Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

Formation of functional groups on graphite during oxygen plasma treatment

Improved sample wettability was obtained by oxygen plasma functionalization of pyrolytic graphite. The samples were exposed to highly dissociated oxygen plasma with the density of 1 × 10¹⁶ m⁻³, the electron temperature of about 5.5 eV and the density of neutral oxygen atoms of 8 × 10²¹ m⁻³ for 20 s. The surface wettability was measured by a contact angle of water drop. The contact angle dropped from original 112° down to about 1°. The functional groups were detected by XPS analyses. The survey spectrum showed a substantial increase of oxygen concentration on the surface, while high-resolution analyses showed additional oxygen was bonded onto the graphite surface in the form of C-O polar functional group responsible for the increase of the surface energy.     

Modulated DSC for gas hydrates analysis

Modulated DSC has been applied to the study of methane, ethane and propane hydrates at different hydrate and ice concentrations. The reversing component of the TMDSC curves, makes it possible to characterize such hydrates. Methane and ethane hydrates show the melting-decomposition peak at a temperatures higher than the ice contained in the sample, while propane hydrate melts and decomposes at lower temperature than the ice present in the sample. The hydrate peaks tend to disappear if the hydrate is stored at atmospheric pressure. Guest size and cavity occupation fix the heat of dissociation and stability of the hydrates, as confirmed by parallel tests on tetrahydrofurane hydrates.     

Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment

This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters. Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.     

On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).     

Impact of photodepletion to amplified spontaneous emission of proton-transfer dyes in polymeric matrices

A six level rate equation system was used to investigate the impact of photodepletion to amplified spontaneous emission (ASE) of intramolecular proton-transfer (IPT) dyes incorporated into polymeric hosts. The model includes the most important transitions for the normal and tautomer form of the molecule as well as intersystem crossing and triplet–triplet transitions. The experimentally observed pulse shape as well as photodepletion phenomena, i.e. a first order exponential decay of the ASE intensity and a shortening in ASE pulse width, have been simulated successfully. Additionally, the model was used to propose an explanation of the unexpected high photodepletion of proton-transfer dyes in solids. The results show that the emission cross section and reabsorption cross section of the tautomer form of the molecule are the most important parameter not only for efficiency but also for photodepletion. The model was tested by comparison with experimental results of 2-(2’-hydroxyphenyl)benzimidazole in polymethylmethacrylate (PMMA), polystyrene (PS) and a 1:1 alternating copolymer matrix PS-co-PMMA. PACS 78.45.th; 42.55.Mv; 42.70.Jk     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

Effect of external Gaussian random field on phonon spectrum of linear atomic chains

We present the theoretical study of the effect of external random field characterized by a Gaussian probability distribution function on the continuous phonon spectrum of one-dimensional (1D) chain, based on the Jacobian matrix method. The cumulative effect of the random field and simple isotopic defect is studied analytically and numerically. The Gaussian random field removes a square-root divergence appearing in the phonon spectrum of ideal 1D chain. The impurity phonon DOS shows strong dependence on the variance and the mean of the random field and exhibits very different behavior from the non-random case: the continuous spectrum is expanded and the δ-peak, describing discrete impurity vibrations in the non-random chain with the impurity, falls into a continuous zone.     

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.