An alternative method for plotting dispersion curves

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.     

Guest Binding Drives Reversible Atropisomerism in Cavitand Hosts

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.

     

Conjugate and cut loci of a two-sphere of revolution with application to optimal control

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.     

Tris(2,2′‐bipyridyl‐N,N′)­iron(II) diperchlorate

The title compound, [Fe(C₁₀H₈N₂)₃](ClO₄)₂, is isomorphous with the Zn^II and Ru^II analogues. A twofold axis passes through the metal atom and the midpoint of the C—C bond joining the two pyridine rings of one of the bi­pyridyl ligands.     

Q-switching of a diode-pumped Nd:YVO4 laser using a quadrupole electro-optic deflector

4 laser and this produced 1.5-ns pulses of 7 kW peak power at a repetition rate of 20 kHz. Received: 11 May 1998     

V:YAG – a new passive Q-switch for diode-pumped solid-state lasers

gsa =3.0×10^-18 cm² and σ_esa=1.4×10^-19 cm² at 1064 nm, and σ_gsa=7.2×10^-18 cm² and σ_esa=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     

The Roles of the Aesthetic in Mathematical Inquiry

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.