A New Method of Synthesis of Monomeric Aryloxide Complexes of Manganese(II): Structures of Manganese Phenoxides

Monomeric manganese(II) complexes of bulky alkyl/ aryl‐substituted phenoxides, [Mn{C₆H_nR_mO}₂(DME)] [ 1 : R = C₆H₅, n = 3, m = 2 (2,6); 2 : R = Me₃C, n = 3, m = 2 (2,6); 3 : R = Me₃C, n = 2, m = 3 (2,4,6)] were prepared in yields of 37, 44 and 72 %, respectively, from the reaction of manganese powder, Hg(C₆F₅)₂ and the corresponding phenol in the presence of a little mercury in dimethoxyethane (DME). The compounds were characterized spectroscopically and by magnetic measurements. The single crystal structures of 1 and 3 and also of the mixed phenoxide complex [Mn{(C₆H₃(C₆H₅)₂‐2,6‐O}{C₆H₃(Me₃C)₂‐2,6‐O}(DME)] 4 are reported.     

Construction of Biorthogonal Multiwavelets Using the Lifting Scheme

The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time–frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.     

On centripetal flows of entities in scale‐free networks with nodes of finite capability

We examine the transmission of entities from the peripheries of scale‐free networks toward their centers when the nodes of the network have finite processing capabilities. We look at varying network utilization, U and find that clogging of the network sets in after a threshold value has been exceeded, and that the congestion sets in at the downstream nodes (those nearer to the collector) having large numbers of upstream neighbors. Investigation of the question of the degree of correlation of several characteristics of scale‐free networks (such as the average path length to the collector <l_(min)> and the average clustering coefficient ) with the dynamics of centripetal flow in them reveals a negative answer: any correlation is indirect and will manifest in the number of producer nodes (which dictate the effective heaviness of the flow) and the interconnectedness of the feeder nodes, those nodes which are immediate neighbors of the collector node. An examination of reinforcement strategies shows dramatic improvements in both the finishing rate, and the average total transmission time, when the more centrally‐placed nodes are reinforced first, showing that the entities spend a large amount of their lifetime waiting in line at those nodes (which constitute the bottlenecks in the network) compared to the nodes in the periphery. Our results reinforce the importance of a network's hubs and their immediate environs, and suggest strategies for prioritizing elements of a network for optimization. © 2014 Wiley Periodicals, Inc. Complexity 21: 283–295, 2015     

Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation

We provide a refined convergence analysis for the SAA (sample average approximation) method applied to stochastic optimization problems with either single or mixed CVaR (conditional value-at-risk) measures. Under certain regularity conditions, it is shown that any accumulation point of the weak GKKT (generalized Karush-Kuhn-Tucker) points produced by the SAA method is almost surely a weak stationary point of the original CVaR or mixed CVaR optimization problems. In addition, it is shown that, as the sample size increases, the difference of the optimal values between the SAA problems and the original problem tends to zero with probability approaching one exponentially fast.     

A rapid and sensitive liquid chromatography/tandem mass spectrometry method for determination of docetaxel in human plasma

A novel, rapid and sensitive isocratic liquid chromatography/tandem mass spectrometry (LC/MS/MS) method was developed for quantification of docetaxel in human plasma with paclitaxel as internal standard. The high sensitivity and specificity of MS/MS detection enabled the use of a small volume of plasma (0.05 mL) and a simple liquid-liquid extraction procedure. Furthermore, a very short run-time (3 min) fulfilled the need for monitoring plasma levels of docetaxel from large-scale clinical studies. The calibration curve for docetaxel was linear over the range 5-1000 ng/mL with coefficients of correlation >0.999 using only 0.05 mL plasma. The intra- and inter-day precisions (CV) of analysis were <7%, and accuracy ranged from 96 to 110%. The applicability of the method was demonstrated in a pharmacokinetic study of a 1-h infusion of docetaxel with dosages of 75 mg/m(2). Possible conjugated metabolites of docetaxel were not detected in patients' samples.