In this paper we study branching laws for certain unitary representations. This is done on the smooth vectors via a version of {\it period integrals}, studied in number theory, and also closely connected to symmetry-breaking operators}, introduced by T.~Kobayashi. We exhibit non-vanishing symmetry breaking operators restriction representation $\Pi$ discrete spectrum real hyperboloids represen...

In an earlier article, atomic radii of elements of Groups 1A 8A were shown to be proportional to their Bohr radii obtained from the first ionization potentials and the constants of proportionality were shown to be simple functions of the Golden ratio. Here it is shown that the above finding holds also for elements of Groups 1B 8B including Lanthanides and Actinides. All the relevant data are pr...

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalised by a discrete cosine transform (DCTII). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

Nowadays, numerical modelings play a key role in analyzing hydraulic problems in fractured rock media. The discrete fracture network model is one of the most used numerical models to simulate the geometrical structure of a rock-mass. In such media, discontinuities are considered as discrete paths for fluid flow through the rock-mass while its matrix is assumed impermeable. There are two main pa...

We find a Lax pair for the geometrically exact discrete Hamiltonian equations for the discrete elastic rod. This is paper III in a series. III. Lax Pair for Discrete Dynamics of Discrete Elastic DNA Shi, McClain, and Hearst