New algorithm for optimal parameter estimation with linear constraints

This paper presents a new algorithm for optimal parameter estimation problems with linear constraints. The algorithm developed is based on least absolute-value approximations. The problem is solved first using a least-error-square technique, where we add to the cost function the equality constraints via Lagrange multipliers, to obtain a good estimate for the residuals of the measurements, having gained this information, we choose a number of measurements with the smallest residuals. This number equals the number of parameters to be estimated minus the number of constraints. Using these measurements together with the constraints, we obtain a number of observations equal to the number of parameters to be estimated. By using this technique, we show that there is no need to either iterate or use linear programming to obtain the estimation.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant A4146.     

An efficient microwave assisted synthesis of N′-aryl/(alkyl)-substituted N-(4-hydroxy-6-phenylpyrimidin-2-yl)guanidines: Scope and limitations

Treatment of N-[(4-hydroxy-6-phenyl)pyrimidin-2-yl]cyanamide with 1° alkyl or arylamines in isopropyl alcohol for only 10 min at 110–120 °C under microwave conditions gave the corresponding N′-alkyl(aryl)guanidine derivatives in excellent yields (65–84%). Isolated yields were greatest when >1.0 equiv. of amines were employed, but excellent results were also obtained when aryl and alkylamines were reacted with a more atom-economical loading (1.0 equiv.; 70% and 72% ave. yields, respectively). Arylamines with either highly electron withdrawing substituents (e.g. CO₂H) or pi-deficient heterocycles (e.g. variously substituted aminopyridines) did not work well under these conditions, and reaction with ureas and/or amino acids did not give detectable products. Work-up was exceedingly simple, and involved simple collection and washing of product on a sintered glass funnel. Products were obtained in analytically pure form and required approximately 1 h to prepare, start to finish.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Membrane chromatography: Protein purification from E. coli lysate using newly designed and commercial anion-exchange stationary phases

This contribution describes the purification of anthrax protective antigen (PA) protein from Escherichia coli lysate using bind-and-elute chromatography with newly designed weak anion-exchange membranes. Protein separation performance of the new AEX membrane adsorber was compared with the commercial Sartobind^® D membrane adsorber and HiTrap™ DEAE FF resin column under preparative scale conditions. Dynamic protein binding capacities of all three stationary phases were determined using breakthrough curve analysis. The AEX membrane showed higher binding capacities than the Sartobind^® D membrane at equivalent volumetric throughput and higher capacities than the HiTrap™ DEAE FF resin column at 15 times higher volumetric throughput. Anion-exchange chromatography was performed using all three stationary phases to purify PA protein. Quantitative SDS-PAGE analysis of effluent fractions showed that the purity of PA protein was higher for membrane adsorbers than the HiTrap™ DEAE FF resin column and was the same for the new AEX membrane and Sartobind^® D membrane adsorbers. The effects of E. coli lysate load volume and volumetric flow rate on PA protein separation resolution using the membrane adsorbers were minor, and the peak elution profile remained un-changed even under conditions where >75% of the total protein dynamic binding capacity of the membranes had been utilized. PA protein peak resolution was higher using pH-gradient elution than with ionic strength gradient elution. Overall, the results clearly demonstrate that membrane chromatography is a high-capacity, high-throughput, high-resolution separation technique, and that resolution in membrane chromatography can be higher than resin column chromatography under preparative conditions and at much higher volumetric throughput.     

Extension of the angular spectrum method to calculate pressure from a spherically curved acoustic source

The angular spectrum method is an accurate and computationally efficient method for modeling acoustic wave propagation. The use of the typical 2D fast Fourier transform algorithm makes this a fast technique but it requires that the source pressure (or velocity) be specified on a plane. Here the angular spectrum method is extended to calculate pressure from a spherical transducer-as used extensively in applications such as magnetic resonance-guided focused ultrasound surgery-to a plane. The approach, called the Ring-Bessel technique, decomposes the curved source into circular rings of increasing radii, each ring a different distance from the intermediate plane, and calculates the angular spectrum of each ring using a Fourier series. Each angular spectrum is then propagated to the intermediate plane where all the propagated angular spectra are summed to obtain the pressure on the plane; subsequent plane-to-plane propagation can be achieved using the traditional angular spectrum method. Since the Ring-Bessel calculations are carried out in the frequency domain, it reduces calculation times by a factor of approximately 24 compared to the Rayleigh-Sommerfeld method and about 82 compared to the Field II technique, while maintaining accuracies of better than 96% as judged by those methods for cases of both solid and phased-array transducers.     

Measuring the effect of demagnetization in stacks of gadolinium plates using the magnetocaloric effect

The effect of demagnetization in a stack of gadolinium plates is determined experimentally by using spatially resolved measurements of the adiabatic temperature change due to the magnetocaloric effect. The number of plates in the stack, the spacing between them and the position of the plate on which the temperature is measured are varied. The orientation of the magnetic field is also varied. The measurements are compared to a magnetostatic model previously described. The results show that the magnetocaloric effect, due to the change in the internal field, is sensitive to the stack configuration and the orientation of the applied field. This may have significant implications for the construction of a magnetic cooling device.     

Ultra-short pulse laser ablation of copper, silver and tungsten: experimental data and two-temperature model simulations

Experimental results of femtosecond laser ablation of the metals copper, silver and tungsten are compared to simulations based on the two-temperature model. The comparison provides new information about the laser-heating process: For the noble metals (Cu, Ag), the energy transport via ballistic electrons must be included, while this effect is negligible for a transition metal (W). The comparison provides values for the range of ballistic electrons in the noble metals. The model calculation is also employed to investigate the dependence of the threshold fluence and melting depth on pulse duration. It is observed that for pulses shorter than approximately 1 ps the threshold fluence and melting depth are independent of the pulse duration, while they increase as τ ^0.47 and τ ^0.51, respectively, for pulses longer than ∼40 ps, in good agreement with approximate analytical expressions predicting a ?{t}\sqrt{\tau} dependence.     

Local Rings of Embedding Codepth 3. Examples

A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a differential graded algebra structure, based on which one can classify local rings of embedding codepth 3. We give examples of algebra structures that have been conjectured not to occur.