆](CymCO₂)₂·4H₂O (3), [Co(CymCO₂)₂(imz)₂] (imz = imidazole, 4), [Co(CymCO₂)₂(bpy)₂]·2PhMe (bpy = 2,2′-bipyridyl, 5), [Ni(CymCO₂)(bpy)₂(H₂O)][CymCO₂]·0.5MePh·2H₂O (6), [Cu(CymCO₂)₂(imz)₂] (7), and [Cu(CymCO₂)₂(bpy)(H₂O)] (8), were obtained and characterized by single-crystal X-ray analysis. Complexes 1–3 are isostructural. Magnetism of the Co complexes 1, 4, and 5 was studied; it was shown that they exhibit the properties of field-induced single-molecule magnets with magnetization reversal barriers (ΔE/k_B) of 44, 13, and 10 K, respectively. Thermal decomposition of complexes 1–8 was studied by means of DSC and TGA methods. The final products of thermolysis of 1–6 in air, according to powder XRD data, are the pure spinel phases MMn₂O₄; for the cases of copper complexes, the mixtures of CuMn₂O₄ and CuO were found in the products.     

Incoherent X-radiation produced by relativistic electrons in crystals

Differential and integral features of incoherent X-radiation, induced by relativistic electrons in crystals, are studied for observation angles θ_γ several times greater than γ^-1, where γ is the projectile Lorentz factor. The existence of sharp maxima and a minimum of the five-folded incoherent differential cross-section as a function of the final electron angles, and a dip minimum when the cross-section is taken as a function of the photon energies, is demonstrated. At near backward observation angles the three-folded cross-section shows a maximum in the region of several keV photon energies. The obtained results allow us to optimize the conditions for coincidence experiments, minimizing the incoherent contribution to the total radiation yield, and helping to analyse results of finite-size detector experiments with crystal targets. Received: 2 July 2001 / Accepted: 26 November 2001     

Mechanism of ethylene hydroformylation on platinum complexes with hydrophosphoryl ligands: a DFT study

The mechanism of ethylene hydroformylation on model organoplatinum hydrides [(R₂PO)₂H]Pt(PR₃)(H)] (R = H, Me, CF₃) was studied within the framework of the density functional theory with the PBE gradient-corrected functional and the TZ2p basis set. The presence of a free coordination site in these square-planar 16-electron platinum complexes provides the possibility of alkene coordination in the first step without energetically unfavorable dissociation of one of the metal-ligand bonds. High strength of the —PR₂O—H....O—R₂ hydrogen bond results in the formation of a bidentate ligand in the coordination sphere of the metal atom. This ligand makes the geometry of the catalytic center rigid, thus enhancing the regioselectivity of the process. The proton can reversibly migrate with ease within the —PR₂O—H... O—R₂ hydrogen bond, thus providing fine adjustment of the electron density in the catalytic center in each reaction step and acting as a molecular switch. The rate-limiting step in the hydroformylation is the CO insertion into the Pt-Et σ-bond. Electron-donating Me groups at the phosphorous atoms hamper, while electron-withdrawing CF₃ groups facilitate, the process.     

NanoFAST: structure-based design of a small fluorogen-activating protein with only 98 amino acids

One of the essential characteristics of any tag used in bioscience and medical applications is its size. The larger the label, the more it may affect the studied object, and the more it may distort its behavior. In this paper, using NMR spectroscopy and X-ray crystallography, we have studied the structure of fluorogen-activating protein FAST both in the apo form and in complex with the fluorogen. We showed that significant change in the protein occurs upon interaction with the ligand. While the protein is completely ordered in the complex, its apo form is characterized by higher mobility and disordering of its N-terminus. We used structural information to design the shortened FAST (which we named nanoFAST) by truncating 26 N-terminal residues. Thus, we created the shortest genetically encoded tag among all known fluorescent and fluorogen-activating proteins, which is composed of only 98 amino acids.

We solved the structure of a fluorogen-activating protein FAST and synthesized the library of potential fluorogens. Using these data, we designed the shortest genetically encoded fluorescent tag among all known.