Surface structure of a "non-amphiphilic" protic ionic liquid

The nanostructure of the ethanolammonium nitrate (EtAN)-air surface has been investigated using X-ray reflectometry (XRR), vibrational sum frequency spectroscopy (VSFS) and neutral impact collision ion scattering spectroscopy (NICISS). The XRR data decays more rapidly than expected for a perfectly sharp interface, indicating a diffuse electron (scattering length) density profile. Modelling of the XRR data using three different fitting routines produced consistent interfacial profiles that suggest the formation of interfacial EtAN clusters. Consistent with this, VSFS reveals that the EtAN surface is predominantly covered by -CH(2)- moieties, with the -NH(3)(+) and -OH groups of the cation buried slightly deeper in the interface. The elemental profiles determined using NICISS also show enrichment of carbon relative to nitrogen and oxygen in the outermost surface layer, which is consistent with the surface cation orientation deduced from VSFS, and with the presence of EtAN aggregates at the liquid surface.     

Ground state periodic solutions for difference equations with discrete p-Laplacian

We use the critical point theory to establish existence results for periodic solutions of some nonlinear boundary value problems involving the discrete p-Laplacian operator. As an application we give an alternative proof to the upper and lower solutions theorem.     

Fixed point theory for a new type of contractive multivalued operators

The aim of this paper is to discuss some basic problems (data dependence, well-posedness, nonself operators, homotopy results, generalized contractions) of the fixed point theory for a new type contractive multivalued operator. The results complement and extend some very recent results proved by M. Kikkawa and T. Suzuki, as well as, other theorems given by M. Frigon and A. Granas, S. Reich, I.A. Rus, etc.     

An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.      

Guided mode resonance in subwavelength metallodielectric free-standing grating for bandpass filtering

We present the experimental study of a free-standing metallic guided-mode resonant structure, for bandpass filtering applications in the mid-IR wavelength range. Structure consists of a subwavelength gold grating with narrow slits deposited on a silicon nitride membrane. High optical transmission is measured with up to 78% transmission at resonance. Angularly resolved spectra are presented revealing Fano-type resonance.     

Convergence Analysis of Spatially Adaptive Rothe Methods

This paper is concerned with the convergence analysis of the horizontal method of lines for evolution equations of the parabolic type. Following a semidiscretization in time by \(S\) -stage one-step methods, the resulting elliptic stage equations per time step are solved with adaptive space discretization schemes. We investigate how the tolerances in each time step must be tuned in order to preserve the asymptotic temporal convergence order of the time stepping also in the presence of spatial discretization errors. In particular, we discuss the case of linearly implicit time integrators and adaptive wavelet discretizations in space. Using concepts from regularity theory for partial differential equations and from nonlinear approximation theory, we determine an upper bound for the degrees of freedom for the overall scheme that are needed to adaptively approximate the solution up to a prescribed tolerance.     

Libera transform of functions with bounded turning

Conditions are determined for the starlikeness of the Libera transform of functions of bounded turning. In addition, several other differential subordinations and differential inequalities are considered.     

Magnetostatic interactions in dense nanowire arrays

We demonstrate the importance of magnetostatic interactions in dense arrays of ferromagnetic nanowires. Beginning from a simple micromagnetic model, we have calculated the interaction field for saturated magnetization in the plane of the array (perpendicular to the axes of the wires) and normal to the plane, using a hybrid (numerical and analytical) strategy. The slope of interaction field versus wire length changes dramatically at the transition between a dipolar regime (at very small lengths) and a monopolar regime (for longer nanowires). We present the interaction fields and the applied fields at saturation for large nanowire arrays. These results are compared with experiment for electrodeposited arrays, and very good agreement is obtained. This shows that the high field behavior of such arrays is dominated by magnetostatic effects and that a nanowire array behaves like a double-sided distribution of magnetic monopoles.