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61.
Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves. 相似文献
62.
Thanh V. Nguyen David J. Sinclair Dr. Anthony C. Willis Dr. Michael S. Sherburn Prof. 《Chemistry (Weinheim an der Bergstrasse, Germany)》2009,15(24):5892-5895
Guest‐love‐ometer : The equilibrium inside–outside atropisomeric ratio of ortho‐substituted phenyl cavitands shows a strong solvent dependence. The competition between the ortho‐substituent and the solvent guest for the bowl cavity leads to a sensitive system for the measurement of relative guest binding affinities.
63.
Bernard Bonnard Jean-Baptiste Caillau Robert Sinclair Minoru Tanaka 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(4):1081-1098
The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control. 相似文献
64.
Abstract— The triplet state characteristics (spectrum, lifetime and quantum yield) for four dye sensi tisers [methylene blue (MB), erythrosin (ER), haematoporphyrin (HP) and riboflavin (RF)] were determined in methanol by laser flash photolysis and singlet oxygen yields (0.60 to 0.48) from time-resolved measurements of the 1270 nm near infrared emission. The reaction of singlet oxygen with four long chain unsaturated phenyl esters [oleate (18: 1), linoleate (18: 2), linolenate (18: 3) and arachidonate (20: 4)] was followed quantitatively using the singlet oxygen luminescence technique and also, after continuous420–700 nm irradiation, by HPLC and other analysis of the isomeric product monohydroperoxides. The overall quantum yield of photooxidation (∼10-2 ) was shown to be consistent with the observed singlet oxygen quenching constants(2–12 times 104 dm3 mol-1 s-1 ) for the four esters studied and the singlet oxygen lifetime in methanol (τ∼ 9 μs). The isomer product distribution was interpreted in terms of a dual singlet oxygen and radical mechanism, the radical contribution increasing with sensitiser in the order ER = MB < HP ≪ RF, but also showing some dependence on substrate unsaturation. Evidence is presented for singlet oxygen quenching by MB and RF ( kO = 1.6 and 6.0 times 107 dm3 mol-1 s-1 ) and for the accelerated photobleaching of the dye sensitisers in the presence of the unsaturated esters. 相似文献
65.
A.M. Malyarevich I.A. Denisov K.V. Yumashev V.P. Mikhailov R.S. Conroy B.D. Sinclair 《Applied physics. B, Lasers and optics》1998,67(5):555-558
gsa =3.0×10-18 cm2 and σesa=1.4×10-19 cm2 at 1064 nm, and σgsa=7.2×10-18 cm2 and σesa=7.4×10-19 cm2 at 1342 nm. Q-switched operation was demonstrated at 1064 nm and 1342 nm from a Nd:YVO4 microchip laser, producing pulses as short as 9.3 ns at 1342 nm with peak powers of 350 W.
Received: 17 March 1998/Revised version: 8 June 1998 相似文献
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Nathalie Sinclair 《Mathematical Thinking and Learning》2004,6(3):261-284
Mathematicians have long claimed that the aesthetic plays a fundamental role in the development and appreciation of mathematical knowledge. To date, however, it has been unclear how the aesthetic might contribute to the teaching and learning of school mathematics. This is due in part to the fact that mathematicians' aesthetic claims have been inadequately analyzed, making it difficult for mathematics educators to discern any potential pedagogical benefits. This article provides a pragmatic analysis of the roles of the aesthetic in mathematical inquiry. It then probes some of the beliefs and values that underlie mathematical aesthetic responses and reveals the important interplay between the aesthetic, cognitive, and affective processes involved in mathematical inquiry. 相似文献
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