Properties of the Central Points in Linear Programming Problems

In this paper we list several useful properties of central points in linear programming problems. We study the logarithmic barrier function, the analytic center and the central path, relating the proximity measures and scaled Euclidean distances defined for the primal and primal–dual problems. We study the Newton centering steps, and show how large the short steps used in path following algorithms can actually be, and what variation can be ensured for the barrier function in each iteration of such methods. We relate the primal and primal–dual Newton centering steps and propose a primal-only path following algorithm for linear programming.     

Stability Monitoring of Electrolytic Conductivity Reference Materials Under Repeated Use Conditions by the Primary Measurement Method

This work presents the results from stability studies for several electrolytic conductivity (EC) reference materials submitted to repeated use conditions, as required by the last version of the ISO 17034 standard. Eight batches of reference materials, composed of water or water/n-propanol and HCl or KCl (at different concentrations), were studied, with nominal EC values ranging from 5 to 12,825 µS·cm−1. The materials were submitted to a simulation of repeated use, with the manipulation of bottles once a week and their storage under refrigeration with air gaps inside them. They were then analyzed once a month by the EC primary measurement method. The measurement results were evaluated to check for deviations from conventional long-term stability monitoring and for variation trends using normalized error and linear regression statistical tests. The results indicated that the repeated use simulation caused deviations in the EC for the 100 and 500 µS·cm−1 reference materials and variation trends in the EC for the 5000 and 12,825 µS·cm−1 reference materials. From the results, the uncertainty related to stability monitoring under repeated use conditions was calculated for each reference material.     

Thionicotinamide SAM on Gold: Adsorption Studies and Electroactivity

STM and impedance results of the self‐assembled monolayer (SAM) formed with thionicotinamide (TNA) on gold indicate the presence of defects that increase with the immersion time of the electrode in the TNA solution affecting the SAM electroactivity toward the electron transfer reaction of the cytochrome c metalloprotein and [Fe(CN)₆]^4? and [Ru(NH₃)₆]³⁺ complexes. It was observed that this electroactivity was also affected by the pH of the electrolyte solution. SERS and STM data indicate sulfur coordination to the surface with contribution of the NH₂ group. From the dependence of the TNA surface coverage on the temperature and concentration in solution, thermodynamic parameters of adsorption were determined.     

Primal-Dual Relationship Between Levenberg–Marquardt and Central Trajectories for Linearly Constrained Convex Optimization

We consider the minimization of a convex function on a bounded polyhedron (polytope) represented by linear equality constraints and non-negative variables. We define the Levenberg–Marquardt and central trajectories starting at the analytic center using the same parameter, and show that they satisfy a primal-dual relationship, being close to each other for large values of the parameter. Based on this, we develop an algorithm that starts computing primal-dual feasible points on the Levenberg–Marquardt trajectory and eventually moves to the central path. Our main theorem is particularly relevant in quadratic programming, where points on the primal-dual Levenberg–Marquardt trajectory can be calculated by means of a system of linear equations. We present some computational tests related to box constrained trust region subproblems.     

A nonlinear programming algorithm based on non-coercive penalty functions

 We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters to these functions: one is used to control the slope and the other controls the deviation from the exact penalty. We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained for non-smooth convex problems under a Slater qualification condition. Received: September 2000 / Accepted: June 2002 Published online: March 21, 2003 Research partially supported by CAPES, Brazil Research partially supported by CNPq, Brazil, and CONICIT, Venezuela. Mathematics Subject Classification (1991): 20E28, 20G40, 20C20     

Interior point algorithms for linear programming with inequality constraints

Interior methods for linear programming were designed mainly for problems formulated with equality constraints and non-negative variables. The formulation with inequality constraints has shown to be very convenient for practical implementations, and the translation of methods designed for one formulation into the other is not trivial. This paper relates the geometric features of both representations, shows how to transport data and procedures between them and shows how cones and conical projections can be associated with inequality constraints.     

Near infrared emission spectroscopy induced by ultrasonic irradiation

Near infrared emission caused by ultrasonic excitation is demonstrated for the first time in this work. The instrument is constituted of an acousto-optical tunable filter-based spectrometer, an ultrasonic processor connected to a titanium alloy ultrasonic probe and a cylindrical borosilicate flask containing the sample to be excited. The radiation emitted by the sample is collected by a concave mirror and sent to the spectrometer. The effects of the position of the probe extremity in relation to a lateral entrance of the borosilicate flask and of the ultrasonic power on the emission signal were studied. The best results were obtained by positioning the probe extremity up to 2mm from the reflexive body (lateral entrance) using 30% of the full ultrasonic incident power and acquiring spectra after 5 min of sonication. The NIR emission spectra resulting from the ultrasonic excitation were in agreement with that obtained by thermal excitation. The proposed technique was utilized to study different poly(dimethylsiloxane) samples having different viscosities.     

Integral low-energy electron Mössbauer spectroscopic studies of the surfaces of carbon nanotube-nanocomposite powders

The surface state of CNTs-Fe-Al₂O₃ and CNTs-Fe-MgAl₂O₄ nanocomposite powders was studied by integral low-energy electron Mössbauer spectroscopy (ILEEMS). Several samples, prepared by reduction of α-(Al,Fe)₂O₃ or (Mg,Fe)Al₂O₄ precursors in a H₂-CH₄ atmosphere, were investigated, demonstrating that ILEEMS is a promising tool completing transmission Mössbauer spectroscopy for the investigation of the metal Fe and iron-carbide particles in the different carbon nanotube systems.     

Use of near infrared emission spectroscopy in the study of supporting materials and stationary phases for liquid chromatography

Near infrared emission spectroscopy (NIRES) has been investigated in the study of different materials employed in liquid chromatography. The samples were heated in a nitrogen atmosphere and the emission spectra were obtained using a lab-made NIRES instrument. Through principal component analysis (PCA) using the raw emission spectra, it was possible to distinguish different materials according to their physical and/or chemical characteristics. Linear relationships between emissivity spectra and the contents of the coating material or the specific surface areas was observed for stationary phases or bare silicas, respectively. Furthermore, the thermal stability of stationary phases could be followed in real time.