X-ray diffraction study of ammonium octamolybdate

Ammonium isopolymolybdate (NH₄)₄[Mo₈O₂₆]·4H₂O was prepared for the first time and studied by X-ray diffraction analysis.     

Bimodal Fluorescence/Magnetic Resonance Molecular Probes with Extended Spin Lifetimes

Bimodal molecular probes combining nuclear magnetic resonance (NMR) and fluorescence have been widely studied in basic science, as well as clinical research. The investigation of spin phenomena holds promise to broaden the scope of available probes allowing deeper insights into physiological processes. Herein, a class of molecules with a bimodal character with respect to fluorescence and nuclear spin singlet states is introduced. Singlet states are NMR silent but can be probed indirectly. Symmetric, perdeuterated molecules, in which the singlet states can be populated by vanishingly small electron-mediated couplings (below 1 Hz) are reported. The lifetimes of these states are an order of magnitude longer than the longitudinal relaxation times and up to four minutes at 7 T. Moreover, these molecules show either aggregation induced emission (AIE) or aggregation caused quenching (ACQ) with respect to their fluorescence. In the latter case, the existence of excited dimers, which are proposed to use in a switchable manner in combination with the quenching of nuclear spin singlet states, is observed     

A Process for Determining Priorities and Weights for Large-Scale Linear Goal Programmes

Many planning models can be formulated as large-scale linear goal-programming problems in which the analyst and user must establish thousands of objective-function weights that reflect the priorities of the many goals. How to select such weights so as to have the resulting optimal solution be a suitable compromise solution is the main focus of this paper. We first describe the problem setting that gave rise to the need, here military personnel planning, and then a process by which a set of goal priorities and objective-function weights can be developed using Saaty's analytic hierarchy process.     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

Mirror and synchronous couplings of geometric Brownian motions

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in general even if the geometric Brownian motions are martingales. On the other hand, we prove that in the cases of the ergodic average and the infinite time horizon criteria, the mirror coupling and the synchronous coupling are always optimal for general (possibly non-martingale) geometric Brownian motions. We show that the two couplings are efficient if and only if they are optimal over a finite time horizon and give a conjectural answer for the efficient couplings when they are suboptimal.