A comprehensive investigation of the chemistry and basicity of a parent amidoruthenium complex

trans-(DMPE)(2)Ru(H)(NH(2)) (1) dehydrogenates cyclohexadiene and 9,10-dihydroanthracene to yield benzene (or anthracene), (DMPE)(2)Ru(H)(2), and ammonia. Addition of fluorene to 1 results in the formation of the ion pair [trans-(DMPE)(2)Ru(H)(NH(3))(+)][A(-)] (A(-) = fluorenide, 4a). Complex 1 also reacts with weak acids A-H (A-H = phenylacetylene, 1,2-propadiene, phenylacetonitrile, 4-(alpha,alpha,alpha-trifluoromethyl)phenylacetonitrile, cyclobutanone, phenol, p-cresol, aniline) to form ammonia and trans-(DMPE)(2)Ru(H)(A) (7, 8, 9a, 9b, 10, 11b, 11c, 12, respectively). In the cases where A-H = phenylacetylene, cyclobutanone, aniline, phenol, and p-cresol, the reaction was observed to proceed via ion pairs analogous to 4a. Compound 1 is reactive toward even weaker acids such as toluene, propylene, ammonia, cycloheptatriene, and dihydrogen, but in these cases deuterium labeling studies revealed that only H/D exchange between A-H and the ND(2) group is observed, rather than detectable formation of ion pairs or displacement products. Addition of triphenylmethane to 1 results in the formation of an equilibrium mixture of 1, triphenylmethane, and the ruthenium/triphenylmethide ion pair 4h. If the energetics of ion-pair association are ignored, this result indicates that the basicity of 1 is similar to that of triphenylmethide. All these observations support the conclusion that the NH(2) group in amido complex 1 is exceptionally basic and as a result prefers to abstract a proton rather than a hydrogen atom from a reactive C-H bond. The energetics and mechanism of these proton-transfer and -exchange reactions are analyzed with the help of DFT calculations.     

Periodic and Homoclinic Solutions of Extended Fisher–Kolmogorov Equations

In this paper we study the existence of periodic solutions of the fourth-order equations u^iv − pu″ − a(x)u + b(x)u³ = 0 and u^iv − pu″ + a(x)u − b(x)u³ = 0, where p is a positive constant, and a(x) and b(x) are continuous positive 2L-periodic functions. The boundary value problems (P₁) and (P₂) for these equations are considered respectively with the boundary conditions u(0) = u(L) = u″(0) = u″(L) = 0. Existence of nontrivial solutions for (P₁) is proved using a minimization theorem and a multiplicity result using Clark's theorem. Existence of nontrivial solutions for (P₂) is proved using the symmetric mountain-pass theorem. We study also the homoclinic solutions for the fourth-order equation u^iv + pu″ + a(x)u − b(x)u² − c(x)u³ = 0, where p is a constant, and a(x), b(x), and c(x) are periodic functions. The mountain-pass theorem of Brezis and Nirenberg and concentration-compactness arguments are used.     

On the Secant method under generalized Lipschitz conditions for the divided difference operator

In this work we introduce for the first time the generalized Lipschitz conditions for the divided difference operator. A positive integrable function, partial case of which is usual Lipschitz constant, is suggested. Under the given conditions the convergence of the Secant method for solving the operator equations in Banach spaces is investigated, the uniqueness ball for the solution is obtained. As a partial case the known results for the Lipschitz constants are received. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic Anisotropy in “Scorpionate” First‐Row Transition‐Metal Complexes: A Theoretical Investigation

