Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.     

Real-time assessment of carbon nanotube alignment in a polymer matrix under an applied electric field via polarized Raman spectroscopy

A technique has been developed utilizing polarized Raman spectroscopy to measure alignment of carbon nanotubes in situ in a polymer matrix under an applied electric field. Previous studies of alignment have been restricted to optically transparent solvents or polymerized specimens that prevent accurate analyses of alignment dynamics in polymers. The effects of electric field strength on the degree of alignment and the time to achieve an aligned state are discussed. The use of in situ, real-time polarized Raman spectroscopy provides a non-invasive technique for assessing carbon nanotube alignment, which can assist in determining processing conditions to improve the mechanical and electrical properties of aligned nanocomposites.     

Fourier analysis of operations that preserve permutations

Fourier inversions of operations identify those with certain symmetries. A general method with invertible matrices over semirings sets up many different inversive schemes, such as disjunctive normal form, algebraic normal form and classical Fourier analysis. First, unary functions are inverted, and then, with tensor products, the same is done for operations of more than one argument. Classical Fourier analysis is applied to inverting operations on a set of k elements by replacing it by the set of \({k^{\rm th}}\) roots of unity. The Fourier transform of an operation preserving rotations of the roots has many coefficients that are zero, in fact, at most \({1/k}\) are non-zero. A related result holds for operations preserving reflections of the roots.     

Backward heat equation with time dependent variable coefficient

Backward heat equation with time dependent variable coefficient is severely ill‐posed in the sense of Hadamard, so we need regularization. In this paper, we consider Backward heat equation with time dependent variable coefficient, and by small perturbing, we obtain an approximation problem. We show this approximation problem is well‐posed with small parameter. Also, we show this approximation system converges to the original problem when parameter goes to zero. Here, we use modified‐quasi boundary value method to regularize this problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.     

Photophysical Study and Biological Applications of Synthetic Chalcone-Based Fluorescent Dyes

A chalcone series (3a–f) with electron push–pull effect was synthesized via a one-pot Claisen–Schmidt reaction with a simple purification step. The compounds exhibited strong emission, peaking around 512–567 nm with mega-stokes shift (∆λ = 93–139 nm) in polar solvents (DMSO, MeOH, and PBS) and showed good photo-stability. Therefore, 3a–f were applied in cellular imaging. After 3 h of incubation, green fluorescence was clearly brighter in cancer cells (HepG2) compared to normal cells (HEK-293), suggesting preferential accumulation in cancer cells. Moreover, all compounds exhibited higher cytotoxicity within 24 h toward cancer cells (IC₅₀ values ranging from 45 to 100 μM) than normal cells (IC₅₀ value >100 μM). Furthermore, the antimicrobial properties of chalcones 3a–f were investigated. Interestingly, 3a–f exhibited antibacterial activities against Escherichia coli and Staphylococcus aureus, with minimum bactericidal concentrations (MBC) of 0.10–0.60 mg/mL (375–1000 µM), suggesting their potential antibacterial activity against both Gram-negative and Gram-positive bacteria. Thus, this series of chalcone-derived fluorescent dyes with facile synthesis shows great potential for the development of antibiotics and cancer cell staining agents.     

Solid-Phase Synthesis of an Insect Pyrokinin Analog Incorporating an Imidazoline Ring as Isosteric Replacement of a trans Peptide Bond

A facile solid-phase synthetic method for incorporating the imidazoline ring motif, a surrogate for a trans peptide bond, into bioactive peptides is reported. The example described is the synthesis of an imidazoline peptidomimetic analog of an insect pyrokinin neuropeptide via a cyclization reaction of an iminium salt generated from the preceding amino acid and 2,4-diaminopropanoic acid (Dap).