Large deflection of a non-linear,elastic, asymmetric Ludwick cantilever beam subjected to horizontal force,vertical force and bending torque at the free end

The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated constant vertical load, to a concentrated constant horizontal load and to a concentrated constant bending torque at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler–Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper.     

Substituent effects on the photophysical properties of amino-aurone-derivatives

ABSTRACT

Aurones are potential candidates to be employed as fluorescent probes or as pharmacophores for biological applications. This work describes a density functional theory (DFT) and time-dependent -DFT study at the PBE0/6-31?+?G(d) level of theory to analyse the structural, electronic and photophysical properties of a series of new proposed 4′-amine-aurone derivatives in its E and Z isomeric conformations. The maximum absorption wavelength of the proposed aurones appears in the range 390???514?nm, while the most allowed emission pathways were computed in the range 493–530?nm. The bathochromic shift of these compounds with respect to the non-substituted aurone is modulated by the acceptor strength of the added 4-substituents, in addition to the ability of the substituents to localise the frontier molecular orbitals over the acceptor benzofuranone moiety without losing the tricyclic planarity, which favours the push–pull nature of these molecules. The influence of the 4-substituent is also evidenced in the Stokes shifts for the whole series; as the electron-withdrawing character of the 4-substituents enhances, higher is the polarisation of the structure resulting in higher Stokes shifts. As a result, -CF₃ and -NO₂ substituents were responsible of larger Stokes shifts, then compounds containing these substituents are proposed as potential fluorescence probes for useful applications in biological systems.     

On cardinal characteristics of Yorioka ideals

Yorioka introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in . We construct a matrix iteration of c.c.c. posets to force that, for many ideals in that class, their associated cardinal invariants (i.e., additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the additivity and cofinality (respectively) of the ideal of Lebesgue measure zero subsets of the real line.     

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...