The dynamic properties of joints, or inter-component connections, are a principal source uncertainty when modelling complex built-up structures. In the present paper, we propose an interval-based sensitivity analysis (SA) to establish contribution, influence, structure’s uncertain joint dynamics towards its coupled admittance. We choose interval SA as it overcomes limitations conventional local...

For any complex vector bundle Ek of rank k over a manifold Mm with Chern classes ci ∈ H2i(Mm, Z) and any non-negative integers l1, · · · , lk we show the existence of a positive number p(m, k) and the existence of a complex vector bundle Êk over Mm whose Chern classes are p(m, k) · li · ci ∈ H2i(Mm, Z). We also discuss a version of this statement for holomorphic vector bundles over projective a...

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi–Yau manifold. In physics such a function appears as the partition function of N = 2 superconformal field theories. In these notes we define the modified ...

We analyse the possible recursive definitions of principal angles and vectors in complex vector spaces and give a new projector based definition. This enables us to derive important properties of the principal vectors and to generalize a result of Björck and Golub (Math. Comput. 1973; 27(123):579–594), which is the basis of today’s computational procedures in real vector spaces. We discuss othe...

We present a technique for constructing simple vector fields with complex behaviour and illustrate this technique with two examples. The examples we construct, besides describing partial behaviour of complicated systems, have an interest of their own as they illustrate complicated behaviour in a tractable way.

Special relativity is one of the monumental achievements of physics of the 20th Century. Whereas Einstein used a coordinate based approach [1], which obscures important geometric aspects of this fundamental theory, many coordinate free geometric languages have since been developed. In [2], D. Hestenes showed how the ideas of special relativity can be elegantly expressed in space-time algebra. T...