CO2 in 1-butyl-3-methylimidazolium acetate. 2. NMR investigation of chemical reactions

The solvation of CO(2) in 1-butyl-3-methylimidazolium acetate (Bmim Ac) has been investigated by (1)H, (13)C, and (15)N NMR spectroscopy at low CO(2) molar fraction (mf) (x(CO(2)) ca. 0.27) corresponding to the reactive regime described in part 1 of this study. It is shown that a carboxylation reaction occurs between CO(2) and Bmim Ac, leading to the formation of a non-negligible amount (~16%) of 1-butyl-3-methylimidazolium-2-carboxylate. It is also found that acetic acid molecules are produced during this reaction and tend to form with elapsed time stable cyclic dimers existing in pure acid. A further series of experiments has been dedicated to characterize the influence of water traces on the carboxylation reaction. It is found that water, even at high ratio (0.15 mf), does not hamper the formation of the carboxylate species but lead to the formation of byproduct involving CO(2). The evolution with temperature of the resonance lines associated with the products of the reactions confirms that they have a different origin. The main byproduct has been assigned to bicarbonate. All these results confirm the existence of a reactive regime in the CO(2)-Bmim Ac system but different from that reported in the literature on the formation of a reversible molecular complex possibly accompanied by a minor chemical reaction. Finally, the reactive scheme interpreting the carboxylation reaction and the formation of acetic acid proposed in the literature is discussed. We found that the triggering of the carboxylation reaction is necessarily connected with the introduction of carbon dioxide in the IL. We argue that a more refined scheme is still needed to understand in details the different steps of the chemical reaction in the dense phase.     

Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and geometric constraint

Mathematical Programming - Some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are...     

一种低功耗快速锁定简易锁相式频率合成器

采用0.5 μm CMOS工艺,设计了一种简易锁相式频率合成器。采用“类锁相环”结构,在传统锁相环频率合成器的基础上,去除了电荷泵和低通滤波器。利用鉴频鉴相器的输出结果作为开关信号,控制压控振荡器的工作状态,使压控振荡器的输出信号在第N个周期返回鉴频鉴相器后立即被关断,直到下一个参考时钟周期来临。分析了电路的结构和工作原理,并对每个模块进行了理论分析。该频率合成器能够快速地产生固定的时钟频率,具有结构简单、功耗低、锁定时间短等优点。仿真结果表明,输入参考时钟为4 MHz时,该频率合成器的输出频率为15.96 MHz,功耗为2.96 mW,锁定时间小于1 μs。     

Structure and luminescence of α-plane GaN on γ-plane sapphire substrate modified by Si implantation

We show the structural and optical properties of non-polar a-plane Ga N epitaxial films modified by Si ion implantation.Upon gradually raising Si fluences from 5×10~(13)cm~(-2)to 5×10~(15)cm~(-2),the n-type dopant concentration gradually increases from 4.6×10~(18)cm~(-2)to 4.5×10~(20)cm~(-2),while the generated vacancy density accordingly raises from3.7×10~(13)cm~(-2)to 3.8×10~(15)cm~(-2).Moreover,despite that the implantation enhances structural disorder,the epitaxial structure of the implanted region is still well preserved which is confirmed by Rutherford backscattering channeling spectrometry measurements.The monotonical uniaxial lattice expansion along the a direction (out-of-plane direction) is observed as a function of fluences till 1×10~(15)cm~(-2),which ceases at the overdose of 5×10~(15)cm~(-2)due to the partial amorphization in the surface region.Upon raising irradiation dose,a yellow emission in the as-grown sample is gradually quenched,probably due to the irradiation-induced generation of non-radiative recombination centers.     

Inner and outer estimates for the solution sets and their asymptotic cones in vector optimization

We use asymptotic analysis to develop finer estimates for the efficient, weak efficient and proper efficient solution sets (and for their asymptotic cones) to convex/quasiconvex vector optimization problems. We also provide a new representation for the efficient solution set without any convexity assumption, and the estimates involve the minima of the linear scalarization of the original vector problem. Some new necessary conditions for a point to be efficient or weak efficient solution for general convex vector optimization problems, as well as for the nonconvex quadratic multiobjective optimization problem, are established.     

A complete characterization of strong duality in nonconvex optimization with a single constraint

We first establish sufficient conditions ensuring strong duality for cone constrained nonconvex optimization problems under a generalized Slater-type condition. Such conditions allow us to cover situations where recent results cannot be applied. Afterwards, we provide a new complete characterization of strong duality for a problem with a single constraint: showing, in particular, that strong duality still holds without the standard Slater condition. This yields Lagrange multipliers characterizations of global optimality in case of (not necessarily convex) quadratic homogeneous functions after applying a generalized joint-range convexity result. Furthermore, a result which reduces a constrained minimization problem into one with a single constraint under generalized convexity assumptions, is also presented.     

Computing the value of information of quadratic decision problems and its non-negativity conditions

Abstract

There are many examples in the literature of non-cooperative games in which players prefer not to have additional information in order to improve their payoff. We present a general quadratic game in which, if one of the players improves his payoff upon obtaining more information, the other player’s payoff worsens in such a way that there is a net social loss due to having more information. How can we ensure this does not occur? The results of this paper are (1) the mathematical expression of the (social) value of information in a quadratic non-cooperative game, and (2) the conditions that ensure the social value of information is non-negative.     

Weak properties and robustness of t-Hill estimators

We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-Hill and t-lgHill. For both estimators we prove weak consistency in moving average settings as well as the asymptotic normality of t-lgHill estimator in iid setting. In cases of contamination with heavier tails than the tail of original sample, t-Hill outperforms several robust tail estimators, especially in small samples. A simulation study emphasizes the fact that the level of contamination is playing a crucial role. The larger the contamination, the better are the t-score moment estimates. The reason for this is the bounded t-score of heavy-tailed distributions (and, consequently, bounded influence functions of the estimators). We illustrate the developed methodology on a small sample data set of stake measurements from Guanaco glacier in Chile.     

Optimal Solutions in an Allocation Process for a Continuum of Traders

We prove an existence theorem in an allocation process for a continuum of traders in the absence of the convexity assumption on the cost function and under the presence of some economic parameters.