NNNO-Heteroscorpionate nickel (II) and cobalt (II) complexes for ethylene oligomerization: the unprecedented formation of odd carbon number olefins

The unprecedented observation of odd carbon number olefins is reported during nickel- catalyzed ethylene oligomerization. Two complexes based on Co (II) and Ni (II) with novel tetradentate heteroscorpionate ligand have been synthesized and fully characterized. These complexes showed the ability to oligomerize ethylene upon activation with various organoaluminum compounds (Et₂AlCl, Et₃Al₂Cl₃, EtAlCl₂, MMAO). Ni (II) based catalytic systems were sufficiently more active (up to 1900 kg·mol (Ni)⁻¹·h⁻¹·atm⁻¹) than Co (II) analogs and have been found to be strongly dependent on the activator composition. The use of PPh₃ as an additive to catalytic systems resulted in the increase of activity up to 4,150 kg·mol (Ni)⁻¹·h⁻¹·atm⁻¹ and in the alteration of selectivity. All Ni (II) based systems activated with EtAlCl₂ produce up to 5 mol. % of odd carbon number olefins; two probable mechanisms for their formation are suggested – metathesis and β-alkyl elimination.     

Distal γ-C(sp3)−H Olefination of Ketone Derivatives and Free Carboxylic Acids

Reported herein is the distal γ-C(sp³)−H olefination of ketone derivatives and free carboxylic acids. Fine tuning of a previously reported imino-acid directing group and using the ligand combination of a mono-N-protected amino acid (MPAA) and an electron-deficient 2-pyridone were critical for the γ-C(sp³)−H olefination of ketone substrates. In addition, MPAAs enabled the γ-C(sp³)−H olefination of free carboxylic acids to form diverse six-membered lactones. Besides alkyl carboxylic acids, benzylic C(sp³)−H bonds also could be functionalized to form 3,4-dihydroisocoumarin structures in a single step from 2-methyl benzoic acid derivatives. The utility of these protocols was demonstrated in large scale reactions and diversification of the γ-C(sp³)−H olefinated products.     

Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis

We present recent work of harmonic and signal analysis based on the complex Hardy space approach.     

Selective ethylene oligomerization with in‐situ‐generated chromium catalysts supported by trifluoromethyl‐containing ligands

A series of pyrrole‐containing diarylphosphine and diarylphosphine oxide ligands were prepared. The catalytic activity of the corresponding in‐situ‐generated chromium catalysts was investigated during selective ethylene oligomerization reactions. Variations in the ligand system were introduced by modifying the diarylphosphine and pyrrole moieties that affect the steric and electronic properties. Minor changes in the ligand structure and the composition of activators significantly changed the catalytic activity, selectivity toward linear alpha‐olefins (LAO) versus polyethylene (PE), and the distribution of oligomeric products. The presence of trifluoromethyl groups on the diphenyl rings in ligand 3 promoted oxidation to form the corresponding phosphine oxide structure, 3o , which dramatically enhanced the catalytic activity of ethylene trimerization. The in‐situ‐generated chromium complex based on 3o activated by DMAO (dry methylaluminoxane)/TIBA (triisobutylaluminum) was used to achieve activity of about 1250 g (mmol of Cr)⁻¹ h⁻¹ with 98.5 mol % 1‐hexene, along with a negligible amount of PE side product. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 444–450     

A steady barycentric Lagrange interpolation method for the 2D higher‐order time‐fractional telegraph equation with nonlocal boundary condition with error analysis

In this paper, we consider the numerical solution of the time‐fractional telegraph equation with a nonlocal boundary condition. A novel barycentric Lagrange interpolation collocation method is developed to solve this equation. Two difficulties have been sorted: the singularity of the integration and the higher accuracy. At the same, we put forward a steady barycentric Lagrange interpolation technique to overcome the new “Runge” phenomenon in computation. Error estimates of the barycentric Lagrange interpolation and the time‐fractional telegraph system for the present method are presented in Sobolev spaces. High convergence rates of the proposed method are obtained and are consisted with the numerical values. Especially in the time dimension, we get the error bound, for h‐refinement and for n_t‐density in the L₂ norms. The numerical results obtained show that the proposed numerical algorithm is accurate and computationally efficient for solving time‐fractional telegraph equation. Experiments demonstrate the high convergence rates of the proposed method are consisted with the theoretical values.     

