Harnack's inequality for quasiminimizers with nonstandard growth conditions

We prove Harnack inequalities for quasiminimizers of the variable exponent Dirichlet energy integral by employing the De Giorgi method.     

A surprising linear type estimate for nonlinear elliptic equations

Pointwise gradient bounds via Riesz potentials, like those available for the Poisson equation, actually hold for p-Laplacian type equations.     

The Sonogashira Coupling of Polymer‐Supported Propargylamine with Aryl Iodides

The Sonogashira coupling reaction of polymer‐supported propargylamine (=prop‐2‐yn‐1‐amine) with aryl iodides in the presence of the [Pd(PPh₃)₂]Cl₂/CuI catalyst system produces 3‐arylprop‐1‐yn‐1‐amines smoothly at room temperature (Scheme). When propargylamine is attached on Wang resin through a carbamate linker, the common problems with amino functionality in palladium‐catalyzed couplings are overcome. The arylpropynamines are cleaved from the polymer with CF₃COOH and converted into chromatographically easily separable acetamides. Our solid‐phase method opens a new pathway toward precursors of pharmacologically interesting arylpropynamines and arylpropanamines.     

Particle-into-liquid sampler on-line coupled with solid-phase extraction-liquid chromatography–mass spectrometry for the determination of organic acids in atmospheric aerosols

In the present study, sample collection and preparation were directly integrated with a chromatographic system by coupling a particle-into-liquid sampler for the first time on-line with solid-phase extraction-liquid chromatography–tandem mass spectrometry. Several organic acids, such as adipic, hydroxyglutaric, mandelic, vanillic, cis-pinonic, pinic, azelaic and sebacic, were used in the research. For sample pretreatment and concentration, strong anion exchange material was used in the extraction. Sampling, extraction and analysis conditions were optimized to obtain reliable information about aerosol chemical composition. To evaluate the performance of the on-line coupled system, half of each sample was analysed on-line and the other half was derivatized and analysed off-line by gas chromatography–mass spectrometry. Comparison of the two techniques with use of t-test showed the results to be in an excellent agreement. Limits of detection of studied acids in on-line system were between 0.1 and 0.9 ng. The on-line coupled system is fast and reliable and a promising tool for the real time analysis of organic acids in atmospheric aerosols.     

Solid-phase extraction of organic compounds in atmospheric aerosol particles collected with the particle-into-liquid sampler and analysis by liquid chromatography-mass spectrometry

Atmospheric aerosol particles, collected with the particle-into-liquid sampler at SMEARII station in Finland in mid-August 2007, were analysed for biogenic acids. The sample pretreatment method, comprising solid-phase extraction with anion exchange and hydrophilic-lipophilic balance materials, was optimized. Extraction efficiencies of solid-phase extraction from 10 and 20 ml samples were about 100%, with average relative standard deviation of 8.9%, in concentration range from 12.5 to 50 ng/ml of the acid. Extraction of aldehydes was less successful, with efficiencies from 69 to 163% and average 10% deviation. Pretreated samples were analysed by reversed phase high performance liquid chromatography with ion trap mass spectrometric detection. Limits of detection achieved for organic acids with the analytical procedure developed ranged from 9 to 27 μg/l of extracted sample, while limits of quantitation were from 31 to 90 μg/l. Oxidation with ozone was used for the preparation of the acid of β-caryophyllene (β-caryophyllinic acid), which was also studied in aerosol samples. MS² experiments were used to confirm the identification of trans-pinic, trans-pinonic and β-caryophyllinic acids. Azelaic, hexadecanoic, cis-pinonic, and cis- and trans-pinic acids were quantitated in the samples with use of authentic standards, while the concentrations of trans-pinonic and β-caryophyllinic acids were determined with cis-pinonic acid as surrogate. Also, the contribution of β-caryophyllene oxidation products to aerosol organic carbon was evaluated. Aldehydes could not be analysed in real samples due to the insufficient extraction. The particle-into-liquid sampler proved to be suitable for the collection of aerosol particles for the elucidation of daily and diurnal variation of selected species. The optimized sample pretreatment, together with the analysis method, offer a promising approach for the study of aerosol chemical composition, where artifact formation is minimal and time resolution is good.     

Controllability method for acoustic scattering with spectral elements

We formulate the Helmholtz equation as an exact controllability problem for the time-dependent wave equation. The problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements. This approach leads to high accuracy in spatial discretization. Moreover, the spectral element method results in diagonal mass matrices, which makes the time integration of the wave equation highly efficient. After discretization, the exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. We illustrate the method with some numerical experiments, which demonstrate the significant improvements in efficiency due to the higher order spectral elements. For a given accuracy, the controllability technique with spectral element method requires fewer computational operations than with conventional finite element method. In addition, by using higher order polynomial basis the influence of the pollution effect is reduced.     

Parallel Integer Optimization for Crew Scheduling

Performance aspects of a Lagrangian relaxation based heuristic for solving large 0-1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Göteborg, Sweden, based on distributing the variables. A lazy variant of this approach which decouples communication and computation is even useful on networks of workstations. Furthermore, we develop a new sequential active set strategy which requires less work and is better adapted to the memory hierarchy properties of modern RISC processors. This algorithm is also suited for parallelization on a moderate number of networked workstations.     

Asymmetrical flow field-flow fractionation technique for separation and characterization of biopolymers and bioparticles

Field-flow fractionation (FFF) is one of the most versatile separation techniques in the field of analytical separation sciences, capable of separating macromolecules in the range 10³–10¹⁵ g mol⁻¹ and/or particles with 1 nm–100 μm in diameter. The most universal and most frequently used FFF technique, flow FFF, includes three types of techniques, namely symmetrical flow FFF, hollow fiber flow FFF, and asymmetrical flow FFF which is most established variant among them. This review provides a brief look at the theoretical background of analyte retention and separation efficiency in FFF, followed by a comprehensive overview of the current status of asymmetrical flow FFF with selected applications in the field of biopolymers and bioparticles.     

Explicit equations for the height and position of the first component shock for binary mixtures with competitive Langmuir isotherms under ideal conditions

Explicit equations for the height c(1)(S) and retention time t(R,1) of the pure first component shock in the case of a narrow rectangular injection pulse of a binary mixture with competitive Langmuir isotherms were derived within the frame of the equilibrium theory. The height of the first shock is obtained as an only positive root of a quartic equation. Hence, it was shown that, for binary Langmuir systems, the individual concentration profiles at the column outlet can be expressed entirely in closed-form. In addition, a novel, simple parametric representation that gives the trajectory of the first shock in the distance-time diagram as a function of c(1)(S) was derived. The practical relevance of the new equations was demonstrated by utilizing them for optimization of batch chromatography. It was shown that c(1)(S) increases and t(R,1) decreases with increasing duration of injection for given feed concentrations when the pure first component plateau is eroded during elution. The derivative of the cycle time with respect to the duration of injection is always more than unity. For this reason, the maximum productivity of more retained component is obtained when the duration of injection is selected so that the purity constraint can be fulfilled by having 100% yield. For the less retained component, an implicit expression for the maximum productivity was derived. When the injected loadings are constant, t(R,1) decreases with increasing feed concentrations while c(1)(S) and the cycle time are independent of them. In addition, the productivities of both components always increase with increasing feed concentrations.