Yang-Baxter operators and scattering amplitudes in N=4\mathcal{N} = 4 super-Yang-Mills theory

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the extended symmetry and to recover as its consequences many known features like cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction, Grassmannian integral representation, $\mathrm{R}$-invariants and on-shell diagram approach.Comment: 32 pages, 10 figures, final version for publicatio

Preliminary Orbit Determination System (PODS) for Tracking and Data Relay Satellite System (TDRSS)-tracked target Spacecraft using the homotopy continuation method

The Preliminary Orbit Determination System (PODS) provides early orbit determination capability in the Trajectory Computation and Orbital Products System (TCOPS) for a Tracking and Data Relay Satellite System (TDRSS)-tracked spacecraft. PODS computes a set of orbit states from an a priori estimate and six tracking measurements, consisting of any combination of TDRSS range and Doppler tracking measurements. PODS uses the homotopy continuation method to solve a set of nonlinear equations, and it is particularly effective for the case when the a priori estimate is not well known. Since range and Doppler measurements produce multiple states in PODS, a screening technique selects the desired state. PODS is executed in the TCOPS environment and can directly access all operational data sets. At the completion of the preliminary orbit determination, the PODS-generated state, along with additional tracking measurements, can be directly input to the differential correction (DC) process to generate an improved state. To validate the computational and operational capabilities of PODS, tests were performed using simulated TDRSS tracking measurements for the Cosmic Background Explorer (COBE) satellite and using real TDRSS measurements for the Earth Radiation Budget Satellite (ERBS) and the Solar Mesosphere Explorer (SME) spacecraft. The effects of various measurement combinations, varying arc lengths, and levels of degradation of the a priori state vector on the PODS solutions were considered

Learning to Live with the New Foreign Nongrantor Trust Rules

The Small Business Job Protection Act of 1996 (the 1996 Act) was intended to deal a heavy blow to the appeal of foreign trusts to U.S. persons. The results were mixed. On the one hand, the 1996 Act imposes an array of reporting requirements, imposes harsh penalties on failures to comply with these requirements, increases the interest charge imposed on taxes paid on distributions of accumulated income from foreign trusts, treats loans of cash from foreign trusts as distributions, and expands the kinds of gifts that can be treated as indirect transfers from foreign trusts. On the other hand, curiously, the 1996 Act encourages the creation of foreign trusts by its adoption of a set of criteria for foreignness that is both more objective than the criteria formerly used and more biased in favor of foreign status. This Article discusses how to create foreign trusts, examines their exposure and the exposure of their U.S. beneficiaries to U.S. income tax, and describes the reporting requirements imposed on their creators, their beneficiaries, and the trusts themselves. In addition to explaining the rules, this Article also considers the extent to which foreign trusts continue to be useful planning tools for U.S. persons