In this work we have analyzed in detail the magnetic anisotropy in a series of hydrotris(pyrazolyl)borate (Tp^?) metal complexes, namely [VTpCl]⁺, [CrTpCl]⁺, [MnTpCl]⁺, [FeTpCl], [CoTpCl], and [NiTpCl], and their substituted methyl and tert‐butyl analogues with the goal of observing the effect of the ligand field on the magnetic properties. In the [VTpCl]⁺, [CrTpCl]⁺, [CoTpCl], and [NiTpCl] complexes, the magnetic anisotropy arises as a consequence of out‐of‐state spin–orbit coupling, and covalent changes induced by the substitution of hydrogen atoms on the pyrazolyl rings does not lead to drastic changes in the magnetic anisotropy. On the other hand, much larger magnetic anisotropies were predicted in complexes displaying a degenerate ground state, namely [MnTpCl]⁺ and [FeTpCl], due to in‐state spin–orbit coupling. The anisotropy in these systems was shown to be very sensitive to perturbations, for example, chemical substitution and distortions due to the Jahn–Teller effect. We found that by substituting the hydrogen atoms in [MnTpCl]⁺ and [FeTpCl] by methyl and tert‐butyl groups, certain covalent contributions to the magnetic anisotropy energy (MAE) could be controlled, thereby achieving higher values. Moreover, we showed that the selection of ion has important consequences for the symmetry of the ground spin–orbit term, opening the possibility of achieving zero magnetic tunneling even in non‐Kramers ions. We have also shown that substitution may also contribute to a quenching of the Jahn–Teller effect, which could significantly reduce the magnetic anisotropy of the complexes studied.     

Bifurcations in basic models of delayed force control

Nonlinear Dynamics - Basic single-degree-of-freedom mechanical models of force control are presented to achieve desired contact forces between actuators and objects. Nonlinear governing equations...     

Novel Template Sorbents for Separation of Americium(III) from Nitric Acid Solutions: Search of Optimal Ion‐Imitator of AmIII

A series of new template sorbents that enable selective and effective sorption of Am^III from 0.5 to 4M HNO₃ solutions containing high concentrations of Fe^III and Zr^IV was synthesized from (ethenyl)(diphenyl)phosphine oxide. La^III, Ce^III, and Pr^III were used as template elements imitating the properties of Am^III. The highest efficiency of separation of Am^III from high amounts of Fe^III and Zr^IV was displayed by the Ce^III‐based sorbent.     

Delay-induced bifurcations in collocated position control of an elastic arm

The interference of the elasticity of a single robotic arm and the unavoidable time delay of its position control is analysed from nonlinear vibrations viewpoint. The simplified mechanical model of two blocks and a connecting spring considers the first vibration mode of the arm, while the collocated proportional-derivative (PD) control uses the state of the first block only and actuates also there. It is assumed that the relevant nonlinearity is the saturation of the delayed control force. The linear stability analysis proves that stabilizable and non-stabilizable parameter regions follow each other periodically even for large spring stiffnesses and for tiny time delays. Hopf bifurcation calculation is carried out after an infinite-dimensional centre manifold reduction, and closed-form algebraic expressions are given for the amplitudes of the emerging oscillations. These results support the experimental tuning of the control gains since the parameters of the arising and often unexpected self-excited vibrations can serve as a guide for this practical procedure.

     

Structural and optical characterization of colloidal Se nanoparticles prepared via the acidic decomposition of sodium selenosulfate

Colloidal selenium nanoparticles (NPs) were synthesized via acidic decomposition of sodium selenosulfate. The effects of synthesis and post-synthesis treatment conditions on the size, structure and size distribution of the Se nanoparticles are discussed. It is shown that the decomposition of sodium selenosulfate with non-oxidative acids (e.g., HCl) in aqueous solutions of polymers (sodium polyphosphate, gelatin, polyvinyl alcohol, polyethyleneglycole) and surfactants (sodium dodecylsulfonate, cetylpyridinium chloride) results in the formation of amorphous 25–200 nm Se nanoparticles converting upon ageing at 90 °C into trigonal 150–250 nm Se nanocrystals. Optical properties (absorption and Raman spectra) of freshly prepared and aged Se nanoparticles both in colloidal solutions and in polymeric (polyvinyl alcohol) films are analyzed.