Pole structure of the Hamiltonian ζ\zeta-function for a singular potential

We study the pole structure of the $\zeta$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $\zeta$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Ge

Strong ellipticity and spectral properties of chiral bag boundary conditions

We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function are analyzed on cylindrical product manifolds of arbitrary even dimension.Comment: 16 pages, LaTeX, References adde

Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm as long as the prescribed angular velocity $\alpha(t)$ of the boundary has bounded total variation. Here we establish convergence in stronger $L^2$ and $L^p$-Sobolev spaces, allow for more singular angular velocities $\alpha$, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently. [LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J., Vanishing viscosity limit for incompressible flow inside a rotating circle, preprint 2006

Discrete Symmetries in the Weyl Expansion for Quantum Billiards

We consider two and three-dimensional quantum billiards with discrete symmetries. We derive the first terms of the Weyl expansion for the level density projected onto the irreducible representations of the symmetry group. As an illustration the method is applied to the icosahedral billiard. The paper was published in J. Phys. A /27/ (1994) 4317-4323Comment: 8 printed pages Latex fil

Abelian Duality

We show that on three-dimensional Riemannian manifolds without boundaries and with trivial first real de Rham cohomology group (and in no other dimensions) scalar field theory and Maxwell theory are equivalent: the ratio of the partition functions is given by the Ray-Singer torsion of the manifold. On the level of interaction with external currents, the equivalence persists provided there is a fixed relation between the charges and the currents.Comment: 11 pages, LaTeX, no figures, a reference added, submitted to Phys. Rev.

Proteomic analysis of Arabidopsis glutathione S-transferases from benoxacor- and copper-treated seedlings

Glutathione S-transferases (GSTs) are involved in many stress responses in plants, for example, participating in the detoxification of xenobiotics and limiting oxidative damage. Studies examining the regulation of this gene family in diverse plant species have focused primarily on RNA expression. A proteomics method was developed to identify GSTs expressed in Arabidopsis seedlings and to determine how the abundance of these proteins changed in response to copper, a promoter of oxidative stress, and benoxacor, a herbicide safener. Eight GSTs were identified in seedlings grown under control conditions, and only one, AtGSTU19, was induced by benoxacor. In contrast, four GSTs, AtGSTF2, AtGSTF6, AtGSTF7, and AtGSTU19, were significantly more abundant in copper-treated seedlings. The different responses to these treatments may reflect the potential for copper to affect many more aspects of plant growth and physiology compared with a herbicide safener. Differences between RNA and protein expression of GSTs indicate that both transcriptional and translational mechanisms are involved in regulation of GSTs under these conditions

Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls

We extend our previous results of simplified expressions for functional determinants for radial Schr\"odinger operators to the computation of vacuum energy, or mass corrections, for static but spatially radial backgrounds, and for domain wall configurations. Our method is based on the zeta function approach to the Gel'fand-Yaglom theorem, suitably extended to higher dimensional systems on separable manifolds. We find new expressions that are easy to implement numerically, for both zero and nonzero temperature.Comment: 30 page

Preferential tau aggregation in von Economo neurons and fork cells in frontotemporal lobar degeneration with specific MAPT variants.

Tau aggregation is a hallmark feature in a subset of patients with frontotemporal dementia (FTD). Early and selective loss of von Economo neurons (VENs) and fork cells within the frontoinsular (FI) and anterior cingulate cortices (ACC) is observed in patients with sporadic behavioral variant FTD (bvFTD) due to frontotemporal lobar degeneration (FTLD), including FTLD with tau inclusions (FTLD-tau). Recently, we further showed that these specialized neurons show preferential aggregation of TDP-43 in FTLD-TDP. Whether VENs and fork cells are prone to tau accumulation in FTLD-tau remains unclear, and no previous studies of these neurons have focused on patients with pathogenic variants in the gene encoding microtubule-associated protein tau (FTLD-tau/MAPT). Here, we examined regional profiles of tau aggregation and neurodegeneration in 40 brain regions in 8 patients with FTLD-tau/MAPT and 7 with Pick's disease (PiD), a sporadic form of FTLD-tau that often presents with bvFTD. We further qualitatively assessed the cellular patterns of frontoinsular tau aggregation in FTLD-tau/MAPT using antibodies specific for tau hyperphosphorylation, acetylation, or conformational change. ACC and mid-insula were among the regions most affected by neurodegeneration and tau aggregation in FTLD-tau/MAPT and PiD. In these two forms of FTLD-tau, severity of regional neurodegeneration and tau protein aggregation were highly correlated across regions. In FTLD-tau/MAPT, VENs and fork cells showed disproportionate tau protein aggregation in patients with V337 M, A152T, and IVS10 + 16 variants, but not in patients with the P301L variant. As seen in FTLD-TDP, our data suggest that VENs and fork cells represent preferentially vulnerable neuron types in most, but not all of the MAPT variants we studied