Continuous Dependence of Entropy Solutions to the Euler Equations on the Adiabatic Exponent and Mach Number

We establish the L ¹-estimates for continuous dependence of entropy solutions to the full Euler equations away from the vacuum on two physical parameters: the adiabatic exponent γ → 1 that passes from the non-isentropic to isothermal Euler equations and the Mach number that passes from the compressible to incompressible Euler equations. Our analysis involves the effective approach developed in our earlier work and additional new techniques that generalize this approach to the setting of the full Euler equations.     

Well‐defined diblock copolymers possessing fluorescent and metal chelating functionalities as novel macromolecular sensors for amines and metal ions

The amino‐ and metal‐ion sensing capability of a novel type of well‐defined block copolymers based on 9‐anthrylmethyl methacrylate (AnMMA; hydrophobic, fluorescent) and 2‐(acetoacetoxy)ethyl methacrylate (AEMA; hydrophobic, metal chelating) has been investigated in organic media. AEMA_x‐b‐AnMMA_y diblock copolymers were prepared for the first time using reversible addition‐fragmentation chain transfer (RAFT) polymerization. All polymers were characterized in terms of molecular weights, polydispersity indices and compositions by size exclusion chromatography and ¹H NMR spectroscopy, respectively. The glass transition (T_g) temperatures of the AEMA_x and AnMMA_x homopolymers and the AEMA_x‐b‐AnMMA_y diblock copolymers were determined using differential scanning calorimetry. These systems were evaluated toward their ability to act as effective dual chemosensors (i.e., amino‐ and metal‐ion sensors) in an organic solvent (chloroform). More precisely, the fluorescence intensity of both the AnMMA_x homopolymers and the AnMMA_x‐b‐AEMA_y diblock copolymers in solution exhibited a significant decrease in the presence of triethylamine. Moreover, the presence of iron (III) cations were also found to significantly affect the fluorescence signal of the anthracene moieties when those were combined in a block copolymer structure with the AEMA units, due to complex formation occurring between the β‐ketoester groups of the AEMA_x segment and the cations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams

In this paper methods to simulate the signals in laser interferometers are proposed. The central part deals with the computation of the photocurrent, subsequent phase demodulation and finally the generation of interferometer signals, such as the longitudinal phase readout, differential wavefront sensing signal, differential power sensing and contrast. Here, fundamental Gaussian beams without astigmatism are assumed. The methods are validated in several examples by comparison with experimental data, with analytical results as well as with an intuitively predictable system.     

Controlling the Emissive,Chiroptical, and Electrochemical Properties of Double [7] Helicenes through Embedded Aromatic Rings

We present here the synthesis and in-depth physicochemical characterization of a double hetero[7]helicene fused with four triazole rings at both helical ends. The comparison of this triazole-fused double helicene with the previously reported all-carbon and thiadiazole-fused analogs revealed the huge impact of the embedded aromatic rings on the photophysical features. The small structural variation of the terminal rings from thiadiazole to triazole caused a dramatic change of the photoluminescence quantum yields (PLQYs) from <1 % to 96 %, while the replacement of the terminal benzene rings with triazole rings induced a tenfold enhancement of the circularly polarized luminescence dissymmetry factor. These observations were well corroborated with transient absorption analysis and/or theoretic calculations. In addition, the triazole-fused double helicene exhibited ambipolar redox behavior, enabling the generation of radical cation and anion species by electrochemical and chemical methods and showing its potential for spin-related applications.     

Ratiometric FRET-based detection of DNA and micro-RNA in solution

A ratiometric method for detecting DNA oligomers in bulk solution based on Förster resonance energy transfer (FRET) is described. The two fluorescence signals (green and red), originating from Cy3 (donor, green) and Cy5 (acceptor, red) labels, are simultaneously detected from the pre-hybridized Cy3oligomerY:Cy5oligomerX system. The ratio of red to green intensities is sensitive to the presence of the single-stranded complimentary oligomer, which replaces single-stranded Cy3oligomerY in the donor:acceptor complex and perturbs the FRET. The detection scheme is generally applicable to the detection of DNA and RNA, and particularly micro-RNA. The proposed method is applicable to various double-stranded various lengths targets (manipulation of the sample preparation conditions, such as temperature, incubation time, denaturizing agent, may be needed).     

