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.     

The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

Raman spectra and binding of CuII to purine nucleotides

Raman spectra of adenosine 5′-monophosphate, poly(rA), guanosine 5′-monophosphate and their Cu^II complexes have been obtained and analysed by referring to spectra of D-, ¹⁵N- and ¹³C-labelled nucleobases. The greatest spectral changes on attachment of Cu^II to these nucleotides are associated with changes in the five-membered ring and suggest that the metal binds preferentially to N-7 of nucleobases. However, in the Cu^II coordinated poly(rA) species, N-1 binding sites are also present to some extent, as deduced from the comparison of the Raman spectrum of the Cu-poly(rA) complex with that of the protonated polynucleotide. In the complexes of guanosine 5′-monophosphate with Cu^II, the guanine residue is located at the anti position with respect to the ribose moiety through the glycosidic bond. In all cases, strong changes are also recorded for characteristic bands of phosphate groups, indicating their participation as ligands surrounding Cu^II.     

Procedure for activating polymers with primary and/or secondary hydroxyl groups

A new facile method using 2-fluoro-1-methylpyridinium toluene-4-sulfonate (FMP) for activating polymeric hydroxyl groups has recently been developed (Refs. 1–2). Such activated polymers are useful for immobilization of enzymes, antibodies and other biomolecules and for affinity matrix development. The activation method involves reacting, at room temperature, the polymer with FMP in the presence of a tertiary amine for 0.5 to 1 hour. The activated hydroxyls react readily with nucleophiles, such as amino or thiol ligands at pH 5–10. The resulting linkages between the ligand and the polymer are respectively stable secondary amine and thioether bonds. The activated polymer remains active and usable for several months when stored at 4°C in either an acidic aqueous solution or an inert anhydrous organic solvent. The “half-life” of the activated groups in non-nucleophilic buffer solution varies from 10 to 300 hours in the pH range of 10 to 6, being most stable at low pH. Both primary and secondary hydroxyl groups of different polymers were facilely activated and shown to react readily with nucleophilic groups of biomolecules. Furthermore, FMP provides a convenient handle for the synthesis of unique conjugates consisting of FMP and a guiding molecule. These conjugates function as an activator of the hydroxyl group of a solid support as well as a molecular guide which orients the position of the ligand to be immobilized. The conjugates make it possible to immobilize ligands in an affinity-directed way.     

Optical modes in nanoscale one-dimensional spin chains

The spin chain systems with one-dimensional magnetic ordering are promising candidates for quantum optical devices. This paper shows how the optical excitation can induce various phonon modes in an ideal Cu-O chain at various lengths. The calculation was carried out at different level theories including configuration interaction singles for excited states, density functional theory and second-order Möller-Plesset perturbation. In general, the number of modes increases with chain length due to growing asymmetry of atomic positions when chain exceeds 5 nm. There were, however, only two basic modes: one is associated with the symmetric oscillation of oxygen and another with the asymmetric motion of the same along the chain. At the length below 4.3 nm, the Raman activity of the symmetric mode (440 cm⁻¹) dominates. From analysis of density of states, this mode may be associated with the excitation across the lowest LUMO bands with changing in spin state.     

Ozonolysis of dipterocarpol and its derivatives

Oxidation of dipterocarpol and its derivatives with ozone gave compounds containing lactone, lactol, alkoxytetrahydrofuran, aldehyde, and methyl ketone fragments in the side chain, as well as 1,2,4-trioxolane fragment in the A ring. The molecular and crystalline structures of dipterocarpol were determined by X-ray analysis.     

Regular conjugated terpolymers comprising two different acceptors and bithiophene donor in repeating group: Effect of strong and weak acceptors on semiconducting properties

Diketopyrrolopyrrole (DPP)‐based terpolymers—P(DPP‐TPyT) and P(DPP‐T3MTT)—bearing bithiophene donating groups and weak accepting units such as pyridine (Py) or methyl thiophene‐3‐carboxylate (3MT), in the polymer backbone, were successfully synthesized. Although the two polymers had similar physical and electrochemical properties, grazing incidence X‐ray diffraction patterns of P(DPP‐TPyT) and P(DPP‐T3MTT) showed mixed and edge‐on orientations, respectively, in thermally annealed films. Accordingly, the P(DPP‐T3MTT) showed twice the hole mobility of P(DPP‐TPyT) in a thin‐film transistor, and a blended film of P(DPP‐T3MTT) and [6,6]‐phenyl‐C71‐butyric acid methyl ester (PC₇₁BM) showed better power conversion efficiency in a polymer solar cell. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1339‐1347     

Construction of [4.3.1]propellanes via molybdenum fischer carbene complexes

Treatment of molybdenum Fischer carbene complexes with 6-methylene-7-octen-1-yne derivatives at 40 degrees C generates substituted tricyclo[4.3.1.0(1,6)]deca-2,4-dienes in good yield. Pentacarbonyl(butylmethoxycarbene)molybdenum(0) afforded the highest cyclization yields (54%), while the analogous chromium carbene complex gave no reaction. The range of dienyne substrates that participate in this reaction is explored and its mechanism is analyzed and discussed.