Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.     

Castelnuovo-Mumford regularity by approximation

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups.     

On the Spectra of Carbon Nano-Structures

An explicit derivation of dispersion relations and spectra for periodic Schrödinger operators on carbon nano-structures (including graphene and all types of single-wall nano-tubes) is provided.     

Degree bounds for syzygies of invariants

Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in (Proc. Amer. Math. Soc. 129 (4) (2001) 955). Here we study minimal free resolutions of invariant rings. For finite linearly reductive groups G it was recently shown in (Adv. Math. 156 (1) (2000) 23, Electron Res. Announc. Amer. Math. Soc. 7 (2001) 5, Adv. Math. 172 (2002) 151) that rings of invariants are generated in degree at most the group order |G|. In characteristic 0 this degree bound is a classical result by Emmy Noether (see Math. Ann. 77 (1916) 89). Given an invariant ring of a finite linearly reductive group G, we prove that the ideal of relations of a minimal set of generators is generated in degree at most ?2|G|.     

Electronic structure and Fermi surface of Bi2Sr2CaCu2O8

Applying angle-resolved photoemission spectroscopy of high angular and energy resolution we have measured the electronic structure of single crystals of Bi₂Sr₂CaCu₂O₈ near the Fermi energy. Along the high symmetry direction X a band is observed to disperse upwards and to cross the Fermi level, whose unoccupied part constitutes the hole-like carriers responsible for the superconductivity. From spectra along the M direction we find evidence for an electron pocket around the M point. The measured band widths appear to be drastically reduced compared with band structure calculations indicating strong electronic correlation effects. From the observation of Fermi-Dirac-like cut-offs in the spectra due to band crossings through the Fermi level we can confirm the existence and, in particular, the shape of the Fermi surface as calculated by band structure calculations.     

The Effect of Preparation Method and Calcination Temperature on the Crystallite Size and Surface Area of Perovskite-Type SrFeO x

We have investigated the synthesis of perovskite-type SrFeO_x (2.5 x 3.0) using three preparative methods: sol-gel, mechanochemical processing and solid state reactions at high temperature of the corresponding oxides. The sample obtained after calcination of the gel from sol-gel method, contained the least amount of strontium carbonate impurity. The amount of strontium carbonate impurity decreased with the increase in calcination temperature. Perovskites obtained have been characterized by X-ray diffraction (XRD) and nitrogen adsorption isotherms. Samples obtained from three methods have been compared with respect to calcination temperature, crystallite size and specific surface area.Issued as NRCC No. 46479.     

Theory of reflectance measurements in quantitative evaluation in TLC and HPTLC. 1. Multilayer model of reflectance and transmittance

In the approach described in this paper, the layer of adsorbent is divided into n sublayers. The radiation density in each sublayer is given by the sum of the transmittance and the reflectance of the adjacent sublayers. Absorption of light by the layer or the substance will diminish this radiation density. Depending upon the factors of reflectance and transmittance some light will pass to the adjacent sublayers. Two polynomials are derived from this readily understood formulation to calculate the reflectance or the transmittance of a layer of finite thickness. The algorithms given describe the reflectance and transmittance encountered in practical measurements with large amounts of substance per spot, as well as with small amounts. There are no restrictions with respect to nonideal scattering or reflection by the adsorbent layer support.     

Derivatization of carboxylic acids with 9-bromomethylacridine using micellar phase-transfer catalysis

Summary Micellar phase-transfer catalysis (MPTC) offers the opportunity to derivatize carboxylic acids directly in an aqueous matrix without prior extraction of the acids into a suitable aprotic solvent. The currently developed MPTC system consists of a non-ionic surfactant, Arkopal N-130, an ion-pair agent, tetrakis-(decyl)-ammonium bromide, and a novel fluorescence reagent, 9-bromomethylacridine. The MPTC system can be applied to the derivatization of many types of carboxylic acids. The reaction rate is affected by the lipophilicity of the acid and by the presence of other functional groups. For lipophilic carboxylic acids the reaction is complete within 5 min at 60°C and pH 7.0.