We construct a representation of qudit multi-controlled unitary operators in terms of many-body angular momentum interactions. The representation is particularly convenient for odd-dimensional systems, with interesting connections to the Pegg-Barnett phase formalism. We illustrate the main points in the special case of qutrits, where simplifications and connections to dipole-quadrupole and quadrupole-quadrupole interactions can be established. We describe the representation of the closely related set of qudit hypergraph states, identifying possible realizations and their main obstacles. Qutrit tripartite controlled unitaries are decomposed in terms of more familiar two-body angular momentum couplings, enabling their implementation in a variety of physical systems. We give then a concrete example of implementation of qutrit unitaries and hypergraph states in optical systems that employs single-photon sources, two-mode cross-Kerr interactions and linear optical operations. Moreover, we define a new set of states, called angular momentum hypergraph states, which are more directly related to the angular momentum representation.

A family of solutions to the Ernst equation is presented, which, in a certain limit, recovers the Yamazaki-Hori solution - an extension of the Tomimatsu-Sato solutions for all integer values of the deformation parameter $\delta$. Our solution also recovers, as a special case, the formulation given by Vein, which is equivalent to the Yamazaki-Hori solution. Furthermore, our construction establishes a connection to a nonlinear differential equation proposed by Cosgrove, which is also associated with the Ernst equation.

We present a partial-sky survey of the radio continuum at 2.3 GHz within the scope of the Galactic Emission Mapping (GEM) project, an observational program conceived and developed to reveal the large-scale properties of Galactic synchrotron radiation through a set of self-consistent surveys of the radio continuum between 408 MHz and 10 GHz. The GEM experiment uses a portable and double-shielded 5.5-m radiotelescope in altazimuthal configuration to map 60-degree-wide declination bands from different observational sites by circularly scanning the sky at zenithal angles of 30 deg from a constantly rotating platform. The observations were accomplished with a total power receiver, whose front-end High Electron Mobility Transistor (HEMT) amplifier was matched directly to a cylindrical horn at the prime focus of the parabolic reflector. The Moon was used to calibrate the antenna temperature scale and the preparation of the map required direct subtraction and destriping algorithms to remove ground contamination as the most significant source of systematic error. We used 484 hours of total intensity observations from two locations in Colombia and Brazil to yield 66% sky coverage from DEC = -51.73 deg to DEC = +34.78 deg. The zero-level uncertainty of the combined survey is 103 mK with a temperature scale error of 5% after direct correlation with the Rhodes/HartRAO survey at 2326 MHz on a T-T plot. The sky brightness distribution into regions of low and high emission in the GEM survey is consistent with the appearance of a transition region as seen in the Haslam 408 MHz and WMAP K-band surveys. Preliminary results also show that the temperature spectral index between 408 MHz and the 2.3 GHz band of the GEM survey has a weak spatial correlation with these regions; but it steepens significantly from high to low emission regions with respect to the WMAP K-band survey.