On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

6-Thia-1-aza-5λ5-phosphabicyclo[3.2.0]hept-3-ene und Isothiocyanatophosphin-sulfide aus (Methylidenamino)phosphinen,Schwefelkohlenstoff und Acetylen- oder Ethylen-Derivaten

6-Thia-l-aza-5λ⁵-phosphabicyclo[3.2.0]hept-3-enes and Isothiocyanatophosphine-sulfides from (Methylidenamino)phosphines, Carbon Disulfide, and Acetylene- or Ethylene Derivatives (Methylidenamino)phosphines react with carbon disulfide to 1,3,2-thiazaphosphete derivatives 2 . Acetylenedicarboxylates give with 2 6-thia-l-aza-5λ⁵-phosphabicyclo[3.2.0]hept-3-enes 4a , b , and acrylates yield isothio-cyanatophosphin-sulfides 5a – c . The structures of 4a and 5a are proven by an X-ray diffraction analysis.     

A highly active fungal β-glucosidase

A highly active thermostable β-glucosidase was purified to homogeneity from a strain ofTrichoderma sp. The enzyme was an extracellular glycoprotein and showed hydrolytic activity toward several β-glucosides. Cellobiose was found to be the substrate of choice for this enzyme. This finding could suggest future technological applications of the purified protein.     

Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons

Upward and downward two-phase heat and mass transfer has been considered in the present paper. The heat and mass transfer with the condenser located below the evaporator has been obtained by inserting an accumulator tank in the liquid line of a loop thermosyphon and enforcing a pressure pulsation. In previous papers these heat transfer devices have been called pulsated two phase thermosyphons (PTPT). A mini PTPT has been experimentally investigated. It has shown a stable periodic heat transfer regime weakly influenced by the position of the condenser with respect to the evaporator. In contrast a classical loop mini thermosyphon (diameter of connecting pipes 4 mm) did not achieve a stable functioning for the investigated level differences between evaporator and condenser lower than 0.37 m. The present study shows that the functioning of a PTPT device does not directly depend on the level difference or the presence of noncondensable gas. In order to obtain a natural circulation in mini or micro loops, a periodically operating heat transfer regime should therefore be considered.     

Chelate polymers: II. Some novel transition metals complexes with azomethine‐containing siloxanes and their polyesters

New Schiff bases of 2,4‐dihydroxybenzaldehyde with siloxane‐α,ω‐diamines having different numbers of siloxane units in the chain have been synthesized and characterized by spectroscopy, elemental and thermal analyses. These azomethines were found to form complexes readily with copper(II), nickel(II), cobalt(II), cadmium(II) and zinc(II). From IR and UV–Vis studies, the phenolic oxygen and imine nitrogen of the ligand were found to be the coordination sites. Thermogravimetric analysis (TGA) data indicate the chelates to be more stable than the corresponding ligands. The melting points increase with shortening of the siloxane segment from azomethine, as well as the result of complexation. The chelates obtained were covalently inserted in polymeric linear structures by polycondensation through the OH‐difunctionalized ligand with 1,3‐bis(carboxypropyl)tetramethyldisiloxane. Direct polycondensation, assisted either by acetic anhydride or N,N′‐dicyclohexylcarbodiimide as dehydrating agent and the complex 4‐(dimethylamino)pyridinium 4‐toluenesulfonate as catalyst, was used for the synthesis of these compound types. The structures of the polymers obtained were confirmed by IR, UV and ¹H NMR. Characterization was undertaken by TGA, solubility tests and viscosity measurements. Copyright © 2003 John Wiley & Sons, Ltd.     

