Estimating scale economies in non-convex production models

The literature on nonparametric frontier technologies lacks a method for the measurement of scale economies in non-convex settings. This paper proposes a general procedure which is based on the minimization of the ray average cost and requires the solution of a single programming problem. Our approach allows for multiple optima to introduce the case of global sub-constant scale economies, and it also permits the estimation of scale economies at a local level. The empirical application investigates the role of replicability and the relationship between global and local indicators. It also points out the managerial implications for companies operating in the Italian public transit industry.     

A low frequency stable plane wave addition theorem

The multilevel fast multipole algorithm (MLFMA) is a well known and very successful method for accelerating the matrix-vector products required for the iterative solution of Helmholtz problems. The MLFMA has an important drawback, namely its inability to handle scattering problems with a lot of subwavelength detail due to the low frequency (LF) breakdown of the MLFMA. There is a need to extend the MLFMA to LF, since alternative methods are less efficient (multipole methods) or hard to implement (spectral methods). In this paper a new addition theorem will be developed that does not suffer from an LF breakdown. Instead it suffers from a high-frequency (HF) breakdown. The new method relies on a novel set of distributions, the so-called pseudospherical harmonics, closely related to the spherical harmonics. These allow the discretization points and translation operators to be calculated in closed form. Hence the method presented in this paper allows the easy implementation of a method that is stable at LF. Furthermore, a combination of the traditional MLFMA and the new method allows for the construction of a broadband MLFMA.     

Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space

We examine curvature properties of twisted surfaces with null rotation axis in Minkowski 3-space. That is, we study surfaces that arise when a planar curve is subject to two synchronized rotations, possibly at different speeds, one in its supporting plane and one of this supporting plane about an axis in the plane. Moreover, at least one of the two rotation axes is a null axis. As is clear from its construction, a twisted surface generalizes the concept of a surface of revolution. We classify flat, constant Gaussian curvature, minimal and constant mean curvature twisted surfaces with a null rotation axis. Aside from pseudospheres, pseudohyperbolic spaces and cones, we encounter B-scrolls in these classifications. The appearance of B-scrolls in these classifications is of course the result of the rotation about a null axis. As for the cones in the classification of flat twisted surfaces, introducing proper coordinates, we prove that they are determined by so-called Clelia curves. With a Clelia curve we mean a curve that has linear dependent spherical coordinates.     

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via ? ₁ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ? ₁ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to ? ₁-constraints, using a gradient method, with projection on ? ₁-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.     

Electronic structure of BaTiO3 using resonant X-ray emission spectroscopy at the Ba-L3 and Ti-K absorption edges

We have studied the electronic properties of the ferroelectric barium titanate BaTiO₃ using two complementary bulk-sensitive spectroscopic probes, resonant X-ray emission spectroscopy (RXES) and X-ray absorption spectroscopy in the partial fluorescence mode (PFY-XAS) at the Ba-L₃ and Ti-K absorption edges. Contrary to a previous study, we found no fine structure in the pre-edge area of the PFY-XAS spectrum at the Ba-L₃ edge, and no temperature-induced spectral change was observed between room temperature and 150 °C. This result is not supportive of the possible presence of the displacement around Ba²⁺ at the Curie temperature. RXES spectra were measured at the Ti-K edge for BaTiO₃, along with SrTiO₃ and La-doped metallic SrTiO₃. The photon energy of the emission peak is found to be nearly constant throughout the absorption edge for all three compounds. We deduce the Ti 3d states to have a delocalized character, in contrast with the Ba 5d states, a property which is consistent with the proposed scenario of the formation of electric dipoles in BaTiO₃.     

Decomposition of Gaseous Sulfide Compounds in Air by Pulsed Corona Discharge

The effectiveness of applying a pulsed corona discharge to the destruction of olfactory pollution in air was investigated. This paper presents a comparative study of the decomposition of three representative sulfide compounds in diluted concentrations: hydrogen sulfide (H₂S), dimethyl sulfide (DMS), and ethanethiol (C₂H₅SH), which could be completely removed when a sufficient but reasonable energy density was deposited in the gas. DMS showed the lowest energy cost (around 30 eV/molecules); C₂H₅SH and H₂S had an EC of respectively 45 eV and 115 eV. The efficiency of the non-thermal plasma process increased with decreasing the initial concentration of sulfide compounds, while the energy yield remained almost unchanged. SO₂ was the only identified byproduct of H₂S decomposition, but the sulfur balance suggests the formation of undetected SO₃. The byproducts analyzed during the degradation of DMS and C₂H₅SH enabled to propose a reaction mechanism, starting with radical attack and breaking of C–S bonds.     

Control of the interfacial reactivity in the Ni/Si system

The reactivity at the Ni/Si interface is studied as a function of the sputtering conditions of the nickel film. Four systems are considered, by combining two different sputtering rates and two distinct base pressures for the deposition of the nickel 10 nm-thick film. The formation of Ni₂Si is revealed at the four interfaces by an X-ray emission spectroscopy study of the interfacial Si 3p occupied valence states. Increasing the sputtering rate is herein evidenced to decrease the quantity of silicide formed at the interface. Moreover, the combination of a high sputtering rate and a low base pressure advantageously prevents against the oxidization of the silicon surface during the metal deposition.     

Ordering of hydrogen bonds in high-pressure low-temperature H2O

The near K-edge structure of oxygen in liquid water and ices III, II, and IX at 0.25 GPa and several low temperatures down to 4 K has been studied using inelastic x-ray scattering at 9884.7 eV with a total energy resolution of 305 and 175 meV. A marked decrease of the preedge intensity from the liquid phase and ice III to ices II and IX is attributed to ordering of the hydrogen bonds in the proton-ordered lattice of the latter phases. Density functional theory calculations including the influence of the Madelung potential of the ice IX crystal correctly account for the remaining preedge feature. Furthermore, we obtain spectroscopic evidence suggesting a possible new phase of ice at temperatures between 4 and 50 K.     

An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography

We propose an iterative algorithm for the minimization of a ? ₁-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in the penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.     

Enantioselective Synthesis of Complex Fused Heterocycles through Chiral Phosphoric Acid Catalyzed Intramolecular Inverse-Electron-Demand Aza-Diels–Alder Reactions

A stable asymmetric intramolecular Povarov reaction has been established to provide an efficient method to access structurally diverse trans,trans-trisubstituted tetrahydrochromeno[4,3-b]quinolines in high stereoselectivities of up to >99:1 diastereomeric ratio and 99 % enantiomeric excess, without any purification step. Additionally, to facilitate large-scale application of this method, a low catalyst loading protocol was employed, 0.2 mol % chiral phosphoric acid, which provided the cycloadducts without any loss in yield and enantioselectivity. Theoretical studies revealed that the reaction occurred through a sequential Mannich reaction and an intramolecular Friedel–Crafts reaction, wherein the phosphoric acid acted as a bifunctional catalyst to activate the para-phenolic dienophile and N-2-hydroxy-2-azadiene simultaneously.