Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket

We establish the Lifschitz-type singularity around the bottom of the spectrum for the integrated density of states for a class of subordinate Brownian motions in presence of the nonnegative Poissonian random potentials, possibly of infinite range, on the Sierpiński gasket. We also study the long-time behaviour for the corresponding averaged Feynman–Kac functionals.     

Generalized Derivatives of Lexicographic Linear Programs

Lexicographic linear programs are fixed-priority multiobjective linear programs that are a useful model of biological systems using flux balance analysis and for goal-programming problems. The objective function values of a lexicographic linear program as a function of its right-hand side are nonsmooth. This work derives generalized derivative information for lexicographic linear programs using lexicographic directional derivatives to obtain elements of the Bouligand subdifferential (limiting Jacobian). It is shown that elements of the limiting Jacobian can be obtained by solving related linear programs. A nonsmooth equation-solving problem is solved to illustrate the benefits of using elements of the limiting Jacobian of lexicographic linear programs.     

Eigenvalues of the matching derangement graph

In this paper, we derive a formula for the eigenvalues of the matching derangement graph. The formula gives an insight regarding the alternating sign conjecture for the eigenvalues of the matching derangement graph. In particular, we show that the alternating sign property holds for certain partitions.     

Quantification of purine basis in their mixtures at femto‐molar concentration levels using FT‐SERS

Surface‐enhanced Raman scattering spectroscopy represents one of the unique techniques for studying nanoscale objects, and its distinctive properties can be used in the process of further analysis. The careful evaluation of the particular influence of selected key‐role experimental parameters (e.g. pH value of measured sample mixture, size and distribution of used nanoparticles) and the influence of reduction agent used in the process of formation of desired nanoparticle objects presents an important task in the further study of surface‐enhanced Raman scattering effect. A broad study of these experimental parameters was performed in this paper. The main aim of the presented work was to a demonstrate an application potential of selected experimental conditions in the determination of three purine bases: adenine, xanthine, and hypoxanthine. The resulting limits of detection are at femtomolar concentration levels for all three studied compounds. Copyright © 2011 John Wiley & Sons, Ltd.     

Blume–Capel model on the antiferromagnetic fcc lattice

In the presence of a uniform external magnetic field, the spin-1 fcc antiferromagnetic Ising model in the four sub-lattice with the nearest-neighbor bilinear and crystal field interactions is investigated by using mean-field theory. The lattice is considered in blocks and each block contains 32 spins. While the central four spins forming a basic tetrahedron structure are allowed to fluctuate, the surrounding 28 spins take the mean-field values. The ground state phase diagram of the system is examined since it provides valuable information to make a prediction of the different phase diagram topologies. The phase diagrams are obtained on the reduced external field versus temperature, (H/|J|−kT/|J|)$(H/\left|J\right|-kT/\left|J\right|)$, plane for selected crystal field interaction values from the ground state phase diagram and it is found that the system exhibits reentrant behavior and some special points such as tricritical, bicritical and triple points.     

Silica‐Protected Micron and Sub‐Micron Capsules and Particles for Self‐Healing at the Microscale

A generalized silica coating scheme is used to functionalize and protect sub‐micron and micron size dicyclopentadiene monomer‐filled capsules and polymer‐protected Grubbs' catalyst particles. These capsules and particles are used for self‐healing of microscale damage in an epoxy‐based polymer. The silica layer both protects the capsules and particles, and limits their aggregation when added to an epoxy matrix, enabling the capsules and particles to be dispersed at high concentrations with little loss of reactivity.

     

Functional MRI using super-resolved spatiotemporal encoding

Recently, new ultrafast imaging sequences such as rapid acquisition by sequential excitation and refocusing (RASER) and hybrid spatiotemporal encoding (SPEN) magnetic resonance imaging (MRI) have been proposed, in which the phase encoding of conventional echo planar imaging (EPI) is replaced with a SPEN. In contrast to EPI, SPEN provides significantly higher immunity to frequency heterogeneities including those caused by B₀ inhomogeneities and chemical shift offsets. Utilizing the inherent robustness of SPEN, it was previously shown that RASER can be used to successfully perform functional MRI (fMRI) experiments in the orbitofrontal cortex — a task which is challenging using EPI due to strong magnetic susceptibility variation near the air-filled sinuses. Despite this superior performance, systematic analyses have shown that, in its initial implementation, the use of SPEN was penalized by lower signal-to-noise ratio (SNR) and higher radiofrequency power deposition as compared to EPI-based methods. A recently developed reconstruction algorithm based on super-resolution principles is able to alleviate both of these shortcomings; the use of this algorithm is hereby explored within an fMRI context. Specifically, a series of fMRI measurements on the human visual cortex confirmed that the super-resolution algorithm retains the statistical significance of the blood oxygenation level dependent (BOLD) response, while significantly reducing the power deposition associated with SPEN and restoring the SNR to levels that are comparable with those of EPI.     

Porous poly(vinylidene fluoride) membrane modified with hyperbranched poly(amine‐ester)

Poly(vinylidene fluoride) (PVDF) membranes were hydrophilic modified with hydroxyl group terminated hyperbranched poly(amine‐ester) (HPAE). Fourier transform infrared spectroscopy (FT‐IR) was used to study the chemical change of PVDF membranes. X‐ray photoelectron spectroscopy (XPS) indicated that some HPAE molecules were retained in PVDF membrane through polymer chain coiling. The presence of HPAE would improve the hydrophilicity of PVDF membrane. Scanning electron microscopy (SEM) was employed to characterize the morphology of different membranes. The thermodynamic stability for PVDF/DMAc/HPAE/Water system was characterized by the determination of the gelation values. Precipitation kinetics for PVDF/DMAc/HPAE/Water system was studied by precipitation time measurement. The water contact angle indicated that the hydrophilicity and the biocompatibility corresponding to protein adsorption of PVDF membrane were improved significantly after blending with hydrophilic HPAE molecules. Copyright © 2011 John Wiley & Sons, Ltd.     

On-chip fabrication of silver microflower arrays as a catalytic microreactor for allowing in situ SERS monitoring

Silver microflower arrays constructed by upright nanoplates and attached nanoparticles were fabricated inside a microfluidic channel, thus a robust catalytic microreactor for allowing in situ SERS monitoring was proposed. On-chip catalytic reduction shows that the silver microflowers have high catalytic activity and SERS enhancement.     

Hydration of humic and fulvic acids studied by DSC

Qualitative and quantitative aspects of hydration of four humic acids (HA) and three fulvic acids (FA) originating from different sources were investigated. DSC experiments at subambient temperatures were carried out in order to monitor differences in ice behavior originating from freezable water surrounding humic molecules. It was found that kinetic effects play a significant role in hydration processes of both HA and FA. In fact, the hydration took part over 21?days which was detected as a progressive decrease in ice melting enthalpy. Simultaneously, the peak shapes and positions changed indicating structural changes in the physical structure of the humic substances. In case of FA, the dependency of melting enthalpy on water concentration showed a linear trend resembling a complete hydration previously observed for water-soluble hydrophilic polymers. In contrast, the melting enthalpy of some HA increased in a step-like way with increasing water content, suggesting preservation of original hydrophobic scaffold during the hydration. The differences between the rather young FA and the rather old HA lead to the conclusion that water can play a significant role in processes of humification. We assume that separation of hydrophobic and hydrophilic domains and thus increase in nanoscale heterogeneity represents an important physical contribution to the overall humification process. It was also demonstrated that the higher content of oxygen in humic molecules is not the only indicator of higher water holding capacity. Instead the porosity of humic matrix seems to contribute as additional parameter into these processes.