Influence of heat treatment conditions on the porosity changes of sulfonated styrene/divinylbenzene copolymers

Sulfonic cation exchangers with two ion exchange group concentrations (0.5 and 2.4 mmol/g, samples A and B, respectively) were obtained by sulfonation of a porous styrene (S) and divinylbenzene (DVB) copolymer with chlorosulfonic acid. Strong thermal decomposition of the sulfonated copolymer A, accompanied by significant changes in its porous structure, starts at ca. 400°C. The char has no sulfonic groups. After heat treatment at 400°C in steam, a sorbent was obtained (yield 65%) that shows higher phenol sorption than the untreated sample when related to the bed volume. The chlorosulfonic derivatives of the initial copolymer were less thermally resistant than the sulfonic ones obtained by hydrolysis. Pyrolysis of the cation exchanger B, in its H+ and Ca²⁺ forms, was carried out at 900°C (yield of both chars close to 30%). By subsequent steam activation at 800°C to a 50% burn-off of the char, sorbents with well-developed, but distinctly different, porous structures were obtained. The activated char from the sulfonated copolymer in its hydrogen form was highly microporous and indicated an effective surface area of 1180 m²/g. However, because of a low contribution of mesopores, its ability to adsorb phenol from the liquid phase was not very high. The activated char from the calcium-doped copolymer, indicating a smaller surface area (580 m²/g) but characterized by a well-developed mesoporosity, was a better sorbent for phenol. © 1994 John Wiley & Sons, Inc.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Nanostructured polymetallaynes of controlled length: Synthesis and characterization of oligomers and polymers from 1,1′‐bis‐(ethynyl)4,4′‐biphenyl bridging Pt(II) or Pd(II) centers

The reactivity of square planar palladium(II) and platinum(II) complexes in trans or cis configuration, namely trans or cis‐[dichlorobis(tributylphosphine)platinum(II)] and trans‐[dichlorobis(tributylphosphine)palladium(II)] with 1,1′‐bis(ethynyl) 4,4′‐biphenyl, DEBP, leading to π‐conjugated organometallic oligomeric and polymeric metallaynes, was investigated by a systematic variation of the reaction conditions. The formation of polymers and oligomers with defined chain length [? M(PBu₃)₂ (C?C? C₆H₄? C₆H₄? C?C? )]_n (n = 3–10 for the oligomers, n = 20–50 for the polymers) depends on the configuration of the precursor Pt(II) and Pd(II) complexes, the presence/absence of the catalyst CuI, and the reaction time. A series of model reactions monitored by XPS, GPC, and NMR ³¹P spectroscopy showed the route to modulate the chain growth. As expected, the nature of the transition metal (Pt or Pd) and the molecular weight of the polymers markedly influence the photophysical characteristics of the polymetallaynes, such as optical absorption and emission behavior. Polymetallaynes with nanostructured morphology could be obtained by a simple casting procedure of polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3311–3329, 2007     

Effect of biotransformation on multispecies plume evolution and natural attenuation

Biological transformation of volatile organic compounds is one of the key factors that influence contaminant-plume evolution and thus natural attenuation. In this study we investigate the effect of biological transformation on the transport of contaminants in the aqueous and gaseous phases. The analysis includes the study of the effect of density-driven advection of contaminants in the gaseous phase on multiphase and multispecies flow, fate and transport modeling in the subsurface. Trichloroethylene (TCE) and its two byproducts, dichloroethylene and vinyl chloride, are analyzed as the target contaminants. Our results indicate that density-driven advection of the gaseous phase, which is initiated by evaporation of TCE as a nonaqueous phase liquid, increases the downward and also the lateral migration of TCE within the unsaturated zone. This process also influences the location of high-concentration zones of the byproducts of TCE in the unsaturated and the saturated zones. Biotransformation of TCE contributes to the reduction of dissolved TCE plume development as expected. The daughter byproducts, which are introduced into the subsurface system, show distinct transport patterns as they are affected by their independent degradation kinetics and density-driven advection. These observations, which are based on our simulation results for biotransformation and transport of TCE and its byproducts, are useful in evaluating the natural attenuation processes, its potential health hazards and also the evaluation of potential plume development at contaminated sites.