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.     

Crystal structural characterization of three chlorosalicylato titanocene compounds

Abstract  Three chlorosalicylato titanocene compounds, namely [(MeCp)₂Ti(O,O′)(OCC₆H₃-5-Cl)]₂ (1), [(MeCp)₂Ti(O,O′)(OCC₆H₂-3,5-Cl₂)] (2) and [(MeCp)₂Ti(O,O′)(OCC₆H-3,5,6-Cl₃)] (3) have been synthesized via the reaction of (MeCp)₂TiCl₂ [MeCp = η⁵-(CH₃)C₅H₄] with the corresponding substituted chlorosalicylic acids in aqueous-organic systems in high yields and characterized by elemental analysis, IR and ¹H NMR spectra. Single-crystal X-ray diffraction analysis shows that geometries at titanium (IV) atoms are distorted tetrahedrons and the exhibited frameworks are constructed through weak interactions, which are H-bonding, π–π stacking and C–H···π interactions. Additional weak interactions, such as Cl···Cl interactions in compound 1, are also present, which help to form and stabilize crystalline materials. It is noticeable that the discriminating framework structures of three compounds due to their weak interactions existing conspicuous changes which result from the number of chlorine atoms on substituted chlorosalicylates. Graphical Abstract  Three to four coordinated chlorosalicylato titanocene compounds, [(MeCp)₂Ti(O,O′)(OCC₆H₃-5-Cl)]₂ (1), [(MeCp)₂Ti(O,O′)(OCC₆H₂-3,5-Cl₂)] (2) and [(MeCp)₂Ti(O,O′)(OCC₆H-3,5,6-Cl₃)] (3) have been synthesized in aqueous-organic system in high yields. Single-crystal X-ray diffraction analysis shows that geometries at titanium (IV) atoms are distorted tetrahedrons and the exhibited frameworks are constructed through weak interactions. The number of chlorine atoms on substituted chlorosalicylates has an effect on their framework structures.      

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.     

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.     

Experimental observation of strongly bound dimers of sulfuric acid: application to nucleation in the atmosphere

Sulfuric acid is a key compound in atmospheric nucleation. Here we report on the observation of a close-to-collision-limited sulfuric acid dimer formation in atmospherically relevant laboratory conditions in the absence of measurable quantities of ammonia or organics. The observed dimer formation rate was clearly higher than the measured new particle formation rate at ～1.5 nm suggesting that the rate limiting step for the nucleation takes place after the dimerization step. The quantum chemical calculations suggested that even in the ultraclean conditions there exist (a) stabilizing compound(s) with (a) concentration(s) high enough to prevent the dimer evaporation. Such a stabilizing compound should be abundant enough in any natural environment and would therefore not limit the formation of sulfuric acid dimers in the atmosphere.