An approximate solution to the integral radiative transfer equation in an optically thick slab

We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ₀?1. We propose two methods transforming this problem to a finite set of the independent problems of the same type set in an atmosphere with optical thickness much less then τ₀. The error estimates are derived. Copyright © 2007 John Wiley & Sons, Ltd.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Synthesis of a new tricyclic 3-(tetrazol-5-yl)pyridine system from 2-(azidomethyl)nicotinonitriles

2-Methyl-3-cyanopyridines were converted into the corresponding 2-azidomethyl derivatives, which then underwent an intramolecular cycloaddition reaction. A novel heterocyclic system containing a 3-(tetrazol-5-yl)pyridine unit was obtained in this way.     

Towards supramolecular fixation of NOX gases: encapsulated reagents for nitrosation

The use of simple calix[4]arenes for chemical conversion of NO2/N2O4 gases is demonstrated in solution and in the solid state. Upon reacting with these gases, calixarenes 1 encapsulate nitrosonium (NO+) cations within their cavities with the formation of stable calixarene-NO+ complexes 2. These complexes act as encapsulated nitrosating reagents; cavity effects control their reactivity and selectivity. Complexes 2 were effectively used for nitrosation of secondary amides 5, including chiral derivatives. Unique size-shape selectivity was observed, allowing for exclusive nitrosation of less crowded N-Me amides 5 a-e (up to 95 % yields). Bulkier N-Alk (Alk>Me) substrates 5 did not react due to the hindered approach to the encapsulated NO+ reagents. Robust, silica gel based calixarene material 3 was prepared, which reversibly traps NO2/N2O4 with the formation of NO+-storing silica gel 4. With material 4, similar size-shape selectivity was observed for nitrosation. The N-Me-N-nitroso derivatives 6 d,e were obtained with approximately 30 % yields, while bulkier amides were nitrosated with much lower yields (<8 %). Enantiomerically pure encapsulating reagent 2 d was tested for nitrosation of racemic amide 5 t, showing modest but reproducible stereoselectivity and approximately 15 % ee. Given high affinity to NO+ species, which can be generated by a number of NOX gases, these supramolecular reagents and materials may be useful for NOX entrapment and separation in the environment and biomedical areas.     

Structural and mechanistic look at the orthoplatination of aryl oximes by dichlorobis(sulfoxide or sulfide)platinum(II) complexes

Structural and mechanistic aspects of orthoplatination of acetophenone and benzaldehyde oximes by the platinum(II) sulfoxide and sulfide complexes [PtCl(2)L(2)] (2, L = SOMe(2) (a), rac-SOMePh (b), R-SOMe(C(6)H(4)Me-4) (c), and SMe(2) (d)) to afford the corresponding platinacycles cis-(C,S)-[Pt(II)(C(6)H(3)-2-CR'=NOH-5-R)Cl(L)] (3, R, R' = H, Me) have been investigated. The reaction of acetophenone oxime with sulfoxide complex 2a in methanol solvent occurs noticeably faster than with sulfide complex 2d due to the fact that the sulfoxide is a much better platinum(II) leaving ligand than the sulfide. Evidence is presented that the orthoplatination is a multistep process. The formation of unreactive dichlorobis(N-oxime)platinum(II) cations accounts for the rate retardation by excess acetophenone oxime and suggests the importance of pseudocoordinatively unsaturated species for the C-H bond activation by Pt(II). A comparative X-ray structural study of dimethyl sulfoxide platinacycle 3b (R = R' = Me) and its sulfide analogue 3e (R = H, R' = Me), as well as of SOMePh complex 3c (R = H, R' = Me), indicated that they are structurally similar and a sulfur ligand is coordinated in the cis position with respect to the sigma-bound phenyl carbon. The differences concern the Pt-S bond distance, which is notably longer in the sulfide complex 3e (2.2677(11) A) as compared to that in sulfoxide complexes 3b (2.201(2)-2.215(2) A) and 3c (2.2196(12) A). Whereas the metal plane is practically a plane of symmetry in 3b due to the H-bonding between the sulfoxide oxygen and the proton at carbon ortho to the Pt-C bond, an S-bonded methyl of SOMePh and SMe(2) is basically in the platinum(II) plane in complexes 3c and 3e, respectively. There are intra- and intermolecular hydrogen bond networks in complex 3b. An interesting structural feature of complex 3c is that the two independent molecules in the asymmetric unit of the crystal reveal an extremely short Pt-Pt contact of 3.337 A.     

Supramolecular fixation of NO2 with calix[4]arenes

Reaction of NO2 with simple calix[4]arenes in chloroform in the presence of a Lewis acid rapidly results in intense coloration caused by the encapsulation of nitrosonium cation.     

Optimal control synthesis for the constrained bilinear biquadratic regulator problem

Optimal process control with control constraints is a challenging task related to many real-life problems. In this paper, a single input continuous time constrained linear quadratic regulator problem, is defined and fully solved. The constraints include both bilinear inequality constraints and customary control force bounds. As a first step, the problem is reformulated as an equivalent constrained bilinear biquadratic optimal control problem. Next, Krotov’s method is used to solve it. To this end, a sequence of improving functions suitable to the problem’s new formulation is constructed and the corresponding successive algorithm is derived. The required computational steps are arranged as an algorithm and proof outlines for the convergence and optimality of the solution are given. The efficiency of the suggested method is demonstrated by numerical example.     

New insights into water‐soluble and water‐coordinated copper 15‐metallacrown‐5 gadolinium complexes designed for high‐field magnetic resonance imaging applications

The development of contrast agents specifically designed for high‐field magnetic resonance imaging (MRI) is required because the relaxation efficiency of classic Gd(III) contrast agents significantly decreases with increasing magnetic field strengths. With an idea of exploring the unique structure of lanthanide (Ln) 15‐MC‐5 metallacrowns, we developed a series of water‐soluble Gd(III) aqua‐complexes, bearing aminohydroxamate (glycine, α‐alanine, α‐phenylalanine and α‐tyrosine) ligands, with increasing number of water molecules directly coordinated to the Gd(III) ion: Gd(H₂O)₄[15‐MC_Cu(II)Glyha‐5](Cl)₃ ( 1 (Gd)), Gd(H₂O)₄[15‐MC_Cu(II)Alaha‐5](Cl)₃ ( 2 (Gd)), Gd(H₂O)₃[15‐MC_{Cu(II)Phalaha}‐5](Cl)₃ ( 3 (Gd)) and Gd(H₂O)₃[15‐MC_Cu(II)Tyrha‐5](Cl)₃ ( 4 (Gd)). In these systems, the Ln(III) central ion is coordinated by five oxygen donor atoms of the ligands and three or four inner‐sphere water molecules. The X‐ray crystal structure of metallacrown Ln(H₂O)_3,4[15‐MC_Cu(II)Rha‐5]³⁺ agrees with density functional theory predictions. The calculations demonstrate that the exchange of coordinated water molecules can proceed easily, resulting in increased relaxivity parameters. The longitudinal relaxivities (r₁) of 1 (Gd)– 4 (Gd) in water at ultrahigh magnetic field of 9.4 T were determined to be 11.5, 14.8, 13.9 and 12.2 mM^?1 s^?1, respectively. The ability to increase the number of Ln(III) inner‐sphere water molecules up to four, the planar metallacrown structure and the rich hydration shell due to strong hydrogen bonds between the [15‐MC‐5] moiety and bulk water molecules provide new opportunities for potential MRI applications.