Origins of the diastereoselectivity in hydrogen bonding directed Diels-Alder reactions of chiral dienes with achiral dienophiles: a computational study

In this study, the origins of diastereoselectivity in the hydrogen bonding assisted Diels-Alder reactions of chiral dienes with achiral dienophiles have been investigated with density functional methods. The distortion/interaction model has been applied to shed light on the origins of selectivity. C9-Substituted chiral anthracene templates (R = (CH(3))(OCH(3))(H), R = (CH(3))(OH)(H), R = (CH(3))(CH(2)CH(3))(H) and R = (-CH(2)-C(CH(3))(OCH(3))(H)) are used to rationalize the role of a stereogenic center and H-bonding on the product distribution ratio. Even though hydrogen bonding increases the reactivity of the diene, the stereoselectivity is reduced because of the hydrogen bonding capacity of both diastereomeric transition states. The interaction energies of the studied anthracene templates with N-methyl maleimide at the transition state correlate linearly with an increase in reactivity. The selectivity is determined by both favorable distortion and interaction energies. The π-facial selectivity induced by the presence of a chiral auxiliary in 1-substituted 1,3-pentadienes (R1 = (CH(3))(OCH(3))(H) and R1 = (CH(3))(OH)(H)) has also been modeled in order to rationalize the role of the stereogenic center and H-bonding on the stereoselectivity of an aliphatic diene. In both parts, the product distribution ratios calculated from Boltzmann distributions based on Gibbs free energies are in reasonable agreement with the experimental results. Finally the role of OH-substituted five-membered pyrrolidine on C9 of anthracene is investigated since the successful usage of the conformationally rigid pyrrolidines in asymmetric synthesis is well known. Overall, both in the acyclic system and in anthracene, the facilitation due to H-bonding is reflected in the interaction energies: the higher the difference in interaction energies in the transition structures of the two diastereomers, the more selective the H-bonding assisted Diels-Alder reaction is.     

An in-service primary teacher’s implementation of mathematical tasks: the case of length measurement and perimeter instruction

The purpose of this paper is to examine the cognitive demand levels of tasks used by an in-service primary teacher during length measurement and perimeter instruction and to examine a possible link between these tasks and the teacher’s mathematical knowledge in teaching. For this purpose, a case study approach was used and the data was drawn from classroom observations, semi-structured interviews, and field notes. Specific tasks from length measurement and perimeter instruction were presented and analyzed according to the Mathematical Tasks Framework. Then, how these tasks gave information about the teacher’s mathematical knowledge in teaching in the length measurement and perimeter topics was examined according to the Knowledge Quartet model. According to the findings of the study, the tasks used during length measurement and perimeter instruction were mostly categorized as low-level tasks. In addition, teacher’s mathematical knowledge in teaching affected the implementation of the tasks.     

Positive solutions of nonlinear multi-point boundary value problems

This paper deals with the existence of positive solutions of nonlinear differential equation

$$\begin{aligned} u^{\prime \prime }(t)+ a(t) f(u(t) )=0,\quad 0<t <1, \end{aligned}$$

subject to the boundary conditions

$$\begin{aligned} u(0)=\sum _{i=1}^{m-2} a_i u (\xi _i) ,\quad u^{\prime } (1) = \sum _{i=1}^{m-2} b_i u^{\prime } (\xi _i), \end{aligned}$$

where \( \xi _i \in (0,1) \) with \( 0< \xi _1<\xi _2< \cdots<\xi _{m-2} < 1,\) and \(a_i,b_i \) satisfy   \(a_i,b_i\in [0,\infty ),~~ 0< \sum _{i=1}^{m-2} a_i <1,\) and \( \sum _{i=1}^{m-2} b_i <1. \) By using Schauder’s fixed point theorem, we show that it has at least one positive solution if f is nonnegative and continuous. Positive solutions of the above boundary value problem satisfy the Harnack inequality

$$\begin{aligned} \displaystyle \inf _{0 \le t \le 1} u(t) \ge \gamma \Vert u\Vert _\infty . \end{aligned}$$

     

Crystallographic Analysis of FCC ? BCT Martensitic Transformation in the Alloy Fe-22% Ni-0.8% C

