Adsorption of block copolymers in nanoporous alumina

We have studied the adsorption of end-attaching block copolymer chains inside the cylindrical pores of nanoporous alumina. Highly asymmetric PS-PEO block copolymers, with a small PEO anchoring block and a long PS dangling block, were allowed to adsorb onto porous alumina substrates with an average pore diameter of ∼200 nm from toluene solution. The adsorption process was monitored using FTIR spectroscopy, whereas depth profile analysis was performed by means of XPS and Ar⁺ ion sputtering. It is found that the PS-PEO adsorption kinetics in porous alumina are ∼4 orders of magnitude slower than the corresponding case of a flat alumina substrate. It appears that chains adsorbed near the pore entrance early on tend to form a barrier for chains entering the pore at later times, thereby slowing down the adsorption process significantly. This effect is much more pronounced for large chains whose dimensions are comparable with the pore diameter. The equilibrium adsorbance value is also affected by chain size due to the additional entropic penalty associated with chain confinement, the adsorbance falling substantially when the chain dimensions become comparable with the pore diameter. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1676–1682, 2010     

Improper hydrogen-bonded cyclohexane C-Hax?Yax contacts: experimental evidence from H NMR spectroscopy of suitable axial cyclohexane models

B3LYP/6-31+G(d,p) calculations predicted the presence of improper hydrogen-bonded C-H_ax?Y_ax contacts of different strength in cyclohexane derivatives;¹ it was predicted that the addition of an appropriate bridging fragment X_ax between an axial substituent Y₁ and a cyclohexane carbon would strengthen the improper hydrogen-bonded contact C-H_ax?Y₁ when the X_ax-Y₁ bond vector bisects the cyclohexane ring. To support the theoretical predictions with experimental evidence for this effect, several 2-substituted adamantane analogues with suitable improper H-bonded C-H_ax?O contacts of different strength were synthesized, as models of the corresponding cyclohexane derivatives, and their ¹H NMR spectra were recorded at 298 K. The ¹H NMR signal separation within the cyclohexane ring γ-CH₂s is increased when the B3LYP/6-31+G(d,p)-calculated strength of the H-bonded C-H_ax?O=C_ax contact interaction is increased.     

Airy trajectory engineering in dynamic linear index potentials

We study the propagation of Airy beams in transversely linear index potentials with a gradient that is dynamically changing along the propagation direction. We find exact solutions in the case of Airy and apodized (Gaussian and exponentially) Airy beams in 1+1 and 2+1 dimensions. More important, we find that the Airy beam can follow any predefined path, in which case the potential gradient is determined as a function of this path.     

Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities

In this Note, we study a class of Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing terms (concave–convex nonlinearities). Using the Ambrosetti–Rabinowitz condition and related topological and variational arguments, we prove a bifurcation result for large values of the parameter.     

Global optimization of general nonconvex problems with intermediate polynomial substructures

This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that exploit these underlying structures. These cutting plane strategies simultaneously convexify linear and nonlinear terms from multiple constraints and are highly effective at tightening standard linear programming relaxations generated by sequential factorable programming techniques. Because the number of available cutting planes increases exponentially with the number of variables, we implement cut filtering and selection strategies to prevent an exponential increase in relaxation size. We introduce algorithms for polynomial substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in BARON at every node in the branch-and-bound tree. A computational study including randomly generated problems of varying size and complexity demonstrates that the exploitation of underlying polynomial substructures significantly reduces computational time, branch-and-bound tree size, and required memory.     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

Phytochemical Differentiation of Saffron (Crocus sativus L.) by High Resolution Mass Spectrometry Metabolomic Studies

The metabolite profiling of saffron (Crocus sativus L.) from several countries was measured by using ultra-performance liquid chromatography combined with high resolution mass spectrometry (UPLC-HR MS). Multivariate statistical analysis was employed to distinguish among the several samples of C. sativus L. from Greece, Italy, Morocco, Iran, India, Afghanistan and Kashmir. The results of this study showed that the phytochemical content in the samples of C. sativus L. were obviously diverse in the different countries of origin. The metabolomics approach was deemed to be the most suitable in order to evaluate the enormous array of putative metabolites among the saffron samples studied, and was able to provide a comparative phytochemical screening of these samples. Several markers have been identified that aided the differentiation of a group from its counterparts. This can be important for the selection of the appropriate saffron sample, in view of its health-promoting effect which occurs through the modulation of various biological and physiological processes.