Max-Plus Stochastic Processes

This paper is concerned with processes which are max-plus counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. Concepts of max-plus martingale and max-plus stochastic differential equation are introduced. The max-plus counterparts of backward and forward PDEs for Markov diffusions turn out to be first-order PDEs of Hamilton–Jacobi–Bellman type. Max-plus additive integrals and a max-plus additive dynamic programming principle are considered. This leads to variational inequalities of Hamilton–Jacobi–Bellman type.     

Separation of natural antioxidants using PDMS electrophoresis microchips coupled with amperometric detection and reverse polarity

This report describes the use of PDMS ME coupled with amperometric detection for rapid separation of ascorbic, gallic , ferulic, p‐coumaric acids using reverse polarity. ME devices were fabricated in PDMS by soft lithography and detection was accomplished using an integrated carbon fiber working electrode aligned in the end‐channel configuration. Separation and detection parameters were investigated and the best conditions were obtained using a run buffer consisting of 5 mM phosphate buffer (pH 6.9) and a detection voltage of 1.0 V versus Ag/AgCl reference electrode. All compounds were separated within 70 s using gated injection mode with baseline resolution and separation efficiencies between 1200 and 9000 plates. Calibration curves exhibited good linearity and the LODs achieved ranged from 1.7 to 9.7 μM. The precision for migration time and peak height provided maximum values of 4% for the intrachip studies. Lastly, the analytical method was successfully applied for the analysis of ascorbic and gallic acids in commercial beverage samples. The results achieved using ME coupled with amperometric detection were in good agreement with the values provided by the supplier. Based on the data reported here, the proposed method shows suitability to be applied for the routine analysis of beverage samples.     

Electrokinetic characterization of hybrid NOA 81-glass microchips: Application to protein microchip electrophoresis with indirect fluorescence detection

A low-cost and straightforward hybrid NOA (Norland optical adhesive) 81-glass microchip electrophoresis device was designed and developed for protein separation using indirect fluorescence detection. This new microchip was first characterized in terms of surface charge density via electroosmotic mobility measurement and stability over time. A systematic determination of the electroosmotic mobility (μ_eo) over a wide pH range (2–10) and at various ionic strengths (20–50 mM) was developed for the first time via the neutral marker approach in an original simple frontal methodology. The evolution of μ_eo was proved consistent with the silanol and thiol functions arising from the glass and the NOA materials, respectively. The repeatability and reproducibility of the measurements on different microchips (RSD < 14%) and within 15 days (less than 5% decrease) were successfully demonstrated. The microchip was then applied for the efficient electrophoretic separation of proteins in a zonal mode coupled with indirect fluorescence detection, which is, to our knowledge, the first proof of concept of capillary zone electrophoresis in this hybrid microsystem.     

Activation energy and nonequilibrium effects in thermal reactions

Calculations of the nonequilibrium rate constant for the model system H₂O₂ + M → 2 OH + M over the temperature range of 300–1900°K, assuming that only vibrational, or that both vibrational and rotational, energy is transferred in a collision, show that (1) inefficient energy transfer leads to a distinctly non-Arrhenius temperature dependence, the nonlinearity being in principle different for different M, and (2) despite different activation energies for different M, the order of M efficiencies is preserved throughout the temperature range. A reversal of M efficiencies can occur only if there is a change of mechanism of the reaction over the temperature range investigated.     

Kinetics of the reaction F + 1,2-dibromo-1,1,2-trifluoroethane

The title reaction was studied in a standard flow system with F atoms produced by RF discharge in F₂-He mixture. Analysis was by gas chromatography using electron capture detection. There were two major products, identified as CF₂BrCF₂H and CF₂BrCF₂Br, plus presumably HF which was not detectable. The overall rate of disappearance of reactant was found to be of mixed one and one-half order, indicating a complex reaction. A mechanism is proposed comprising six steps and involving two radical species CF₂Br?FBr (R₁) and CF₂Br?F₂. The 300 K rate constant for the initial step F + reactant → HF + R₁ is evaluated to be 2.2 × 10^?13 cm³/molec·s, which fits in with rates of other saturated hydrocarbon reactants containing one hydrogen atom, thus supporting the view that in this class of reactants the rates of reactions of the type F + saturated hydrocarbon depend mainly on the number of hydrogen atoms in the reactant.     

