Eigenvalue bounds for elliptic operators

Lower bounds for the real parts of the points in the spectrum of elliptic equations are derived. These bounds, depending only on the diameter L of the domain G and on the maximum norm M of the coefficients a, b, are optimal. They are always positive and thus the spectrum is bounded away from the imaginary axis. This result is then used to prove an “anti-dynamo theorem” for magnetic fields with plane symmetry in the case of a compressible steady flow surrounded by a perfect conductor.     

The oxidative decarboxylation of polyaminocarboxylic acids

Summary The rates of oxidation of four chelating agents, NTA, EDTA, CDTA, and DTPA with Ce(IV), in sulfuric acid media, were determined spectrophotometrically by a stopped-flow technique. The reductive ability is in the order CDTA > EDTA > DTPA > NTA. The influence of varying the acidity of the medium was studied, and in each case a maximum in the rate constant vs. [H⁺] plot was observed. A possible interpretation of the reactivities and the influence of acidity is advanced.

---

Oxydative Decarboxylierung von PolyaminocarbonsäurenII. Vergleichende kinetische Untersuchung der Oxydation von NTA, ÄDTA, CDTA und DTPA mit Ce(IV) in saurer Lösung

Zusammenfassung Die Oxydationsgeschwindigkeiten von 4 Chelaten (NTA, ÄDTA, CDTA und DTPA) mit Ce(IV) in saurer Lösung wurden spektrophotometrisch mit Hilfe der stopped-flow-Technik bestimmt. Die Reduzierfähigkeit nimmt in der Reihenfolge CDTA > ÄDTA > DTPA > NTA ab. Der Einfluß verschiedener Säuregehalte in der Lösung wurde untersucht, und in jedem Fall wurde ein Maximum in der graphischen Darstellung der Geschwindigkeitskonstante gegen [H⁺] beobachtet. Eine mögliche Erklärung des Reaktionsvermögens und des Säureeinflusses wird gegeben.

---

---

Part I: Z. Anal. Chem. 246, 231 (1969).     

The Chemistry of Coumarin Derivatives. Part 5. Unusual course of the reaction of 4-hydroxycoumarin and aliphatic aldehydes

The reaction of 4-hydroxycoumarin and certain aliphatic aldehydes affords 1:1 or complex 2:2 adducts besides (or in place) of the expected 2:1 bis(coumarin) adducts. Reaction with heptanal, cyclohexanecarbaldehyde, and pivalaldehyde are reported as representative. The structure of the reaction products was established by spectroscopical techniques, including X-ray analysis, and their formation was mechanistically rationalized. Some of the 1:1 adducts are synthetically useful for the preparation of 3-alkyl-4-hydroxycoumarins.     

Optical and Electrical Properties of Polymerizing Plasmas and Their Correlation with DLC Film Properties

Diamond-like carbon (DLC) films were grown from radiofrequency plasmas of acetylene-argon mixtures, at different excitation powers, P. The effects of this parameter on the plasma potential, electron density, electron temperature, and plasma activity were investigated using a Langmuir probe. The mean electron temperature increased from about 0.5 to about 7.0 eV while the mean electron density decreased from about 1.2 × 10⁹ to about 0.2 × 10⁹ cm^–3 as P was increased from 25 to 150 W. Both the plasma potential and the plasma activity were found to increase with increasing P. Through actinometric optical emission spectrometry, the relative concentrations of CH, [CH], and H, [H], in the discharge were mapped as a function of the applied power. A rise in [H] and a fall in [CH] with increasing P were observed and are discussed in relation to the plasma characteristics and the subimplantation model. The optical properties of the films were calculated from ultraviolet-visible spectroscopic data; the surface resistivity was measured by the two-point probe method. The optical gap, E _G, and the surface resistivity, _s, fall with increasing P. E _G and _s are in the ranges of about 2.0–1.3 eV and 10¹⁴–10¹⁶ /, respectively. The plasma power also influences the film self-bias, V _b, via a linear dependence, and the effect of V _b on ion bombardment during growth is addressed together with variation in the relative densities of sp² and sp³ bonds in the films as determined by Raman spectroscopy.     

