We comment on the necessity of a unified approximative scheme within relativistic cosmology which would allow us to classify different cosmological models in a systematic way. We also report on recent progresses in formulating a cosmological post-Newtonian approximation and the problems related to such a scheme.

The extended model concept links migration velocity analysis and waveform inversion. This abstract presents a method to solve a partially linearized version of the full waveform inversion problem with model extension. Linearization separates the model of the earth into the smooth long scale background model and the short scale model. Extended waveform inversion allows the short scale model to d...

We consider a framework for learning additive classifiers based on regularized empirical risk minimization, where the regularization favors “smooth” functions. We present representations of classifiers for which the optimization problem can be efficiently solved. The first family of such classifiers are derived from a penalized spline formulation due to Eilers and Marx, which is modified to ena...

In this paper, we study the existence and uniqueness of a degenerate parabolic equation, with nonhomogeneous boundary conditions, coming from the linearization of the Crocco equation [12]. The Crocco equation is a nonlinear degenerate parabolic equation obtained from the Prandtl equations with the so-called Crocco transformation. The linearized Crocco equation plays a major role in stabilizatio...

We suggest a new spin-4 self-dual model (parity singlet) and parity doublet in $D=2+1$. They are of higher order derivatives described by totally symmetric rank-4 tensor without extra auxiliary fields. Despite the they ghost free. find gauge invariant field combinations which allow us to show that canonical structure (spin-3) models follows same pattern its spin-2 (spin-1) counterpart after red...

A scheme to achieve a wideband linearized silicon Mach-Zehnder (MZ) modulator is proposed. The modulator consists of a single MZ interferometer with identical reverse-biased silicon diode phase shifters in both arms, driven in a push-pull configuration. It is shown that the 3rd order nonlinearity of the modulator can be eliminated by canceling the nonlinearities from the silicon phase shifters ...

We consider polynomial maps described by so-called (multivariate) linearized polynomials. These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps without mixed terms over a characteristic zero field, we will only obtain (up to a linear transformation of the variables) triangular maps, which are the most b...

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. In this paper we use techniques from the spatial operator algebra to obtain closed form operator expressions for two types of linearized dynamics models, the Linearized Inverse and Forward Dynamics Models. We rst develop spatially recursive algorithms of O(n) and O(n) complexity ...

A nonlinear controllable plant, under mild technical conditions, admits a precompensator with the following property: along control trajectories joining pairs of states, the composite system (precompensator plus plant) is, up to first order, isomorphic to a parallel connection of integrators. Appeared in IEEE Trans.Autom.Control, Vol.32, 10, Oct.1987, pp877-888 *Research supported in part by US...

We are now ready to consider the solutions of GR for the case of weak gravitational fields. This encompasses Newtonian gravity, as well as a few extensions thereof. In addition to its importance in e.g. the solar system, our study of linearized gravity will prepare us for the discussion of some of the weak-field experimental tests of GR (Lecture XI). It will also illustrate some of the issues t...