The Tolerance Approach to Sensitivity Analysis of Matrix Coefficients in Linear Programming: General Perturbations

In the tolerance approach to sensitivity analysis of matrix coefficients in a linear programme, the maximum tolerance percentage characterizes the largest percentage within which selected matrix coefficients may vary simultaneously and independently while retaining the same set of optimal basic variables. While it is difficult to calculate exactly the maximum tolerance percentage under perturbations in multiple rows or columns, we show herein how it can be approximated.     

Electrokinetic control of fluid in plastified laser-printed poly(ethylene terephthalate)-toner microchips

The application of plastified laser-printed poly(ethylene terephthalate)(PET)-toner microchips to capillary electrophoresis was investigated. Electroosmotic flow was observed in the direction of the cathode for the buffer system studied (phosphate, pH 3–10). Average electroosmotic mobilities of 1.71×10^–4 to 4.35×10^–4 cm² V^–1 s^–1 were observed from pH 3 to 10. This variation suggests that silica fillers in the toner and on the surface of the polymer dominate the zeta potential of the material, which is also confirmed by XPS measurements. Dopamine and catechol were used as model analytes for microchip electrophoresis in combination with electrochemical detection. Results show that these two analytes can be efficiently separated and detected electrochemically with the plastified laser-printed PET-toner microchips.     

Analytical solution of vibrational–rotational energy transfer in the dissociation and relaxation of N2, Br2, and CO at high temperature

An approximate analytical solution of relaxation in a low-pressure system with exponential transition probabilities is given for vibrational–rotational energy transfer in the dissociation of diatomics. The main assumption is that the rotational degrees of freedom are in thermal equilibrium at all times, and that the barrier to dissociation in the vibrational–rotational plane is linear and asymmetric. The theory is applied to high-temperature dissociations of N₂, Br₂, and CO in excess argon, with satisfactory agreement with available experimental data.     

Rapid separation of post‐blast explosive residues on glass electrophoresis microchips

This study describes the development of an analytical methodology based on the use of microchip electrophoresis (ME) devices integrated with capacitively coupled contactless conductivity detection (C⁴D) for the separation and detection of inorganic anions in post‐blast explosive residues. The best separation condition was achieved using a running buffer composed of 35 mmol/L lactic acid, 10 mmol/L histidine and 0.070 mmol/L cetyl(trimethyl ammonium) bromide. For C⁴D measurements, the highest sensitivity was obtained applying a 700 kHz sinusoidal wave with excitation voltage of 20 V_pp. The separation of Cl^?, NO₃^?, NO₂^?, SO₄^2?, ClO₄^? and ClO₃^? was performed within ca. 150 s with baseline resolution and efficiencies between 4.4 × 10⁴ and 1.7 × 10⁵ plates/m. The found limits of detection ranged between 2.5 and 9.5 μmol/L. Last, real samples of post‐blast explosive residues were analyzed on the ME‐C⁴D devices obtaining successfully the determination of Cl^?, NO₃^? and SO₄^2?. The achieved concentration values varied between 12.8–72.5 mg/L for Cl^?, 1.7–293.1 mg/L for NO₃^? and 1.3–201.3 mg/L for SO₄^2?. The data obtained using ME‐C⁴D devices were in good agreement with the concentrations found by ion chromatography. The approach reported herein has provided short analysis time, instrumental simplicity, good analytical performance and low cost. Furthermore, the ME‐C⁴D devices emerge as a powerful and portable analytical platform for on‐site analysis demonstrating to be a promising tool for the crime scene investigation.