Chromium‐Mediated Dearomatization: Application to the Synthesis of Racemic 15‐Acetoxytubipofuran and Asymmetric Synthesis of Both Enantiomers

An efficient dearomatization process of [Cr(arene)(CO)₃] complexes initiated by a nucleophilic acetaldehyde equivalent is detailed. It generates in a one‐pot reaction three C? C bonds and two stereogenic centers. This process allowed a rapid assembly of a cis‐decalin ring system incorporating a homoannular diene unit in just two steps starting from aromatic precursors (Scheme 2). The method was applied to the total synthesis of the eudesmane‐type marine furanosesquiterpene (±)‐15‐acetoxytubipofuran ( 2 ). Two routes were successfully used to synthesize the γ‐lactone precursor of the furan ring. The key step in the first approach was a Pd‐catalyzed allylic substitution (Scheme 3), while in the second approach, an Eschenmoser–Claisen rearrangement was highly successful (Scheme 4). The Pd‐catalyzed allylic substitution could be directed to give either the (normal) product with overall retention as major diastereoisomer or the unusual product with inversion of configuration (see Table). For the synthesis of the (?)‐enantiomer (R,R)‐ 2 of 15‐acetoxytubipofuran, an enantioselective dearomatization in the presence of a chiral diether ligand was implemented (Scheme 7), while the (+)‐enantiomer (S,S)‐ 2 was obtained via a diastereoselective dearomatization of an arene‐bound chiral imine auxiliary (Scheme 8). Chiroptical data suggest that a revision of the previously assigned absolute configuration of the natural product is required.     

Solid State NMR and TG/MS Study on the Transformation of Methyl Groups During Pyrolysis of Preceramic Precursors to SiOC Glasses

The sol-gel method was used to prepare two different starting gels containing SiCH₃-groups for the preparation of SiOC ceramics. To understand the role of Si—H bonds in the incorporation of carbon into the SiOC network, gels prepared from a 1:2 mixture of triethoxysilane and methyldiethoxysilane (T^HD^H2) and solely methyltriethoxysilane (T^Me) were investigated. Thermogravimetric analysis coupled with mass spectroscopy (TG-MS) in inert atmosphere was performed to attain an insight into the decomposition reactions involved during gel-glass transformation. Samples calcined at different temperatures up to 1000°C were characterized by ²⁹Si and ¹³C magic angle spinning nuclear magnetic resonance (MAS-NMR) spectroscopy. The presence of SiH groups in the starting gel allows an efficient conversion of Si—CH₃ groups into CSi₄ sites at lower temperatures. As a result, despite a much lower amount of carbon in the starting T^HD^H2 gel (C/Si = 0.33) compared to the T^Me gel (C/Si = 1), the amount of carbon inserted into the SiOC network of both glasses is equivalent, but the T^Me sample contains the 10 fold amount of free carbon.     

Potential energy surface and rovibrational states of the ground Ar-HI complex

A potential energy surface for the ground electronic state of the Ar-HI van der Waals complex is calculated at the coupled-cluster with single and double excitations and a noniterative perturbation treatment of triple excitations [CCSD(T)] level of theory. Calculations are performed using for the iodine atom a correlation consistent triple-zeta valence basis set in conjunction with large-core Stuttgart-Dresden-Bonn relativistic pseudopotential, whereas specific augmented correlation consistent basis sets are employed for the H and Ar atoms supplemented with an additional set of bond functions. In agreement with previous studies, the equilibrium structure is found to be linear Ar-I-H, with a well depth of 205.38 cm(-1). Another two secondary minima are also predicted at a linear and bent Ar-H-I configurations with well depths of 153.57 and 151.57 cm(-1), respectively. The parametrized CCSD(T) potential is used to calculate rovibrational bound states of Ar-HI/Ar-DI complexes, and the vibrationally averaged structures of the different isomers are determined. Spectroscopic constants are also computed from the CCSD(T) surface and their comparison with available experimental data demonstrates the quality of the present surface in the corresponding configuration regions.     

