Computing devices,mathematics education and mathematics: Sexton’s omnimetre in its time

Material objects can tell us much about mathematical practice. In 1899, Albert Sexton, a Philadelphia mechanical engineer, received the John Scott Medal of the Franklin Institute for his invention of the omnimetre. This inexpensive circular slide rule was one of a host of computing devices that became common in the United States around 1900. It is inscribed “NUMERI MUNDUM REGUNT”. In part because of instruments such as the omnimetre, numbers increasingly ruled the practical world of the late 19th and early 20th century. This changed not only engineering, but mathematics education and mathematical work.     

PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.     

Quantitative model for prediction of hydrodynamic size of nonionic reverse micelles

The sizes of nonionic reverse micelles were investigated as a function of the molecular structure of the surfactant, the type of oil, the total concentration of surfactant [NP], the ratio of surfactant to total surfactant (r), the water to surfactant molar ratio (omega), temperature, salt concentration, and polar phase. The basis of our investigation was a mixture of nonylphenol polyethoxylates--NP4 and NP7, various polar phases, and several oils. Micelle sizes were determined using dynamic light scattering (DLS). A central composite experimental design was used to quantitatively model micelle size as a function of omega, surfactant concentration, and r. The model has demonstrated the capability of predicting the mean diameter of micelles from 4 to 13 with a precision of +/-2 nm as measured by DLS. This quantitative correlation between the size of reverse micelles and the synthetic variables provides the foundation for choosing experimental conditions to control reverse micelle size. In turn, this allows control of the size of nanoparticles synthesized within them.     

Separation and characterisation of five polar herbicides using countercurrent chromatography with detection by negative ion electrospray ionisation mass spectrometry.

Five polar herbicides were separated and characterised using high-speed analytical countercurrent chromatography (HSACCC) in conjunction with online electrospray mass spectrometry (ESI-MS). The countercurrent chromatography used a standard isocratic biphasic solvent system of hexane/ethyl acetate/methanol/water in reverse phase to effect the separation of these five environmentally important compounds. The chromatograph was coupled to a triple quadrupole mass spectrometer via a standard electrospray liquid chromatography interface that was able to give mass spectra in negative ion mode of each compound. Limits of detection are reported for this series of compounds along with representative negative ion ESI-MS data and calibrations for the separation.     

Correlation between biological activity and energies of electronic transitions in benzodiazepines. Negative ion mass spectrometry and ultraviolet absorption spectroscopy study of some derivatives

A correlation between the energies of electronic singlet transitions in benzodiazepines and their biological activity, which was revealed earlier by means of negative ion mass spectrometry with resonance electron capture, has been verified with a UV absorption spectroscopy investigation. Also, it has been noted that the energies of electronic singlet transitions in benzodiazepines are close in value to the ionization energies of atoms Cs, Rb, K, Na, Li and Tl, the cations of which are known to play an important role in nerve cell excitation processes. Copyright 1999 John Wiley & Sons, Ltd.     

Nitrogen atom exchange between molybdenum,tungsten and carbon. A convenient method for N-15 labeling

The compound (ButO)3W identical to N serves to exchange the nitrogen atoms between nitriles (MeC identical to N and PhC identical to N), itself and (ButO)3Mo identical to N in solution at room temperature.     

Gas-phase deprotonation of arylalkylamines. A collision-induced dissociation study

The collision-induced dissociation (CID) of deprotonated arylalkylamines of general formula R(1)C(6)H(4)CHR(2)CH(2)NR(3)(2) (where R(1) = H, OH, F or NO(2); R(2) = H or OH; R(3) = H or CH(3)) generated by negative chemical ionization with H(2)O and D(2)O as ionizing reagents, is discussed. The negative chemical ionization mass spectra show that, in the absence of a hydroxy group in the aromatic ring, deprotonation takes place at the benzylic position whereas the proton is lost from the OH group when present. The nitro compound forms only M(-.) ions. The CID spectra of the deprotonated molecules show that fragmentations are strongly dependent on the structural features of the molecules, namely the presence or absence of substituents in the aromatic ring or aliphatic chain. Copyright 1999 John Wiley & Sons, Ltd.