Reductive Methylation of Homogeneous Primary β-Lauryl/myristyl 7/3 Polyethyleneoxy n = 3–18 Ethylamines under Phase-Transfer Catalysis Conditions

Homogeneous tertiary N,N-dimethyl-N-β-lauryl/myristyl 7/3 polyethyleneoxy n = 3–18 ethylamines, LM(EO)_nAT, are niche intermediates in the synthesis of homogeneous N-alkyl (C₁–C₁₈)-N,N-dimethyl-N-β-lauryl/myristyl 7/3 polyethyleneoxy n = 3–18 ethylammonium chlorides (unitary degree of oligomerization of ethylene oxide in the polyoxyethylene chain). This paper synthetically presents the dependence of the reductive methylation yields of homogeneous primary β-lauryl/myristyl 7/3 polyethyleneoxy n = 3–18 ethylamines, LM(EO)_nAP, on the reaction time (10–90 min), the temperature (70 °C), the molar ratio formic aldehyde /LM(EO)_nAP (1.1/1–2.5/1), the molar ratio HCOOH/LM(EO)_nAP (5/1), the degree of oligomerization of ethylene oxide in the homogeneous polyoxyethylene chain in the 3,6,9,12,18 series, and the structure of the phase-transfer catalysts. The steric effects of hydrophobic groups CH₃ and C₁₈H₃₇ grafted onto the ammonium function, and the micellar phenomena in the vicinity of their critical micellar concentration, directly proportional to the homogeneous degree of oligomerization, were highlighted. In all cases, a steady increase in reductive methylation yields was observed, with even quantitative values obtained. The high purity of the homologous series LM(EO)_nAT will allow their personalization as reference structures for the study of the evolution of basic colloidal characteristics useful in forecasting technological applications. LM(EO)_nAP were obtained either by direct amidoethylation (nucleophilic addition under basic catalysis of homogeneous lauryl/myristyl 7/3 polyethoxylated n = 3, 6, 9, 12, 18 alcohols, LM(EO)_nOH, to acrylamide monomer) or by cyanoethylation of LM(EO)_nOH under basic catalysis at 25–50 °C, in the presence of Fe²⁺ cations as oligomerization/polymerization inhibitor, followed by partial acid hydrolysis of homogeneous β-alkyl (C₁₂H₂₅/C₁₄H₂₉) 7/3 polyethyleneoxy n = 3, 6, 9, 12, 18 propionitriles, LM(EO)_nPN, to β-alkyl (C₁₂H₂₅/C₁₄H₂₉) 7/3 polyethyleneoxy n = 3, 6, 9, 12, 18 propionamides, LM(EO)_nPD, which led to LM(EO)_nAP by Hoffmann degradation. Homogeneous higher tertiary polyetheramines LM(EO)_nAT were structurally characterized.     

Interpreting a graph and constructing its derivative graph: stability and change in students’ conceptions

This present study investigated engineering students’ conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the incorporation of computers for the purposes of seeing the power of visualization, investigating worked examples given in steps and solving various questions related to the worked examples, assisting conceptual understanding, and/or providing feedback besides lectures in the classroom. Students were tested before and after being exposed to instruction on differentiation and integration by a diagnostic test measuring their understanding of major aspects of calculus. Follow-up interviews were conducted with 18 students. Analyses of the results revealed that A-level student's performance was improving more than non-A-level students, particularly in computer groups. The analyses of the students’ written and oral responses in all groups indicated that prototypes, poor understanding of the notion of limit, confusion between the process and the product, and difficulties in using graphical information to give meaning to symbolic representation account for the errors and the misconceptions identified.     

A role for M -matrices in modelling population growth

Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results, which are illustrated using simple examples. The material is presented in a format that makes it appropriate as background material for interesting applications based modelling assignments on undergraduate programmes in the mathematical sciences, applied sciences, economics and technology. All relevant properties of both positive-time systems and M-matrices are presented and clarified at the outset.     

Solvability of the ideal of all weight zero elements in bernstein algebras

We use a computer to verify that the ideal N of all weight zero elements of any (not necessarily finite dimensional) Bernstein algebra is solvable of index ≤4. We also use a computer to verify that N ² is nilpotent of index ≤9. We give three examples of Bernstein algebras which show that various hypotheses like finite dimensionality, finitely generatedA ² = A, are separately not enough to force N to be nilpotent.