Effect of methoxyl groups on the NMR spectra: configuration and conformation of natural and synthetic indanic and tetralinic structures

Here, we studied the influence of the methoxyl groups attached at C‐7 and C‐2′ of natural and synthetic 1‐arylindanes on the chemical shift of the signal of bibenzylic hydrogen and carbon atoms and J_1,2 coupling constants. This influence was also analysed in natural 1‐aryltetralins and related compounds that possess methoxyl and/or hydroxyl groups bound at C‐8 and C‐2′. The methoxyl groups attached at C‐7 in indanes or at C‐8 in tetralins produce a deshielding signal at H‐1 and shield at C‐1 and a strong decrease in the value of J_1,2 due to the pseudoequatorial location adopted by the aryl group bound at C‐1, avoiding an ‘A^1,3 strain’. Furthermore, compounds with hydroxyl or methoxyl groups in C‐2′, in the absence of substituents of C‐7 or C‐8, present a strong deshielding signal at H‐1, strong shield of the C‐1 signal and a decrease in the value of J_1,2. This is attributed to the stereoelectronic effects of the methoxyl or hydroxyl groups, which we have called ‘Asarone effect’. NOESY experiments were conducted to confirm the configuration and conformation of some of the compounds included in this work. This study shows that both effects, A^1,3 strain and Asarone effect, must be taken into account when the structure of natural indanes and tetralins is analysed by using ¹H‐NMR and ¹³C‐NMR spectra. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermal photon production in a strongly coupled anisotropic plasma

Journal of High Energy Physics - For the homogeneous configuration given by the long string limit of the folded string with a spin in AdS 3 and a spin and a winding number in S 1, we solve the...     

Bounds on the Dimension of Trivariate Spline Spaces: A Homological Approach

We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by applying homological techniques. We give an insight of different ways of approaching this problem by exploring its connections with the Hilbert series of ideals generated by powers of linear forms, fat points, the so-called Fröberg–Iarrobino conjecture, and the weak Lefschetz property.     

On the hyperbolic order

We define the hyperbolic order of any locally injective holomorphic function between arbitrary hyperbolic domains of the complex plane and study the relation between the hyperbolic order and the Schwarzian derivative for locally injective holomorphic functions from the unit disk into itself.