An Inverse Theorem for the Uniformity Seminorms Associated with the Action of {{\mathbb {F}^{\infty}_{p}}}

Let ${\mathbb {F}}Let \mathbb F{\mathbb {F}} a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra uniformity seminorm U ^k (X) for an ergodic action (T_g)_{g ? \mathbb F^w}{(T_{g})_{{g} \in \mathbb {F}^{\omega}}} of the infinite abelian group \mathbb F^w{\mathbb {F}^{\omega}} on a probability space X = (X, B, m){X = (X, \mathcal {B}, \mu)} is generated by phase polynomials f: X ? S¹{\phi : X \to S^{1}} of degree less than C(k) on X, where C(k) depends only on k. In the case where k ￡ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} we obtain the sharp result C(k) = k. This is a finite field counterpart of an analogous result for \mathbb Z{\mathbb {Z}} by Host and Kra [HK]. In a companion paper [TZ] to this paper, we shall combine this result with a correspondence principle to establish the inverse theorem for the Gowers norm in finite fields in the high characteristic case k ￡ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} , with a partial result in low characteristic.     

Co-pyrolysis of macroalgae and lignocellulosic biomass

Synergistic effect of co-pyrolysis of macroalgae [Enteromorpha prolifera (EP)] and lignocellulosic biomass [rice husk (RH)] in a fixed bed reactor for maximum and enhanced biofuels yield has been investigated. The main and interaction effects of three effective co-pyrolysis parameters (pyrolysis temperature, feedstock blending ratio, and heating rate) were also modeled and simulated to determine the yield rates of bio-oil and bio-char, respectively. Optimization studies were, then, performed to predict the optimal conditions for maximum yields using the central composite circumscribed experimental design in Design Expert^® software 8.0.6. Analysis of variance was carried out to determine whether the fit of the multiple regressions is significant for the second-order model. Normal pyrolysis oils from EP, RH, and co-pyrolysis oils obtained from different feedstock blending ratios were examined using the gas chromatography-mass spectrometry to identify their compositions. Some vital properties of oils and bio-chars such as the heating value, water content, elemental compositions, and specific gravity were also determined, which unveiled that synergistic effect exists between EP and RH during co-pyrolysis, and this led to increase in products’ yields and improved co-pyrolysis products’ quality.

     

Cellular properties and population asymptotics in the population balance equation

Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.     

Heterogeneous liquid phase oxidation of ethylbenzene to acetophenone with graphene carbon-based catalyst

The series of graphene materials and N-doped graphene materials were successfully synthesized and improved by high-temperature treatment with trace iron oxide. XRD, Raman, FT-IR, TEM and XPS were employed for these catalysts. The catalytic performance of these catalysts was investigated in the selective oxidation of ethylbenzene with tert-butyl hydroperoxide as oxidant. The impacts of temperature, mass of catalysts, reaction time and oxidants on the selective oxidation of ethylbenzene were also investigated. The N-doped graphene materials exhibit greatly remarkable catalytic performance than others. The conversion of ethylbenzene is more than 90% and the selectivity of acetophenone is more than 95% at 353 K. Graphene can be used as catalyst owing to its unique structures and chemical properties. The characterization tests show that the doping of N atoms can create more defects and more active sites in the N-doped graphene materials which could greatly improve the catalytic performance. Furthermore, such cost-effective graphene-based catalysts possess good stability and could be reused at least five times without remarkable loss of the catalytic activity.     

Theory of three-dimensional alignment by intense laser pulses

We introduce a theoretical framework for study of three-dimensional alignment by moderately intense laser pulses and discuss it at an elementary level. Several features of formal interest are noted and clarified. Our approach is nonperturbative, treating the laser field within classical and the material system within quantum mechanics. The theory is implemented numerically using a basis set of rotational eigenstates, transforming the time-dependent Schrodinger equation to a set of coupled differential equations where all matrix elements are analytically soluble. The approach was applied over the past few years to explore different adiabatic and nonadiabatic three-dimensional alignment approaches in conjunction with experiments, but its formal details and numerical implementation were not reported in previous studies. Although we provide simple numerical examples to illustrate the content of the equations, our main goal is to complement previous reports through an introductory discussion of the underlying theory.     

