The Supreme Court, Due Process and State Income Taxation of Trusts

What are the constitutional limits on a state\u27s power to tax a trust with no connection to the state, other than the accident that a potential beneficiary lives there? The Supreme Court of the United States will take up this question this term in the context of North Carolina Department of Revenue v. Kimberley Rice Kaestner 1992 Family Trust. The case involves North Carolina\u27s income taxation of a trust with a contingent beneficiary, meaning someone who is eligible, but not certain, to receive a distribution or benefit from the trust, who resides in that state. Part I of this Article explains the background of Kaestner Trust and frames the constitutional questions that will be before the Court at oral arguments on April 16, 2019. Part II examines how and why due process applies in the state income taxation context, with a particular emphasis on how familiar concepts of general and specific jurisdiction apply uneasily to donative trusts. Part III articulates the reasons that the Court should hold that a state has no constitutional authority to impose a tax on trust income where the trust\u27s only connection with the forum state is the residence of a contingent beneficiary. Kaestner Trust is the most important due process case involving trusts that the Court has decided in over sixty years; it bears directly on the fundamental meaning of due process

Superpotentials and Quiver Algebras for Semisimple Hopf Actions

We consider the action of a semisimple Hopf algebra $H$ on an $m$-Koszul Artin-Schelter regular algebra $A$. Such an algebra $A$ is a derivation-quotient algebra for some twisted superpotential $\mathsf{w}$, and we show that the homological determinant of the action of $H$ on $A$ can be easily calculated using $\mathsf{w}$. Using this, we show that the smash product $A\,\#\,H$ is also a derivation-quotient algebra, and use this to explicitly determine a quiver algebra $\Lambda$ to which $A\,\#\,H$ is Morita equivalent, generalising a result of Bocklandt-Schedler-Wemyss. We also show how $\Lambda$ can be used to determine whether the Auslander map is an isomorphism. We compute a number of examples, and show how several results for the quantum Kleinian singularities studied by Chan-Kirkman-Walton-Zhang follow using our techniques

Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode

An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude $\rho(t)$ decouples from the phase due to the spatial homogeneity of the equilibrium, and the resulting one-dimensional dynamics is analyzed using an expansion in $\rho$. As the linear growth rate $\gamma$ vanishes, the expansion coefficients diverge; a rescaling $\rho(t)\equiv\gamma^2\,r(\gamma t)$ of the mode amplitude absorbs these singularities and reveals that the mode electric field exhibits trapping scaling $|E_1|\sim\gamma^2$ as $\gamma\rightarrow0$. The dynamics for $r(\tau)$ depends only on the phase $e^{i\xi}$ where $d\epsilon_{{k}} /dz=|{\epsilon_{{k}}}|e^{-i\xi/2}$ is the derivative of the dielectric as $\gamma\rightarrow0$.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the Author ([email protected]); paper accepted by Physical Review Letter

A Search for Radio Emission from the Young 16-ms X-ray Pulsar PSR J0537-6910

PSR J0537-6910 is a young, energetic, rotation-powered X-ray pulsar with a spin period of 16 ms located in the Large Magellanic Cloud. We have searched for previously undetected radio pulsations (both giant and standard) from this pulsar in a 12-hour observation taken at 1400 MHz with the Parkes 64-m radio telescope. The very large value of the magnetic field at the light cylinder radius suggests that this pulsar might be emitting giant radio pulses like those seen in other pulsars with similar field strengths. No radio emission of either kind was detected from the pulsar, and we have established an upper limit of ~ 25 mJy kpc^2 for the average 1400-MHz radio luminosity of PSR J0537-6910. The 5-sigma single-pulse detection threshold was ~ 750 mJy for a single 80-us sample. These limits are likely to be the best obtainable until searches with greatly improved sensitivity can be made with next-generation radio instruments.Comment: 4 pages, including 1 figure and 2 tables. Accepted for publication in Advances in Space Research; Proceedings of Session E1.4 of the 35th COSPAR Scientific Assembly, Paris, July 18-25 2004, "Young Neutron Stars and Supernova Remnants", edited by C. Rakowski and S. Chatterje

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]