Novel synthesis of alkoxy substituted oxa[9]helicenes by the reaction of helical quinone with alcohols

The reaction of helical quinone with alcohols in the presence of Brønsted acid such as para-toluenesulfonic acid (pTSA) or HCl proceeded smoothly to produce the corresponding alkoxy substituted oxa[9]helicenes in good yields.     

Crystal supramolecularity in 2,2′-iminodipyridinium tetrahalometallate(II) salts: Supramolecular motifs that control tetrahedral halometallate solid state structures

N⁺–H$?$Br–M and (π)C–H$?$Br–M hydrogen bond synthons have been exploited in the crystallization of a series of 2,2′-iminodipyridinium(2+) dication (hereafter 2,2′-imdipyH₂), (C₁₀H₁₁N₃)[MX₄] salts (M = Co and Hg; X = Cl and Br) and 2,2′-iminodipyridinium(1+) cation (hereafter 2,2′-imdipyH), (C₁₀H₁₀N₃)₂[MX₄] salts (M = Co, Hg; X = Cl and Br). Intermolecular interactions and crystal supramolecularity adopted in these structures were analyzed and compared with reported similar structures, (C₁₀H₁₁N₃)[CuCl₄] and (C₁₀H₁₀N₃)₂[CoCl₄]. In these salts only one structural form for the halometallate species is observed namely mononuclear tetrahedral. The crystal supramolecularity in the (2,2′-imdipyH₂)[MX₄] series corresponds to three distinct structural motifs: Parallel ribbons of infinitely connected cyclic dimers of two dications and two anions found in the isomorphous salts of [CoCl₄]^2? and [CuCl₄]^2?; and cyclic dimer hearing-bone packing motif found in the isomorphous dication salts of [CoBr₄]^2? and [HgBr₄]^2?. Infinitely helical layers based on alternating $?$anion$?$two stacked cations $?$anion$?$ two stacked cations$?$ are found in the isomorphous salts of (2,2′-imdipyH)₂[CoCl₄] and (2,2′-imdipyH)₂[HgBr₄].     

Typing of unknown microorganisms based on quantitative analysis of fatty acids by mass spectrometry and hierarchical clustering

Rapid identification of unknown microorganisms of clinical and agricultural importance is not only critical for accurate diagnosis of infections but also essential for appropriate and prompt treatment. We describe here a rapid method for microorganisms typing based on quantitative analysis of fatty acids by iFAT approach (Isotope-coded Fatty Acid Transmethylation). In this work, lyophilized cell lysates were directly mixed with 0.5M NaOH solution in d3-methanol and n-hexane. After 1 min of ultrasonication, the top n-hexane layer was combined with a mixture of standard d0-methanol derived fatty acid methylesters with known concentration. Measurement of intensity ratios of d3/d0 labeled fragment ion and molecular ion pairs at the corresponding target fatty acids provides a quantitative basis for hierarchical clustering. In the resultant dendrogram, the Euclidean distance between unknown species and known species quantitatively reveals their differences or shared similarities in fatty acid related pathways. It is of particular interest to apply this method for typing fungal species because fungi has distinguished lipid biosynthetic pathways that have been targeted for lots of drugs or fungicides compared with bacteria and animals. The proposed method has no dependence on the availability of genome or proteome databases. Therefore, it is can be applicable for a broad range of unknown microorganisms or mutant species.     

General boundary stabilization of memory type in thermoelasticity of type III

In this paper, we consider a multi-dimensional system of thermoelasticity type III with a viscoelastic damping acting on a part of the boundary. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases.     

Idempotents and the multiplicative group of some totally bounded rings

In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2^ℵ0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.     

General decay of solutions of a nonlinear system of viscoelastic wave equations

This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered.     

A study on densities of sets of points and lines

In this paper, firstly, our purpose is to give the relationship among the densities of the sets of collinear points, the relationship among the densities of the sets of noncollinear points, and the relationship among the densities of the sets of the intersecting lines in Euclidean plane, respectively. In addition to that, we define the density formulas for the sets of points and lines under the two‐parameter planar Euclidean motion. By means of these results, we obtain essential properties that explain the connection among the densities of the sets of points and among the densities of the sets of intersecting lines under the two‐parameter planar Euclidean motion.     

On Jacobi fields

We define curves on a Riemannian manifold as integrals of generalized Jacobi fields. We show that the force term that deviates the trajectory from the geodesic motion can be constructed as a functional of the metric tensor. These curves can be interpreted as particles (observers) coupled nonminimally with gravitation that can provide a class of residual observers for the inevitable singularity—as shown in the text.This essay received an honorable mention (1976) from the Gravity Research Foundation-Ed.     

Cycloshydratation de dios in presence D'HMPT

1,4 and 1,5-diols heated with 0.3 equivalent of HMPA undergo cyclodehydration leading to tetrahydrofurans and tetrahydropyrans.     

On the coupling of MIXED-FEM and BEM for an exterior Helmholtz problem in the plane

Summary This paper deals with an elliptic boundary value problem posed in the plane, with variable coefficients, but whose restriction to the exterior of a bounded domain reduces to a Helmholtz equation. We consider a mixed variational formulation in a bounded domain that contains the heterogeneous medium, coupled with a boundary integral method applied to the Helmholtz equation in . We utilize suitable auxiliary problems, duality arguments, and Fredholm alternative to show that the resulting formulation of the problem is well posed. Then, we define a corresponding Galerkin scheme by using rotated Raviart-Thomas subspaces and spectral elements (on the interface). We show that the discrete problem is uniquely solvable and convergent and prove optimal error estimates. Finally we illustrate our analysis with some results from computational experiments.