Dog and tricks: some mathematics for students of graphics

This paper describes how parametric cubic splines and cubicBezier curves may be used in designing a two dimensional shape.A simple aerofoil shape is designed using both methods. Themathematics is described and the shape drawn using Excel. Theeffect of varying parameters is shown in both methods.     

Coprecipitation of Naphthol Azosulfonates with Organic Coprecipitants and Its Use in Flow-Injection Analysis

The coprecipitation of azo compounds based on 4-nitrophenyl- and 4-sulfophenyldiazonium naphthol sulfonates as their diphenylguanidinium ion-pair complexes with analogous compounds of naphthalene-2-sulfonic acid and 4-phenylsulfodiazonium is investigated. The optimization of the coprecipitation is considered based on the notions of the driving force of the cocrystallization of impurities. The optical characteristics of colored ion-pair complexes are measured. It is found that the water solubility is decreased most substantially for azosulfonates with hydrophobic nitro groups and with no more than two sulfo groups in different aromatic nuclei, which can lead to a decrease in the detection limit due to preconcentration by coprecipitation, which stimulates the thermodynamic flux of concentrate elution. Coprecipitation is combined with flow-injection analysis in the on-line mode, and new procedures are developed for determining naphthol sulfonates and related azo compounds with the detection limit equal to 0.003–0.006 mg/50 mL.     

Resonant Phenomena in Slowly Irregular Rectangular Waveguides

A waveguide with a rectangular cross section of size and orientation slowly changing along the length of the waveguide is considered. Methods of the canonical perturbation theory are used to describe the ray dynamics in the waveguide. As the size and orientation of the cross section slowly change along the ray trajectory, certain resonance conditions may be satisfied. The phenomena of scattering on resonance and capture into resonance is studied. These phenomena lead to destruction of the adiabatic invariance in the system. Bibliography: 12 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 173–179     

The solution of the neutron transport equation in a slab with anisotropic scattering

The neutron transport equation for a slab geometry with the extremely anisotropic scattering kernel is considered. The albedo and transmission factors are calculated using the variation method. The effect of the extremely anisotropic parameter on the variation of the slab albedo and transmission factor is calculated. The obtained results are compared with the published data.     

Homotopic Theory of Bundles whose Fibers Are Matrix Algebras

In this paper, we consider homotopic properties of bundles of algebras, matrix Grassmanians, and homotopy functors connected with bundles of algebras.     

Efficiency of shear surface wave transformation by the motion of the confining domain wall

The transformation of a shear surface magnetoelastic wave by the motion of the 180° confining domain wall in a ferromagnet is considered. Changes in the wave spectrum due to the motion of the wall are correlated with the variations of the energies of the elastic and magnetic subsystems. The efficiency of surface wave transformation by the domain wall motion is estimated in terms of energy. The frequency dependences of the mean energy density of the wave are found. It is shown that the energy density grows with wall velocity.     

Influence of Pretreatment of Expanded Graphite on Its Sorption Properties with Respect to Petroleum

Petroleum sorption on expanded graphite prepared from residual graphite hydrosulfate at 300-900°C was studied as influenced by pretreatment of the sorbent with water.     

Degradation of Metal 2-Acrylamido-2-methylpropanesulfonate-N-Vinylpyrrolidine Copolymers in Aqueous Solutions Containing Different Cations

The influence of single- and double-charged cations on degradation of metal 2-acrylamido-2-methylpropanesulfonate-N-vinylpyrrolidine copolymers in aqueous solutions in the presence of potassium peroxodisulfate, K₂S₂O₈, at 50 and 70°C was studied by viscosimetry.