Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.     

An Efficient Method for the Synthesis of Acyl-diazenes Using NaNO_2/NaHSO_4·H_2O

Azo compounds are widely utilized as analytic reagents and dyes1, they can also be used in material of non-linear optics, material of optics information storing in laser disks, and dyes with oil solubility in photochromy in modern technology2. Recently, many noteworthy studies have shown that some azo compounds possess excellent optical memory and photoelectric properties3,4. For example, polymer scaffolds bearing azobenzene-potential are useful for optical information storage, azo-dye doped…     

Rapid chiral analysis based on liquid-phase cyclic chemiluminescence

Rapid chiral analysis has become one of the important aspects of academic and industrial research. Here we describe a new strategy based on liquid-phase cyclic chemiluminescence (CCL) for rapid resolution of enantiomers and determination of enantiomeric excess (ee). A single CCL measurement can acquire multistage signals that provide a unique way to examine the intermolecular interactions between chiral hosts and chiral guests, because the lifetime (τ) of the multistage signals is a concentration-independent and distinguishable constant for a given chiral host–guest system. According to the τ values, CCL allows discrimination between a wide range of enantiomeric pairs including chiral alcohols, amines and acids by using only one chiral host. Even the chiral systems hardly distinguished by nuclear magnetic resonance and fluorescence methods can be distinguished easily by CCL. Additionally, the τ value of a mixture of two enantiomers is equal to the weighted average of each enantiomer, which can be used for the direct determination of ee without the need to separate the chiral mixture and create calibration curves. This is extremely crucial for the cases without readily available enantiomerically pure samples. This strategy was successfully applied to monitoring of the Walden inversion reaction and analysis of chiral drugs. The results were in good agreement with those obtained by high-performance liquid chromatography, indicating the utility of CCL for routine quick ee analysis. Mechanism study revealed that the τ value is possibly related to the activity of the chiral substance to catalyze a luminol–H₂O₂ reaction. Our research provides an unprecedented and general protocol for chirality differentiation and ee determination, which is anticipated to be a useful technology that will find wide application in chirality-related fields, particularly in asymmetric synthesis and the pharmaceutical industry.

Rapid chiral analysis has become one of the important aspects of academic and industrial research.     

Organic functionalization of the sidewalls of carbon nanotubes by diels-alder reactions: a theoretical prediction

[structure: see text] The viability of the Diels-Alder (DA) cycloaddition of conjugated dienes onto the sidewalls of single-wall carbon nanotubes is assessed by means of a two-layered ONIOM(B3LYP/6-31G:AM1) approach. Whereas the DA reaction of 1,3-butadiene on the sidewall of an armchair (5,5) nanotube is found to be unfavorable, the cycloaddition of quinodimethane is predicted to be viable due to the aromaticity stabilization at the corresponding transition states and products.     

Highly regioselective construction of spirocycles via phosphine-catalyzed [3 + 2]-cycloaddition

A direct entry to spirocycles with low to moderate regioselectivity was achieved by triphenylphosphine-catalyzed [3 + 2]-cycloaddition of active exo-methylenecycles (1) and ethyl 2,3-butadienoate (2). The regioselectivity of the reaction was greatly improved by using the bulky tert-butyl ester of the 2,3-butadienoate (5). The regioselectivity of the reaction was further enhanced by using the tert-butyl 2-butynoate as the substrate. This protocol provided an efficient entry to the skeleton of spirocarbocycles, especially spiro[4.n]alkanes.