Heavy traffic analysis of M/G/1 type queueing systems with Markov-modulated arrivals

M/G/1 type queueing systems whose arrival rate is a function of an independent continuous time Markov chain are considered. We suggest a simple analytical approach which allows rigorous mathematical analysis of the stationary characteristics under heavy traffic. Their asymptotic behaviour is described in terms of characteristics of the modulating process (defined as a solution of a set of linear algebraic equations). The analysis is based on certain “semi-explicit” formulas for the performance characteristics. This research was supported by INTAS under grant No. 96-0828.     

Optimal portfolio for nonstationary security market

A new interpretation of the classical portfolio problem is suggested. It is based on the optimization on the conditional expectation of a utility function where the conditional expectation is calculated taking into account all information available at the moment of decision making. This approach allows to show that the risk is a sequence of forecasting errors. Main classes of forecasting algorithms are described and compared. A similarity between some variants of solutions to the modified portfolio problem and the traditional technical analysis recommendations is shown. The scheme is essentially important for nonstationary nonequilibrium security market. Some results of its practical application to the Russian bond market are presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal nonlinear passage through a quantum critical point

We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power law in time. The optimal power is proportional to the logarithm of the total passage time multiplied by universal critical exponents characterizing the phase transition. We support our results by the general scaling analysis and by explicit calculations for the transverse-field Ising model.     

On the existence of non-monotone non-oscillating wavefronts

We present a monostable delayed reaction–diffusion equation with the unimodal birth function which admits only non-monotone wavefronts. Moreover, these fronts are either eventually monotone (in particular, such is the minimal wave) or slowly oscillating. Hence, for the Mackey–Glass type diffusive equations, we answer affirmatively the question about the existence of non-monotone non-oscillating wavefronts. As it was recently established by Hasik et al. and Ducrot et al., the same question has a negative answer for the KPP-Fisher equation with a single delay.     

Probing the effect of anion structure on the physical properties of cationic 1,2,3‐triazolium‐based poly(ionic liquid)s

To extensively explore the influence of anion structure on the physical properties of poly(ionic liquid)s (PILs) a series of PILs having main‐chain 1,2,3‐triazolium cations was synthesized via copper(I)‐catalyzed azide‐alkyne 1,3‐dipolar cycloaddition (CuAAC) followed by N‐alkylation with iodomethane and anion metathesis with different metal salts, that is, Li(CF₃SO₂)₂N, Li(CF₃CF₂SO₂)₂N, K(FSO₂)₂N, K(CF₃SO₂)N(CN), Ag(CN)₂N, and sodium 4,5‐dicyano‐1,2,3‐triazolate. To isolate the effect of anion on physical properties of PILs, a common iodide precursor was used to maintain constant the average degree of polymerization (DP_n) and chain dispersity. Detailed structure/properties relationship analyses demonstrated a lack of correlation between anion chemical structure, ionic conductivity, and glass transition temperatures. Among synthesized series, the PIL derivative having bis(trifluoromethylsulfonyl)imide counter anion showed the best compromise in performance: low glass transition temperature (T_g = ?68 °C), high thermal stability (T_onset = 340 °C) and superior ionic conductivity (σ_DC = 8.5 × 10^{? 6} S/cm at 30 °C), which makes it an interesting candidate for various key modern electrochemical applications. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2191–2199     

2-Hydroperfluoropropyl azide—a versatile reagent for the oxidative fluorination of organic compounds of trivalent phosphorus

2-Hydroperfluoropropyl azide CF₃CHFCF₂N₃, 1 , an inexpensive, readily available, and stable (easy to store) compound, is suggested as an effective fluorinating reagent for different classes of trivalent organophosphorus compounds in accordance with the general scheme R₃P → R₃PF₂. Generally, the reactions are performed without solvent, the highly volatile CF₃ CHFCN being the main by-product. The fluorination is usually an exothermic process, but slight heating is necessary in the case of alkyldifluorophosphites. The unusual Arbuzov rearrangement, accompanied by isomerization of an isobutyl or neopentyl group into a tert-group, ROPF₂ → t-R′POF₂, under the action of a catalytic amount of 1 , was observed.     

ChemInform Abstract: Ab initio MO Study of Diverse Si3H3+ Isomers.

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