Buckling of a continuous beam resting on a tensionless elastic foundation

In this paper, a solution is presented to the buckling problem of a continuous beam resting on a tensionless foundation model that was proposed by Winkler and by Reissner.     

Adjacency matrix concepts for the analysis of the interconnection of networks

A mathematical theory is developed for an imagined device termed a “junctor”. A junctor could be used to interconnect two n-terminal networks giving rise to another n-terminal network. Actually a junctor is itself a simple network with three banks of n-terminals internally connected in some fashion by perfectly conducting wires. Adjacency matrices are formulated to analyze various junctors and their current flows. The main problem treated concerns conditions which would ensure that the junctor operation is associative.     

Definition in science teaching

Summary Definitions, I have suggested, have both a function and a form. The function pursued and the form used should depend on the situation and on the term being defined. In the situation described at the outset, Mr. Beta should probably have seen to it that a stipulation of some sort was given-just in order to get on with the task at hand. The stipulation might have been based upon a true reported definition-or it might not-depending on political considerations and the linguistic flexibility of the people concerned. Since no one involved could plausibly have been trying to embody a program in a definition of dough, a programmatic definition was not appropriate in that situation.Several different forms for a definition of dough might reasonably have been used, but in this case the old reliable classification form was probably best, because of its completeness, neatness, and brevity. Two reasonable alternatives are the equivalent-expression form and the range form. The synonym, example-nonexample, and operational forms were probably not appropriate.My main point is that there is not just one way to define. I hope that my delineation of some major possibilities and variations will help those who read this article to be flexible in handling problems of definition when they arise; and they arise more often than most people realize.An ealier draft of this article was presented at a colloquium at the University of Illinois in honor of Professor B. Othanel Smith at his retirement.