The infinitesimal deformation (ID) approach is applied to analyse the crystallography involved in the fcc to bct martensitic transformation for the case of (101)_γ[<formula><overline>1</overline>01</formula>]_γ twinning shear as LIS (lattice invariant shear) system in the alloy Fe-22% Ni-0.8% C. Analytical solutions are derived for habit plane orientation, orientation relationships between austenite and martensite phases, and the magnitude of the total shape deformation, etc. In order to compare numerical solutions with the ID approach and phenomenological crystallographic theory, the corresponding crystallographic parameters are calculated by using the Ledbetter and Dunn (L-D) theory. The numeric values obtained are compared with the predictions of the phenomenological crystallographic theories, and with experimental results.     

Molar Volume Calculation of Molten Ag–Au–Cu and Cu–Ag–In Alloy Systems Using General Solution Model

Russian Journal of Physical Chemistry A - However, up to the present, there was few reports on the density of the molten Ag–Au–Cu and Cu–Ag–In alloy systems. In this work,...     

Thermodynamic description of the viscosity of liquid solder alloys with minor Co impurities

Because of the increasing complexity and cost of experiments carried out, the data for the multi-component alloy systems have frequently been obtained by numerical modelling. It is clear that the related calculations require reliable data dealing with the pure components and binary alloy systems. Selecting the reliable data concerning the pure components from the literature, the viscosities for the SAC and (SAC)_1?x Co_x solder alloys have been calculated using different viscosity models (geometric and physical). The viscosity decreases as the amount of tin content increases in the SAC387 alloy while the addition of the cobalt to SAC387 solder results in the increasing of the viscosity. Moreover, by computing the root mean square values between theoretical and experimental viscosities, it can be concluded that the lowest value among all models is that of obtained by Kaptay equation.     

Copper + nickel-in-charcoal (Cu-Ni/C): a bimetallic, heterogeneous catalyst for cross-couplings

A new heterogeneous catalyst composed of copper and nickel oxide particles supported within charcoal has been developed. It catalyzes cross-couplings that traditionally use palladium, nickel, or copper, including Suzuki-Miyaura reactions, Buchwald-Hartwig aminations, vinylalane alkylations, etherifications of aryl halides, aryl halide reductions, asymmetric conjugate reductions of activated olefins, and azide-alkyne "click" reactions.     

Electroanalytical investigation and determination of pefloxacin in pharmaceuticals and serum at boron-doped diamond and glassy carbon electrodes

The anodic behavior and determination of pefloxacin on boron-doped diamond and glassy carbon electrodes were investigated using cyclic, linear sweep, differential pulse and square wave voltammetric techniques. In cyclic voltammetry, pefloxacin shows one main irreversible oxidation peak and additional one irreversible ill-defined wave depending on pH values for both electrodes. The results indicate that the process of pefloxacin is irreversible and diffusion controlled on boron-doped diamond electrode and irreversible but adsorption controlled on glassy carbon electrode. The peak current is found to be linear over the range of concentration 2 × 10⁻⁶ to 2 × 10⁻⁴ M in 0.5 M H₂SO₄ at about +1.20 V (versus Ag/AgCl) for differential pulse and square wave voltammetric technique using boron-doped diamond electrode. The repeatability, reproducibility, precision and accuracy of the methods in all media were investigated. Selectivity, precision and accuracy of the developed methods were also checked by recovery studies. The procedures were successfully applied to the determination of the drug in pharmaceutical dosage forms and humans serum samples with good recovery results. No electroactive interferences from the excipients and endogenous substances were found in the pharmaceutical dosage forms and biological samples, respectively.     

Nonlinear Response of Cylindrical Shells to Random Excitation

An analytical study of nonlinear flexural vibrations of cylindrical shells to random excitation is presented. Donnell's thin-shell theory is used to develop the governing equations of motion. Thermal effects for a uniform temperature rise through the shell thickness are included in the formulation. A Monte Carlo simulation technique of stationary random processes, multi-mode Galerkin-like approach and numerical integration procedures are used to develop nonlinear response solutions of simply-supported cylindrical shells. Numerical results include time domain response histories, root-mean-square values and histograms of probability density. Comparison of Monte Carlo results is made to those obtained by statistical linearization and the Fokker–Planck equation.