Creating hierarchical models of protein families based on Expressed Sequence Tags: the "Sprockets" analysis pipeline

We have created an analysis pipeline called Sprockets, which can be used to classify proteins into various hierarchical “families”, and build searchable models of these families. The construction of these families is based on data from Expressed Sequence Tags (ESTs) and Coding DNA Sequences (CDSs), making Sprockets clusters especially suitable for studying gene families in organisms for which the completely sequenced genome does not (yet) exist. The pipeline consists of two main parts: pair-wise analysis and grouping of sequences with Z-score statistics, followed by hierarchical splitting of clusters into alignable protein families. Various computational and statistical techniques applied in Sprockets allow it to act like a massive and selective multiple sequence alignment engine for combining individual sequence collections and related public sequences. The end result is a database of gene Hidden Markov Models, each related to the other by three levels of similarity: secondary structure, function and evolutionary origin. For a sample 20,000 EST set from Lactuca spp., Sprockets provided a 9% improvement in mapping of function to unknown sequences over traditional pair-wise search methods and InterPro mapping.     

The neglected Pt-N(sulfonamido) bond in Pt chemistry. New fluorophore-containing Pt(II) complexes useful for assessing Pt(II) interactions with biomolecules

Treatment of cis-Pt(Me2SO)2Cl2 with DNSH-tren afforded [Pt(DNSH-tren)Cl]Cl and with DNSH-dienH, under increasingly more basic conditions, led to Pt(DNSH-dienH)Cl(2), Pt(DNSH-dien)Cl, and Pt(DNS-dien). (DNSH = 5-(dimethylamino)naphthalene-1-sulfonyl, linked via a sulfonamide group to tris(2-aminoethyl)amine (DNSH-tren) and diethylenetriamine (DNSH-dienH); the H's in DNSH-dienH designate protons sometimes lost upon Pt binding, i.e., sulfonamide NH for the dienH moiety and H8 for the DNSH moiety). Respectively, the three neutral DNSH-dienH-derived complexes are difunctional, monofunctional, and nonfunctional and exhibit decreasing fluorescence in this order as the dansyl group distance to Pt decreases. 2D NMR data establish that Pt(DNS-dien) has a Pt-C8 bond and a Pt-N(sulfonamido) bond. Pt(DNSH-dien)Cl and [Pt(DNSH-tren)Cl]Cl bind to N7 of 6-oxopurines (e.g., 5'-GMP, 3'-IMP, and 9-ethylguanine) and sulfur of methionine (met). Competition and challenge reactions for Pt(II) with met and 5'-GMP typically reveal that met binding is favored kinetically but that 5'-GMP binding is favored thermodynamically. This common type of behavior was found for [Pt(DNSH-tren)Cl]Cl. In contrast, Pt(DNSH-dien)Cl had reduced kinetic selectivity for met. This unusual behavior undoubtedly arises as a consequence of the bound Pt-N(sulfonamido) group, which donates strongly to Pt (as indicated by relatively upfield dien NH signals) and which places the bulky DNSH moiety close to the monofunctional reaction site. The decrease in the relatively upfield shifts of the DNSH group signals indicates that this group stacks with the purine. This stacking could explain the unprecedented, relatively low reactivity of a Pt complex bearing a dien-type ligand toward met vs 5'-GMP.     

Novel example of a chain structure formed by 1,4-dioxane and cobalt(II) links. Chain [Co3(mu-OOCCF3)4(mu-H2O)2(OOCCF3)2(H2O)2(C4H8O2)].2C4H8O2

The trimer [Co3(mu-OOCCF3)4(mu-H2O)2(OOCCF3)2(H2O)2(C4H8O2)].2C4H8O2. (1) is composed of three tetragonally distorted Co(II) centers bridged by four trifluoroacetates and two bridging water molecules. 1,4-Dioxane is coordinated at a distance of 2.120(3) A from the terminal cobalt Co2; the remaining oxygen of this 1,4-dioxane links the terminal cobalt to a neighbor trimer, forming a one-dimensional chain. The crystal structure displays a network of hydrogen bonds between four noncoordinated 1,4-dioxane molecules and the coordinated terminal water molecules. The magnetic properties of 1 were analyzed with the use of the Hamiltonian including isotropic exchange interactions between real spins of a high-spin Co(II), spin-orbit coupling and a low-symmetry crystal field acting within the (4)T(1g) ground manifold of each cobalt ion. A weak antiferromagnetic exchange interaction between cobalt ions in 1 was found. The results of the magnetic model are in good agreement with the experimental observations.     

Ratiometric FRET-based detection of DNA and micro-RNA on the surface using TIRF detection

A new FRET-based method for the ratiometric detection of DNA oligomers on a surface using TIRF detection mode is reported. The dual-labeled system consisting of two hybridized oligomers, Cy3oligoY:Cy5oligoX was immobilized on the surface, and the total internal reflection fluorescence (TIRF) was used to detect emission signals from the surface. Two signals, green and red, which originated from the green donor Cy3 and the red acceptor Cy5, have been simultaneously detected. When the target single-stranded complimentary oligomer was present in the solution, this oligomer replaced the Cy3oligoY in the donor:acceptor complex on the surface and the ratio of red-to-green signal was dramatically changed. This detection scheme is generally applicable to the detection of DNA or RNA on a surface.