The fundamental band ν2 of D2CO

The ν₂ band of D₂¹³CO in the region of 1570-1760 cm⁻¹ has been analyzed with high accuracy. The limits of the quantum numbers J and K_a are 50 and 16, respectively. The number of the assigned transitions is 3858. A local anharmonic resonance ν₂/2ν₄ at K_a =  8-12 was observed. The Watson’s A-reduced Hamiltonian and anharmonic resonance term were fitted to the observed transitions. The fit resulted in the band center and rotational parameters of the ν₂ band as well as the effective parameters for the 2ν₄ band and anharmonic resonance parameter. The rms deviation of the transitions in the ν₂ band was 0.000364 cm⁻¹.     

Self‐Assembly of Amphiphilic Janus Dendrimers into Mechanically Robust Supramolecular Hydrogels for Sustained Drug Release

Compounds that can gelate aqueous solutions offer an intriguing toolbox to create functional hydrogel materials for biomedical applications. Amphiphilic Janus dendrimers with low molecular weights can readily form self‐assembled fibers at very low mass proportion (0.2 wt %) to create supramolecular hydrogels (G′?G′′) with outstanding mechanical properties and storage modulus of G′>1000 Pa. The G′ value and gel melting temperature can be tuned by modulating the position or number of hydrophobic alkyl chains in the dendrimer structure; thus enabling exquisite control over the mesoscale material properties in these molecular assemblies. The gels are formed within seconds by simple injection of ethanol‐solvated dendrimers into an aqueous solution. Cryogenic TEM, small‐angle X‐ray scattering, and SEM were used to confirm the fibrous structure morphology of the gels. Furthermore, the gels can be efficiently loaded with different bioactive cargo, such as active enzymes, peptides, or small‐molecule drugs, to be used for sustained release in drug delivery.     

Comparison of Microwave-Assisted Digestion Methods and Selection of Internal Standards for the Determination of Rh, Pd and Pt in Dust Samples by ICP-MS

Different temperature-pressure controlled microwave-assisted digestion methods were compared for the digestion of dust samples prior to the determination of rhodium and platinum by inductively coupled plasma mass spectrometry (ICP-MS). The results obtained for platinum and rhodium in the digested reference material (BCR-723, road dust) were generally in good agreement with the certified values. However, the determination of matrix elements (Zn, Rb, Sr, Y, Hf and Pb) showed clear differences between the digestion methods. In addition, different internal standards were compared in the determination rhodium, palladium and platinum by ICP-MS. According to the results, even serious non-spectral interferences can be corrected by choosing a suitable internal standard or combination of internal standards.     

Determination of the Dissociation Constants of Urocanic Acid Isomers in Aqueous Solutions

(E)- and (Z)-Urocanic acids are endogenous chemicals in the normal mammalian skin. The first and the second thermodynamic dissociation constants (pK _a1 and pK _a2) of urocanic acid isomers were determined using UV spectrophotometry in aqueous solutions. The values with standard deviation (pK _a1 = 3.43 ± 0.12 and pK _a2 = 5.80 ± 0.04) and (pK _a1 = 2.7 ± 0.3 and pK _a2 = 6.65 ± 0.04) were obtained to (E)- and (Z)-urocanic acids, respectively. The second dissociations were studied also by potentiometric titration in aqueous sodium chloride solutions up to the isotonic salt concentration (0.154 mol dm⁻³), and the second thermodynamic dissociation constants as well as activity parameters for both isomers were determined at temperature 25°C and for (E)-urocanic acid also at 37°C. The obtained pK _a2 values were close to those found by UV spectrophotometry. The equations for the calculation of the second stoichiometric dissociation constants of urocanic acid isomers on molality and molarity scale in aqueous sodium chloride solutions were derived. The obtained pK _a1 and pK _a2 values for (Z)-urocanic acid appear to be essentially lower than some previously reported values in literature.     

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior.     

Bisfunctionalized Janus molecules

[reaction: see text] Bisfunctionalized dendritic multiester molecules were synthesized by combined protection-deprotection and divergent-convergent-divergent sequences in high yields leading to dendritic molecules that combine two functionally different surfaces, polar aliphatic arborol and nonpolar gallate ether moieties, resulting in a two-faced Janus molecule.     

NP-completeness of the hamming salesman problem

It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.     

Hirota's method and the search for integrable partial difference equations. 1. Equations on a 3 × 3 stencil

Hirota's bilinear method (‘direct method’) has been very effective for constructing soliton solutions to many integrable equations. The construction of one-soliton solution (1SS) and two-soliton solution (2SS) is possible even for non-integrable bilinear equations, but the existence of a generic three-soliton solution (3SS) imposes severe constraints and is in fact equivalent to integrability. This property has been used before in searching for integrable partial differential equations, and in this paper we apply it to two-dimensional (2D) partial difference equations defined on a 3 × 3 stencil. We also discuss how the obtained equations are related to projections and limits of the 3D master equations of Hirota and Miwa, and find that sometimes a singular limit is needed.     

Sequential action of two flavoenzymes, PgaE and PgaM, in angucycline biosynthesis: chemoenzymatic synthesis of gaudimycin C

Tailoring steps in aromatic polyketide antibiotic biosynthesis are an important source of structural diversity and, consequently, an intriguing focal point for enzymological studies. PgaE and PgaM from Streptomyces sp. PGA64 are representatives of flavoenzymes catalyzing early post-PKS reactions in angucycline biosynthesis. This in vitro study illustrates that the chemoenzymatic conversion of UWM6 into the metabolite, gaudimycin C, requires multiple closely coupled reactions to prevent intermediate degradation. The NMR structure of gaudimycin C confirms that the reaction cascade involves C12- and C12b-hydroxylation, C2,3-dehydration, and stereospecific ketoreduction at C6. Enzymatic 18O incorporation studies verify that the oxygens at C12 and C12b derive from O2 and H2O, respectively. The results indicate that PgaM deviates mechanistically from flavoprotein monooxygenases, and suggest an alternative catalytic mechanism involving a quinone methide intermediate.