Functions of singular random matrices with applications

This article describes how the Jacobian is found for certain functions of a singular random matrix, both in the general case and in that of a non-negative, definite random matrix. The Jacobian of the transformationV=S ² is found whenS is non-negative definite; in addition, the Jacobian of the transformationY=X ⁺ is determined whenX ⁺ is the generalized, or Moore-Penrose, inverse ofX. Expressions for the densities of the generalized inverse of the central beta and F singular random matrices are proposed. Finally, two applications in the field of Bayesian inference are presented. This work was supported in part by the research project 39017E of CONACYT-México This article was written during the first author's stay as a Visiting Professor in the Department of Statistics at the University of Granada, Spain     

Chip making's singular future

Making chips a single wafer at a time can reduce chip oversupply and help ensure sustainable growth in the semiconductor industry.     

Experimental Investigations of Colloidal Silica Grouting in Porous Media

This paper presents the results of an experimental investigation performed to understand the processes influencing the injection of colloidal silica grout into porous media. Based on the combined analysis of grout injection pressures and the visually observed grout distribution patterns, three major processes, gelation, shear, and viscous fingering, have been identified to occur during grout injection. The results demonstrate the dynamic interplay between grout viscosity variations and the resulting flow instabilities.     

Synthesis of hexagonal Al2−x Cr x O3 nanodisks by a thermal decomposition of mesoporous Cr4+:Al2O3 powders

Monodispersed hexagonal Al_2−x Cr _x O₃ nanodisks are synthesized through a reactive doping of Cr⁶⁺ cations in a hydrogenated mesoporous AlO(OH)·αH₂O powder followed by annealing at 1,200 °C in air. The reaction was carried out by a drop wise addition of an aqueous Cr⁶⁺ solution (0.5–1.0 M) to AlO(OH)·αH₂O, at room temperature. Al_2−x Cr _x O₃ nanostructure formation was controlled by the nucleation and growth from the intermediate amorphous mesoporous Cr⁴⁺:Al₂O₃ composites in the temperature range 400–1,000 °C. The nanodisks of ∼50 nm diameter and thickness of ∼16 nm is observed in the sample with x of 0.2 and similar nanodisks with a low dimension is observed at a higher value of x of 1.6 (after 2 h of heating at 1,200 °C). The Cr³⁺ ↔ Al³⁺ substitution, x ≤ 1.2, inhibits grain growth in small crystallites. The crystallites in x = 0.2 composition have 43 nm diameter while it is 15 nm in those with x = 1.2 composition.     

Characterization of Catheter Dynamics During Percutaneous Transluminal Catheter Procedures

Remote catheter navigation systems are being developed to reduce the occupational risk of the intervening physician. Despite the success of such systems, development has occurred with little fundamental knowledge of the catheter dynamics applied by the interventionalist. This paper characterizes the kinematics of a catheter during manipulation, the minimum applied force/torque during interventional procedures, and the maximum force/torque applied by an operator to overcome vasculature friction. Ten operators manipulated a 6F catheter inside a specialized catheter movement sensor to determine the velocities and accelerations of catheter motion. A mass-spring apparatus was constructed to measure the forces and torques required to overcome introducer sheath and vasculature friction. Results showed the catheter was manipulated at peak velocities and accelerations of (muplusmnsigma) : 360 plusmn 180 mmldrs^-1 and 22200 plusmn 14000 mmldrs^-2, and 19 plusmn 7 radldrs^-1 and 900 plusmn 510 radldrs^-2, for axial and radial directions of motion, respectively. A minimum force of 0.29 plusmn 0.06 N and a torque of 1.15 plusmn0.3 mNldrm was required to move the catheter through the introducer sheath; while the observed maximum applied torque was 15 mNldrm to overcome vasculature friction. The implications of these results for future design optimization of an intuitive remote catheter navigation system are considered.     

Two step sequential treatment of pulp and paper mill effluent by Cryptococcus albidus and Emericella nidulans var. nidulans in 2L bioreactor

A number of studies had shown biological treatment of pulp and paper mill effluent. However, almost all the studies have focused on reduction in physical and chemical parameters. Toxicity analysis, though very important, has been neglected. Thus in this study genotoxicity along with colour and lignin content were studied. Treatment of effluent, generated at the pulping stage in pulp and a paper mill, was done using two fungal strains, Cryptococcus albidus and Emericella nidulans var. nidulans, in sequential manner in 2 L bioreactor. Two different treatments were given. In treatment (I) effluent was first treated by C. albidus (stage A) and this treated effluent was further treated by E. nidulans var. nidulans (stage B). In treatment (II) effluent was first treated by E. nidulans var. nidulans (stage C) and this treated effluent was further treated by C. albidus (stage D). Treatment (I) was more efficient than treatment (II) with 71%, 51%, 44% and 70% reduction in colour, lignin, COD and genotoxicity, respectively. Class distribution of comets also showed that treatment (I) was more efficient than treatment (II). Colour content showed very good correlation (r² = 0.99) with effluent toxicity. The effluent treatment process (I) can be scaled up for industrial use. © 2011 Canadian Society for Chemical Engineering     

A rapid tool for strategic internal analysis of manufacturing firms

This paper examines strengths and weaknesses of companies in the context of the value chain as a way to assess a manufacturing firm. For doing this, the executives of 20 companies were interviewed and asked about the strengths and weaknesses they thought their companies had. The responses were classified according to the elements of the value chain and new sub-classifications were created. In this way, it was possible to discover the main concerns the executives had about their company and to see if there were some comonality in their responses. It was found that the main concerns were in the areas of Production and Sales, as opposed to Finances, Human Resources, Technology and Procurement. As a result, a proposition is made about the use of this value chain and its dimensions as a way for rapid internal assessment of a manufacturing firm. A case study is presented in which the developed tool was implemented. An internal analysis of a company was undertaken in few hours.     

Removal of Phosphorous from Steel Produced by Melting Sponge Iron in Induction Furnace

In secondary route of steelmaking, production through induction melting furnace contributes about 31 % of India’s total steel production. The main raw materials used are steel scrap, cast iron and sponge iron. In India, majority of the induction furnaces are operated using acidic lining of silica based ramming mass to produce structural steel where basicity cannot be maintained to remove phosphorous and sulphur. In the present work, efforts are being made to generate the experimental data for refining of steel in 750 kg induction furnace. The basicity is maintained by addition of CaO and MgO in the form of flux. The slag is made oxidizing in nature by addition of sponge iron in the bath. Oxidation potential of the slag is fulfilled by presence of FeO in sponge iron. In every single heat, samples of slag and metal are collected. The degree of dephosphorization obtained is as high as 82 %.