Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Regioselective cycloaddition of C-carbamoylnitrones to methyl (E)-2-(2-phenylcyclopropylidene)acetate and methyl (E)-2-methylidene-3-phenylcyclopropane-1-carboxylate

N-Aryl-C-(arylcarbamoyl)nitrones regioselectively add to methyl 2-(2-phenylcyclopropylidene)-acetate and methyl 2-methylidene-3-phenylcyclopropanecarboxylate to give in each case two diastereoisomeric 5-oxa-6-azaspiro[2.4]heptane-4-carboxylates.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Review of stationary phases for microelectromechanical systems in gas chromatography: feasibility and separations

This review covers the recent development of stationary phases for chip-based gas chromatography (GC). Portable systems for rapid and reliable analysis are urgently needed. One way to achieve this is to miniaturize the entire analysis. Because the column is the central component of the GC system and determines the feasibility and quality of separation, this review focuses on stationary phases reported in the literature and their use in different fields during the last two decades, with emphasis on different methods for introducing the stationary phase into the GC column.     

Self-assembled free-floating nanomaterials from sequence-defined polymers

Sequence-defined polymers can be programmed to self-assemble into precise nanostructures for applications in biosensing, drug delivery, optics, and molecular computation. Inspired by the natural self-assembly processes present in biological protein and DNA systems, sets of molecular design rules have emerged across materials classes as instructions to build a variety of tunable structures. This review highlights recent advances in self-assembled sequence-defined and sequence-specific polymers across peptides, peptoids, DNA, and non-biological synthetic materials, with a focus on synthesis, assembly processes and overall structure. Specifically, these self-assembled structures are free-floating, as such constructs can potentially serve as a platform for the aforementioned applications. Emphasis is placed on the molecular design of polymers that self-assemble into zero-dimensional, one-dimensional, two-dimensional, or three-dimensional nanostructures. With the development of automated syntheses and increasing control over self-assembly, future work may focus on emerging classes of compatible hybrid materials with exciting directions toward new architectures and applications.     

Impedance Response of a Thin Film on an Electrode: Deciphering the Influence of the Double Layer Capacitance

The different contributions of the interfacial capacitance are identified in the case of passive materials or thin protective coatings deposited on the electrode surface. The method is based on a graphical analysis of the EIS results to determine both the passive-film capacitance in the high-frequency domain and the double-layer capacitance in the low-frequency domain. The proposed analysis is shown to be independent of the physicochemical origins of the frequency dispersion of the interfacial capacitances which results, from an analysis point of view of the experimental results, in the use of a constant-phase element However, for a correct evaluation of the thin-film properties such as its thickness, the high-frequency data must be corrected for the double-layer contribution. In particular, it is shown that if the double-layer capacitance gives a frequency-dispersed response, it is necessary to correct the high-frequency part for the double-layer constant-phase elements. This is first demonstrated on synthetic data and then used for the determination of the thickness of thin oxide film formed on Al in neutral pH solution.     

Halide Anion Triggered Reactions of Michael Acceptors with Tropylium Ion

Tropylium bromide undergoes noncatalyzed, regioselective additions to a large variety of Michael acceptors. In this way, acrylic esters are converted into β-bromo-α-cycloheptatrienylpropionic esters. The reactions are interpreted as nucleophilic attack of bromide ions at the electron-deficient olefins and the approach of the tropylium ion to the incipient carbanion. Quantum chemical calculations were performed to elucidate the analogy to the amine- or phosphine-catalyzed Rauhut–Currier reactions. Subsequent synthetic transformations of the bromo-cycloheptatrienylated adducts are reported.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.