This paper concerns the implementation of the QR factorization by Givens and Householder transformations on vector computers . Following the analysis of Dongarra, et al. [1984] for Gaussian elimination, various ijk forms for both Givens and Householder transformations are investigated. Conclusions concerning which of these forms have desirable or undesirable properties for vector computers are ...

We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (suc...

We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (suc...

In this paper, we classify quasi-conformally flat generalized Sasakian-space forms under the assumption that characteristic vector field is Killing. Also Weyl-symmetric forms.

The language of modern mechanics is calculus on manifolds, and exterior calculus is an important part of that. It consists of objects like differential forms, general tensors and vector fields on manifolds, and operators that act on these. While the smooth exterior calculus has a long history going back to Cartan, Lie, Grassmann, Hodge, de Rham and many others, the need for a discrete calculus ...

Jacobi forms can be considered as vector valued modular forms, and Jacobi forms of critical weight correspond to vector valued modular forms of weight 1 2 . Since the only modular forms of weight 1 2 on congruence subgroups of SL(2,Z) are theta series the theory of Jacobi forms of critical weight is intimately related to the theory of Weil representations of finite quadratic modules. This artic...

The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.