Octahedral Rhenium Cluster Complexes with 1,2-Bis(4-pyridyl)ethylene and 1,3-Bis(4-pyridyl)propane as Apical Ligands

A series of eight new octahedral rhenium cluster complexes with the general formula trans-[{Re₆Q₈}L₄X₂] (Q = S or Se; L = 1,2-Bis(4-pyridyl)ethylene (bpe) or 1,3-Bis(4-pyridyl)propane (bpp); X = Cl or Br) was synthesized and investigated. While bpe is a ligand with a conjugated aromatic system, bpp represents a molecule of opposite type and has independent aromatic systems of the two pyridine rings. It was shown that this difference in the electronic structure of the ligands has a fundamental effect on the electronic structure, electrochemical and luminescent properties of the corresponding cluster complexes. Specifically, the [{Re₆Q₈}(bpe)₄X₂] complexes in solutions show multiple quasi-reversible electrochemical transitions associated with reduction of the organic ligands. At the same time, the trans-[{Re₆Q₈}(bpp)₄X₂] complexes show multielectron quasi-irreversible reduction processes, which correlate with the mixed character of the lowest unoccupied molecular orbitals of these complexes. All the obtained new compounds exhibit red photoluminescence. The photophysical parameters (emission lifetimes and quantum yields) measured for the bpp complexes exceed those revealed for bpe complexes by more than an order of magnitude.     

New Erdős-Kac Type Theorems for Signed Measures on Square-Free Integers

We consider a family of signed measures supported on the set of square-free numbers. We prove some local limit theorems for the prime divisor counting function ω(n) and establish new Erd?s-Kac type results.     

Duality in Finite Element Exterior Calculus and Hodge Duality on the Sphere

Foundations of Computational Mathematics - Finite element exterior calculus refers to the development of finite element methods for differential forms, generalizing several earlier finite element...     

Regularization of Monotone Variational Inequalities with Mosco Approximations of the Constraint Sets

In this paper we study the convergence and stability in reflexive, smooth and strictly convex Banach spaces of a regularization method for variational inequalities with data perturbations. We prove that, when applied to perturbed variational inequalities with monotone, demiclosed, convex valued operators satisfying certain conditions of asymptotic growth, the regularization method we consider produces sequences which converge weakly to the minimal-norm solution of the original variational inequality, provided that the perturbed constraint sets converge to the constraint set of the original inequality in the sense of a modified form of Mosco convergence of order ≥1. If the underlying Banach space has the Kadeč–Klee property, then the sequence generated by that regularization method is strongly convergent. Mathematics Subject Classifications (2000) Primary: 47J0G, 47A52; secondary: 47H14, 47J20.     

Formation of cyclopropanone during cytochrome P450-catalyzed N-dealkylation of a cyclopropylamine

The role of single electron transfer (SET) in P450-catalyzed N-dealkylation reactions has been studied using the probe substrates N-cyclopropyl-N-methylaniline (2a) and N-(1'-methylcyclopropyl)-N-methylaniline (2b). In earlier work, we showed that SET oxidation of 2a by horseadish peroxidase leads exclusively to products arising via fragmentation of the cyclopropane ring [Shaffer, C. L.; Morton, M. D.; Hanzlik, R. P. J. Am. Chem. Soc. 2001, 123, 8502-8508]. In the present study, we found that liver microsomes from phenobarbital pretreated rats (which contain CYP2B1 as the predominant isozyme) oxidize [1'-(13)C, 1'-(14)C]-2a efficiently (80% consumption in 90 min). Disappearance of 2a follows first-order kinetics throughout, indicating a lack of P450 inactivation by 2a. HPLC examination of incubation mixtures revealed three UV-absorbing metabolites: N-methylaniline (4), N-cyclopropylaniline (6a), and a metabolite (M1) tentatively identified as p-hydroxy-2a, in a 2:5:2 mole ratio, respectively. 2,4-Dinitrophenylhydrazine trapping indicated formation of formaldehyde equimolar with 6a; 3-hydroxypropionaldehyde and acrolein were not detected. Examination of incubations of 2a by (13)C NMR revealed four (13)C-enriched signals, three of which were identified by comparison to authentic standards as N-cyclopropylaniline (6a, 33.6 ppm), cyclopropanone hydrate (11, 79.2 ppm), and propionic acid (12, 179.9 ppm); the fourth signal (42.2 ppm) was tentatively determined to be p-hydroxy-2a. Incubation of 2a with purified reconstituted CYP2B1 also afforded 4, 6a, and M1 in a 2:5:2 mole ratio (by HPLC), indicating that all metabolites are formed at a single active site. Incubation of 2b with PB microsomes resulted in p-hydroxylation and N-demethylation only; no loss or ring-opening of the cyclopropyl group occurred. These results effectively rule out the participation of a SET mechanism in the P450-catalyzed N-dealkylation of cyclopropylamines 2a and 2b, and argue strongly for the N-dealkylation of 2a via a carbinolamine intermediate formed by a conventional C-hydroxylation mechanism.     