Quantum mechanics/molecular mechanics investigation of the chemical reaction in Dpo4 reveals water-dependent pathways and requirements for active site reorganization

The nucleotidyl-transfer reaction coupled with the conformational transitions in DNA polymerases is critical for maintaining the fidelity and efficiency of DNA synthesis. We examine here the possible reaction pathways of a Y-family DNA polymerase, Sulfolobus solfataricus DNA polymerase IV (Dpo4), for the correct insertion of dCTP opposite 8-oxoguanine using the quantum mechanics/molecular mechanics (QM/MM) approach, both from a chemistry-competent state and a crystal closed state. The latter examination is important for understanding pre-chemistry barriers to interpret the entire enzyme mechanism, since the crystal closed state is not an ideal state for initiating the chemical reaction. The most favorable reaction path involves initial deprotonation of O3'H via two bridging water molecules to O1A, overcoming an overall potential energy barrier of approximately 20.0 kcal/mol. The proton on O1A-P(alpha) then migrates to the gamma-phosphate oxygen of the incoming nucleotide as O3' attacks P(alpha), and the P(alpha)-O3A bond breaks. The other possible pathway in which the O3'H proton is transferred directly to O1A on P(alpha) has an overall energy barrier of 25.0 kcal/mol. In both reaction paths, the rate-limiting step is the initial deprotonation, and the trigonal-bipyramidal configuration for P(alpha) occurs during the concerted bond formation (O3'-P(alpha)) and breaking (P(alpha)-O3A), indicating the associative nature of the chemical reaction. In contrast, the Dpo4/DNA complex with an imperfect active-site geometry corresponding to the crystal state must overcome a much higher activation energy barrier (29.0 kcal/mol) to achieve a tightly organized site due to hindered O3'H deprotonation stemming from larger distances and distorted conformation of the proton acceptors. This significant difference demonstrates that the pre-chemistry reorganization in Dpo4 costs approximately 4.0 to 9.0 kcal/mol depending on the primer terminus environment. Compared to the higher fidelity DNA polymerase beta from the X-family, Dpo4 has a higher chemical reaction barrier (20.0 vs 15.0 kcal/mol) due to the more solvent-exposed active site.     

Optimal design of nanoplasmonic materials using genetic algorithms as a multiparameter optimization tool

An optimal control approach based on multiple parameter genetic algorithms is applied to the design of plasmonic nanoconstructs with predetermined optical properties and functionalities. We first develop nanoscale metallic lenses that focus an incident plane wave onto a prespecified, spatially confined spot. Our results illustrate the mechanism of energy flow through wires and cavities. Next we design a periodic array of silver particles to modify the polarization of an incident, linearly polarized plane wave in a desired fashion while localizing the light in space. The results provide insight into the structural features that determine the birefringence properties of metal nanoparticles and their arrays. Of the variety of potential applications that may be envisioned, we note the design of nanoscale light sources with controllable coherence and polarization properties that could serve for coherent control of molecular, electronic, or electromechanical dynamics in the nanoscale.     

Octahydroxypyridine[4]arene self-assembles spontaneously to form hexameric capsules and dimeric aggregates

In recent years it has been observed that resorcin[4]arenes and pyrogallol[4]arenes form hydrogen-bonded hexameric capsules in nonpolar solvents. In the present study we have used NMR spectroscopy, with an emphasis on diffusion NMR, to investigate the self-assembly and the aggregation mode of solutions of octahydroxypyridine[4]arene (1 b) in chloroform. In spectroscopic studies, the hexameric capsule of C-undecylresorcin[4]arene (2 b) was used as a reference compound and in some cases also as an internal reference. The current diffusion NMR spectroscopy study shows, in contrast to a previous report, that compound 1 b self-assembles spontaneously into hexameric and dimeric aggregates in solutions in chloroform. The (1)H NMR and diffusion NMR spectroscopic studies on a solution of 1 b in CHCl(3) show the presence of new upfield-shifted peaks, which diffuse with the same diffusion coefficient as the hexameric peaks in the spectrum. Therefore, these new upfield-shifted peaks were attributed to encapsulated CHCl(3) molecules. Interestingly, diffusion NMR measurements showed that the addition of trifluoroacetic acid (6.7 equiv), which had no effect on the hexameric capsules of 2 b, led to the disassembly of the hexamer and the dimer of 1 b into its monomers. Therefore, we conclude that compound 1 b self-assembles spontaneously into hexameric capsules in nonpolar organic solvents, as do resorcin[4]arenes 2 b and 2 c and pyrogallol[4]arenes 3 a and 3 b.