Formation of the paramagletic Ni(I) π-allyl complex in the Ni(allyl)2 - (2,6-diisopropylphenyl)diazabutadiene system

It has been shown that the reaction of Ni(allyl)₂ with (2,6-diisopropylphenyl)diazabutadiene gives the imino-amide Ni complex (1). The imino-amide moiety of this complex undergoes some complicated rearrangements resulting in spontaneous formation of a paramagnetic π-allyl Ni(I) complex. Nickel complexes formed in the system have been studied with ESR, FTIR, 2D NMR, and mass spectrometry. The structure of complex 1 was studied with X-ray diffraction.     

Combining electrophoresis with detection under ultraviolet light and multiple ultrafiltration for isolation of humic fluorescence fractions

Polyacrylamide gel electrophoresis of chernozem soil humic acids (HAs) followed by observation under UV (312 nm) excitation light reveals new low molecular weight (MW) fluorescent fractions. Ultrafiltration of HAs sample in 7 M urea on a membrane of low nominal MW retention (NMWR, 5 kDa) was repetitively used for separation of fluorescent and non-fluorescent species. Thirty ultrafiltrates and the final retentate R were obtained. Fluorescence maxima of separate ultrafiltrates were different and non-monotonously changed in the range of 475–505 nm. Fluorescence maxima of less than 490 nm were detected only in the four first utrafiltrates. For further physical–chemical analyses all utrafiltrates were combined into a fraction called UF < 5 (NMW < 5 kDa). Retentate R demonstrated very weak fluorescence under 270 nm excitation, while fluorescence intensity of UF < 5 was about six times higher than of the bulk HAs. Fraction UF < 5 was further ultrafiltrated on membranes of MNWR 3 kDa and 1 kDa, yielding three subfractions UF3-5, UF1-3 and UF < 1 with NMW 3–5 kDa, 1–3 kDa and <1 kDa, respectively. The validation of the UF procedure was performed by size exclusion chromatography on Sephadex G-25 column. The fluorescence maxima were found to be at 505, 488 and 465 nm for UF3-5, UF1-3 and UF < 1, respectively, with increasing of fluorescence intensity from UF3-5 to UF1-3 to UF < 1 fraction. EPR analysis showed that the amount of free radicals was the largest in retentate R and drastically decreased in fluorescent ultrafiltrates. The results demonstrate that more than one fluorophore is present in chernozem soil HAs complex.     

Chemical reactions modulated by mechanical stress: extended Bell theory

A number of recent studies have shown that mechanical stress can significantly lower or raise the activation barrier of a chemical reaction. Within a common approximation due to Bell [Science 200, 618 (1978)], this barrier is linearly dependent on the applied force. A simple extension of Bell's theory that includes higher order corrections in the force predicts that the force-induced change in the activation energy will be given by -FΔR - ΔχF(2)∕2. Here, ΔR is the change of the distance between the atoms, at which the force F is applied, from the reactant to the transition state, and Δχ is the corresponding change in the mechanical compliance of the molecule. Application of this formula to the electrocyclic ring-opening of cis and trans 1,2-dimethylbenzocyclobutene shows that this extension of Bell's theory essentially recovers the force dependence of the barrier, while the original Bell formula exhibits significant errors. Because the extended Bell theory avoids explicit inclusion of the mechanical stress or strain in electronic structure calculations, it allows a computationally efficient characterization of the effect of mechanical forces on chemical processes. That is, the mechanical susceptibility of any reaction pathway is described in terms of two parameters, ΔR and Δχ, both readily computable at zero force.     

Metric tangent spaces to Euclidean spaces

We prove that the metric spaces pretangent to a finite-dimensional Euclidean or unitary space E are isometric to E. As a consequence of this result, we describe the metric pretangent spaces at the nonsingular points of smooth surfaces. It is also proved that there exist the spaces pretangent to the Hilbert space l ₂ , which are not isometric to it.     

Perturbed Markov Chains with Damping Component

The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.

     

Numerical solution of the problem of computational time reversal in a quadrant

The problem of computational time reversal is posed as the inverse problem of the determination of an unknown initial condition with a finite support in a hyperbolic equation, given the Cauchy data at the lateral surface. Two such two-dimensional inverse problems are solved numerically in the case when the domain is a quadrant and the Cauchy data are given at finite parts of the coordinate axes. The previously obtained Lipschitz stability estimate implies refocusing of the time-reversed wave field in the case of a small amount of noise in the data. It also indicates the possibility of good performance of a proper numerical method. Such performance is demonstrated in this paper for a particular problem and a particular numerical method.     

Relation of orbital integrals on SO(5) and PGL(2)

We relate the “Fourier” orbital integrals of corresponding spherical functions on thep-adic groups SO(5) and PGL(2). The correspondence is defined by a “lifting” of representations of these groups. This is a local “fundamental lemma” needed to compare the geometric sides of the global Fourier summation formulae (or relative trace formulae) on these two groups. This comparison leads to conclusions about a well known lifting of representations from PGL(2) to PGSp(4). This lifting produces counter examples to the Ramanujan conjecture.     

Photo‐Induced Electron Transfer Between Photosystem 2 via Cross‐linked Redox Hydrogels

Photosystem 2 (PS2) that catalyses light driven water splitting in photosynthesis was ‘wired’ to electrode surfaces via osmium‐containing redox polymers based on poly(vinyl)imidazol. The redox polymer hydrogel worked as both immobilization matrix and electron acceptor for the enzyme. Upon illumination, the enzymatic reaction could be switched on and a catalytic current was observed at the electrode. The catalytic current is directly dependent on the intensity of light used for the excitation of PS2. A typical current density of 45 μA cm^?2 at a light intensity of 2.65 mW cm^?2 could be demonstrated with a significantly improved operational stability.     

The dihydrofuran template approach to furofuran synthesis

Flash vacuum pyrrolysis of vinyl epoxides provides cis-dihydrofuran carboxylic esters in good yields and diastereoselectivities, which, on base-promoted epimerisation afford the complementary trans series. The compounds provide a viable template for a Lewis acid promoted cyclisation to provide the 2,6-diaryl-3,7-dioxabicyclo[3.3.0]octane core found in the furofuran series of natural lignans. This strategy is stereodivergent and can be controlled to provide the exo-exo, exo-endo or endo-endo stereochemistries. The approach has been exemplified in syntheses of the sesamyl furofurans (+/-)-epiasarinin and (+/-)-asarinin.