Stiff convergence of force-gradient operator splitting methods

We consider force-gradient, also called modified potential, operator splitting methods for problems with unbounded operators. We prove that force-gradient operator splitting schemes retain their classical orders of accuracy for linear time-dependent partial differential equations of parabolic and Schrödinger types, provided that the solution is sufficiently regular.     

Non-existence of generalized splitting methods with positive coefficients of order higher than four

We prove that generalized exponential splitting methods making explicit use of commutators of the vector fields are limited to order four when only real coefficients are admitted. This generalizes the restriction to order two for classical splitting methods with only positive coefficients.     

The Groups LS and Morphisms of Quadratic Extensions

For a morphism of quadratic extensions of antistructures, groups similar to the groups of obstructions to splitting along one-sided submanifolds are defined. These groups are a natural generalization of the splitting obstruction groups. The results obtained open additional possibilities for constructing groups and natural maps in L-theory.     

A class of exhaustive cone splitting procedures in conical algorithms for concave minmization

A class of exhaustive cone splitting procedures is developed and is shown to perform substantially better than the bisection procedure in conical algorithms for concave minimization. Computational experiments are reported and discussed.     

Variable Selection in Regression via Repeated Data Splitting

Abstract

A new algorithm—backward elimination via repeated data splitting (BERDS)—is proposed for variable selection in regression. Initially, the data are partitioned into two sets {E, V}, and an exhaustive backward elimination (BE) is performed in E. For each p value cutoff α used in BE, the corresponding fitted model from E is validated in V by computing the sum of squared deviations of observed from predicted values. This is repeated m times, and the α minimizing the sum of the m sums of squares is used as the cutoff in a final BE on the entire data set. BERDS is a modification of the algorithm BECV proposed by Thall, Simon, and Grier (1992). An extensive simulation study shows that, compared to BECV, BERDS has a smaller model error and higher probabilities of excluding noise variables, of selecting each of several uncorrelated true predictors, and of selecting exactly one of two or three highly correlated true predictors. BERDS is also superior to standard BE with cutoffs .05 or .10, and this superiority increases with the number of noise variables in the data and the degree of correlation among true predictors. An application is provided for illustration.     

Iron-Doped Nickel Molybdate with Enhanced Oxygen Evolution Kinetics

Electrochemical water splitting is one of the potential approaches for making renewable energy production and storage viable. The oxygen evolution reaction (OER), as a sluggish four-electron electrochemical reaction, has to overcome high overpotential to accomplish overall water splitting. Therefore, developing low-cost and highly active OER catalysts is the key for achieving efficient and economical water electrolysis. In this work, Fe-doped NiMoO₄ was synthesized and evaluated as the OER catalyst in alkaline medium. Fe³⁺ doping helps to regulate the electronic structure of Ni centers in NiMoO₄, which consequently promotes the catalytic activity of NiMoO₄. The overpotential to reach a current density of 10 mA cm⁻² is 299 mV in 1 m KOH for the optimal Ni_0.9Fe_0.1MoO₄, which is 65 mV lower than that for NiMoO₄. Further, the catalyst also shows exceptional performance stability during a 2 h chronopotentiometry testing. Moreover, the real catalytically active center of Ni_0.9Fe_0.1MoO₄ is also unraveled based on the ex situ characterizations. These results provide new alternatives for precious-metal-free catalysts for alkaline OER and also expand the Fe-doping-induced synergistic effect towards performance enhancement to new catalyst systems.     

Spectroscopic Determination of the Electronic Structure of a Uranium Single-Ion Magnet

Early actinide ions have large spin-orbit couplings and crystal field interactions, leading to large anisotropies. The success in using actinides as single-molecule magnets has so far been modest, underlining the need for rational strategies. Indeed, the electronic structure of actinide single-molecule magnets and its relation to their magnetic properties remains largely unexplored. A uranium(III) single-molecule magnet, [U^III{SiMe₂NPh}₃-tacn)(OPPh₃)] (tacn=1,4,7-triazacyclononane), has been investigated by means of a combination of magnetic, spectroscopic and theoretical methods to elucidate the origin of its static and dynamic magnetic properties.