Cyclic voltammetry of Th(IV) in the room-temperature ionic liquid [Me3NnBu][N(SO2CF3)2

A Th(IV) compound, [Th(TFSI)4(HTFSI)].2H2O [where TFSI = N(SO2CF3)2], has been synthesized and characterized using elemental analysis, thermogravimetric analysis, and vibrational spectroscopy. The analysis suggests that the TFSI anion coordinates to the metal center via the sulfonyl oxygens as well as provides evidence for the coordination of HTFSI. The voltammetric behavior of this compound has been studied in the room-temperature ionic liquid [Me3NnBu][TFSI], and results show that Th(IV) is reduced to Th(0) in this ionic liquid in a single reduction step. Analysis of cyclic voltammograms shows that an insoluble product is being formed at the electrode surface, which is attributed to the formation of ThO2 by reaction with water. The E0 value for the reduction of Th(IV) to Th(0) has been determined to be -2.20 V (vs Fc+/Fc; -1.80 V vs SHE). A comparison of this E0 value with those obtained for Th(IV) reduction in a LiCl-KCl eutectic (400 degrees C), water, and nonaqueous solvents shows that the reduction in [Me3NnBu][TFSI] is easier to accomplish than that in these other solvents.     

Existence of Hartree–Fock excited states for atoms and molecules

For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree–Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree–Fock theory, of the famous Zhislin–Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree–Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree–Fock functional satisfies the Palais–Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.     

A Family of Monotone Quantum Relative Entropies

We study here the elementary properties of the relative entropy ${\mathcal{H}_\varphi(A, B) = {\rm Tr}[\varphi(A) - \varphi(B) - \varphi'(B)(A - B)]}$ for φ a convex function and A, B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ′ is operator monotone. We use this to appropriately define ${\mathcal{H}_\varphi(A, B)}$ in infinite dimension.     

Free radical rearrangements of organocobaloximes: alkynyl to cycloalkylidene and hexenyl to cyclopentylmethyl

Under irradiation by tungsten light in pyridine solution, several substituted alkylcobaloximes undergo rearrangement to more stable substituted alkyl- or alkenyl-cobaloximes. When the same reactions are carried out in the presence of carbon tetrachloride or chloroform, no rearranged organocobaloximes are obtained, but a variety of organic products are obtained derived from the interception of transient organic radicals by the halogenated solvent. The rearrangements are rationalised in terms of a reversible homolysis of the carbon-cobalt bond, rearrangement of the organic radical and recapture by the cobalt(II) fragment to give complexes that are more stable to irradiation than their precursors.     

The growth function of some free products of groups

We give some hypotheses under which it, is easy to compute the growth function of free products and HNN extensions.     

The creation of actuarial science

Actuarial science was created more than 300 years ago. The article traces the influences which led to this development, which has been of such fundamental significance for calculations involving risk and finance and has enabled life assurance companies and pension funds to be financed on scientific principles. Actuarial techniques are nowadays starting to be applied in wider fields and it is suggested that the history of actuarial science could be taught in sixth forms and universities to students of risk and finance.     

Derivation of Hartreeʼs theory for generic mean-field Bose systems

In this paper we provide a novel strategy to prove the validity of Hartree?s theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the known case of trapped Bose gases, this can be shown using the strong quantum de Finetti theorem, which gives the structure of infinite hierarchies of k-particles density matrices. Here we deal with the case where some particles are allowed to escape to infinity, leading to a lack of compactness. Our approach is based on two ingredients: (1) a weak version of the quantum de Finetti theorem, and (2) geometric techniques for many-body systems. Our strategy does not rely on any special property of the interaction between the particles. In particular, our results cover those of Benguria–Lieb and Lieb–Yau for, respectively, bosonic atoms and boson stars.     

Semi-classical limit of the Levy–Lieb functional in Density Functional Theory

In a recent work, Bindini and De Pascale have introduced a regularization of N-particle symmetric probabilities that preserves their one-particle marginals. In this short note, we extend their construction to mixed quantum fermionic states. This enables us to prove the convergence of the Levy–Lieb functional in Density Functional Theory, to the corresponding multi-marginal optimal transport in the semi-classical limit. Our result holds for mixed states of any particle number N, with or without spin.