Length functions of 2-dimensional right-angled Artin groups

Morgan and Culler proved that a minimal action of a free group on a tree is determined by its translation length function. We prove an analogue of this theorem for 2-dimensional right-angled Artin groups acting on CAT(0) rectangle complexes.     

On learning process of a newsvendor with censored demand information

A behavioural study on the newsvendor problem without demand distribution knowledge or realized demands is conducted. We configure a censored-information scenario, where only sales data in history are provided. With laboratory experiments, we analyse participants ordering levels and ordering oscillations over time. It is observed that participants perform a significant learning process in the censored-information scenario. Moreover, we find that participants make orders by anchoring on the previous-period sales and adjusting to an adapted inventory level. On the basis of the observations, we propose an exponential-type learning (EXP) model to describe the behaviour of decision makers. Comparing with a chasing model that is popularly used in the full-information scenario, the EXP model is more recommended in the censored-information scenario.     

The Least-Perimeter Partition of a Sphere into Four Equal Areas

We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.     

Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition

Domain decomposition methods for solving the coupled Stokes–Darcy system with the Beavers–Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and the results of computational experiments are presented to illustrate the convergence.     

Synthesis and Characterization of a Stable Nickelocenium Dication Salt

We report the synthesis and characterization of the nickelocenium cations [NiCp₂]⋅⁺ and [NiCp₂]²⁺ as their [F-{Al(OR^F)₃}₂]⁻ (Cp = C₅H₅; R^F=C(CF₃)₃) salts. Diamagnetic [NiCp₂]²⁺ represents the first example for the isolation of an unsubstituted parent metallocene dication. Both salts were generated by reacting neutral NiCp₂ with [NO]⁺[F-{Al(OR^F)₃}₂]⁻ in 1,2,3,4-tetrafluorobenzene (4FB). The salts were characterized by single crystal X-ray diffraction (XRD), indicating shorter metal-ligand bond lengths for the higher charged salt. Powder XRD shows the salts to be phase pure, cyclic voltammetry in 4FB gave quasi reversible redox waves at −0.44 (0→1) and +1.17 V (1→2) vs Fc/Fc⁺. The ¹H NMR of [NiCp₂]²⁺ is a singlet at 8.6 ppm, whereas paramagnetic [NiCp₂]⋅⁺ is significantly shifted upfield to −103.1 ppm.     

Palladium-catalyzed alkylation of 1,4-dienes by C-H activation

Activated: the title reaction proceeds with a broad range of nucleophiles and variously substituted 1,4-dienes under mild conditions, and provides direct access to the corresponding 1,3-diene-containing products with high regio- and stereocontrol (see scheme; 2,6-DMBQ=2,6-dimethylbenzoquinone, EWG=electron-withdrawing group). This is the first catalytic allylic C-H alkylation that proceeds in the absence of sulfoxide ligands.