Nonstationary Stokes system in weighted Sobolev spaces

We consider an initial‐boundary value problem for nonstationary Stokes system in a bounded domain Omega??³ with slip boundary conditions. We assume that Ω is crossed by an axis L. Let us introduce the following weighted Sobolev spaces with finite norms: and where ?(x) = dist{x, L}. We proved the result. Given the external force f∈L_{2, ?µ}(Ω^T), initial velocity v₀∈H(Ω), µ∈?₊\? there exist velocity v∈H(Ω^T) and the pressure p, ?p∈L_{2, ?µ}(Ω^T) and a constant c, independent of v, p, f, such that As we consider the Stokes system in weighted Sobolev spaces the following two things must be used:

• 1. the slip boundary condition and
• 2. the Helmholtz–Weyl decomposition.

Copyright © 2010 John Wiley & Sons, Ltd.     

Ultrafast nonadiabatic dynamics of [Fe(II)(bpy)(3)](2+) in solution

The ultrafast relaxation of aqueous iron(II)-tris(bipyridine) upon excitation into the singlet metal-to-ligand charge-transfer band (1MLCT) has been characterized by femtosecond fluorescence up-conversion and transient absorption (TA) studies. The fluorescence experiment shows a very short-lived broad 1MLCT emission band at approximately 600 nm, which decays in < or =20 fs, and a weak emission at approximately 660 nm, which we attribute to the 3MLCT, populated by intersystem crossing (ISC) from the 1MLCT state. The TA studies show a short-lived (<150 fs) excited-state absorption (ESA) below 400 nm, and a longer-lived one above 550 nm, along with the ground-state bleach (GSB). We identify the short-lived ESA as being due to the 3MLCT state. The long-lived ESA decay and the GSB recovery occur on the time scale of the lowest excited high-spin quintet state 5T2 lifetime. A singular value decomposition and a global analysis of the TA data, based on a sequential relaxation model, reveal three characteristic time scales: 120 fs, 960 fs, and 665 ps. The first is the decay of the 3MLCT, the second is identified as the population time of the 5T2 state, while the third is its decay time to the ground state. The anomalously high ISC rate is identical in [RuII(bpy)3]2+ and is therefore independent of the spin-orbit constant of the metal atom. To reconcile these rates with the regular quasi-harmonic vibrational progression of the 1MLCT absorption, we propose a simple model of avoided crossings between singlet and triplet potential curves, induced by the strong spin-orbit interaction. The subsequent relaxation steps down to the 5T2 state dissipate approximately 2000 cm-1/100 fs. This rate is discussed, and we conclude that it nevertheless can be described by the Fermi golden rule, despite its high value.     

Random quantum operations

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Φ and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.     

Limit theorems for random walks

We consider a random walk $S_{\tau }$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau }$ converges in the Skorohod space to the symmetric $\alpha$-stable process $B^{\alpha }$. We also prove asymptotic formula for the transition function of $S_{\tau }$ similar to the Pólya’s asymptotic formula for $B^{\alpha }$.     

Characterisation of anodic oxide films on zirconium formed in sulphuric acid: XPS and corrosion resistance investigations

Present work describes investigations of a two-step process consisting of galvanostatic anodising in a 1 M H₂SO₄ solution at 100 mA cm⁻² up to the limiting voltages of 20, 60, 80, 100 and 120 V, directly after which potentiostatic regime was employed and the current was allowed to drop. The total treatment time (5 min) was held constant for all samples. The treatment was carried out to improve the corrosion resistance of zirconium in physiological conditions, which was determined by electrochemical evaluation in Ringer’s solution. XPS studies revealed that after anodising sulphur was incorporated into the oxide film in the form of sulphated zirconia. The maximum content of sulphate in the oxide layer was observed after anodising at 80 V. Anodising at higher voltages resulted in formation of coatings with decreasing amount of sulphur. It was found that there is a strong correlation between the sulphur content in the oxide layers and the measured corrosion current density. On the other hand, the pitting corrosion resistance seemed to be unaffected by the presence of S and it was improving with the increasing limiting voltage of the treatment.

     

X‐ray investigations of bicyclic α‐methyl­ene‐δ‐valerolactones. II. (4aS,8aS)‐4a‐Methyl‐3‐methyl­eneper­hydro­chromen‐2‐one

The title compound, C₁₁H₁₆O₂, adopts a semifolded conformation with the δ‐lactone and cyclo­hexane rings almost perpendicular to one another. The β‐methyl substituent occupies an axial position with respect to the cyclo­hexane ring. The δ‐lactone moiety adopts a slightly distorted half‐chair arrangement, while the cyclo­hexane ring exists in an almost ideal chair conformation.     

Structurally tailored carbon xerogels produced through a sol–gel process in a water–methanol–inorganic salt solution

The impact of solvent composition as well as inorganic salt content and type on carbon xerogel structure was investigated. Carbon xerogels were derived from the sol–gel polycondensation of resorcinol with furfural in a water–methanol–inorganic salt solution. As inorganic salts, NaCl, NH₄ClO₄ and FeCl₃ were used. In order to conduct an accurate examination of the carbon xerogel structures and textures, inorganic salts were removed prior to carbonization. The xerogel structures can be tailored according to the water/methanol ratio and, to a lesser extent, according to the inorganic salt content and type in the starting solution. As a result, a significant amount of salt can be introduced to the gel network of the desired structure. The morphology and physical properties of the organic xerogels, carbon xerogels and their composites were characterized by means of SEM, N₂ sorption and XRD. It was found that samples derived from mixtures with FeCl₃ manifest well developed mesoporosity and depleated microporosity in comparison to samples prepared from mixtures with NaCl and NH₄ClO₄. Iron ions chemically bond to the xerogel matrix and cause its partial graphitization during the carbonization process, resulting in enhanced mesoporosity.     

Topotecan dynamics,tautomerism and reactivity—1H/13C NMR and ESI MS study

Topotecan (TPT) is in clinical use as an antitumor agent, hycamtin^?. Because of this, it requires both biologically and chemically useful information to be available. TPT acts by binding to the covalent complex formed by nicked DNA and topoisomerase I. This has a poisonous effect since inserted into the single‐strand nick and TPT inhibits its religation. We used NMR to trace TPT dynamics, tautomerism and solvolysis products in various solvents and conditions. Chemical stability was assessed in methanol and DMSO as compared to water, and the regioselectivity of the N‐ and O‐methylation was studied using various alkylating agents. The reaction products of quaternization of the nitrogen atom and methylation of the oxygen atom were characterized by means of ESI MS, ¹H/¹³C‐HMBC and ‐HSQCAD NMR. We have focused on the NMR characterization of TPT with an anticipation that its aggregation, tumbling properties and the intramolecular dipolar interactions will be a common feature for other compounds described in this article. These features can also be useful in tracing the interactions of this class of topoisomerase I (TopoI) poisons with DNA. Moreover, the results explained shed light on the recently disclosed problem of lack of stability of TPT in the heart tissue homogenate samples using the analytical assays developed for this class of compounds carried out in the presence of methanol. Copyright © 2010 John Wiley & Sons, Ltd.