A New Way of Using Semidefinite Programming with Applications to Linear Equations mod p

We introduce a new method of constructing approximation algorithms for combinatorial optimization problems using semidefinite programming. It consists of expressing each combinatorial object in the original problem as a constellation of vectors in the semidefinite program. When we apply this technique to systems of linear equations mod p with at most two variables in each equation, we can show that the problem is approximable within (1 − κ(p))p, where κ(p) > 0 for all p. Using standard techniques, we also show that it is NP-hard to approximate the problem within a constant ratio, independent of p.     

Simultaneous 36 kHz PLIF/chemiluminescence imaging of fuel,CH2O and combustion in a PPC engine

The requirements on high efficiency and low emissions of internal combustion engines (ICEs) raise the research focus on advanced combustion concepts, e.g., premixed-charge compression ignition (PCCI), partially premixed compression ignition (PPCI), reactivity controlled compression ignition (RCCI), partially premixed combustion (PPC), gasoline compression ignition (GCI) etc. In the present study, an optically accessible engine is operated in PPC mode, featuring compression ignition of a diluted, stratified charge of gasoline-like fuel injected directly into the cylinder. A high-speed, high-power burst-mode laser system in combination with a high-speed CMOS camera is employed for diagnostics of the autoignition process which is critical for the combustion phasing and efficiency of the engine. To the authors’ best knowledge, this work demonstrates for the first time the application of the burst-system for simultaneous fuel tracer planar laser induced fluorescence (PLIF) and chemiluminescence imaging in an optical engine, at 36?kHz repetition rate. In addition, high-speed formaldehyde PLIF and chemiluminescence imaging are employed for investigation of autoignition events with a high temporal resolution (5 frames/CAD). The development of autoignition together with fuel or CH₂O distribution are simultaneously visualized using a large number of consecutive images. Prior to the onset of combustion the majority of both fuel and CH₂O are located in the recirculation zone, where the first autoignition also occurs. The ability to record, in excess of 100 PLIF images, in a single cycle brings unique possibilities to follow the in-cylinder processes without the averaging effects caused by cycle-to-cycle variations.     

Existence Results for Quasistatic Contact Problems with Coulomb Friction

We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique. \par Accepted 15 May 2000. Online publication 6 October 2000.     

Asymmetric hydrogenation of trisubstituted olefins with iridium-phosphine thiazole complexes: a further investigation of the ligand structure

New chiral bidentate phoshine thiazoles have been prepared and successfully applied as ligands in the homogeneous iridium-catalyzed asymmetric hydrogenation of aryl alkenes and aryl alkene esters. The ligands are designed to be highly modular and have one common chiral intermediate, from which diversity can be introduced at a late stage in the synthetic pathway. It was found that a six-member-ring backbone of the rigid ligand structure was preferred over seven- or five-member rings. In this study it is shown that the substituent pattern of the ligands has a major influence on the stereochemical outcome of the products. By applying the selectivity model proposed in this study, it is possible to match different substrates against different catalysts. In this way, good to excellent enantioselectivity can be obtained for typically difficult substrates. Geometrically different derivatives of alpha- and beta-methyl cinnamic acid ethyl esters were hydrogenated, to demonstrate the validity of the selectivity model and to verify the importance of steric and electronic matching of the catalyst and the substrate.     

Crystallization of mesoporous silica SBA-15 in a high pressure hydrothermal environment

Mesoporous silica SBA-15 (with ～6?nm pore size and ～6?nm wall thickness) was exposed to a hydrothermal environment at 2 and 5?GPa. The p,T quenched products were investigated by powder X-ray diffraction and transmission electron microscopy. Infrared spectroscopy and thermogravimetric analysis of a sample subjected to 5?GPa at room temperature suggests functionalization of both inner and outer pore surface by silanol. Partial transformation to nano-sized (20–50?nm) coesite crystals with nonfaceted morphology was observed during short equilibration times of 2?h at 125°C, which is significantly below the melting point of water (～250°C). Untransformed SBA-15 maintained intact pore structure. At 175°C and during 8?h, SBA-15 transformed completely into faceted coesite crystals with dimensions 100–300?nm, suggesting Ostwald ripening and thus significant mass transport in the solid water environment. At 2?GPa the melting point of water is near 70°C. Partial transformation to nano-sized α-quartz was observed at 65°C and during 2?h. Untransformed SBA-15 partially pore collapsed. The reduced pore stability of SBA-15 at 2?GPa is attributed to the presence of liquid water in the pores due to melting point depression of confined water.     

Thermodynamics and structure of liquid surfaces investigated directly with surface analytical tools**

Measuring directly the composition, the distribution of constituents as function of the depth and the orientation of molecules at liquid surfaces is essential for determining physicochemical properties of liquid surfaces. While the experimental tools that have been developed for analyzing solid surfaces can in principal be applied to liquid surfaces, it turned out that they had to be adjusted to the particular challenges imposed by liquid samples, e.g. by the unavoidable vapor pressure and by the mobility of the constituting atoms/molecules. In the present work it is shown, how electron spectroscopy and ion scattering spectroscopy have been used for analyzing liquid surfaces. The emphasis of this review is on using the structural information gained for determining the physicochemical properties of liquid surfaces.     

Multimode interferometer for guided matter waves

Atoms can be trapped and guided with electromagnetic fields, using nanofabricated structures. We describe the fundamental features of an interferometer for guided matter waves, built of two combined Y-shaped beam splitters. We find that such a device is expected to exhibit high contrast fringes even in a multimode regime, analogous to a white light interferometer.     

Rational approximation to functions likex α in integral norms

Основной результат р аботы касается поряд ков рациональных прибли жений вН ^p функций типа Маркова—Стилть еса с некоторыми спец иальными условиями на меры. Как следствие, получено распростра нение на случай иррац иональных показателей а тех оце нок порядка рациональных прибли жений функцийx ^α вL ^p [0,1], 1<р <∞, которые ранее были из вестны для рациональных а.     

A fragment of triosephosphate isomerase competes with the vasoactive intestinal polypeptide (VIP) for binding to the VIP receptor.

A 28-residue N-terminal fragment of triosephosphate isomerase, TIM(1-28), has been purified from porcine upper intestine. It competes with VIP for binding to the VIP receptor on rat liver plasma membranes with an IC50 value of 2.8 mM, about 1000 times higher than that for VIP binding to the membranes. Except for a single positional identity and the number of amino acid residues, the amino acid sequences of TIM(1-28) and VIP are unrelated as regards primary structure. However, the ability to bind to the same receptor site may indicate common three-dimensional structural properties.