Extended generalised variances, with applications

Extended generalised variances, with applications

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

Theory of Generalised Biquandles and Its Applications to Generalised Knots

In this thesis we present a range of different knot theories and then generalise them. Working with this, we focus on biquandles with linear and quadratic biquandle functions (in the quadratic case we restrict ourselves to functions with commutative coefficients). In particular, we show that if a biquandle is commutative, the biquandle function must have non-commutative coefficients, which ties...

Matrix variances with projections

The quantum variance of a self-adjoint operator depends on a density matrix whose particular example is a pure state (formulated by a projection). A general variance can be obtained from certain variances of pure states. This is very different from the probabilistic case.

Stochastic properties of generalised Yule models, with biodiversity applications.

The Yule model is a widely used speciation model in evolutionary biology. Despite its simplicity many aspects of the Yule model have not been explored mathematically. In this paper, we formalise two analytic approaches for obtaining probability densities of individual branch lengths of phylogenetic trees generated by the Yule model. These methods are flexible and permit various aspects of the t...