General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios.     

Optical and hydrophilic properties of Cr doped TiO2-SiO2 nanostructure thin film

Cr doped TiO₂-SiO₂ nanostructure thin film on glass substrates was prepared by a sol-gel dip coating process. X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) were used to characterize the structural and chemical properties of the films. A UV-vis spectrophotometer was used to measure the transmittance spectra of the thin film. The hydrophilicity of the thin film during irradiation and storage in a dark place was measured by a contact angle analyzer. The results indicated that Cr doping has a significant effect on the transmittance and super-hydrophilicity of TiO₂-SiO₂ thin film.     

Use of Faraday instabilities to enhance fuel pulverisation in air-blast atomisers

The atomization of liquids into a spray is an important process in many industrial applications and particularly in the aero-engine sector. Conventional air-blast injectors in aircraft engines today use aerodynamic shearing effects to atomize the liquid fuel. However, at operating conditions where the air velocity is below 30 m/s (such as ground start and high altitude restart) the atomization quality is poor. Consequently combustion is less efficient with high pollutant emissions. The objective of this study is to validate a new concept of injector which couples the shearing effects with the principle of ultrasonic atomization. The latter consists of using piezoelectric actuators to generate the oscillations of a wall in contact with the liquid film. This excitation perpendicular to the liquid film surface creates Faraday instabilities at the liquid/air interface. Amplitudes higher than a defined threshold value induce the break-up of ligaments and the formation of droplets. To cite this article: M. Boukra et al., C. R. Mecanique 337 (2009).     

Effect of Sudden Expansion on Entrainment and Spreading Rates of a Jet Issuing from Asymmetric Nozzles

Turbulent free jets issuing from five different nozzle geometries; smooth pipe, contracted circular, rectangular, triangular, and square, are experimentally investigated by using TSI 2-D laser Doppler velocimetry (LDV) to assess the effect of nozzle geometry and quarl (i.e. a cylindrical sudden expansion) on jet entrainment and spreading. The centerline mean velocity decay and the jet half-velocity width, which are indicators of jet entrainment and spreading rates, are determined for each nozzle’s flow configuration, i.e. with and without sudden expansion. Furthermore, turbulence quantities, such as the flow mean velocities and their mean fluctuating components, as well as Reynolds shear stresses, are all measured along the centerline plane of the jet to facilitate understanding the extent of the effect of nozzle’s geometry (i.e. nozzle’s orifice shape and sudden expansion) on jet’s entrainment and spreading. The main results show that the jet flow with the presence of sudden expansion exhibits higher rates of entrainment and spreading than without. In addition, these results reveal that sudden expansion exercises a greater effect on the asymmetric jet characteristics, especially for the triangular and rectangular nozzles compared to their axisymmetric counterparts (i.e. circular contracted nozzle).     

New mononuclear copper(II) complexes from β-diketone and β-keto ester N-donor heterocyclic ligands: structure,bioactivity, and molecular simulation studies

Four new mononuclear copper(II) complexes with methyl acetoacetate and benzoylacetone in the presence of 1,10-phenanthroline and 2,2′-bipyridine were synthesized and characterized by elemental analyses, FT-IR, and UV–Vis spectroscopy. The molecular structures of complexes [Cu(MAA)(bpy)(ClO₄)] (1a), [Cu(bzac)(bpy)]ClO₄ (2a), [Cu(MAA)(phen)(ClO₄)] (1b) and [Cu(bzac)(phen)(ClO₄)] (2b) were determined by single crystal X-ray diffraction technique. 1a, 1b, and 2b are five coordinate with a distorted square pyramidal geometry and the structure of 2a consists of isolated [Cu(bzac)(bpy)]⁺ cations and perchlorate counter anions. The electrochemical studies of copper complexes in acetonitrile solution showed that Cu^II/Cu^I reduction processes are electrochemically irreversible. Cytotoxic activity of complexes was screened, including an MTT assay against gastric cancer cell line (MKN-45). The four Cu(II) complexes exhibited lethal effects against MKN-45 cell lines and the half maximal inhibitory concentration (IC₅₀) values obtained were much lower in comparison with 5-fluorouracil. In addition, MTT and migration studies revealed that benzoylacetone complexes are more active than complexes of methyl acetoacetate against the MKN-45 cancer cell lines. Docking simulations of Cu(II) complexes on DNA revealed that the most stable adducts with DNA bind in the minor groove. All complexes display a binding specificity to the A/T rich regions.     

Distinguishing between evidence and its explanations in the steering of atomic clocks

Quantum theory reflects within itself a separation of evidence from explanations. This separation leads to a known proof that: (1) no wave function can be determined uniquely by evidence, and (2) any chosen wave function requires a guess reaching beyond logic to things unforeseeable. Chosen wave functions are encoded into computer-mediated feedback essential to atomic clocks, including clocks that step computers through their phases of computation and clocks in space vehicles that supply evidence of signal propagation explained by hypotheses of spacetimes with metric tensor fields.     

Stability and hyperstability of orthogonally $$*$$- m-ho mo morphis ms in orthogonally Lie $$C^*$$C-algebras: a fixed point approach

Recently Eshaghi et al. introduced orthogonal sets and proved the real generalization of the Banach fixed point theorem on these sets. In this paper, we prove the real generalization of Diaz–Margolis fixed point theorem on orthogonal sets. By using this fixed point theorem, we study the stability of orthogonally \(*\)-m-homomorphisms on Lie \(C^*\)-algebras associated with the following functional equation:

$$\begin{aligned} \begin{aligned}&f(2x+y)+f(2x-y)+(m-1)(m-2)(m-3)f(y)\\&\quad =2^{m-2}[f(x+y)+f(x-y)+6f(x)]. \end{aligned} \end{aligned}$$

for each \(m=1,2,3,4.\). Moreover, we establish the hyperstability of these functional equations by suitable control functions.