Improving discrimination in data envelopment analysis: PCA–DEA or variable reduction

Within the data envelopment analysis context, problems of discrimination between efficient and inefficient decision-making units often arise, particularly if there are a relatively large number of variables with respect to observations. This paper applies Monte Carlo simulation to generalize and compare two discrimination improving methods; principal component analysis applied to data envelopment analysis (PCA–DEA) and variable reduction based on partial covariance (VR). Performance criteria are based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. A trade-off was observed with both methods improving discrimination by reducing the probability of the latter error at the expense of a small increase in the probability of the former error. A comparison of the methodologies demonstrates that PCA–DEA provides a more powerful tool than VR with consistently more accurate results. PCA–DEA is applied to all basic DEA models and guidelines for its application are presented in order to minimize misclassification and prove particularly useful when analyzing relatively small datasets, removing the need for additional preference information.     

Interfacial long traveling waves in a two‐layer fluid with variable depth

Long wave propagation in a two‐layer fluid with variable depth is studied for specific bottom configurations, which allow waves to propagate over large distances. Such configurations are found within the linear shallow‐water theory and determined by a family of solutions of the second‐order ordinary differential equation (ODE) with three arbitrary constants. These solutions can be used to approximate the true bottom bathymetry. All such solutions represent smooth bottom profiles between two different singular points. The first singular point corresponds to the point where the two‐layer flow transforms into a uniform one. In the vicinity of this point nonlinear shallow‐water theory is used and the wave breaking criterion, which corresponds to the gradient catastrophe is found. The second bifurcation point corresponds to an infinite increase in water depth, which contradicts the shallow‐water assumption. This point is eliminated by matching the “nonreflecting” bottom profile with a flat bottom. The wave transformation at the matching point is described by the second‐order Fredholm equation and its approximated solution is then obtained. The results extend the theory of internal waves in inhomogeneous stratified fluids actively developed by Prof. Roger Grimshaw, to the new solutions types.     

Spread of a catalytic branching random walk on a multidimensional lattice

For a supercritical catalytic branching random walk on ${\mathbb{Z}}^d$, $d\in \mathbb{N}$, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in ${\mathbb{R}}^d$ which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.     

Affiliated subspaces and infiniteness of von Neumann algebras

We show that the structural properties of von Neumann algebra s are connected with the metric and order theoretic properties of various classes of affiliated subspaces. Among others we show that properly infinite von Neumann algebra s always admit an affiliated subspace for which (1) closed and orthogonally closed affiliated subspaces are different; (2) splitting and quasi‐splitting affiliated subspaces do not coincide. We provide an involved construction showing that concepts of splitting and quasi‐splitting subspaces are non‐equivalent in any GNS representation space arising from a faithful normal state on a Type I factor. We are putting together the theory of quasi‐splitting subspaces developed for inner product spaces on one side and the modular theory of von Neumann algebra s on the other side.     

Local Particles Numbers in Critical Branching Random Walk

Critical catalytic branching random walk on an integer lattice ? ^d is investigated for all d∈?. The branching may occur at the origin only and the start point is arbitrary. The asymptotic behavior, as time grows to infinity, is determined for the mean local particles numbers. The same problem is solved for the probability of the presence of particles at a fixed lattice point. Moreover, the Yaglom type limit theorem is established for the local number of particles. Our analysis involves construction of an auxiliary Bellman–Harris branching process with six types of particles. The proofs employ the asymptotic properties of the (improper) c.d.f. of hitting times with taboo. The latter notion was recently introduced by the author for a non-branching random walk on ? ^d .     

Photothermal image flow cytometry in vivo

The capability of photothermal (PT) microscopy to image moving, unlabeled cells in real time in vivo is demonstrated in a study of circulating red and white blood cells in blood and lymph microvessels of rat mesentery. Potential applications of this optical tool, called PT flow cytometry, are discussed.     

On the application of a ZrO2‐based solid electrolyte in isotope ratio mass spectrometry

The application of a high‐temperature electrochemical reactor based on stabilized zirconium dioxide (0.9 ZrO₂0.1 Y₂O₃) for organic gas sampling in continuous‐flow isotope‐ratio mass spectrometry (CF‐IRMS) has been found to be efficient. This solid electrolyte reactor (SER) can also be used as a chromatographic detector for the quantitative measurements of organic gases. A three‐electrode SER system was studied. Complete stoichiometric oxidation of organic gases has been achieved at 900–950°C due to the large catalytic surface area of the porous platinum coating. At this temperature, the oxygen ions formed from the oxygen of ambient air on the outer surface of the reactor migrate through the solid electrolyte under the action of the applied electric field and allow combustion of gases being analyzed to be effected. It should be noted that oxygen gas was not introduced into the gas‐carrier flow. Similar results for the measurements of carbon isotope ratios were obtained at the oxidation of hydrocarbon gases in both the standard and the solid electrolyte reactors. Copyright © 2009 John Wiley & Sons, Ltd.     

Energy transfer (EnT) photocatalysis enabled by gold-N-heterocyclic carbene (NHC) complexes

We present the use of gold sensitizers [Au(SIPr)(Cbz)] (PhotAu 1) and [Au(IPr)(Cbz)] (PhotAu 2) as attractive alternatives to state-of-the-art iridium-based systems. These novel photocatalysts are deployed in [2 + 2] cycloadditions of diallyl ethers and N-tosylamides. The reactions proceed in short reaction times and in environmentally friendly solvents. [Au(SIPr)Cbz] and [Au(IPr)(Cbz)] have higher triplet energy (E_T) values (66.6 and 66.3 kcal mol⁻¹, respectively) compared to commonly used iridium photosensitizers. These E_T values permit the use of these gold complexes as sensitizers enabling energy transfer catalysis involving unprotected indole derivatives, a substrate class previously inaccessible with state-of-the-art Ir photocatalysts. The photosynthesis of unprotected tetracyclic spiroindolines via intramolecular [2 + 2] cycloaddition using our simple mononuclear gold sensitizer is readily achieved. Mechanistic studies support the involvement of triplet–triplet energy transfer (TTEnT) for both [2 + 2] photocycloadditions.

We present the use of gold sensitizers [Au(SIPr)(Cbz)] (PhotAu 1) and [Au(IPr)(Cbz)] (PhotAu 2) as attractive alternatives to state-of-the-art iridium-based systems.