Filing for Bankruptcy and Untying the Knot? Not Without Strings Attached

(Excerpt) Substantive consolidation is an equitable remedy used sparingly by bankruptcy courts to consolidate the bankruptcy estates of two debtors. Although it originated in the corporate context, consolidating the estates of two corporate entities or a corporate entity and an individual debtor, its application has extended to consumer bankruptcy. The consolidation of the bankruptcy estates of two debtor spouses has been addressed and recognized by the Second, Third, Fourth, Sixth, Eighth, and Eleventh Circuit Courts. Part I of this article briefly examines the authority legitimizing substantive consolidation. Part II analyzes the remedy’s corporate origins and the differing approaches taken by the circuit courts. Part III explores its expansion into the consumer context, particularly debtor spouses, and the Eighth Circuit’s decision in Boellner v. Dowden, which was the first time a circuit court affirmed an order substantively consolidating the separate estates of debtor spouses. This article concludes that debtors in the process of ending their marital relationship should take concrete steps to legalize that dissolution prior to filing for bankruptcy if they want to reduce the risk that their bankruptcy estates will be substantively consolidated

Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity

We present an implicit-explicit well-balanced finite volume scheme for the Euler equations with a gravitational source term which is able to deal also with low Mach flows. To visualize the different scales we use the non-dimensionalized equations on which we apply a pressure splitting and a Suliciu relaxation. On the resulting model, we apply a splitting of the flux into a linear implicit and an non-linear explicit part that leads to a scale independent time-step. The explicit step consists of a Godunov type method based on an approximative Riemann solver where the source term is included in the flux formulation. We develop the method for a first order scheme and give an extension to second order. Both schemes are designed to be well-balanced, preserve the positivity of density and internal energy and have a scale independent diffusion. We give the low Mach limit equations for well-prepared data and show that the scheme is asymptotic preserving. These properties are numerically validated by various test cases

Solute carriers involved in energy transfer of mitochondria form a homologous protein family

AbstractThe sequences of three mitochondrial carriers involved in energy transfer, the ADP/ATP carrier, phosphate carrier and uncoupling carrier, are analyzed. Similarly to what has been previously reported for the ADP/ATP carrier and the uncoupling protein, now also the phosphate carrier is found to have a tripartite structure comprising three similar repeats of approx. 100 residues each. The three sequences show a fair overall homology with each other. More significant homologies are found by comparing the repeats within and between the carriers in a scheme where the sequences are spliced into repeats, which are arranged for maximum homology by allowing possible insertions or deletions. A striking conservation of critical residues, glycine, proline, of charged and of aromatic residues is found throughout all nine repeats. This is indicative of a similar structural principle in the repeats. Hydropathy profiles of the three proteins and a search for amphipathic α-spans reveal six membrane-spanning segments for each carrier, providing further support for the basic structural identity of the repeats. The proposed folding pattern of the carriers in the membrane is exemplified with the phosphate carrier. A possible tertiary arrangement of the repeats and the membranespanning helices is shown. The emergence of a mitochondrial carrier family by triplication and by divergent evolution from a common gene of about 100 residues is discussed

AnAll Speed SecondOrder IMEXRelaxation Scheme for the Euler Equations

We present an implicit-explicit finite volume scheme for the Euler equations. We start from the non-dimensionalised Euler equations where we split the pressure in a slow and a fast acoustic part. We use a Suliciu type relaxation model which we split in an explicit part, solved using a Godunov-type scheme based on an approximate Riemann solver, and an implicit part where we solve an elliptic equation for the fast pressure. The relaxation source terms are treated projecting the solution on the equilibrium manifold. The proposed scheme is positivity preserving with respect to the density and internal energy and asymptotic preserving towards the incompressible Euler equations. For this first order scheme we give a second order extension which maintains the positivity property. We perform numerical experiments in 1D and 2D to show the applicability of the proposed splitting and give convergence results for the second order extension