Let M be a C∞ manifold (without corners) and let E ⊆ TM be a subbundle of the tangent bundle. In class we discussed the notion of integral manifolds for E in M (as well as maximal ones), essentially as a generalization of the theory of integral curves for vector fields. Roughly speaking, in the special case that E is a trivial line bundle we are in the setup of integral curves for (non-vanishin...

We give an expression for the most general input-output map associated with the members of a certain important large family of causal time-invariant linear systems. This expression is a uniform limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution, and we relate this to the concepts of an impulse response and a q-response...

A dynamic reduced order model using integral manifold theory has been derived, which can be used to simulate the DOIG wind turbine using a double-winding representation of the generator rotor. The model is suitable for use in transient stability programs that can be used to investigate large power systems. The behavior of a wind farm and the network under various system disturbances was stu...

Line Integral Convolution (LIC), introduced by Cabral and Leedom in 1993, is a powerful technique for generating striking images of vector data. Based on local ltering of an input texture along a curved stream line segment in a vector eld, it is possible to depict directional information of the vector eld at pixel resolution. The methods suggested so far can handle structured grids only. Now we...

The Kitware Software Developer's Quarterly Newsletter contains articles related to the development of Kitware projects in addition to a myriad of software updates, news and other content relevant to the open source community. In this issue, Utkarsh Ayachit illustrates the LIC implementations in VTKEdge, VTK and ParaView which will allow users to exploit the processing power provided by modern G...

Toeplitzmatrices are characterized by a special structure that can be exploited in order to obtain fast linear system solvers. These solvers are difficult to parallelize due to their low computational cost and their closely coupled data operations. We propose to transform the Toeplitz system matrix into a Cauchy-like matrix since the latter can be divided into two independent matrices of half t...

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

The surface integral that measures the solid angle subtended by a planar aperture at a point in space is transformed to a line integral over the boundary of the aperture. The problem is divided into three distinct cases, and in each case a transformation is established. The results have a direct application to the problem of converting the Kirchhoff integral of diffraction by an aperture on a p...