Regularization methods for a class of variational inequalities in banach spaces

In this paper, we introduce two regularization methods, based on the Browder-Tikhonov and iterative regularizations, for finding a solution of variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gateaux differentiate norm.     

Design and identification of high performance steel alloys for structures subjected to underwater impulsive loading

Martensitic and austenitic steel alloys were designed to optimize the performance of structures subjected to impulsive loads. The deformation and fracture characteristics of the designed steel alloys were investigated experimentally and computationally. The experiments were based on an instrumented fluid–structure interaction apparatus, in which deflection profiles are recorded using a shadow Moiré technique combined with high speed imaging. Fractographic analysis and post-mortem thickness reduction measurements were also conducted in order to identify deformation and fracture modes. The computational study was based on a modified Gurson damage model able to accurately describe ductile failure under various loading paths. The model was calibrated for two high performance martensitic steels (HSLA-100 and BA-160) and an austenitic steel (TRIP-120). The martensitic steel (BA-160) was designed to maximize strength and fracture toughness while the austenitic steel (TRIP-120) was designed to maximize uniform ductility, in other words, to delay necking instability. The combined experimental–computational approach provided insight into the relationships between material properties (strength, uniform ductility, and post-necking ductility) and blast resistance of structures. In particular, the approach allowed identification of material/structure performances by identifying impulse-center deflection behavior and the impulse leading to panel fracture.     

Synthesis and optoelectronic behavior of conjugated polymer poly(3‐hexylthiophene) grafted on multiwalled carbon nanotubes

A nanocomposite of multiwalled carbon nanotubes (CNTs) and poly(3‐hexylthiophene) (P3HT) was prepared by grafting P3HT uniformly on the surface of CNTs (P3HT/P3HT‐g‐CNT) via a “grafting from” method with the coating thicknesses controlled. It was found that as the coating thickness decreased, the crystallinity of the P3HT decreased, along with significant red‐shifting of Raman that signified alterations of chain conformation. Furthermore, although the photoluminescence (PL) peak remained unchanged when grafted on CNTs, modifications of P3HT energy gap was observed, indicating variations of vibronic levels arising from the grafting. Moreover, broadening of the PL emission took place that suggested decreasing of lifetimes of the photo‐generated species when grafted on CNTs. Bilayer photovoltaic devices with the (6,6)‐phenyl C61‐butyric acid methyl ester as the electron acceptor have shown that the nanocomposite P3HT/P3HT‐g‐CNT performed much more efficiently as the electron donor, in both photocurrent density and power conversion efficiency, compared with the neat P3HT. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

The Hukuhara–Kneser property for a nonlinear integral equation

Applying a structure theorem of Krasnosel’skii and Perov, we show that the solution set of a nonlinear integral equation satisfies the classical Hukuhara–Kneser property.     

Single-atom ligand changes affect breathing in an extended metal-organic framework

2-Phenylpyridine-5,4'-dicarboxylic acid (1, dcppy), a derivative of 4,4'-biphenyldicarboxylic (2, bpdc) was used as the organic linking component for several metal-organic frameworks (MOFs). The pyridine component of 1 does not interfere with the solvothermal synthetic procedure, and hence both 1 and 2 form similar isoreticular MOFs. Zr(4+)-based UiO-67-dcppy, Al(3+)-based DUT-5-dcppy, Zn(2+)-based DMOF-1-dcppy, and interpenetrated Zn(2+)-based BMOF-1-dcppy were readily synthesized from 1. Similarly, isostructural frameworks from 2 were prepared (UiO-67, DUT-5, DMOF-1-bpdc, and interpenetrated BMOF-1-bpdc). The structures and physical properties of these frameworks were characterized by powder X-ray diffraction (PXRD), single X-ray diffraction (XRD), thermogravimetric analysis (TGA), and gas sorption analysis. Generally, frameworks prepared from 1 or 2 displayed similar properties; however, gas sorption data showed that BMOF-1-dcppy displayed a very large hysteresis with N(2) and CO(2) suggestive of possible framework flexibility. In contrast, the analogous framework prepared from 2 (BMOF-1-bpdc) showed low uptake of N(2) and CO(2). The substantial difference in the gas sorption behavior of these MOFs is attributed to the pyridine nature of 1 that results in weakened π-π interactions between the interpenetrated nets.     

Friedel–Crafts acylation using bismuth triflate in [BMI][PF6]

Bismuth trifluoromethanesulfonate was found to be a good catalyst for the Friedel–Crafts acylation. Bismuth triflate immobilized in an ionic liquid was the most efficient catalytic system. Bismuth triflate in [BMI][PF₆] catalyzes this reaction under microwave irradiation allowing the rapid synthesis of aryl ketones in excellent yields. The catalyst system was easily recovered and reused several times.     

On qualitative properties of differential-algebraic equations

Linear systems of ordinary differential equations with identically degenerate coefficient matrix before the derivative of the unknown vector function are considered. The structure of general solutions and the notion of singular point of such systems are discussed. From the comparison of the properties of the “perturbed” and original problems, a sufficient criterion for the Lyapunov asymptotic stability of the zero solution is obtained.     

Structural and low temperature Raman scattering studies in SrTi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> nanoparticles synthesized by sol–gel method

We investigate effects of Co dopant concentration on the structure and low temperature Raman scattering properties in SrTi_1−x Co _x O₃ (x = 0.00, 0.10, 0.20, 0.30) nanoparticles prepared by sol–gel method. The dopant induced changes are studied by XRD, and Raman scattering measurements. The results show an average particle size of about 20 nm depending on the Co content and the lattice parameters decrease as increasing the Co content. In the Raman spectra, a broad structure in the region 100–500 cm⁻¹ is almost absent and the peaks in the region 600–800 cm⁻¹ show different weights with respect to SrTiO₃, relating to structural changes. The anomalous change in the area ratio of Raman peaks as function of temperature suggests a phase transition in our samples in the range of 110–130 K. These results indicate that the Co ion has replaced the site of Ti in unit cell. This novel route also demonstrates the advantage of synthesizing the compound with low annealing temperature.     

Configurational entropy: an improvement of the quasiharmonic approximation using configurational temperature

One challenge in computational biophysics and biology is to develop methodologies able to estimate accurately the configurational entropy of macromolecules. Among many methods, the quasiharmonic approximation (QH) is most widely used as it is simple in both theory and implementation. However, it has been shown that this method becomes inaccurate by overestimating entropy for systems with rugged free energy landscapes. Here, we propose a simple method to improve the QH approximation, i.e., to reduce QH entropy. We approximate the potential energy landscape of the system by an effective harmonic potential, and request that this potential must produce exactly the configurational temperature of the system. Due to this constraint, the force constants associated with the effective harmonic potential are increased, or equivalently, entropy of motion governed by this effective harmonic potential is reduced. We also introduce the effective configurational temperature concept which can be used as an indicator to check the anharmonicity of the free energy landscape. To validate the new method we compare it with the recently developed expansion approximate method by calculating entropy of one simple model system and two peptides with 3 and 16 amino acids either in gas phase or in explicit solvent. We show that the new method appears to be a good choice in practice as it is a compromise between accuracy and computational speed. A modification of the expansion approximate method is also introduced and advantages are discussed in some detail.