Periodic Solutions of Pendulum-Like Perturbations of Singular and Bounded $${\phi}$$-Laplacians

In this paper we study the existence and multiplicity of periodic solutions of pendulum-like perturbations of bounded or singular f{\phi}-Laplacians. Our approach relies on the Leray-Schauder degree and the upper and lower solutions method.     

Surfaces Generation by Blending Interpolation on a Triangle with One Curved Side

We use some interpolation operators and some Bernstein type operators for construction of surfaces which satisfy some given conditions.     

FRET Enhancement in Aluminum Zero‐Mode Waveguides

Zero‐mode waveguides (ZMWs) can confine light into attoliter volumes, which enables single molecule fluorescence experiments at physiological micromolar concentrations. Of the fluorescence spectroscopy techniques that can be enhanced by ZMWs, Förster resonance energy transfer (FRET) is one of the most widely used in life sciences. Combining zero‐mode waveguides with FRET provides new opportunities to investigate biochemical structures or follow interaction dynamics at micromolar concentrations with single‐molecule resolution. However, prior to any quantitative FRET analysis on biological samples, it is crucial to establish first the influence of the ZMW on the FRET process. Here, we quantify the FRET rates and efficiencies between individual donor–acceptor fluorophore pairs that diffuse into aluminum zero‐mode waveguides. Aluminum ZMWs are important structures thanks to their commercial availability and the large amount of literature that describe their use for single‐molecule fluorescence spectroscopy. We also compared the results between ZMWs milled in gold and aluminum, and found that although gold has a stronger influence on the decay rates, the lower losses of aluminum in the green spectral region provide larger fluorescence brightness enhancement factors. For both aluminum and gold ZMWs, we observed that the FRET rate scales linearly with the isolated donor decay rate and the local density of optical states. Detailed information about FRET in ZMWs unlocks their application as new devices for enhanced single‐molecule FRET at physiological concentrations.     

Crown ethers at the aqueous solution-air interface. Part 2. Electrolyte effects, ethylene oxide hydration and temperature behaviour

Vibrational Sum Frequency Spectroscopy (VSFS) was employed to study adsorbing films of 4-Nitro Benzo-15-Crown-5 (NB15C5) and Benzo-15-Crown-5 (B15C5) at the aqueous solution-air interface. The surface of the solution is strongly influenced by the presence of crown ether species. Changes in the orientation of NB15C5 were monitored as a function of solution concentration, by targeting the ratio of peak intensities of the CN and NO(2) vibrational modes. The water of hydration has also been probed as a function of crown concentration, salt concentration, and temperature. The latter study strongly suggests that the surface can be treated as a charged interface, and that the associated ordered water decreases with increasing ionic strength of the bulk solution.     

Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices

Let Ω⊂R² be a simply connected domain, let ω be a simply connected subdomain of Ω, and set A=Ω?ω. Suppose that J is the class of complex-valued maps on the annular domain A with degree 1 both on ∂Ω and on ∂ω. We consider the variational problem for the Ginzburg-Landau energy Eλ among all maps in J. Because only the degree of the map is prescribed on the boundary, the set J is not necessarily closed under a weak H¹-convergence. We show that the attainability of the minimum of Eλ over J is determined by the value of cap(A)—the H¹-capacity of the domain A. In contrast, it is known, that the existence of minimizers of Eλ among the maps with a prescribed Dirichlet boundary data does not depend on this geometric characteristic. When cap(A)?π (A is either subcritical or critical), we show that the global minimizers of Eλ exist for each λ>0 and they are vortexless when λ is large. Assuming that λ→∞, we demonstrate that the minimizers of Eλ converge in H¹(A) to an S¹-valued harmonic map which we explicitly identify. When cap(A)<π (A is supercritical), we prove that either (i) there is a critical value λ₀ such that the global minimizers exist when λ<λ₀ and they do not exist when λ>λ₀, or (ii) the global minimizers exist for each λ>0. We conjecture that the second case never occurs. Further, for large λ, we establish that the minimizing sequences/minimizers in supercritical domains develop exactly two vortices—a vortex of degree 1 near ∂Ω and a vortex of degree −1 near ∂ω.     

A variational problem with lack of compactness for H(S;S) maps of prescribed degree

We consider, for maps in H^1/2(S¹;S¹), a family of (semi)norms equivalent to the standard one. We ask whether, for such a norm, there is some map in H^1/2(S¹;S¹) of prescribed topological degree equal to 1 and minimal norm. In general, the answer is no, due to concentration phenomena. The existence of a minimal map is sensitive to small perturbations of the norm. We derive a sufficient condition for the existence of minimal maps. In particular, we prove that, for every given norm, there are arbitrarily small perturbations of it for which the minimum is attained. In case there is no minimizer, we determine the asymptotic behavior of minimizing sequences. We prove that, for such minimizing sequences, the energy concentrates near a point of S¹. We describe this concentration in terms of bubbling-off of circles.     

On using lens-assisted hologram interferometry to investigate semiconductor device behaviour

The paper analyses some of the causes that limit the performance of the hologram interferometry method when used for the study of the behaviour of semiconductors devices. Then some results are shown obtained by the authors using a method of lens-assisted microscope hologram interferometry for studying such structures. The method allows detection of defects and, besides, it renders quantitatively the structure local non-uniformities during the normal operation of the semiconductor devices.     

Effect of the interface on separation in multicapillary gas chromatography-based hyphenated techniques for speciation analysis of organometallic compounds

This paper reports the effect of transfer line (TL) internal diameter (i.d.) on gas chromatographic separation characteristics such as efficiency and speed, when a multicapillary (MC) column is used for speciation analysis of mercury. Five different TL consisting of fused-silica capillaries with 0.15, 0.20, 0.25, 0.32, and 0.53 mm i.d. are compared. The separation efficiency and total chromatographic run time are critically affected by the i.d. of the TL. Narrow capillaries (i.d.0.20 mm) produce minimum peak dispersion whereas wide capillaries result in narrow peaks and shorter chromatographic analysis times. A thermodynamic approach is proposed to describe the motion of the analytes through the separation column and TL. The model provides good agreement with the experimental data for high pressures (35 psig) and wide TL (0.25 mm i.d.).Dedicated to the memory of Wilhelm Fresenius     

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].