Raman scattering from magnons in CoCl2 and FeCl2

One-magnon Raman scattering has been observed in the metamagnets CoCl₂ and FeCl₂. The k = 0 magnon energies are 16 ± 1 cm^-1 at 21 K and 16.4 ± 0.4 cm^-1 at 12 K, respectively and these values are in good agreement with previous AFMR and neutron scattering results. A search for two-magnon scattering in both compounds was unsuccessful, largely because of masking from nearby first-order phonons and a weak temperature dependent broad band at 140 cm^-1 in CoCl₂, which is assigned to two-phonon scattering from acoustic phonons.     

Transition De Phase Metamagnetique Du Bromure Ferreux

In a magnetic field parallel to the magnetization axis of an antiferromagnetic Fe Br₂ single crystal, a caracteristic metamagnetic behaviour is observed. The transition from an antiferromagnetic phase to a paramagnetic phase is studied by help of magnetization measurements in a steady field (H < 60 kOe). The measurement precision has allowed a detailed study of the magnetization isotherms, caracteristic of a first order magnetization phase transition (T < T_c = 4, 7 K) and of a second order phase transition (T_c < T < T_N = 14, 2 K).We have observed an original phase diagram. In a certain temperature and field range, the ordered phase is stable on the high temperature side of the transition point. Some theoretical studies in an Ising model, or in the hypothesis of a strong magnetoelastic coupling forecast the existence of such a magnetic phase diagram.At present, we proceed to a theoretical study, in a molecular field approximation, of the magnetic phase diagram of compounds similar to Fe Br₂ where we take into account the relative values of parameters J₁, J₂ and D associated with ferromagnetic and antiferromagnetic interactions and crystalline anisotropy.     

Solution phase synthesis of a library of tetrasubstituted pyrrole amides

An efficient strategy for the solution-phase parallel synthesis of a library of pyrrole-amides is described. Key reactions include functional homologation of beta-ketoesters with a set of aldehydes followed by oxidation to produce a series of differently substituted 1,4-dicarbonyl compounds. Rapid cyclization using a microwave-assisted Paal-Knorr reaction provided a set of 24 pyrrole esters that were further functionalized through a trimethylaluminum-mediated aminolysis to obtain a larger library of 288 diverse pyrrole-3-amides. The tetrasubstitution allows a good exploration of the chemical space around the central pyrrole core. The last step was entirely automated with a Bohdan Myriad personal synthesizer.     

Elemental chemical analysis of submerged targets by double-pulse laser-induced breakdown spectroscopy

Double-pulse laser-induced plasma spectroscopy (DP-LIPS) is applied to submerged targets to investigate its feasibility for elemental analysis. The role of experimental parameters, such as inter-pulse delay and detection time, has been discussed in terms of the dynamics of the laser-induced bubble produced by the first pulse and its confinement effect on the plasma produced by the second laser pulse. The analytical performance of this technique applied to targets in a water environment are discussed. The elemental analysis of submerged copper alloys by DP-LIPS has been compared with conventional (single-pulse) LIBS in air. Theoretical investigation of the plasma dynamics in water bubbles and open air has been performed.     

RBFOpt: an open-source library for black-box optimization with costly function evaluations

We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the solution methodology implemented in the open-source library RBFOpt, available on COIN-OR. The algorithm is based on the Radial Basis Function method originally proposed by Gutmann (J Glob Optim 19:201–227, 2001.  https://doi.org/10.1023/A:1011255519438), which builds and iteratively refines a surrogate model of the unknown objective function. The two main methodological contributions of this paper are an approach to exploit a noisy but less expensive oracle to accelerate convergence to the optimum of the exact oracle, and the introduction of an automatic model selection phase during the optimization process. Numerical experiments show that RBFOpt is highly competitive on a test set of continuous and mixed-integer nonlinear unconstrained problems taken from the literature: it outperforms the open-source solvers included in our comparison by a large amount, and performs slightly better than a commercial solver. Our empirical evaluation provides insight on which parameterizations of the algorithm are the most effective in practice. The software reviewed as part of this submission was given the Digital Object Identifier (DOI)  https://doi.org/10.5281/zenodo.597767.     

Representation of MV-algebras by regular ultrapowers of [0, 1]

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable way, thus providing a sort of “canonical” set of values for the functional representation.     

An integral formulation procedure for the solutions to Helmholtz's equation in spherically symmetric media

Starting from Helmholtz's equation in inhomogeneous media, the associated radial second‐order equation is investigated through a Volterra integral equation. First the integral equation is considered in a sphere. Boundedness, uniqueness and existence of the (regular) solution are established and the series form of the solution is provided. An estimate is determined for the error arising when the series is truncated. Next the analogous problem is considered for a spherical layer. Again, boundedness, uniqueness and existence of two base solutions are established and error estimates are determined. The procedure proves more effective in the sphere. Copyright © 2009 John Wiley & Sons, Ltd.