Comment on "Some novel delta-function identities"

We show that a form for the second partial derivative of $1/r$ proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that restriction.Comment: 4 page Comment on an AJP paper. The second version modifies the discussion and corrects some misprints. This version will appear in AJP

Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid

Virtual Las Vegas: Regulate or Prohibit?

With online gambling becoming increasingly accessible and popular, state and federal politicians are asking themselves how to make the prohibition on online gambling effective. Nevertheless, questions still linger as to whether outright prohibition is truly the right answer

Convergence in Karmarkar's Algorithm for Linear Programming

Karmarkar’s algorithm is formulated so as to avoid the possibility of failure because of unbounded solutions. A general inequality gives an easy proof of the convergence of the iterations. It is shown that the parameter value α = 0.5 more than doubles the originally predicted rate of convergence. To go from the last iterate to an exact optimal solution, an O(n^3) termination algorithm is prescribed. If the data have maximum bit length independent of n, the composite algorithm is shown to have complexity 0(n^4.5 log n)

Rigid body motion in special relativity

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term `rigid body' in relativistic straight line motion. We show that the definition of `rigid body' in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe: 1. The motion of a rigid body undergoing constant acceleration to a given velocity. 2. The acceleration of a rigid body due to an applied impulse. 3. Collisions between rigid bodies.Comment: Extended the discussion,and added reference

Quantity and number

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity