Molar absorptivities of U(VI), U(IV), and Pu(III) in nitric acid solutions of various concentrations relevant to developing nuclear fuel recycling flowsheets

Journal of Radioanalytical and Nuclear Chemistry - The activity and osmotic coefficients of fission product systems CsOH?+?CsCl, CsOH?+?CsBr and CsOH?+?CsI are...     

Exciton Interactions,Excimer Formation,and [2π+2π] Photodimerization in Nonconjugated Curcuminoid-BF2 Dimers

We describe the synthesis of a series of covalently linked dimers of quadrupolar curcuminoid-BF₂ dyes and the detailed investigation of their solvent-dependent spectroscopic and photophysical properties. In solvents of low polarity, intramolecular folding induces the formation of aggregated chromophores, the UV/Vis absorption spectra of which display the optical signature characteristic of weakly-coupled H-aggregates. The extent of folding and, in turn, of ground-state aggregation is strongly dependent on the nature of the flexible linker. Steady-state and time-resolved fluorescence emission spectroscopies show that the Frenkel exciton relaxes into a fluorescent symmetrical excimer state with a long lifetime. Furthermore, our in-depth studies show that a weakly emitting excimer lies on the pathway toward a photocyclomer. Two-dimensional ¹H NMR spectroscopy and density functional theory (DFT) allowed the structure of the photoproduct to be established. To our knowledge, this represents the first example of a [2π+2π] photodimerization of the curcuminoid chromophore.     

Formation of helical beams by use of Pancharatnam-Berry phase optical elements

Spiral phase elements with topological charges based on space-variant Pancharatnam-Berry phase optical elements are presented. Such elements can be achieved by use of continuous computer-generated space-variant subwavelength dielectric gratings. We present a theoretical analysis and experimentally demonstrate spiral geometrical phases for infrared radiation at a wavelength of 10.6microm .     

Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design

In this paper, we propose a path relinking procedure for the fixed-charge capacitated multicommodity network design problem. Cycle-based neighbourhoods are used both to move along paths between elite solutions and to generate the elite candidate set by a tabu-like local search procedure. Several variants of the method are implemented and compared. Extensive computational experiments indicate that the path relinking procedure offers excellent results. It systematically outperforms the cycle-based tabu search method in both solution quality and computational effort and offers the best current meta-heuristic for this difficult class of problems.     

Notes on the Kazhdan–Lusztig Theorem on Equivalence of the Drinfeld Category and the Category of $\boldsymbol{U}_{\!\boldsymbol q}{\boldsymbol {\mathfrak g}}$-Modules

We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category \({\mathcal D}({\mathfrak g},\hbar)\) of \({\mathfrak g}\)-modules and the category of finite dimensional \(U_q{\mathfrak g}\)-modules, \(q=e^{\pi i\hbar}\), for \(\hbar\in{\mathbb C}\setminus{\mathbb Q}^*\). Aiming at operator algebraists the result is formulated as the existence for each \(\hbar\in i{\mathbb R}\) of a normalized unitary 2-cochain \({\mathcal F}\) on the dual \(\hat G\) of a compact simple Lie group G such that the convolution algebra of G with the coproduct twisted by \({\mathcal F}\) is *-isomorphic to the convolution algebra of the q-deformation G _q of G, while the coboundary of \({\mathcal F}^{-1}\) coincides with Drinfeld’s KZ-associator defined via monodromy of the Knizhnik–Zamolodchikov equations.     

On a conjecture of Vorst

Let k be an infinite perfect field of positive characteristic such that strong resolution of singularities holds over k. We prove that a localization of a d-dimensional commutative k-algebra R of finite type is K _d+1-regular if and only if it is regular. This partially affirms a conjecture of Vorst.     

On Anosov energy levels of hamiltonians on twisted cotangent bundles

LetT ^* M denote the cotangent bundle of a manifoldM endowed with a twisted symplectic structure [1]. We consider the Hamiltonian flow generated (with respect to that symplectic structure) by a convex HamiltonianH: T ^* M, and we consider a compact regular energy level ofH, on which this flow admits a continuous invariant Lagrangian subbundleE. When dimM3, it is known [9] that such energy level projects onto the whole manifoldM, and thatE is transversal to the vertical subbundle. Here we study the case dimM=2, proving that the projection property still holds, while the transversality property may fail. However, we prove that in the case whenE is the stable or unstable subbundle of an Anosov flow, both properties hold.     

Convergence de mesures spectrales aléatoires et applications à des principes d'invariance

Nous présentons un cadre unificateur pour un certain nombre de résultats connus de convergence en loi pour des processus admettant une représentation linéaire par rapport à un bruit blanc faible pour lequel il existe un principe dinvariance faible. Nous montrons que ce principe dinvariance est équivalent à la convergence dune suite de mesures aléatoires spectrales. Ceci permet daffaiblir les hypothèses usuelles et donc dobtenir des résultats nouveaux de convergence en loi, notamment pour des processus à longue portée.     

Optimal Paths for Symmetric Actions in the Unitary Group

Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold.