Ratio-based RTS determination in weight-restricted DEA models

This paper provides computationally efficient approaches for determining to which returns to scale (RTS) class a unit belongs in weight-restricted Data Envelopment Analysis (DEA) models. A non-traditional computational algorithm is introduced. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. Some theorems and algorithms are given. Computational advantages of the provided results are discussed and one of the algorithms is illustrated using real world data.     

Measuring position and momentum together

We describe an operational scheme for determining both the position and momentum distributions in a large class of quantum states, together with an experimental implementation.     

Effect of molecular size on the parity-non-conserving contributions to the nuclear magnetic resonance shielding constant

We present density-functional theory studies on the effects of molecular size on the parity-violating contribution to the nuclear magnetic shielding constant. We focus on models with different backbone and side chain lengths, as well as the details of geometry optimization for certain helical polysilylenes and investigate the parity-violating contribution to the shielding constant of the ²⁹Si nucleus of the backbone. Our calculations show that the molecular geometry has a large influence on the magnitude of the parity-violating shielding contribution, a result that is in line with the previous studies on much smaller molecules. In addition, we find convergence in the magnitude of the PV effect with respect to system size, when using geometries that preserve the helical Si backbone structure optimized for the largest of the present systems. This can be interpreted in terms of the non-size-extensive nature of the parity-violating operator influencing the leading-order effect on nuclear magnetic shielding, as opposed to the size-extensive interaction affecting the energy difference between enantiomers. Our molecules are truncated models of large polysilylene systems, for which a difference in the ²⁹Si chemical shift between enantiomers has been observed to be 0.06 ppm (Fujiki in Macromol Rapid Commun 22, 669–674, 2001). As expected based on earlier first principles studies of small molecules, we do not find support for the difference to be of the parity-violating origin. Instead, the predicted parity-violation-induced splitting of the ²⁹Si resonance is found to converge at values around 10^?8 ppm with increasingly large Si backbone.     

Experimental and theoretical treatment of hydrogen splitting and storage in boron-nitrogen systems

Hydrogen gas serves as a reducing agent and hydrogen atom source in numerous industrially important chemical processes and also has a great potential as a clean power source for fuel cells. In this respect, the reversible storage of hydrogen and the development of new metal-free hydrogenation catalysts are important tasks. Here, we review the recent literature, primarily on cases where the split H₂ forms an N-H?H-B dihydrogen bond. In these systems dihydrogen interaction was found to be the key actor in the hydrogen liberating process. Accordingly, the intramolecular ansa-aminoboranes (where B and N atoms are situated within each other’s range) can reversibly activate hydrogen. Moreover, the theoretical studies of the hydrogen splitting by bulky Lewis acid-Lewis base systems are discussed.     

ChemInform Abstract: AunHgm Clusters: Mercury Aurides,Gold Amalgams,or van der Waals Aggregates?

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Systematic Gaussian basis-set limit using completeness-optimized primitive sets. A case for magnetic properties

We discuss the connection between the completeness of a basis set, measured by the completeness profiles introduced by Chong (Can J Chem 1995, 73, 79) at a certain exponent interval, and the possibility of reproducing molecular properties that arise either in the region close to the atomic nuclei or in the valence region. We present a scheme for generating completeness-optimized Gaussian basis sets, in which a preselected range of exponents is covered to an arbitrary accuracy. This is done by requiring Gaussian functions, the exponents of which are selected without reference to the atomic structure, to span the range with completeness profile as close to unity as wanted with as few functions as possible. The initial exponent range can be chosen suitable for calculations of molecular energetics or other valence-like properties. By extending the exponent range, properties requiring augmentation of the basis at a given angular momentum value and/or in a given distance range from the nucleus may be straightforwardly and systematically treated. In this scheme a universal, element-independent exponent set is generated in an automated way. The relation of basis-set completeness and performance in the calculation of magnetizability, nuclear magnetic shielding, and spin-spin coupling is tested with the completeness-optimized primitive sets and literature basis sets.     

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.