Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold $\overline{M}$. We first assume the pull back Weitzenböck operator of $\overline{M}$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of $\overline{M}$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when $\overline{M}$ is the space form.     

Contributions to the Optimization of a Caprolactam Production Plant by Radiotracer Techniques

Residence time spectra and material distributions in an operating caprolactam production plant were measured by means of sodium 24, bromine 82 and technetium 99m. The results of the tracerexperiments contributed to an optimization of the plant.     

Stereoselective Synthesis of Alkenyl Alcohols Using Dissolving Metal (Ca,Na) Reduction

Use of the calcium-ethylenediamine and sodium-liquid ammonia reduction systems for the ring opening of dihydropyran derivatives was studied. (Z)-Alkenyl alcohols and (E)-alkenyl alcohols were stereoselectively synthesized respectively.     

La(O-i-Pr)3 CATALYZED THREE-COMPONENT CONDENSATION REACTION: A CONVENIENT SYNTHESIS OF N,N-DIALKYL-α-CYANOAMINES

ABSTRACT

In the presence of 10 mol% of La(O-i-Pr)₃, a three-component condensation reaction of aldehyde, secondary amine and trimethylsilylcyanide proceeded smoothly to afford N,N-dialkyl-α-cyanoamine in good yield.     

Two coordination polymers based on 2,2′-biimidazoles and d10 metal ions: syntheses,structures, and luminescence

Two d¹⁰ metal coordination polymers, [Zn(µ-Me₂biim)Cl₂] _n (1) and [Cd₃(MeHbiim)₂(1,4-BDC)₃] _n (2) (Me₂biim?=?N,N′-dimethyl-2,2′-biimidazole, MeHbiim?=?N-methyl-2,2′-biimidazole, 1,4-BDC?=?1,4-benzenedicarboxylate), were synthesized under hydrothermal conditions and characterized by elemental analysis, infrared spectroscopy, thermogravimetric analysis, and single-crystal X-ray crystallography. Complex 1 features an infinite neutral zigzag 1-D chain. Interchain hydrogen-bonding interactions further extend the 1-D arrangement to generate a 2-D supramolecular architecture. Complex 2 features a 3-D coordination polymer with α-Po net topology, based on linear trinuclear {Cd₃O₁₄N₄} clusters. Both complexes have high thermal stability and exhibit strong luminescence at room temperature.     

Exhaled breath condensate: Determination of non-volatile compounds and their potential for clinical diagnosis and monitoring. A review

Exhaled breath condensate is a promising, non-invasive, diagnostic sample obtained by condensation of exhaled breath. Starting from a historical perspective of early attempts of breath testing towards the contemporary state-of-the-art breath analysis, this review article focuses mainly on the progress in determination of non-volatile compounds in exhaled breath condensate. The mechanisms by which the aerosols/droplets of non-volatile compounds are formed in the airways are discussed with methodological consequences for sampling. Dilution of respiratory droplets is a major problem for correct clinical interpretation of the measured data and there is an urgent need for standardization of EBC. This applies also for collection instrumentation and therefore various commercial and in-house built devices are described and compared with regard to their design, function and collection parameters. The analytical techniques and methods for determination of non-volatile compounds as potential markers of oxidative stress and lung inflammation are scrutinized with an emphasis on method suitability, sensitivity and appropriateness. The relevance of clinical findings for each group of possible non-volatile markers of selected pulmonary diseases and methodological recommendations with emphasis on interdisciplinary collaboration that is essential for future development into a fully validated clinical diagnostic tool are given.     

α- or β-Substituted functional phthalocyanines bearing thiophen-3-ylmethanol substituents: synthesis,characterization, aggregation behavior and antioxidant activity

The tetra α- or β-thiophene substituted metal and metal-free phthalocyanines (Pcs) M[Pc(α-OCH₂Thiopen)₄] and M[Pc(β-OCH₂Thiopen)₄] {(α-ThMet-MPc), (β-ThMet-MPc) [ThMet: Thiophene methoxy], M = Zn(II), Co(II) and, 2H} were synthesized from the corresponding 3’-(thiophen-3-ylmethoxy)phthalonitrile or 4’-(thiophen-3-ylmethoxy)phthalonitrile (ThMePN). The structural characterization, spectral, and antioxidant properties of a series of new Pcs were also presented. Both α- and β-substituted Pc complexes increased solubility in polar solvents, such as THF, DMF, and DMSO. FT-IR, ¹H-NMR, ¹³C-NMR, UV–vis, MALDI-TOF/MS spectral, and elemental analysis data were used to characterize the compounds. The aggregation behaviors of 3–8 were also investigated at different concentrations in THF. Antioxidant test methods, α,α-diphenyl-β-picrylhydrazyl radical scavenging activity, metal chelating activity, and reducing power, were used to determine the antioxidant activities. 6 showed very good ferrous ion chelating activity of 81 ± 1%. 6, 5, 4, and 3 showed better reducing power than trolox, ascorbic, acid and butylated hydroxytoluene, commercially used antioxidants.     

Iron(III)-catalyzed synthesis of selenoesters from α-amino carbonyl derivatives at room temperature

An Fe(III)-catalyzed efficient method has been developed for the synthesis of selenoester derivatives in high yields through the coupling of α-amino carbonyl/glycine derivatives and diselenides under ambient air. A library of benzoselenoate derivatives having a variety of substituents has been synthesized. A plausible reaction pathway has been predicted. Experimental results suggest that the reaction proceeds through a radical pathway. Operational simplicity, compatibility with various α-amino carbonyls and diselenides, high yields, fast reaction and mild reaction conditions are the notable advantages of this procedure. We have also shown the practical application of the synthesized selenoesters which is useful to generate peptide bonds in biological sciences.     

Nano-bio interface study between Fe content TiO2 nanoparticles and adenosine triphosphate biomolecules

The advent of nano-biotechnology has inspired the interface interaction study between engineered nanoparticles (NPs) and biomolecules. The interaction between Fe content titanium dioxide (TiO₂) NPs and adenosine triphosphate (ATP) biomolecules has been envisioned. The effect of Fe content in TiO₂ matrix was studied using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The increase in Fe content caused a decrease in particle size with change in morphology from spherical to one-dimensional rod structure. The Fe incorporation in the TiO₂ matrix reduced the transition temperature from anatase to rutile (A-R) phase along with formation of haematite phase of iron oxide at 400°C. The interaction of Fe content TiO₂ NPs with ATP molecule has been studied using spectroscopic method of Raman scattering and infrared vibration spectrum along with TEM. Fe content in TiO₂ has enhanced the interaction efficiency of the NPs with ATP biomolecules. Raman spectroscopy confirms that the NPs interact strongly with nitrogen (N₇) site in the adenine ring of ATP biomolecule. Engineering of Fe content TiO₂ NP could successfully tune the coordination between metal oxide NPs with biomolecules, which could help in designing devices for biomedical applications.     

High-efficiency α-benzoyloxylation and hydroxylation of β-keto amides by phase transfer catalysis

A facile and efficient protocol for α-benzoyloxylation and α-hydroxylation of β-keto amides by phase-transfer catalysis is presented. This methodology provides mild and practical access to a variety ofα-oxygenated β-keto amides. Furthermore, α-benzoyloxylation products can be easily converted into α-hydroxylation compounds, which are useful synthetic precursors of biological targets.