Mapping Class Groups of Nonorientable Surfaces

We obtain a finite set of generators for the mapping class group of a nonorientable surface with punctures. We then compute the first homology group of the mapping class group and certain subgroups of it. As an application we prove that the image of a homomorphism from the mapping class group of a nonorientable surface of genus at least nine to the group of real-analytic diffeomorphisms of the circle is either trivial or of order two.     

On Some Second Order Differential Equations with Convergent Solutions

Via a special integral transformation, asymptotic integration results for ordinary differential equations are used to establish accurate asymptotic developments for radial solutions of the elliptic equation Δu + K(|x|)e ^u = 0, |x| > x ₀ > 0, in the bidimensional case.     

Reaction of electron rich heterocycles with electrophiles. Formylation of indoles via thiomethylation

The formylation of indoles 1 by dithiocarbenium-ions 2 is discussed. The reaction proceeds to thioacetals 4 under mild conditions. Longer reaction times yield bisindolylmonomethylcyanines 5–6 . Generally, the reaction is inhibited by the presence of electron-withdrawing groups at the pyrrol nucleus of indole 1 , e.g. an acetyl group.     

Zinc perchlorate catalyzed one-pot amination-annulation of α-cyanomethyl-β-ketoesters in water. Regioselective synthesis of 2-aminopyrrole-4-carboxylates

In this paper, we report the efficient and regioselective synthesis of 2-aminopyrrole-4-carboxylates as derivatives of conformationally restricted analogues of γ-amino butyrates (GABA) via a zinc perchlorate catalyzed amination-annulation of α-cyanomethyl-β-ketoesters under mild reaction conditions in water.     

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).     

An experimental study on an oscillating loop heat pipe consisting of three interconnected columns

This paper presents some experimental results of an extensive research on a novel oscillating heat pipe. The heat pipe is formed of three interconnected columns as different from the pulsating heat pipe designs. The dimensions of the heat pipe considered in this study are large enough to neglect the effect of capillary forces. Thus, the self-oscillation of the system is driven by the gravitational force and the phase lag between the evaporation and condensation processes. The overall heat transfer coefficient is found to be approximately constant irrespective of heat load for the experimental cases considered. The results are also compared with the previously published data by other investigators for water as the working fluid and for the same heat input range. The experimental data for the time variation of the liquid column heights and the vapor pressure are correlated algebraically, convenient for practical uses.     

Chemical profile by LC–MS/MS,GC/MS and antioxidant activities of the essential oils and crude extracts of two Euphorbia species

In this study, it was aimed to investigate the chemical composition and antioxidant activities of two Euphorbia species. The major component of the fatty acid compositions obtained from the petroleum ether extracts was identified as palmitic acid for Euphorbia gaillardotii and Euphorbia macroclada. The main constituents of the essential oils were identified as arachidic acid for E. gaillardotii and tetratetracontane for E. macroclada. Among the 27 studied compounds, hesperidin, rutin, hyperoside and quinic, malic, gallic and tannic acids were found to be the most abundant compounds in the two Euphorbia species. The methanol extracts of E. gaillardotii and E. macroclada showed strong antioxidant activity in all tested methods. Particularly, IC₅₀ values of E. macroclada methanol extract that was the richest in terms of total phenolic-flavonoid contents were found to be lower than α-tocopherol and butylated hydroxytoluene in β-carotene bleaching, 2,2-diphenyl-1-picrylhydrazyl free and ABTS cation radical scavenging methods.     

A far-red emitting probe for unambiguous detection of mobile zinc in acidic vesicles and deep tissue

Imaging mobile zinc in acidic environments remains challenging because most small-molecule optical probes display pH-dependent fluorescence. Here we report a reaction-based sensor that detects mobile zinc unambiguously at low pH. The sensor responds reversibly and with a large dynamic range to exogenously applied Zn²⁺ in lysosomes of HeLa cells, endogenous Zn²⁺ in insulin granules of MIN6 cells, and zinc-rich mossy fiber boutons in hippocampal tissue from mice. This long-wavelength probe is compatible with the green-fluorescent protein, enabling multicolor imaging, and facilitates visualization of mossy fiber boutons at depths of >100 μm, as demonstrated by studies in live tissue employing two-photon microscopy.