Stochastic control for a class of random evolution models

We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton-Bellman-Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.     

High Electromagnetic Field Enhancement of TiO2 Nanotube Electrodes

We present the fabrication of TiO₂ nanotube electrodes with high biocompatibility and extraordinary spectroscopic properties. Intense surface‐enhanced resonance Raman signals of the heme unit of the redox enzyme Cytochrome b₅ were observed upon covalent immobilization of the protein matrix on the TiO₂ surface, revealing overall preserved structural integrity and redox behavior. The enhancement factor could be rationally controlled by varying the electrode annealing temperature, reaching a record maximum value of over 70 at 475 °C. For the first time, such high values are reported for non‐directly surface‐interacting probes, for which the involvement of charge‐transfer processes in signal amplification can be excluded. The origin of the surface enhancement is exclusively attributed to enhanced localized electric fields resulting from the specific optical properties of the nanotubular geometry of the electrode.     

Structural Relevance of Intramolecular H-Bonding in Ortho-Hydroxyaryl Schiff Bases: The Case of 3-(5-bromo-2-hydroxybenzylideneamino) Phenol

A new Schiff base compound, 3-(5-bromo-2-hydroxybenzylideneamino)phenol (abbreviated as BHAP) was synthesized and characterized by ¹H- and ¹³C- nuclear magnetic resonance and infrared spectroscopies. DFT/B3LYP/6-311++G(d,p) calculations were undertaken in order to explore the conformational space of both the E- and Z- geometrical isomers of the enol-imine and keto-amine tautomers of the compound. Optimized geometries and relative energies were obtained, and it was shown that the most stable species is the E-enol-imine form, which may exist in four low-energy intramolecularly hydrogen-bonded forms (I, II, V, and VI) that are almost isoenergetic. These conformers were concluded to exist in the gas phase equilibrium with nearly equal populations. On the other hand, the infrared spectra of the compound isolated in a cryogenic argon matrix (10 K) are compatible with the presence in the matrix of only two of these conformers (conformers II and V), while conformers I and VI convert to these ones by quantum mechanical tunneling through the barrier associated with the rotation of the OH phenolic group around the C–O bond. The matrix isolation infrared spectrum was then assigned and interpreted with help of the DFT(B3LYP)/6-311++G(d,p) calculated infrared spectra for conformers II and V. In addition, natural bond orbital (NBO) analysis was performed on the most stable conformer of the experimentally relevant isomeric form (E-enol-imino conformer V) to shed light on details of its electronic structure. This investigation stresses the fundamental structural relevance of the O–H···N intramolecular H-bond in o-hydroxyaryl Schiff base compounds.     

A generalization of rational Bernstein–Bézier curves

This paper is concerned with a generalization of Bernstein–Bézier curves. A one parameter family of rational Bernstein–Bézier curves is introduced based on a de Casteljau type algorithm. A subdivision procedure is discussed, and matrix representation and degree elevation formulas are obtained. We also represent conic sections using rational q-Bernstein–Bézier curves. AMS subject classification (2000)  65D17     

Synthesis and analysis of thermal characteristics of polybenzoxazine based on phenol and 3‐Amino phenyl boronic acid

In this work, 3‐amino phenyl boronic acid (AB) was used as an aniline derivative in the preparation of polybenzoxazine based on phenol. In order to investigate the effect of boronic acid on thermal characteristics, polybenzoxazines based on pure aniline and 50% aniline and AB mixture were also prepared and analyzed. Significant improvements in thermal characteristics, increase in thermal stability and char yield, was recorded for the polymers based on AB or its mixture. This behavior was associated with crosslinked structures generated by condensation reactions of B? OH groups. Morphologic and thermal characteristics of polybenzoxazines samples were investigated by NMR, FTIR, DSC, TGA, and direct pyrolysis mass spectrometry (DP‐MS) techniques. Application of DP‐MS technique also supplied additional information on crosslinked structures produced by boronic acid units. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1711–1716     

Viscoelastic behavior of poly(ether imide) incorporated with multiwalled carbon nanotubes

There is significant potential in improving the mechanical, electrical, and thermal properties of engineering plastics, including poly(ether imide) (PEI), with various nanoinclusions such as multiwalled carbon nanotubes (MWCNTs). However, this potential can only be fully realized through a thorough understanding of the rheological behavior and the thermomechanical histories that the nanocomposites are exposed to during their preparation and the resulting effective properties. In this study, nanocomposites of PEI and MWCNTs were prepared using a solution processing method under different dispersion conditions, and the viscoelastic material functions of the nanocomposites were characterized as functions of concentration of CNTs in the 1–5% by weight range (volume fraction, ? = 0.006–0.03) and temperature. The storage modulus and magnitude of complex viscosity values of the PEI nanosuspensions increased by as much as 3500% and 800%, respectively, at ? = 0.03, along with similar orders of magnitude increases observed or predicted in other viscoelastic material functions. Such increases reflect how nanotube incorporation and network formation can drastically alter the flow and deformation behavior of the PEI/CNT nanosuspensions at processing‐relevant temperatures and deformation rates. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Disruption of protein-protein interactions using nanoparticles: inhibition of cytochrome c peroxidase

Functionalized gold nanoparticles bind selectively to cytochrome c or cytochrome c peroxidase and inhibit enzyme turnover.