Discreteness of interior transmission eigenvalues revisited

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.     

Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.     

Spiro-sulfamidate and sulfate nucleosides via 2′ and 3′-C-branched-chain sugars and nucleosides

C-branched-chain sugars and nucleosides were obtained by organocatalysis from ulose derivatives. After a reduction step, the corresponding 1,3-diol was derivatized into 3′-spiro-sulfamidates and unexpected sulfates by treatment with a Burgess reagent. Deprotection of the Boc-derivatives was carried out while preserving the cyclic sulfate. An example of ring opening of the cyclic sulfate derivative with sodium azide leading to the corresponding 3′-C-azidoalkyl branched-chain nucleosides is given.     

The effect of boric acid on the vapour liquid equilibrium of aqueous potassium carbonate

Aqueous potassium carbonate has seen renewed interest as a viable solvent for pre and post combustion carbon capture and storage. However, slow reaction kinetics may require the addition of a rate promoter such as boric acid to improve efficiency. The vapour liquid equilibrium of 30 weight percent potassium carbonate with 0, 3 and 5 weight percent boric acid was investigated at 50 and 70 °C using a dynamic inert gas stripping method. By estimating the boric acid reactions an Electrolyte-NRTL model was able to fit this data and literature results very closely.     

Physical and chemical analysis of elemental sulfur formation during galena surface oxidation

The surface oxidation of sulfide minerals, such as galena (PbS), in aqueous solutions is of critical importance in a number of applications. A comprehensive understanding of the formation of oxidation species at the galena surface is still lacking. Much controversy over the nature of these oxidation products exists. A number of oxidation pathways have been proposed, and experimental evidence for the formation of elemental sulfur, metal polysulfides, and metal-deficient lead sulfides in acidic conditions has been shown and argued. This paper provides further insight into the electrochemical behavior of galena at pH 4.5. Utilizing a novel experimental system that combines in situ electrochemical control and AC mode atomic force microscopy (AFM) surface imaging, the formation and growth of nanoscopic domains on the galena surface are detected and examined at anodic potentials. AFM phase images indicate that these domains have different material properties to the underlying galena. Continued oxidation results in nanoscopic pitting and the formation of microscopic surface domains, which are confirmed to be elemental sulfur by Raman spectroscopy. Further clarification of the presence of elemental sulfur is provided by Cryo-XPS. Polysulfide and metal-deficient sulfide could not be detected within this system.     

A fluorescent, shape-persistent dendritic host with photoswitchable guest encapsulation and intramolecular energy transfer

A fluorescent and photoresponsive host based on rigid polyphenylene dendrimers (PPDs) has been synthesized. The key building block for the divergent dendrimer buildup is a complex tetracyclone 12 containing azobenzenyl, pyridyl, and ethynyl entities. The rigidity of polyphenylenes is of crucial importance for a site-specific placement of different functions: eight azobenzene (AB) moieties into the rigid scaffold, a fluorescent perylenetetracarboxdiimide (PDI) into the core, and eight pyridin functions into the interior cavities. AB moieties of host-1 undergo reversible cis-trans photoisomerization and are photostable, as confirmed by various techniques: UV-vis, (1)H NMR, size exclusion chromatography, and fluorescence correlation (FCS). In this system, AB moieties act as photoswitchable hinges and enable control over (i) molecular size, (ii) intramolecular energy transfer between AB and PDI, and (iii) encapsulation and release of guest molecules. The presence of PDI allows not only following the effect of cis-trans photoisomerization on molecular size with highly sensitive FCS but also monitoring the efficiency of the intramolecular energy transfer process (from AB to PDI) by time-resolved optical spectroscopy. Pyridyl functions were incorporated to facilitate guest uptake via hydrogen bonds between the host and guests. Also, we have demonstrated that the photoswitchability of the host can be utilized to actively encapsulate guest molecules into its interior cavities. This novel, light-driven encapsulation mechanism could enable the design of new drug delivery systems.     

An improvement of the Nevanlinna-Gundersen theorem

A well-known result of Nevanlinna states that for two nonconstant meromorphic functions f and g on the complex plane C and for four distinct values aj∈C∪{∞}, if νf−aj=νg−aj for all 1?j?4, then g is a Möbius transformation of f. In 1983, Gundersen generalized the result of Nevanlinna to the case where the above condition is replaced by: min{νf−aj,1}=min{νg−aj,1} for j=1,2 and νf−aj=νg−aj for j=3,4. In this paper, we prove that the theorem of Gundersen remains valid to the case where min{νf−aj,1}=min{νg−aj,1} for j=1,2, and min{νf−aj,2}=min{νg−aj,2} for j=3,4. Furthermore, we work on the case where {aj} are small functions.     

On the stability of gradient polynomial systems at infinity

We first define the notion of the infimum at infinity of a polynomial function and the notion of stability at infinity near the fiber of the gradient descent system. Then we prove that the gradient descent system is stable at infinity near the fiber of the infimum value at infinity.     

Oleanolic triterpene saponins from the roots of Panax bipinnatifidus

Ten oleanane-type saponins (1-10), including three new compounds, namely bifinosides A-C (1-3), were isolated from the roots of Panax bipinnatifidus SEEM. Their structures were elucidated on the basis of chemical and spectroscopic methods.     

The reduction of Ag+ in metallic silver on pseudomelanin films allows for antibacterial activity but does not imply unpaired electrons

Dopamine-melanin films produced through the oxidation of dopamine in the presence of oxygen as an oxidant allow to reduce silver ions onto silver particles as already described in the paper by Lee et al. (H. Lee, S.M. Dellatore, W.M. Miller, P.B. Messersmith, Science 318 (2007) 426.). This reduction process has to occur through the oxidation of moieties present in the melanin film. This investigation shows that the free radicals present in the pseudomelanin film, quantified by means of electron spin resonance spectroscopy (ESR) for the first time, are not used in the transformation of Ag(+) cations to deposit silver. The ESR signal is hardly affected by the deposition of silver particles. On the other hand, X-ray photoelectron spectroscopy shows a small increase in the density of quinone groups and a small decrease of catechol groups on the surface of the film during the deposition of silver. This suggests that the deposited pseudomelanin films contain a significant fraction of catechol groups able to trigger reduction processes of metallic cations. These silver nanoparticles remain adherent to the melanin films and allow for a quantitative killing of Escherichia coli over a broad range of bacterial dilutions. However, the presence of the bacteria induces a release of the nanoparticles. The pseudomelanin films cannot be reused again for a silver ion reduction step. Nevertheless, the easy preparation of the pseudomelanin-silver composite and its effective one shot bacterial killing activity renders the strategy presented in this paper attractive. Some fundamental questions about redox process allowed by the pseudomelanin films will also be asked.