Phenyl Sulphonyl Acetaldehyde Diethyl Acetal: A New Robust 1,2-Diol Protective Group

Abstract

A simple preparation of a novel resilient protective group for 1,2-diols is described herein which is remarkably stable in the presence of extremely harsh basic conditions as well as acidic media. The title reagent's versatility is detailed with numerous examples.

     

Connectivity interdiction

We consider the problem of maximally decreasing the edge-connectivity of an edge-weighted graph by removing a limited set of edges. This problem, which we term connectivity interdiction, falls into a large family of so-called interdiction problems, which have been considered in a variety of contexts. Whereas little is known about the approximability of most interdiction problems, we show that connectivity interdiction admits a PTAS, and a natural special case of it can even be solved efficiently.     

基于组合预测模型在高校招生人数预测中的应用研究

引进诱导有序加权平均算子,建立诱导有序加权平均组合预测模型,借助它对四川省普通高等学校招生人数进行预测.通过两个误差指标值的比较,说明这种方法的合理性,从而为教育部门制定相关的就业体制提供依据.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.     

What are the Factors that Determine the Number of People Coming to China?

This paper studies the factors that affect people coming to China. We select the spending of United States and South Korea, GDP, railway transportation capacity of China as observations. Based on the data from 1988 to 2015, we use the ordinary least squares analysis regression model and present a most reasonable regression equation. It is found that South Korea’s spending is negative to the number of visitors, whereas the spending of US is positive. On comparing the effect of other variables, the growth of railway transportation capacity and the overseas travel expenses of South Korea or United States, have almost no significant impact on the number of people coming to China. However, as China economic growth increasing rapidly, more and more people are willing to come.     

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For linear quantile regression model, this paper proves that the test statistics, besed on smoothed empirical likelihood (SEL) method and least absolute deviation (LAD) method, both converge weakly to a noncentral Chi-square distribution under the local alternatives $H_1:\beta=\beta_0+a_n$, where $\beta$ is the true parameter. Simulation results show that the SEL method is more efficient than the LAD method.     

Pathwise superhedging for time-dependent barrier options on càdlàg paths—Finite or infinite tradeable European,One-Touch,lookback or forward starting options

We establish pathwise duality using simple predictable trading strategies for the robust hedging problem associated with a barrier option whose payoff depends on the terminal level and the infimum of a càdlàg strictly positive stock price process, given tradeable European options at all strikes at a single maturity. The result allows for a significant dimension reduction in the computation of the superhedging cost, via an alternate lower-dimensional formulation of the primal problem as a convex optimization problem, which is qualitatively similar to the duality which was formally sketched using linear programming arguments in Duembgen and Rogers [10] for the case where we only consider continuous sample paths. The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn–Banach theorem. We later adapt this result to include additional tradeable One-Touch options using the Kertz and Rösler (1990) condition. We also compute the superhedging cost when in the more realistic situation where there is only finite tradeable European options; for this case we obtain the full duality in the sense of quantile hedging as in Soner (2015), where the superhedge works with probability $1?\epsilon$ where $\epsilon$ can be arbitrarily small), and we obtain an upper bound for the true pathwise superhedging cost. In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes. This set up is designed to approximate the more realistic situation where we have a finite number of tradeable Europeans at both maturities plus a finite number of tradeable forward starting options.¹