On <Emphasis Type="Italic">C</Emphasis>*-algebras related to constrained representations of a free group

We consider representations of the free group F ₂ on two generators for which the norm of the sum of the generators and their inverses is bounded by some number μ ∈ [0, 4]. These μ-constrained representations determine a C*-algebra A _μ for each μ ∈ [0, 4]. If μ = 4, this gives the full group C*-algebra of F ₂. We prove that these C*-algebras form a continuous bundle of C*-algebras over [0, 4] and evaluate their K-groups.     

Structural stability and robustness to bounded rationality for non-compact cases

We study the model M consisting of “general games” with noncompact action space, together with an associated abstract rationality function. We prove that M is structurally stable and robust to ϵ-equilibria for “almost all” parameters. As applications, we investigate structural stability and robustness to bounded rationality for noncooperative games, multiobjective optimizations and fixed point problems satisfying existence and some continuity conditions. Specifically, we introduce concrete rationality functions for such three kinds of problems with both payoffs and strategy sets, objective functions and domain spaces, and correspondence and domain spaces as parameters, respectively, and show the generic structural stability and robustness to bounded rationality for the corresponding model Ms.     

Wavelength-modulation-spectroscopy for real-time, in situ NO detection in combustion gases with a 5.2 μm quantum-cascade laser

A mid-infrared absorption strategy with calibration-free wavelength-modulation-spectroscopy (WMS) has been developed and demonstrated for real-time, in situ detection of nitric oxide in particulate-laden combustion-exhaust gases up to temperatures of 700 K. An external-cavity quantum-cascade laser (ECQCL) near 5.2 μm accessed the fundamental absorption band of NO, and a wavelength-scanned, 1f-normalized WMS with second-harmonic detection (WMS-2f/1f) strategy was developed. Due to the external-cavity laser architecture, large nonlinear intensity modulation (IM) was observed when the wavelength was modulated by injection-current modulation, and the IM indices were also found to be strongly wavelength-dependent as the center wavelength was scanned with piezoelectric tuning of the cavity. A quantitative model of the 1f-normalized WMS-2f signal was developed and validated under laboratory conditions. A sensor was subsequently designed, built and demonstrated for real-time, in situ measurements of NO across a 3 m path in the particulate-laden exhaust of a pulverized-coal-fired power plant boiler. The 1f-normalized WMS-2f method proved to have better noise immunity for non-absorption transmission, than wavelength-scanned direct absorption. A 0.3 ppm-m detection limit was estimated using the R15.5 transition near 1927 cm⁻¹ with 1 s averaging. Mid-infrared QCL-based NO absorption with 1f-normalized WMS-2f detection shows excellent promise for practical sensing in the combustion exhaust.     

基于目标在回路的三路光纤传输激光相干合成实验

实验验证了一种利用目标回光在远场实现相干合成的技术——目标在回路技术.建立了目标在回路相干合成的物理模型,利用可同时调整光程和光束倾斜的自适应光纤光源准直器,同时补偿合成光束间的平移和倾斜相差,实现了基于目标在回路的三路光纤传输激光间相干合成,获得了接近理想情况的合成效果.文章为在实际大气环境中实现多路相干组束的长距离传输提供了参考.     

Vanishing viscosity limit of Navier–Stokes Equations in Gevrey class

In this paper, we consider the inviscid limit for the periodic solutions to Navier–Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier–Stokes equation is independent of viscosity, and that the solutions of the Navier–Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover, the convergence rate in Gevrey class is presented. Copyright © 2017 John Wiley & Sons, Ltd.     

Inverse Anisotropic Curvature Flow from Convex Hypersurfaces

In this paper, we study the inverse anisotropic curvature flow from strictly convex hypersurfaces. We show the long-time existence and the convergence to the Wulff shape after rescaling, under certain conditions on the general speed functions.     

An improved NSGA-III algorithm based on elimination operator for many-objective optimization

Due to the low selection pressure of the Pareto-dominance relation and the ineffectivity of diversity maintenance schemes in the environmental selection, the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) fail to handle many-objective optimization problems. The recently presented non-dominated sorting genetic algorithm III (NSGA-III) employs the uniformly distributed reference points to significantly promote population diversity, but the convergence based on the Pareto-dominance relation could still be enhanced. For this purpose, an improved NSGA-III algorithm based on elimination operator (NSGA-III-EO) is proposed. In the proposed algorithm, the elimination operator first identifies the reference point with maximum niche count and then employs the penalty-based boundary intersection distance to rank the individuals associated with it. To this end, the selection scheme is used to remove the worse individuals rather than to select the superior individuals. The proposed NSGA-III-EO is tested on a number of well-known benchmark problems with up to fifteen objectives and shows the competitive performance compared with five state-of-the-art MOEAs. Additionally, it is also tested on constrained problems having a large number of objectives and shows good performance.     

Stereoselective Synthesis of Trisubstituted Vinylboronates from Ketone Enolates Triggered by 1,3‐Metalate Rearrangement of Lithium Enolates

An unprecedented stereoselective synthesis of trisubstituted vinylboronates is reported to proceed by direct borylation of lithium ketone enolates under transition‐metal‐free conditions. The stereospecific C?O borylation of lithium enolates was triggered by a carbonyl‐induced 1,3‐metalate rearrangement via a C‐bound boron enolate. DFT calculations and control experiments revealed that the stereoselectivity is controlled by sterics. A variety of stereospecific trisubstituted vinylboronates, together with several tetrasubstituted vinylboronates, were conveniently synthesized with the newly developed methodology. Based on the transformation of stereospecific vinylboronate, a single isomer of Dienestrol was efficiently obtained.     

Synthesis,structures, and electrochemistry of diiron toluene-3,4-dithiolate complexes containing phosphine ligands

Transition Metal Chemistry - In this paper, four diiron toluene-3,4-dithiolate complexes with phosphine ligands were synthesized and characterized. Treatment of complex...     

Recyclable MoO3 nanobelts for photocatalytic degradation of Rhodamine B by near infrared irradiation

Molybdenum trioxide (MoO₃) represented an excellent photocatalytic performance with many applications, including degradation of organic contaminants and splitting of water. This paper presented a new route to synthesize MoO₃ nanobelts with high aspect ratios and crystallinity by a hydrothermal technique. This work showed that the as-synthesized nanobelts exhibited strong photocatalytic activity to degrade an organic dye of Rhodamine B (RhB) in aqueous solution under the exposure of the light source in the near infrared wavelength range, significantly improving the photocatalytic activity of the nanobelts. The results also showed that for a small concentration of RhB at 7.5 mg/L a complete photodegradation (for a given MoO₃ nanobelts quantity of 0.1 g) can be reached after exposing for 60 min. For all concentrations of the RhB solution, the photodegradation exhibited an exponential dependence on the exposure time followed by a sudden shutdown, but no complete photodegradation can be reached. Also, the residual quantity of RhB in solution after the photocatalytic reaction was determined by the initial RhB concentration. The photocatalytic degradation can be interpreted by the pseudo–first-order equation for the absorption of liquid/solid based on solid capacity; thus, photocatalytic degradation can be attributed to the interaction between the photoexcited electrons in the substrate and the antibonding orbital of the RhB in solution. The sudden shutdown was due to the inability of the photoexcited electrons in the substrate hopping to the antibonding orbital of RhB in the presence of the RhB intermediate products from the degraded RhB. In addition, this work showed that the photocatalytic reaction can be recovered after a thermal treatment of postreacted MoO₃ nanobelts, enhancing the utilization efficiency of the catalysis.