Study of the Surface Tensions of Binary Mixtures of Isomeric Chlorobutanes with Methyl tert-Butyl Ether

In the present work we report experimental surface tensions for binary mixtures of isomeric chlorobutanes with methyl tert-butyl ether from 283.15 to 303.15 K, measured with a drop volume tensiometer. From these experimental data the corresponding surface tension deviations were calculated and correlated using a Redlich-Kister type polynomial. Finally, we include the calculation of excess surface compositions for all of the mixtures from 288.15 K to 308.15 K.     

Effect of confinement space on adsorption energy and electronic structure of molecule-metal pairs

Structural Chemistry - The adsorption of molecules on metal surfaces within confined spaces is key to industrially relevant processes such as catalytic conversions, separations, or gas storage....     

The NLS Equation in Dimension One with Spatially Concentrated Nonlinearities: the Pointlike Limit

In the present paper, we study the following scaled nonlinear Schrödinger equation (NLS) in one space dimension: $$ i\frac{\rm d}{{\rm d}t}\psi^{\varepsilon}(t)=-\Delta\psi^{\varepsilon}(t) +\frac{1}{\varepsilon}V\left(\frac{x}{\varepsilon} \right)|\psi^{\varepsilon}(t)|^{2\mu}\psi^{\varepsilon}(t)\quad \varepsilon > 0\,\quad V\in L^1(\mathbb{R},(1+|x|){\rm d}x) \cap L^\infty(\mathbb{R}).$$ This equation represents a nonlinear Schrödinger equation with a spatially concentrated nonlinearity. We show that in the limit \({\varepsilon\to 0}\) the weak (integral) dynamics converges in \({H^1(\mathbb{R})}\) to the weak dynamics of the NLS with point-concentrated nonlinearity: $$ i\frac{{\rm d}}{{\rm d}t} \psi(t) =H_{\alpha} \psi(t) .$$ where H _α is the Laplacian with the nonlinear boundary condition at the origin \({\psi'(t,0+)-\psi'(t,0-)=\alpha|\psi(t,0)|^{2\mu}\psi(t,0)}\) and \({\alpha=\int_{\mathbb{R}}V{\rm d}x}\) . The convergence occurs for every \({\mu\in \mathbb{R}^+}\) if V ≥  0 and for every  \({\mu\in (0,1)}\) otherwise. The same result holds true for a nonlinearity with an arbitrary number N of concentration points.     

Molecular structure,experimental and theoretical 1H and 13C NMR chemical shift assignment of cyclic and acyclic α,β‐unsaturated esters

The experimental ¹H and ¹³C NMR spectra of 13 phenyl cinnamates and four 4‐methylcoumarins were investigated and their chemical shifts assigned on the basis of the two‐dimensional spectra. For the unsubstituted cinnamic acid phenyl ester, optimized molecular structures were calculated at a B3LYP/6‐311++G(d,p) level of theory. ¹H and ¹³C NMR chemical shifts were also calculated with the GIAO method at the B3LYP/6‐311 + G(2d,p) level of theory. The comparison between experimental and calculated NMR chemical shift suggests that the experimental spectra are formed from the superposition spectra of the two lowest energy conformers of the compound in solution. The most stable s‐cis configuration found in our studies is also the conformation adopted for a related phenyl cinnamate in solid state. The experimental results were analyzed in terms of the substituent effects. Copyright © 2013 John Wiley & Sons, Ltd.     

On the <Emphasis Type="Italic">Λ</Emphasis>CDM Universe in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

In the context of the so-called Gauss–Bonnet gravity, where the gravitational action includes function of the Gauss–Bonnet invariant, we study cosmological solutions, especially the well-known ΛCDM model. It is shown that the dark energy contribution and even the inflationary epoch can be explained in the frame of this kind of theories with no need of any other kind of component. Other cosmological solutions are constructed and the rich properties that this kind of theories provide are explored.