The solution of an optimal power ow (OPF) problem in rectangular form by an interior-point method (IPM) for nonlinear programming is described. When formulated in rectangular form, some OPF variants have quadratic objective and quadratic constraints. Such quadratic features allow for ease of matrix setup and inexpensive incorporation of higher-order information in a predictor-corrector procedur...

We prove that the separating space of an epimorphism from a Lie–Banach algebra onto the (continuous) derivation algebra Der(A) of a Banach algebra A consists of derivations which map into the radical of A.

This paper presents the derivation, simulation, and implementation of a nonlinear tracking control law for a hydraulic servosystem. An analysis of the nonlinear system equations is used in the derivation of a Lyapunov function that provides for exponentially stable force trajectory tracking. This control law is then extended to provide position tracking. The proposed controller is simulated and...

Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations higher Frobenius kernels reduces to first kernel. In preceding paper in this series, deforming distribution algebra a kernel yielded family deformations called reduced enveloping algebras. we prove Steinberg decomposition can be similarly deformed, allowing us reduce representa...

In the late 1980s, Friedlander and Parshall studied representations of a family algebras which were obtained as deformations distribution algebra first Frobenius kernel an algebraic group. The representation theory these tells us much about Lie in positive characteristic. We develop analogue this for higher kernels, answering 30 year old question posed by Parshall. also examine their case speci...

We define, for each subset $S$ of the set $\mathcal{P}$ primes, an $S_n$-module $Lie_n^S$ with interesting properties. $Lie_n^\emptyset$ is well-known representation $Lie_n$ $S_n$ afforded by free Lie algebra, while $Lie_n^\mathcal{P}$ module $C\!onj_n$ conjugacy action on $n$-cycles. For arbitrary $Lie_n^{S}$ interpolates between representations and $C\!onj_n.$ consider symmetric exterior powe...

It is well known that anomaly cancellations for D16 Lie algebra are at the root of the first string revolution. For E8 Lie algebra, cancellation of anomalies is the principal fact leading to the existence of heterotic string. They are in fact nothing but the 6th order cohomologies of corresponding Lie algebras. Beyond 6th order, the calculations seem to require special care and it could be that...