We discuss the twistor correspondence between complex vector bundles over a self-dual four-dimensional manifold and holomorphic bundles over its twistor space and describe the moduli space of self-dual Yang-Mills fields in terms of Čech and Dolbeault cohomology sets. The cohomological description provides the geometric interpretation of symmetries of the self-dual Yang-Mills equations.

The relatively small package capacity (less than 5 kb) of adeno-associated virus (AAV) vectors has been effectively doubled with the development of dual-vector heterodimerization approaches. However, the efficiency of such dual-vector systems is limited not only by the extent to which intermolecular recombination occurs between two independent vector genomes, but also by the directional bias re...

We show in this paper that Eq. (1) can be solved exactly in linear time. The procedure aims at solving a dual formulation of Eq. (1) involving the dual norm of ‖.‖ denoted by ‖.‖∗ and defined as ‖κ‖∗ = max‖z‖≤1 zκ for any vector κ in R. We first derive a dual problem based on conic duality [Boyd and Vandenberghe, 2004]. The rationale for using conic duality is to come up with a dual problem wit...

We show in this paper that Eq. (1) can be solved exactly in linear time. The procedure aims at solving a dual formulation of Eq. (1) involving the dual norm of ‖.‖ denoted by ‖.‖∗ and defined as ‖κ‖∗ = max‖z‖≤1 zκ for any vector κ in R. We first derive a dual problem based on conic duality [Boyd and Vandenberghe, 2004]. The rationale for using conic duality is to come up with a dual problem wit...

On the total space of a G−complex vector bundle E is defined the gauge transformations. A gauge complex invariant Lagrangian determines a special complex nonlinear connection for which the associated Chern-Lagrange and Bott complex connections are gauge invariant. The complex field equations are determined with respect to these associated gauge complex connections. By complex Legendre transform...

This project consists of a rambling introduction to some basic notions in multilinear algebra. The central purpose will be to show that the div, grad, and curl operators from vector calculus can all be thought of as special cases of a single operator on differential forms. Not all of the material presented here is required to achieve that goal. However, all of these ideas are likely to be usefu...

When does there exist an optimal generating Lagrangian multi-plier vector (that generates an optimal solution of an integer programming problem in a Lagrangian relaxation formulation), and in cases of nonexistence, can we produce the existence in some other equivalent representation space? Under what conditions does there exist an optimal primal-dual pair in integer programming? This paper cons...

Background: Aedes aegypti is the main vector of the yellow fever and dengue virus. This mosquito has become the major indirect cause of morbidity and mortality of the human worldwide. Dengue virus activity has been reported recently in the western areas of Saudi Arabia. There is no vaccine for dengue virus until now, and the control of the disease depends on the control of the vector. Objectiv...

BEIDOU AND GPS DUAL CONSTELLATION VECTOR TRACKING DURING IONOSPHERE SCINTILLATION AT EQUATORIAL REGION