Nodal and spectral minimal partitions -- The state of the art in 2015 --

In this article, we propose a state of the art concerning the nodal and spectral minimal partitions. First we focus on the nodal partitions and give some examples of Courant sharp cases. Then we are interested in minimal spectral partitions. Using the link with the Courant sharp situation, we can determine the minimal k-partitions for some particular domains. We also recall some results about the topology of regular partitions and Aharonov-Bohm approach. The last section deals with the asymptotic behavior of minimal k-partition

On spectral minimal partitions II, the case of the rectangle

In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-\frac a2,\frac a2[\times ] -\frac b2,\frac b2[$, with $0< a\leq b$. It has been observed in \cite{HHOT} that when $0<\frac ab < \sqrt{\frac 38}$ the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles $]-\frac a2,\frac a2[\times ] -\frac b2,-\frac b6[$, $]-\frac a2,\frac a2[\times ] -\frac b6,\frac b6[$ and $]-\frac a2,\frac a2[\times ] \frac b6, \frac b2[$. We will describe a possible mechanism of transition for increasing $\frac ab$ between these nodal minimal 3-partitions and non nodal minimal 3-partitions at the value $\sqrt{\frac 38}$ and discuss the existence of symmetric candidates for giving minimal 3-partitions when $\sqrt{\frac 38}<\frac ab \leq 1$. Numerical analysis leads very naturally to nice questions of isospectrality which are solved by introducing Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle

Against Divine Truthmaker Simplicity

Divine Simplicity has it that God is absolutely simple. God exhibits no metaphysical complexity; he has neither proper parts nor distinct intrinsic properties. Recently, Jeffrey Brower has put forward an account of divine simplicity that has it that God is the truthmaker for all intrinsic essential predications about him. This allows Brower to preserve the intuitive thought that God is not a property but a concrete being. In this paper, I provide two objections to Brower’s account that are meant to show that whatever merits this account of divine simplicity has, plausibility is not one of them

Site-dependent charge transfer at the Pt(111)-ZnPc interface and the effect of iodine

The electronic structure of ZnPc, from sub-monolayers to thick films, on bare and iodated Pt(111) is studied by means of X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS) and scanning tunneling microscopy (STM). Our results suggest that at low coverage ZnPc lies almost parallel to the Pt(111) substrate, in a non-planar configuration induced by Zn-Pt attraction, leading to an inhomogeneous charge distribution within the molecule and charge transfer to the molecule. ZnPc does not form a complete monolayer on the Pt surface, due to a surface-mediated intermolecular repulsion. At higher coverage ZnPc adopts a tilted geometry, due to a reduced molecule-substrate interaction. Our photoemission results illustrate that ZnPc is practically decoupled from Pt, already from the second layer. Pre-deposition of iodine on Pt hinders the Zn-Pt attraction, leading to a non-distorted first layer ZnPc in contact with Pt(111)-I $\left(\sqrt{3}\times\sqrt{3}\right)$ or Pt(111)-I $\left(\sqrt{7}\times\sqrt{7}\right)$, and a more homogeneous charge distribution and charge transfer at the interface. On increased ZnPc thickness iodine is dissolved in the organic film where it acts as an electron acceptor dopant.Comment: 12 pages, 9 figure

Superconductivity in domains with corners

We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the normal state occurs. We discuss and clarify the definition of this field and obtain a complete asymptotic expansion for it in the large $\kappa$ regime. Furthermore, we discuss nucleation of superconductivity at the boundary

Outside-in disk evolution in the LMC

From the analysis of the color-magnitude diagrams and color functions of four wide LMC fields located from ~2 to 6 kpc from the kinematic center of the LMC we present evidence that, while the oldest population is coeval in all fields, the age of the youngest component of the dominant stellar population gradually increases with galactocentric distance, from currently active star formation in a field at 2.3 deg, to 100 Myr, 0.8 Gyr, and 1.5 Gyr in fields at 4.0 deg, 5.5 deg, and 7.1 deg, respectively. This outside-in quenching of the star formation in the LMC disk is correlated with the decreasing HI column density (which is < 2x 10^{20} cm^{-2} in the two outermost fields with little or no current star formation. Other work in the literature hints at similar behavior in the stellar populations of irregular galaxies, and in M33. This is observational evidence against the inside-out disk formation scenario in low-mass spirals and irregular galaxies. Alternatively, it could be that the age distribution with radius results from interplay between the evolution with time of the star-forming area of the LMC and the subsequent outward migration of the stars.Comment: 6 pages, 2 figures, ApJ Letters, in pres

Collagen α5 and α2(IV) chain coexpression: Analysis of skin biopsies of Alport patients

Alport syndrome is a collagen type IV disease caused by mutations in the COL4A5 gene with the X-linked form being most prevalent. The resultant α5(IV) collagen chain is a component of the glomerular and skin basement membranes (SBMs). Immunofluorescent determination of the α5(IV) chain in skin biopsies is the procedure of choice to identify patients. In 30% of patients, however, the mutant protein is still found in the SBM resulting in a normal staining pattern. In order to minimize or eliminate false results, we compared the distribution of the α2(IV) chain (another SBM component) and the α5(IV) chain by standard double label immunofluorescence (IF) and by confocal laser scanning microcopy. The study was performed on 55 skin biopsies of patients suspected of Alports and five normal control specimens. In normal skin, IF showed the classical linear pattern for both collagens along the basement membrane. Additionally, decreased α5(IV) was found in the bottom of the dermal papillary basement membrane. Confocal analysis confirmed the results and show α5(IV) focal interruptions. In suspected patients, both techniques showed the same rate of abnormal α5(IV) expression: segmental in women and absent in men. Our results show a physiological variation of α5(IV) location with focal interruptions and decreased expression in the bottom of the dermal basement membrane. Comparison of α5(IV) with α2(IV) expression is simple and eliminates technical artifacts