Energies of knot diagrams

We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals considered are the sum of two terms, the uniformization term (which tends to make the curvature of the knot uniform) and the resistance term (which, in particular, forbids crossing changes). We define an infinite family of uniformization functionals, depending on an arbitrary smooth function $f$ and study the simplest nontrivial case $f(x)=x^2$, obtaining neat normal forms (corresponding to minima of the functional) by making use of the Gauss representation of immersed curves, of the phase space of the pendulum, and of elliptic functions

The Soviet Union and The Middle East: The High Cost of Influence

A common concern harbored by many Americans regarding the current Middle Eastern situation has been the ostensibly growing measure of Soviet influence over Arab regimes in the area

Thurgood Marshall: Man of Character

As a result of his historic achievements, Thurgood Marshall changed the face of America. Although the changes have not been so swift in recent years as they were at the height of Marshall\u27s career, progress will continue and the direction is certain. In the end, that progress toward the achievement of equality for all will be Thurgood Marshall\u27s greatest legacy. Thurgood Marshall\u27s life was a unique conjunction of person and place, of talent and destiny. He was an American original, a man of character whose contributions to the Republic redeemed its most cherished values

Soviet Policy Toward the Middle East Since the October 1973 Arab-Israeli War

It comes as no surprise that the long-term Soviet goal in the Middle East is to diminish, if not to replace, Western and particularly United States influence. However, at least since the Yom Kippur War, the states and the political forces in the Middle East are subjects and are no longer objects of international politics