Periodic motion or oscillation is a common phenomenon which exists in almost all disciplines of physical and engineering systems. Limit cycle is one of the source generating periodic motion, and its study plays an important role in the research of nonlinear dynamical systems. A related wellknown problem to limit cycle is Hilbert’s 16th problem [Hilbert, 1902], which has attracted many mathemati...

Extended Abstract: I will only summarise the evidence for the transmission of the calculus from India to Europe in the 16th c. CE, since it has been considered elsewhere. Briefly, unlike the wild claims of transmission from “Greece”, typically advanced without serious evidence by Western historians in the last three centuries, the standard of evidence I use is a legal standard of evidence which...

In 1948 Miroslav Katětov showed that if the cube X3 of a compact space X satisfies the separation axiom T5 then X must be metrizable. He asked whether X3 can be replaced by X2 in this metrization result. In this note we prove the consistency of this implication.

Newcomb’s problem is a decision puzzle whose difficulty and interest stem from the fact that the possible outcomes are probabilistically dependent on, yet causally independent of, the agent’s options. The problem is named for its inventor, the physicist William Newcomb, but first appeared in print in a 1969 paper by Robert Nozick [12]. Closely related to, though less well-known than, the Prison...

This talk will come in four parts. First, I will introduce the Riemann hypothesis (RH) as it was first introduced, using the Riemann zeta function, and discuss briefly its connection to number theory and prime numbers. Second, I will make this connection explicit by discussion a famous problem equivalent to RH. Third, I will examine the generalised Riemann hypothesis (GRH) and, finally, will li...

We show that Tsirelson’s problem concerning the set of quantum correlations and Connes’ embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg’s QWEP conjecture) are essentially equivalent. Specifically, Tsirelson’s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the...

We analyse the one-dimensional motion of a uniform thin fibre which is pulled upwards from a horizontal plane by a constant vertical force exerted against the homogeneous gravitational field. The solution of the equation of motion which describes this variable mass problem is discussed and the character of the resulting damped oscillations is described. 1. Historical background and formulation ...