Axisymmetric vibrations of circular plates of linearly varying thickness

Summary Free axisymmetric vibrations of circular plates of linearly varying thickness have been studied on the basis of classical theory of plates. The differential equation governing the motion of such plates have been solved by Frobenius method. The transverse displacement has been expressed as an infinite power series in the radial coordinate. Frequency parameters have been computed for the first three modes of vibration for clamped as well as simply supported circular plates corresponding to different values of taper constant.

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Zusammenfassung Auf Grund der klassischen Scheibentheorie werden die freien axialsymmetrischen Schwingungen der Kreisscheibe mit linear veränderlicher Dicke studiert. Die Differentialgleichung der Bewegung wird mit Hilfe der Methode von Frobenius gelöst. Die transversale Verschiebung wird als eine Reihe der radialen Koordinaten ausgedrückt. Die Schwingungsparameter werden für die ersten drei Eigenschwingungen sowohl für die eingespannte als auch für die aufgelegte Kreisscheibe für verschiedene Werte des Anzugs berechnet.

     

Simultaneous sizing and electrophoretic mobility measurement of sub-micron particles using Brownian motion

The size and surface chemistry of micron scale particles are of fundamental importance in studies of biology and air particulate pollution. However, typical electrophoretic measurements of these and other sub‐micron scale particles (300 nm–1 μm) cannot resolve size information within heterogeneous mixtures unambiguously. Using optical microscopy, we monitor electrophoretic motion together with the Brownian velocity fluctuations – using the latter to measure size by either the Green–Kubo relation or by calibration from known size standards. Particle diameters are resolved to ±12% with 95% confidence. Strikingly, the size resolution improves as the particle size decreases due to the increased Brownian motion. The sizing ability of the Brownian assessed electrophoresis method described here complements the electrophoretic mobility resolution of the traditional CE.     

Reactions between arylhydrazinium chlorides and 2‐chloroquinoline‐3‐carbaldehydes: molecular and supramolecular structures of a hydrazone,a 4,9‐dihydro‐1H‐pyrazolo[3,4‐b]quinoline and two 1H‐pyrazolo[3,4‐b]quinolines

Hydrazone derivatives exhibit a wide range of biological activities, while pyrazolo[3,4‐b]quinoline derivatives, on the other hand, exhibit both antimicrobial and antiviral activity, so that all new derivatives in these chemical classes are potentially of value. Dry grinding of a mixture of 2‐chloroquinoline‐3‐carbaldehyde and 4‐methylphenylhydrazinium chloride gives (E)‐1‐[(2‐chloroquinolin‐3‐yl)methylidene]‐2‐(4‐methylphenyl)hydrazine, C₁₇H₁₄ClN₃, (I), while the same regents in methanol in the presence of sodium cyanoborohydride give 1‐(4‐methylphenyl)‐4,9‐dihydro‐1H‐pyrazolo[3,4‐b]quinoline, C₁₇H₁₅N₃, (II). The reactions between phenylhydrazinium chloride and either 2‐chloroquinoline‐3‐carbaldehyde or 2‐chloro‐6‐methylquinoline‐3‐carbaldehyde give, respectively, 1‐phenyl‐1H‐pyrazolo[3,4‐b]quinoline, C₁₆H₁₁N₃, (III), which crystallizes in the space group Pbcn as a nonmerohedral twin having Z′ = 3, or 6‐methyl‐1‐phenyl‐1H‐pyrazolo[3,4‐b]quinoline, C₁₇H₁₃N₃, (IV), which crystallizes in the space group R. The molecules of compound (I) are linked into sheets by a combination of N—H…N and C—H…π(arene) hydrogen bonds, and the molecules of compound (II) are linked by a combination of N—H…N and C—H…π(arene) hydrogen bonds to form a chain of rings. In the structure of compound (III), one of the three independent molecules forms chains generated by C—H…π(arene) hydrogen bonds, with a second type of molecule linked to the chains by a second C—H…π(arene) hydrogen bond and the third type of molecule linked to the chain by multiple π–π stacking interactions. A single C—H…π(arene) hydrogen bond links the molecules of compound (IV) into cyclic centrosymmetric hexamers having (S₆) symmetry, which are themselves linked into a three‐dimensional array by π–π stacking interactions.