New organocatalysts derived from tartaric and glyceric acids for direct aldol reactions

The synthesis of several new pyrrolidine based asymmetric organocatalysts derived from tartaric, glyceric acids and a pyrrolidine moiety is described with a study of their application in the development of an enantioselective aldol protocol. The influence of different proton donor groups, such as a primary hydroxyl or a carboxylic acid group, or their absence, on the efficiency of the organocatalyst was studied. The configuration of the tartrate derived catalysts and the presence of the rigid butane-2,3-diacetal were found to have a strong influence on the stereoselective outcome of the aldol reaction.     

The impact of time on the heat resistance of self-compacting high-performance concrete incorporated with recycled martials

The influence of time on the mechanical behavior of concrete after exposure to elevated temperatures has been studied. Twenty-one self-compacting high-performance concrete mixtures with different incorporation amounts of coarse recycled concrete aggregate (RCA) and three unprocessed waste powder materials have been tested at age of 270 days for residual compressive and flexural strength after exposure to fire. The results have been compared to the results for the same concrete, which have been studied at age of 90 days. A new parameter has been introduced for comparing the responses of concrete to elevated temperatures at different ages; this parameter was the “heat resistance” which expresses the total area under the curve of the relative residual strength (compressive or flexural) after exposing to six temperature degrees (20, 150, 300, 500, 600, and 800 °C). The results showed that the age of concrete has an influence on the response of concrete to elevated temperatures. The heat resistance of compressive strength enhanced with age but the concrete behaved with a tendency different to that at the age of 90 days. The heat resistance of flexural strength has not been affected or slightly decreased but not with more than 10% to that at the age of 90 days. The used waste powder materials were unprocessed waste fly ash, waste cellular concrete powder and waste perlite powder; they proved that using any of them up to 15% as a replacement for cement with 0% or 25% of RCA enhanced the concrete resistance for the fire with time. The main two reasons for changing of residual strength with the time were the changing of water content and the proceeding of hydration of the binder. In general, long ages testing properties of concrete simulate the real behavior of concrete structures accurately.

     

One-bond 1J(15N,H) coupling constants at sp2-hybridized nitrogen of Schiff bases,enaminones and similar compounds: A theoretical study

¹J(¹⁵N,H) coupling constants for enaminones and NH-forms of intramolecularly hydrogen-bonded Schiff bases as model compounds for sp²-hybridized nitrogen atoms are evaluated using density functional theory (DFT) to find the optimal functionals and basis sets. Ammonia is used as a test molecule and its one-bond coupling constant is compared with experiment. A methylamine Schiff base of a truncated molecule of gossypol is used for checking the performance of selected B3LYP, O3LYP, PBE, BHandH, and APFD density functionals and standard, modified, and dedicated basis sets for coupling constants. Both in vacuum and in chloroform, modeled by the simple continuum model of solvent, the modified basis sets predict significantly better the ¹J(¹⁵N,H) value in ammonia and in the methylamine Schiff base of a truncated molecule of gossypol than the standard basis sets. This procure is then used on a broad set of intramolecularly hydrogen-bonded molecules, and a good correlation between calculated and experimental one-bond NH coupling constants is obtained. The ¹J(¹⁵N,H) couplings are slightly overestimated. The calculated data show for hydrogen-bonded NH interatomic distances that the calculated values depend on the NH bond lengths. The shorter the bond lengths, the larger the ¹J(¹⁵N,H). A useful correlation between ¹J(¹⁵N,H) and NH bond length is derived that enables realistic predictions of one-bond NH coupling constants. The calculations reproduce experimentally observed trends for the studied molecules.