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81.
Hee-Kap Ahn Sang Won Bae Otfried Cheong Joachim Gudmundsson 《Discrete and Computational Geometry》2008,40(3):414-429
The aperture angle
α(x,Q) of a point x
∉
Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q⊂C is the minimum aperture angle of any x∈C∖Q with respect to Q. We show that for any compact convex set C in the plane and any k>2, there is an inscribed convex k-gon Q⊂C with aperture angle approximation error
. This bound is optimal, and settles a conjecture by Fekete from the early 1990s.
The same proof technique can be used to prove a conjecture by Brass: If a polygon P admits no approximation by a sub-k-gon (the convex hull of k vertices of P) with Hausdorff distance σ, but all subpolygons of P (the convex hull of some vertices of P) admit such an approximation, then P is a (k+1)-gon. This implies the following result: For any k>2 and any convex polygon P of perimeter at most 1 there is a sub-k-gon Q of P such that the Hausdorff-distance of P and Q is at most
.
This research was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-311-D00763).
NICTA is funded through the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian
Research Council. 相似文献
82.
83.
Griffiths DV Al-Jeboori MJ Cheong YK Duncanson P Harris JE Salt MC Taylor HV 《Organic & biomolecular chemistry》2008,6(3):577-585
Dialkyl heteroaroylphosphonates based on thiophene, pyrrole or furan have been prepared and their reactions with trimethyl phosphite investigated. Deoxygenation of the carbonyl groups in these heteroaroylphosphonates occurs to give carbene intermediates, which then undergo further reaction. In the case of the furan-3-oylphosphonates and those systems containing a thiophene or pyrrole ring, the major reaction pathway involves intermolecular trapping of the carbene intermediates by the trimethyl phosphite, leading to the formation of ylidic phosphonates that can be readily converted into the corresponding 1,1-bisphosphonates. However, in some furan-2-oylphosphonates the carbenes generated undergo ring-opening to initially give acyclic alkynylphosphonates which may react further to give other novel phosphorus compounds. The effects of substituents on the extent to which intermolecular trapping of the initially formed carbene competes with intramolecular rearrangement has been investigated. The latter process appears to be suppressed by a substituent at the 5-position of the furan ring, the resulting ylidic phosphonates being a rare example of an efficient intermolecular trapping of a furan-2-yl carbene. 相似文献
84.
85.
Jeon Y Sung J Kim D Seo C Cheong H Ouchi Y Ozawa R Hamaguchi HO 《The journal of physical chemistry. B》2008,112(3):923-928
Mixtures of ionic liquid (IL, 1-butyl-3-methylimidazolium tetrafluoroborate, [BMIM][BF4]) and water with varying concentrations were studied by attenuated total reflection infrared absorption and Raman spectroscopy. Changes in the peak intensities and peak positions of CHx (x = 1, 2, 3) vibration modes of the cation of the IL and OH vibration modes of the water molecules were investigated. Peaks from normal-mode stretch vibrations of CH bonds belonging to the imidazolium ring of the cation did not change their positions, while those from the terminal methyl group of the butyl chain blueshifted by approximately 10 cm-1 with the addition of water. On the other hand, change in the spectral shape in the OH stretch vibration region shows hydrogen-bonding network of water molecules breaking down rapidly as the IL is added. Trends in the change of the peak positions and the peak intensities suggested qualitative change of the intermolecular structure in the [BMIM][BF4] + H2O mixture at 32 +/- 2 and 45 +/- 2 mol/L of water concentration. 相似文献
86.
Lee JD Kim SK Kim TJ Han WS Lee YJ Yoo DH Cheong M Ko J Kang SO 《Journal of the American Chemical Society》2008,130(30):9904-9917
A series of group 13 main group complexes with pi,sigma-type bonding interaction of the formula [{(eta (5)-RC 2B 9H 9)(CH 2)(eta (1)-NMe 2)}MMe] (M = Al, R = H 5, Me 6; Ga, R = H 7, Me 8; In, R = H 9, Me 10) was produced by the reaction of group 13 metal alkyls (MMe 3; M = Al, Ga, In) with the dicarbollylamine ligands, nido-8-R-7,8-C 2B 9H 10-7-(CH 2)NHMe 2 (R = H 1, Me 2). The reactions of 1 and 2 with AlMe 3 in toluene initially afforded tetra-coordinated aluminum complexes with sigma,sigma-type bonding interaction, [{(eta (1)-RC 2B 9H 10)(CH 2)(eta (1)-NMe 2)}AlMe 2] (R = H 3, Me 4), which readily underwent further methane elimination to yield the corresponding constrained geometry complexes (CGCs, 5 and 6) of aluminum with pi,sigma-bonding interaction. However, the reactions between 1 and 2 and MMe 3 (M = Ga, In) in toluene produced gallium and indium pi,sigma-CGCs of 7 and 10 directly, not proceeding through sigma,sigma-intermediates. The structures of group 13 metal CGCs were established by X-ray diffraction studies of 5, 6, and 8, which authenticated a characteristic eta (5):eta (1)-coordination mode of the dicarbollylamino ligand to the group 13 metals. A similar pi,sigma-bonding interaction was also established in ethylene-bridged dicarbollylethylamine series. Thus, aluminum