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141.
142.
For any two points p and q in the Euclidean plane, define LUNpq = { v | v ∈ R2, dpv < dpq and dqv < dpq}, where duv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUNpq(V) = V ∩ LUNpq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUNpq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUNpq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn2) time. Let Ec = {epq| p ∈ V and q ∈ V}. Then Gc = (V,Ec) is a complete graph. For any subset F of Ec, define the maximum distance of F as maxepq∈Fdpq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph Gc whose maximum distance is the minimum among all Hamiltonian cycles in graph Gc. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian. 相似文献
143.
Translated from Matematicheskie Zametki, Vol. 49, No. 5, pp. 37–44, May, 1991. 相似文献
144.
N. B. Voznesensky E. V. Gavrilov A. P. Zhevlakov V. K. Kirillovskiĭ P. V. Orlov 《Technical Physics》2007,52(2):271-275
Methods and schemes to inspect the EUV mirror shape are developed on the basis of a point diffraction interferometer with computer processing of interferograms. A measurement accuracy to within 0.001 of a wavelength in the visual range is achieved. 相似文献
145.
V. V. AntiĆ M. P. AntiĆ M. N. Govedarica P. R. DvorniĆ 《Journal of polymer science. Part A, Polymer chemistry》2007,45(11):2246-2258
The kinetics of the formation of poly(carbosiloxane), as well as of alkyl-substituted poly(siloxane), by Karstedt's catalyst catalyzed hydrosilylation were investigated. Linear poly(carbosiloxane), poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene], (PTMDSE), was obtained by hydrosilylation of 1,3-divinyltetramethyldisiloxane (DVTMDS) and 1,1,3,3-tetramethyldisiloxane (TMDS), while alkyl-substituted poly(siloxane), poly(methyldecylsiloxane), (PMDS), was synthesized by hydrosilylation of poly(methylhydrosiloxane) (PMHS) and 1-decene. To investigate the kinetics of PTMDSE formation, two series of experiments were performed at reaction temperatures ranging from 25 to 56 °C and with catalyst concentrations ranging from 7.0 × 10−6 to 3.1 × 10−5 mol Pt/mol CHCH2. A series of experiments was performed at reaction temperatures ranging from 28 to 48 °C, with catalyst concentrations of 7.0 ×10−6 mol of Pt per mol of CHCH2, when kinetics of PMDS formation was investigated. All reactions were carried out in bulk, with equimolar amounts of the reacting Si H and CHCH2 groups. The course of the reactions was monitored by following the disappearance of the Si H bands using quantitative infrared spectroscopy. The results obtained showed typical first order kinetics for the PTMDSE formation, consistent with the proposed reaction mechanism. In the case of PMDS an induction period occurred at lower reaction temperatures, but disappeared at 44 °C and the rate of Si H conversion also started to follow the first-order kinetics. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2246–2258, 2007 相似文献
146.
Mary E. Neubert DAVID G. ABDALLAH Jr Sandra S. Keast Julie M. Kim Soonnam Lee Ryan M. Stayshich Margaret E. Walsh Rolfe G. Petschek Shin-Tson Wu 《Liquid crystals》2003,30(6):711-731
New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.
Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature. 相似文献
Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature. 相似文献
147.
148.
149.
Ph. Komninou Th. Kehagias A. Delimitis G.P. Dimitrakopulos J. Kioseoglou E. Dimakis A. Georgakilas Th. Karakostas 《Superlattices and Microstructures》2004,36(4-6):509
The structural properties of InN thin films, grown by rf plasma-assisted molecular beam epitaxy on Ga-face GaN/Al2O3(0001) substrates, were investigated by means of conventional and high resolution electron microscopy. Our observations showed that a uniform InN film of total thickness up to 1 μm could be readily grown on GaN without any indication of columnar growth. A clear epitaxial orientation relationship of , was determined. The quality of the InN film was rather good, having threading dislocations as the dominant structural defect with a density in the range of 109–1010 cm−2. The crystal lattice parameters of wurtzite InN were estimated by electron diffraction analysis to be a=0.354 nm and c=0.569 nm, using Al2O3 as the reference crystal. Heteroepitaxial growth of InN on GaN was accomplished by the introduction of a network of three regularly spaced misfit dislocation arrays at the atomically flat interface plane. The experimentally measured distance of misfit dislocations was 2.72 nm. This is in good agreement with the theoretical value derived from the in-plane lattice mismatch of InN and GaN, which indicated that nearly full relaxation of the interfacial strain between the two crystal lattices was achieved. 相似文献
150.
Sanzhizhapov D. B. Tonevitskii Yu. V. Mognonov D. M. Doroshenko Yu. E. 《Russian Journal of Applied Chemistry》2003,76(4):619-622
New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined. 相似文献