Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Ultrastructure of the excretory system of Trilocularia acanthiaevulgaris (Cestoda, Tetraphyllidea).

The fine structure of the excretory system in the juvenile (plerocercoid-like) form of Trilocularia acanthiaevulgaris is described. The flame cell bears a bunch of 50-70 cilia, which are anchored in the cytoplasm by means of basal bodies possessing striated rootlets. All the cilia in the

E-Commerce Innovations in the Personal Tax System of the United Kingdom

This study finds evidence that attempts to reduce costs and error rates in the Inland Revenue through the use of e-commerce technology are flawed. While it is technically possible to write software that will record tax data, and then transmit it to the Inland Revenue, there is little demand for this service. The key finding is that the tax system is so complex that many people are unable to complete their own tax returns. This complexity cannot be overcome by well-designed software. The recommendation is to encourage the use of agents to assist taxpayers or simplify the tax system. The Inland Revenue is interested in saving administrative costs and errors by encouraging electronic submission of tax returns. To achieve these objectives, given the raw data it would seem clear that the focus should be on facilitating the work of agents.

Instability and dynamics of two nonlinearly coupled laser beams in a plasma

The nonlinear interaction between two laser beams in a plasma is investigated in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schrodinger equations that are coupled with the slow plasma density response. A nonlinear dispersion relation is derived and used to study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations. (c) 2006 American Institute of Physics.