pi,sigma-CGCs of dicarbollylethylamine, [{(eta (5)-RC 2B 9H 9)(CH 2) 2(eta (1)-NBz 2)}AlMe] (R = H 17, Me 18), were prepared by the trans-metalation of the [{(eta (5)-RC 2B 9H 9)(CH 2) 2(eta (1)-NBz 2)}Ti(NMe 2) 2] (R = H 15, Me 16) with AlMe 3. However, only sigma,sigma-bonded complexes of the formula [{(eta (1)-RC 2B 9H 9)(CH 2) 2(eta (1)-NBz 2)}AlMe 2] (R = H 13, Me 14) were isolated by the reaction between [ nido-7-8-R-7,8-C 2B 9H 10-(CH 2) 2HNBz 2] (R = H 11, Me 12) and AlMe 3. When methane-elimination reactions between metal alkyls and dicarbollylamines were carried out with either the gallium atom or monobenzyl aminoethyl tethered ligands, [ nido-7-H 2NBz(CH 2) 2-8-R-7,8-C 2B 9H 10] (R = H 21, Me 22), desired pi,sigma-CGCs, [{(eta (5)-RC 2B 9H 9)(CH 2) 2(eta (1)-NBz 2)}GaMe] (R = H 19, Me 20) or [{(eta (5)-RC 2B 9H 9)(CH 2) 2(eta (1)-NHBz)}AlMe] (R = H 23, Me 24), were generated, respectively. DFT calculation on 5 provides evidence of existence of pi,sigma-bonding of dicarbollylamine ligand to the aluminum atom: pi-bonding interaction of a dicarbollyl unit becomes intensified in the presence of a weak sigma-bonding amine-tethered group. Furthermore, preference for the formation of pi,sigma-bonding was predicted by optimizing a reaction profile including sigma,sigma- and pi,sigma-structures as well as transition state structures for each methylene- and ethylene-spaced ligand system, 3-5 and 14- 18, to reveal that pi,sigma-bonding interaction is more favorable in the case of a methylene-tethered ligand system. 相似文献
87.
Zhang H Mitsumori S Utsumi N Imai M Garcia-Delgado N Mifsud M Albertshofer K Cheong PH Houk KN Tanaka F Barbas CF 《Journal of the American Chemical Society》2008,130(3):875-886
The development of enantioselective anti-selective Mannich-type reactions of aldehydes and ketones with imines catalyzed by 3-pyrrolidinecarboxylic acid and related pyrrolidine derivatives is reported in detail. Both (3R,5R)-5-methyl-3-pyrrolidinecarboxylic acid and (R)-3-pyrrolidinecarboxylic acid efficiently catalyzed the reactions of aldehydes with alpha-imino esters under mild conditions and afforded anti-Mannich products with high diastereo- and enantioselectivities (anti/syn up to 99:1, up to >99% ee). For the reactions of ketones with alpha-imino esters, (R)-3-pyrrolidinecarboxylic acid was an efficient catalyst (anti/syn up to >99:1, up to 99% ee). Evaluation of a series of pyrrolidine-based catalysts indicated that the acid group at the beta-position of the pyrrolidine ring of the catalyst played an important role in forwarding the carbon-carbon bond formation and in directing anti-selectivity and enantioselectivity. 相似文献
88.
89.
Prabal Datta Barua Wai Yee Chan Sengul Dogan Mehmet Baygin Turker Tuncer Edward J. Ciaccio Nazrul Islam Kang Hao Cheong Zakia Sultana Shahid U. Rajendra Acharya 《Entropy (Basel, Switzerland)》2021,23(12)
Optical coherence tomography (OCT) images coupled with many learning techniques have been developed to diagnose retinal disorders. This work aims to develop a novel framework for extracting deep features from 18 pre-trained convolutional neural networks (CNN) and to attain high performance using OCT images. In this work, we have developed a new framework for automated detection of retinal disorders using transfer learning. This model consists of three phases: deep fused and multilevel feature extraction, using 18 pre-trained networks and tent maximal pooling, feature selection with ReliefF, and classification using the optimized classifier. The novelty of this proposed framework is the feature generation using widely used CNNs and to select the most suitable features for classification. The extracted features using our proposed intelligent feature extractor are fed to iterative ReliefF (IRF) to automatically select the best feature vector. The quadratic support vector machine (QSVM) is utilized as a classifier in this work. We have developed our model using two public OCT image datasets, and they are named database 1 (DB1) and database 2 (DB2). The proposed framework can attain 97.40% and 100% classification accuracies using the two OCT datasets, DB1 and DB2, respectively. These results illustrate the success of our model. 相似文献
90.
Won Jung Yoon Jae Hoon Ryu Cheolhoon Cheong Kyu Yong Choi 《Macromolecular theory and simulations》1998,7(3):327-332
Molecular weight averages have long been used as a measure of polymer molecular weight properties in industrial polymer manufacturing processes. With a kinetic model, it is possible to directly calculate the polymer chain length distribution by integrating an infinite number of the polymer population balance equations. However, when the polymer chain length is very large, such a direct integration of polymer population balance equations can be computationally demanding. In this paper, the method of finite molecular weight moments is applied to the calculation of polymer chain length distribution in a batch free radical thermal polymerization of styrene. The weight fraction of a finite chain length interval is directly calculated in conjunction with a kinetic model. The method of calculation is illustrated through model simulations. 相似文献