Selective two-step oxidation of μ2-S ligands in trigonal prismatic unit {Re3(μ6-C)(μ2-S)3Re3} of the bioctahedral cluster anion [Re12CS17(CN)6]6–

An oxidation of cluster anion [Re(12)CS(17)(CN)(6)](6-) by H(2)O(2) in water has been investigated. It was shown that selective two-step oxidation of bridging μ(2)-S-ligands in trigonal prismatic unit {Re(3)(μ(6)-C)(μ(2)-S)(3)Re(3)} takes place. The first stage runs rapidly, whereas the speed of the second stage depends on intensity of ultraviolet irradiation of the reaction mixture. Each stage of the reaction is accompanied by a change in the solution's color. In the first stage of the oxidation, the cluster anion [Re(12)CS(14)(SO(2))(3)(CN)(6)](6-) is produced, in which all bridging S-ligands are turned into bridging SO(2)-ligands. The second stage of the oxidation leads to formation of the anion [Re(12)CS(14)(SO(2))(2)(SO(3))(CN)(6)](6-), in which one of the SO(2)-ligands underwent further oxidation forming the bridging SO(3)-ligand. Seven compounds containing these anions were synthesized and characterized by a set of different methods, elemental analyses, IR and UV/vis spectroscopy, and quantum-chemical calculations. Structures of some compounds based on similar cluster anions, [Cu(NH(3))(5)](3)[Re(12)CS(14)(SO(2))(3)(CN)(6)]·9.5H(2)O, [Ni(NH(3))(6)](3)[Re(12)CS(14)(SO(2))(3)(CN)(6)]·4H(2)O, and [Cu(NH(3))(5)](2.6)[Re(12)CS(14)(SO(2))(3)(CN)(6)](0.6)[{Re(12)CS(14)(SO(2))(2)(SO(3))(CN)(5)(μ-CN)}{Cu(NH(3))(4)}](0.4)·5H(2)O, were investigated by X-ray analysis of single crystals.     

Direct AFM measurements of adhesion forces between calcium oxalate monohydrate and kidney epithelial cells in the presence of Ca2+ and Mg2+ ions

Adhesion forces between the calcium oxalate monohydrate (COM, whewellite) crystal and the layer of the epithelial kidney cells have been directly measured under buffer solutions by using atomic force microscope (AFM). Two renal epithelial lines, MDCK (a collecting duct line) and LLC-PK1 (a proximal tubular line), were used. All experiments were conducted in buffer solutions containing additional Ca(2+) and Mg(2+) ions in the various concentrations. For MDCK-cells, the obtained values of the adhesion force were in the range 0.12-0.51 nN and 0.12-0.20 nN for Ca(2+) and Mg(2+), respectively. No adhesion force (larger than 0.05 nN) has been found for LLC-PK1 cells. The "critical" concentrations of ions, near which the adhesion force (for MDCK-cells) was maximal, were found to be 100 mM. The "critical" concentration of ions and the tendency of the adhesion forces with the changing ions concentration, confirm earlier results of Lieske et al. [J.C. Lieske, G. Farell, S. Deganello, Urol. Res. 32 (2004) 117-123], in which the affinity (rather than the adhesion force) between the COM micro-crystals and the layer of the MDCK-cells were measured, calculating the radioactive signal of radioactive (14)C COM-crystals stuck to the cells. We believe that the aggregation of the COM crystals does not occur in the bulk urine due to short travel time through the nephron. If so, the kidney stone formation is determined by COM-seeding on the tubules walls. The further growth of the stone on the seed can take practically unlimited time because the COM crystal is practically is not soluble in water or urine solutions. The value of the adhesion force can be useful for evaluation of the adhesion energy or probability of the COM-aggregates to stick to the kidney epithelium under the urine flow. This probability is calculated taking into account the adhesion force, F(ad), and hydrodynamic driving force of the flow. This probability reflects the opportunity of the small aggregates to grow and form the kidney stones.