Autonomous linear lossless systems

We define a lossless autonomous system as one having a quadratic differential form associated with it called an energy function, which is positive and which is conserved. We define an oscillatory system as one which has all its trajectories bounded on the entire time axis. In this paper, we show that an autonomous system is lossless if and only if it is oscillatory. Next we discuss a few properties of energy functions of autonomous lossless systems and a suitable way of splitting a given energy function into its kinetic and potential energy components

Algebraic Geometry Approach in Gravity Theory and New Relations between the Parameters in Type I Low-Energy String Theory Action in Theories with Extra Dimensions

On the base of the distinction between covariant and contravariant metric tensor components, a new (multivariable) cubic algebraic equation for reparametrization invariance of the gravitational Lagrangian has been derived and parametrized with complicated non - elliptic functions, depending on the (elliptic) Weierstrass function and its derivative. This is different from standard algebraic geometry, where only two-dimensional cubic equations are parametrized with elliptic functions and not multivariable ones. Physical applications of the approach have been considered in reference to theories with extra dimensions. The s.c. "length function" l(x) has been introduced and found as a solution of quasilinear differential equations in partial derivatives for two different cases of "compactification + rescaling" and "rescaling + compactification". New physically important relations (inequalities) between the parameters in the action are established, which cannot be derived in the case $l=1$ of the standard gravitational theory, but should be fulfilled also for that case.Comment: 4 pages; no figures; Talk at the Grassmannian Conference in Fundamental Cosmology "Grasscosmofun'09" (14-19 September 2009, University of Szczecin, Poland); prepared for the Proceedings of the Conference, which will appear in a special issue of the journal "Annalen der Physik" (Leipzig); "Ann.der Phys." style files use

A globally convergent matricial algorithm for multivariate spectral estimation

In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate spectral estimation, and test its effectiveness through simulation. Simulation shows that, in the case of short observation records, this method may provide a valid alternative to standard multivariable identification techniques such as MATLAB's PEM and MATLAB's N4SID