The Five Point Conic Section: Exploration with Computer Software

This article investigates computer graphing of conic sections. It is shown how five points determine the formula of a conic section, and the determinant is used as a computational device to find the coefficients in the formula. The article is written in the “rule-of-threeform” using symbolic, numerical and graphical techniques. It is suitable for classroom enrichment where a computer is available.     

The photoelastic determination of the stresses in vibrating cantilevered beams

A method of determining the dynamic stresses in vibrating cantilevered beams using photoelasticity is presented. The method uses the basic principles of photomechanics and the optic-stress laws. A high-intensity strobe light is timed with the frequency of vibration so that the beam image appears to be stationary. Data are recorded with a camera and analyzed to provide an experimental solution. The theoretical solution is derived from the Bernoulli-Euler equation of motion. Two basic types of beams were investigated, an aluminum beam coated with a birefringent material to simulate an actual structural member and a birefringent model that was dynamically similar to the aluminum beam. The feasibility of extending the technique to more complicated shapes is suggested by this investigation. The experimental results and feasibility of the concept are verified by close correlation with the analytical solution.     

Kohlenhydrate

Ohne Zusammenfassung     

On the problem of constraints in minimally coupled relativistic wave equations for particles of unique mass

We study the problem of a possible change in the number of constraints in linear relativistic wave equations (-iβ _μ ∂ ^μ +m)ψ=0 for particles of unique mass, on introduction of minimal coupling to an external electromagnetic field. Complementing our earlier work in which we obtained conditions for non-loss of constraints in equations characterised by the minimalβ-algebraβ ₀ ⁵ =β ₀ ³ we derive here the conditions for such theories not to generate more constraints than in the free case. The results are illustrated by considering specific equations and a fallacy in certain conclusions of Kobayashi and Shamaly on this problem is pointed out.     

Ordinary linear differential equations involving random functions

Physical processes which can be represented by symbolic differential equations involving random functions are cited and studied. The solutions of these equations are obtained using Ramakrishnan’s recent phenomenological interpretation of integrals of random functions.     

Eine Methode, um im Laboratorium einen continuirlichen und gleichm?ssigen Strom von Acetylen

Ohne Zusammenfassung