The use of Raman microscopy and laser desorption ionization mass spectrometry in the examination of synthetic organic pigments in modern works of art

Synthetic organic pigments are widely used in modern and contemporary works of art. They have been examined by a variety of techniques including spectroscopic methods such as Fourier transform infrared spectroscopy, Raman, and X‐ray powder diffraction as well as chromatographic or mass spectrometric techniques such as pyrolysis‐gas chromatography/mass spectrometry and laser desorption ionization mass spectrometry (LDI–MS). Often, a combination of techniques has been used to examine these pigments. This paper describes use of Raman spectroscopy to create a database of colorants including two pigments not previously reported, PO1 and PO2. Then, using Raman spectroscopy in combination with LDI–MS, samples from modern works of art by artists including Mark Rothko, Barnett Newman, and José de Rivera were examined in order to identify the pigments present. One finding was that Rothko used a variety of red pigments over the course of his career including PR11 which has not been previously reported in artwork, and PO2 found with its positional isomer PR1. Knowledge of the colorants serves to inform conservators about display and treatment decisions. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

On Weighted Poincaré Inequalities

We are concerned with the problem of finding sharp summability conditions on the weights which render certain weighted inequalities of Poincaré - type true. The conditions we find consist of proper integral balances between the growths of the rearrangements of the weights.     

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].     

Theoretical investigation of EPR and optical spectra of Mo(V) in [Mo6O19][N(C4H9)4]3 salt

The electron paramagnetic resonance (EPR) spectral data (the g factors and hyperfine structure constants) and d–d transition spectra for the tetragonal Mo⁵⁺ centre in [Mo₆O₁₉][N(C₄H₉)₄]₃ salt are theoretically investigated from the complete diagonalization method (CDM) for a 4d¹ ion in tetragonally compressed octahedron. The theoretical results are in good agreement with the experimental data. The dependency of the g factors of the ground state on the R_∥(MoO bond length) has been studied. It is shown that the g factors varied with the R_∥ approximately in a linear way.     

Intersection Poincaré Polynomial for Nagaraj–Seshadri moduli space

We compute Betti numbers of both the components of the moduli space of rank 2 semi‐stable torsion‐free sheaves with fixed determinant over a reducible nodal curve with two smooth components intersecting at a node. We also compute the intersection Betti numbers of the moduli space.     

Multi-Conjugate Adaptive Optics for ELTs: constraints and limitations

We present how enlarging the size of a telescope from the current 10 meter telescope to the future 100 meter Extremely Large Telescopes increases the complexity of a classical or multiconjugate adaptive optics instrument. We point out elements or parameters of the system for which it is critical to propose new ideas as solutions and we study the effect of the increase of the diameter on the point spread function of an MCAO and a Ground Layer AO system. To cite this article: R. Ragazzoni et al., C. R. Physique 6 (2005).     

Tuning for the first 9-cell TESLA cavity of PKU

A method based on circuit model is used to tune the first home-made 9-cell TESLA type superconducting niobium cavity at Peking University.After tuning,a flat field profile with a final π-mode frequency within 3 kHz of target frequency is achieved.The field flatness is measured by a bead-pull method,and the relative electric field is calculated from the frequency shift perturbed by the bead stepping along the axis of the cavity.     

Path bundles on n-cubes

A path bundle is a set of 2^a paths in an n-cube, denoted Q_n, such that every path has the same length, the paths partition the vertices of Q_n, the endpoints of the paths induce two subcubes of Q_n, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n>0 is odd and 0?a?n-⌈log₂(n+1)⌉.     

On the complexity of some subgraph problems

We study the complexity of the problem of deciding the existence of a spanning subgraph of a given graph, and of that of finding a maximum (weight) such subgraph. We establish some general relations between these problems, and we use these relations to obtain new NP-completeness results for maximum (weight) spanning subgraph problems from analogous results for existence problems and from results in extremal graph theory. On the positive side, we provide a decomposition method for the maximum (weight) spanning chordal subgraph problem that can be used, e.g., to obtain a linear (or O(nlogn)) time algorithm for such problems in graphs with vertex degree bounded by 3.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.