Abstract: WAN is a child friendly educational card game that can be used to teach the concepts of trigonometric functions and identities or can be played as a simple card game by anyone over seven years old. The game uses all six basic trigonometric functions and their squares. These trigonometric functions are represented by various shapes and colors on the cards. Mathematical operations are determined by how the cards are placed. The game is played by creating card hands representing functions and operations that equal the number one. These card hands are called WAN hands.

Abstract: The regeneration of HF alkylation acid in an alkylation unit is improved by withdrawing a vapor stream from the HF regenerator tower and condensing the stream to form a liquid fraction which is accumulated in a side distillation zone; the collected liquid fraction, comprising HF acid, water and some stripping medium is distilled in a batch or continuous type operation to drive off the HF acid (along with stripping medium) and the vapor is returned to the regenerator-stripper vessel. The distillation of the sidedraw liquid is continued until the composition of the liquid attains the azeotropic value or as near to that value as desired. The azeotrope, comprising water and acid can then be dropped out of the distillation vessel for disposal by neutralization in the conventional way.

Abstract: The regeneration of HF alkylation acid in an alkylation unit is improved by withdrawing a vapor stream from the HF regenerator tower and condensing the stream to form a liquid fraction which is accumulated in a side distillation zone; the collected liquid fraction, comprising HF acid, water and some stripping medium is distilled in a batch or continuous type operation to drive off the HF acid (along with stripping medium) and the vapor is returned to the regenerator-stripper vessel. The distillation of the sidedraw liquid is continued until the composition of the liquid attains the azeotropic value or as near to that value as desired. The azeotrope, comprising water and acid can then be dropped out of the distillation vessel for disposal by neutralization in the conventional way.

Abstract: A ball holder for a ball-point pen is arranged to have a ball socket with a ball seat having a plurality of convex surfaces formed on concave shoulder surfaces. A writing ball inserted in the ball socket is supported by a single ball contact point on each of the ball seat convex surfaces. Concavities are provided between adjacent convex surfaces and shoulder surfaces for collecting and supplying ink to a surface of the writing ball.