The dataset generated by a large-scale numerical simulation may include thousands of timesteps and hundreds of variables describing different aspects of the modeled physical phenomena. In order to analyze and understand such data, scientists need the capability to explore simultaneously in the temporal, spatial, and variable domains of the data. Such capability, however, is not generally provid...

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. ...

The configuration space of a physical system is a differentiable manifold M. The state of a system is given by a point x in M and a tangent vector v at x, the velocity of the configuration. Call the tangent bundle T M of M the state space of the system (though the phrase " velocity phase space " is often used). A dynamical variable is a possibly time-dependent function on state space. Newtonian...

We consider a new state-space parametrization for linear time series models: data driven coordinates (DDC), which provides an atlas for the manifold of (stable) p×m transfer functions of fixed McMillan degree n. Hence, DDC has similar desirable properties as more traditional overlapping parametrizations and better than classical canonical forms. Moreover, the choice of charts can be done in a d...

The present paper deals with the quantum coordinates of an event in spacetime, individuated by a quantum object. It is known that these observables cannot be described by selfadjoint operators. We describe them by means of a normalized positive operator valued (POV) measure in the Minkowski spacetime, satisfying a suitable covariance condition with respect to the Poincaré group. This POV measur...

Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...