Titanium-catalyzed [6π+2π]-cycloaddition of Si-containing alkynes to bis(1,3,5-cycloheptatriene-7-yl)alkanes

The reaction between Si-containing alkynes and bis(1,3,5-cycloheptatriene-7-yl)alkanes in the presence of the two-component catalyst Ti(acac)₂Cl₂-Et₂AlCl, led to the selective formation of mono- and bis-adducts – {9-[4-(2,4,6-cycloheptatrienyl)alkyl]-8-alkyl(phenyl)bicyclo[4.2.1]nona-2,4,7-triene-7-yl}(trimethyl)silanes and bis(7-trimethylsilyl-8-alkyl(phenyl)bicyclo[4.2.1]nona-2,4,7-triene-7-yl)alkanes in 78–86% yield. The structures of the obtained cycloadducts were confirmed by ¹H and ¹³C NMR spectroscopy.     

Sensing and fixation of NO2/N2O4 by calix[4]arenes

An approach toward visual detection and chemical utilization of NO(2)/N(2)O(4) is proposed, which employs simple calix[4]arenes. Exposure of tetra-O-alkylated calix[4]arenes 1 and 2, possessing either a cone or a 1,3-alternate conformation, to NO(2)/N(2)O(4), both in chloroform solution and in the solid state, results in deeply colored calixarene-nitrosonium (NO(+)) complexes. In the presence of a Lewis acid, such as SnCl(4), stable calixarene-NO(+) complexes 7 and 8 were isolated in a quantitative yield and characterized by UV-vis, FTIR, high-resolution (1)H NMR spectroscopy and elemental analysis. NO(+) is found encapsulated within the calixarene cavity, and stable charge-transfer complexes result with K(ass) > 10(6) M(-1) (CDCl(3)). The NO(+) encapsulation was also demonstrated in titration experiments with calixarenes 1, 2, and 5 and commercially available NO(+)SbF(6)(-) salt in chloroform. The complexation process is reversible, and the complexes dissociate upon addition of water and alcohol, recovering the parent calixarenes. Attachment of functionalized calix[4]arenes to silica gel was demonstrated, which afforded a solid material 15 capable of visual detection and entrapment of NO(2)/N(2)O(4). Calixarene-NO(+) complexes can be utilized for the NO(+) transfer processes and nitrosation reactions. The NO(+) guest transfer between two calixarene containers 2 and 5 was achieved and studied by UV-vis and (1)H NMR spectroscopy. Chemical fixation of NO(2)/N(2)O(4) was demonstrated through their quantitative transformation into the calixarene-NO(+) complex and its use as a nitrosonium transfer agent in the synthesis of N-nitrosoamides. These results may lead toward novel nitrogen oxides storing materials.     

Interchange-tunneling splitting in HCl dimer in helium nanodroplets

Midinfrared spectra of HCl dimers have been obtained in helium nanodroplets. The interchange-tunneling (IT) splitting in the vibrationally excited state of the bonded H-Cl stretching band (nu(2)) in (H(35)Cl-H(37)Cl) dimers was measured to be 2.7+/-0.2 cm(-1), as compared to 3.7 cm(-1) in free dimer. From the splitting, the strength of the IT coupling in liquid helium of 0.85+/-0.15 cm(-1) was obtained, which is about a factor of 2 smaller than in the free dimer. The results are compared with the previous spectroscopic study of (HF)(2) in He droplets as well as the theoretical study of (HF)(2) and (HCl)(2) dimers in small He clusters.     

Queueing model of a hybrid channel with faster link subject to partial and complete failures

This paper presents a Markovian queueing model for a hybrid channel consisting of two links with different throughputs. The busy faster link is assumed to be unreliable, with possible partial and complete failures. Partial failures lead to a reduction in the service rate, while complete failure stops the service. Repairs return the faster server to a non-failed state. The problem of the optimal allocation of customers between the servers is considered. The optimality of a threshold-based policy that depends on the failure state of the faster server is proved. The dynamic behaviour of the system for the given threshold policy is described by a four-dimensional Markov process that can be treated as a QBD process with a large number of boundary states. Stationary analysis of the system is performed by means of a matrix-geometric approach, and the main performance measures are derived.     

Model-Free Approach beyond the Borders of Its Applicability

Model calculations presented in this article show that commonly used methodology of¹⁵N relaxation data analysis completely fails in detecting nanosecond time scale motions if the major part of the molecule is involved in these motions. New criteria are introduced for the detection of such cases, based on the dependence of the apparent overall correlation time, derived from theT₁/T₂ratio, on the spectrometer frequency. Correctly estimating the overall rotation correlation time τ_Rwas shown to play the key role in model-free data analysis. It is found, however, that in cases of slow internal motions with characteristic times of more than 3–4 ns, the effective τ_Rprovided by theT₁/T₂ratio for individual amide nitrogens can be used for the characterization of the fast picosecond internal dynamics.     

Recovery and suppression of the detonation of hydrogen-air mixtures at an obstacle with orifices

A numerical simulation of the interaction of detonation waves with an obstacle having orifices and an analysis of the results were performed. The calculations were conducted using the 3D GasDynamicTool code for a model gas with parameters of detonation corresponding to a hydrogen-air stoichiometric mixture under normal conditions. Within the framework of the assumptions made, it was shown that, upon interaction with a perforated partition, a detonation wave experiences disintegration accompanied by the formation of unsteady jets of detonation products, with each one being preceded by a shock wave. The simulations demonstrated that the reinitiation of detonation downstream from the partition is determined by the dynamics of the ignition caused by the interaction between the converging shock waves formed ahead of the jets outflowing from neighboring orifices.     

Coherent versus incoherent Raman scattering: molecular coherence excitation and measurement

We present a comparative analysis of spontaneous and coherent Raman scattering on pyridine. The instantaneous excitation of the molecular coherence is done by a pair of ultrashort preparation pulses. Then, a long narrowband probe pulse is scattered off the molecular vibrations. The described hybrid technique allows for the single-shot acquisition of a background-free coherent Raman spectrum within the excitation band and its straightforward comparison with the spontaneous Raman measurements, performed in the same setup. We report a 10(5)-fold increase in the efficiency of the Raman scattering process due to the broadband pump-Stokes preparation. The coherence magnitude (approximately 0.5x10(-3)) is inferred experimentally, without a priori knowledge about the molecular structure.     

Several formulas for special values of the Bell polynomials of the second kind and applications

In the paper, the authors establish several explicit formulas for special values of the Bell polynomials of the second kind, connect these formulas with the Bessel polynomials, and apply these formulas to give new expressions for the Catalan numbers and to compute arbitrary higher order derivatives of elementary functions such as the since, cosine, exponential, logarithm, arcsine, and arccosine of the square root for the variable.