Post-Dissolution Liabilities of Shareholders and Directors for Claims Against Dissolved Corporations

This Article initially will explore the nature and extent of shareholders\u27 and directors\u27 liabilities for contingent claims against the dissolved corporation by examining section 105 of the Model Business Corporation Act and the case law of those states that have adopted the Model Act.\u27 Two purposes underlying the Model Act are uniformity and progressive resolution of issues inadequately resolved by the common law or earlier statutes. An exhaustive analysis of the case law under section 105 of the Model Act, however,reveals that both purposes have been frustrated, if not defeated. First, uniformity among jurisdictions, as well as within each Model Act state, is defeated by the overwhelming inconsistency in the case law. Litigants presently can choose precedent to support almost any position they seek to argue. Moreover, section 105 itself does not resolve clearly any of the major post-dissolution liability issues. Its ambiguous language has furnished litigants and courts with little guidance in determining the legislatively intended answers to key issues

On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations

We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.Comment: We have modified the definition of Lipschitz well-posedness, in order to allow for a possible loss in regularity of the solution ma

Second-order gravitational self-force

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page

Emergence of fractal behavior in condensation-driven aggregation

We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision. We solved the model exactly by using scaling theory for the case whereby a particle, say of size $x$, grows by an amount $\alpha x$ over the time it takes to collide with another particle of any size. It is shown that the particle size spectra of such system exhibit transition to dynamic scaling $c(x,t)\sim t^{-\beta}\phi(x/t^z)$ accompanied by the emergence of fractal of dimension $d_f={{1}\over{1+2\alpha}}$. One of the remarkable feature of this model is that it is governed by a non-trivial conservation law, namely, the $d_f^{th}$ moment of $c(x,t)$ is time invariant regardless of the choice of the initial conditions. The reason why it remains conserved is explained by using a simple dimensional analysis. We show that the scaling exponents $\beta$ and $z$ are locked with the fractal dimension $d_f$ via a generalized scaling relation $\beta=(1+d_f)z$.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

Bone mass does not correlate with the serum fibroblast growth factor 23 in hemodialysis patients

Circulating fibroblast growth factor 23 (FGF23) increases renal phosphate excretion, decreases bone mineralization and is markedly increased in hemodialysis patients. Bone cells express fibroblast growth receptor 1, suggesting that FGF23 could alter bone mineralization by means of a direct effect on the skeleton and/or secondarily due to hypophosphatemia. To distinguish between these possibilities we measured serum concentrations of FGF23, parathyroid hormone, phosphate, calcium, and markers of bone remodeling, and assessed bone mineral density in 99 hemodialysis patients. FGF23 concentrations were increased in all hemodialysis patients, even in those without hyperphosphatemia, and positively correlated with serum phosphate but not with parathyroid hormone. Hemodialysis did not decrease the serum FGF23 concentration. We found no significant correlation between serum FGF23 levels and bone mineral density. Further analysis by gender or T-score did not modify these results. Serum markers of bone remodeling significantly correlated with parathyroid hormone but not with FGF23 levels. The increase in serum FGF23 concentration in hemodialysis patients cannot be solely ascribed to hyperphosphatemia. Our study suggests that the effects of FGF23 on bone mineralization are mainly due to hypophosphatemia and not a direct effect on bone

Conformal scattering for a nonlinear wave equation on a curved background

The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities. The proof is achieved in three steps. A priori linear estimates are obtained via an adaptation of the Morawetz vector field in the Schwarzschild spacetime and a method used by H\"ormander for the Goursat problem. A well-posedness result for the characteristic Cauchy problem on a light cone at infinity is then obtained. This requires a control of the nonlinearity uniform in time which comes from an estimates of the Sobolev constant and a decay assumption on the nonlinearity of the equation. Finally, the trace operators on conformal infinities are built and used to define the conformal scattering operator

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

Support varieties for selfinjective algebras

Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true

Influence of primary particle density in the morphology of agglomerates

Agglomeration processes occur in many different realms of science such as colloid and aerosol formation or formation of bacterial colonies. We study the influence of primary particle density in agglomerate structure using diffusion-controlled Monte Carlo simulations with realistic space scales through different regimes (DLA and DLCA). The equivalence of Monte Carlo time steps to real time scales is given by Hirsch's hydrodynamical theory of Brownian motion. Agglomerate behavior at different time stages of the simulations suggests that three indices (fractal exponent, coordination number and eccentricity index) characterize agglomerate geometry. Using these indices, we have found that the initial density of primary particles greatly influences the final structure of the agglomerate as observed in recent experimental works.Comment: 11 pages, 13 figures, PRE, to appea

Johnson-Kendall-Roberts theory applied to living cells

Johnson-Kendall-Roberts (JKR) theory is an accurate model for strong adhesion energies of soft slightly deformable material. Little is known about the validity of this theory on complex systems such as living cells. We have addressed this problem using a depletion controlled cell adhesion and measured the force necessary to separate the cells with a micropipette technique. We show that the cytoskeleton can provide the cells with a 3D structure that is sufficiently elastic and has a sufficiently low deformability for JKR theory to be valid. When the cytoskeleton is disrupted, JKR theory is no longer applicable