Conversion of Natural Narciclasine to Its C-1 and C-6 Derivatives and Their Antitumor Activity Evaluation: Some Unusual Chemistry of Narciclasine

During the search for a general, efficient route toward the synthesis of C-1 analogues of narciclasine, natural narciclasine was protected and converted to its C-1 enol derivative using a novel semi-synthetic route. Attempted conversion of this material to its triflate in order to conduct cross-coupling at C-1 resulted in a triflate at C-6 that was successfully coupled with several functionalities. Four novel compounds were fully deprotected after seven steps and subjected to evaluation for cytotoxic activity against three cancer cell lines. Only one derivative showed moderate activity compared to that of narciclasine. Spectral and physical data are provided for all new compounds.     

An Investigation of the Separate Flow and Stall-delay for Horizontal-Axis Wind Turbine

The flow characteristics and stall delay phenomenon of a stall regulated wind turbine rotor due to blade rotation in steady state non-yawed conditions are investigated. An incompressible Reynolds-averaged Navier-Stokes solver is applied to carry out the separate flow cases at high wind speeds from 11 m/s to 25 m/s with an interval of 2 m/s. The objective of the present research effort is to validate a first-principles based approach for modeling horizontal axis wind turbines (HAWT) under stalled flow conditions using NREL/Phase VI rotor data. The computational results are compared with the predicted values derived by a new stall-delay model and blade element momentum (BEM) method. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Genus mapping class groups are not Kähler

The goal of this note is to prove that the mapping class groups of closed orientable surfaces of genus 2 (with punctures) are not Kähler. An application to compactifications of the moduli space of genus curves (with punctures) is given.

     

Quantitative approximation by fractional smooth general singular operators

In this article we study the fractional smooth general singular integral operators on the real line, regarding their convergence to the unit operator with fractional rates in the uniform norm. The related established inequalities involve the higher order moduli of smoothness of the associated right and left Caputo fractional derivatives of the engaged function. Furthermore we produce a fractional Voronovskaya type result giving the fractional asymptotic expansion of the basic error of our approximation.We finish with applications to fractional trigonometric singular integral operators. Our operators are not in general positive.     

The 1/N Expansion of Tensor Models Beyond Perturbation Theory

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.     

Raman spectra and lattice dynamics of cubic gauche nitrogen

The lattice dynamical properties of the cubic gauche phase of nitrogen are computed using density functional perturbation theory. The structure is found to be stable up to at least 250 GPa. Based on the dynamical data we derive the thermodynamical properties. We also determine the Raman spectra with both peak position and intensity and find excellent agreement with the experimental data, with the A mode dominating the spectra at all pressures.     

Quenching of fluorophore-labeled DNA oligonucleotides by divalent metal ions: implications for selection, design, and applications of signaling aptamers and signaling deoxyribozymes

Recent years have seen a dramatic increase in the use of fluorescence-signaling DNA aptamers and deoxyribozymes as novel biosensing moieties. Many of these functional single-stranded DNA molecules are either engineered to function in the presence of divalent metal ion cofactors or designed as sensors for specific divalent metal ions. However, many divalent metal ions are potent fluorescence quenchers. In this study, we first set out to examine the factors that contribute to quenching of DNA-bound fluorophores by commonly used divalent metal ions, with the goal of establishing general principles that can guide future exploitation of fluorescence-signaling DNA aptamers and deoxyribozymes as biosensing probes. We then extended these studies to examine the effect of specific metals on the signaling performance of both a structure-switching signaling DNA aptamer and an RNA-cleaving and fluorescence-signaling deoxyribozyme. These studies showed extensive quenching was obtained when using divalent transition metal ions owing to direct DNA-metal ion interactions, leading to combined static and dynamic quenching. The extent of quenching was dependent on the type of metal ion and the concentration of supporting monovalent cations in the buffer, with quenching increasing with the number of unpaired electrons in the metal ion and decreasing with the concentration of monovalent ions. The extent of quenching was independent of the fluorophore, indicating that quenching cannot be alleviated simply by changing the nature of the fluorescent probe. Our results also show that the DNA sequence and the local secondary structure in the region of the fluorescent tag can dramatically influence the degree of quenching by divalent transition metal ions. In particular, the extent of quenching is predominantly determined by the fluorophore location with respect to guanine-rich and duplex regions within the strand sequence. Examination of the effect of both the type and concentration of metal ions on the performance of a fluorescence-signaling aptamer and a signaling deoxyribozyme confirms that judicious choice of divalent transition metal ions is important in maximizing signals obtained from such systems.     

Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations

We establish one-to-one transformations and self-maps between nonlinear diffusion equations in nonhomogeneous media, where the density function is given by a power. We use these transformations to deduce new interesting self-similar, radially symmetric solutions of the equations. In particular, Barenblatt, dipole and focusing Aronson-Graveleau type solutions are deduced, and some equations with singular potentials are studied. The new solutions are example of interesting or unexpected mathematical features of these equations, providing also natural candidates for the asymptotic behavior.