Imine insertion into a late metal-carbon bond to form a stable amido complex

An arylrhodium(I) complex containing a labile dative ligand was prepared, and its reactivity toward aryl imines was investigated. The arylrhodium(I) complex (DPPE)Rh(C5H5N)(p-tol), 2, was isolated in 65% yield from [(DPPE)Rh(mu-Cl)]2, pyridine, and p-tolyllithium. Reaction of 2 with the aldimine (p-tol)CH=N(C6H4-p-CO2Me) (3a-Tol) gave the Rh amide insertion product 4 in 88% isolated yield. The solid-state structure of 4 was determined by single-crystal X-ray diffraction. The reaction of 2 with the electron-neutral and electron-rich aldimines (Ph)CH=NPh (3b) and (p-tol)CH=N(C6H4-p-OMe) (3c) also appeared to involve insertion, but the amido complexes formed from these insertions were not stable. Thus, reaction of 2 with 3b, followed by addition of Et3NHCl, gave the amine and ketimine products (Ph)(p-tol)CH-NHPh, 5, and (p-tol)(Ph)C=N(Ph), 6, in 25% and 50% yields. Several lines of data indicate that these products are formed by a sequence of transformations involving insertion of imine to give a Rh amide intermediate, beta-hydrogen elimination, cyclometalation to form a bound imine and H2, and protonolysis of the metallacycle upon addition of Et3NHCl. Consistent with this proposal, the proposed metallacycle containing the ortho-metalated ketimine ligand (p-tol)2C=N(C6H4-p-OMe) was isolated and characterized by single-crystal X-ray diffraction.     

Fully aromatic thermotropic liquid crystalline polyesters of substituted 4,4′-biphenols. IV. Homopolyesters with terephthalic acid and copolyesters with terephthalic acid and 4-hydroxybenzoic acid

A series of fully aromatic thermotropic polyesters based on mono-, di-, and tetra-substituted biphenols was prepared by the melt polycondensation method and examined for their thermotropic behavior by a variety of experimental techniques. The homopolyesters obtained from substituted biphenols containing either one phenyl or two phenyl groups as substituent(s) and TA formed nematic melts, but the homopolymers of the substituted biphenols containing either four sec-butyl groups or two tert-butyl groups with TA had melting transitions, T_m, above 400°C. Thus, it was not possible to determine whether they formed nematic melts. On copolymerization with 30 mol % HBA most of the resulting copolyesters had much lower T_m values, compared to those of respective homopolyesters, and the copolymers of the biphenol monomer containing the tert-butyl groups formed a nematic melt at an observable temperature. However, the copolymer of the biphenol with sec-butyl groups still had a T_m above 400°C. © 1993 John Wiley & Sons, Inc.     

Quantitative electrochemical formation of phosphotungstate heteropolyanion blues

The optical and ESR spectra of electrochemically reduced phosphotungstate and polyphosphotungstate anions in phosphoric acid were examined as quantitative functions of W⁵⁺ concentration. The optical spectra obey Beer-Lambert laws and are similar to the spectra of reduced silicotungstate anions, indicating the secondary nature of the central cluster in the keggin structure with regard to interactions with the reduction electron. ESR spectra indicate an equivalent correspondence for the W⁵⁺ concentration and unpaired spins for the reduced polyphosphotungstate anion but for the reduced phosphotungstate anion monomer the unpaired spin concentration estimated by ESR was much lower than the W⁵⁺ concentration. Reacting reduced phosphotungstate anions with oxygen showed a I-electron reduction of the oxygen molecule with concomitant oxidation of W⁵⁺ to W⁶⁺ and possibly production of high-molecular-weight, polyanion clusters.     

Combinatorial invariants for nets of conics in $$\mathrm {PG}(2,q)$$ PG ( 2 , q )

Designs, Codes and Cryptography - The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics...     

The finite element approximation of a coupled reaction-diffusion problem with non-Lipschitz nonlinearities

Summary. A coupled semilinear elliptic problem modelling an irreversible, isothermal chemical reaction is introduced, and discretised using the usual piecewise linear Galerkin finite element approximation. An interesting feature of the problem is that a reaction order of less than one gives rise to a "dead core" region. Initially, one reactant is assumed to be acting as a catalyst and is kept constant. It is shown that error bounds previously obtained for a scheme involving numerical integration can be improved upon by considering a quadratic regularisation of the nonlinear term. This technique is then applied to the full coupled problem, and optimal and error bounds are proved in the absence of quadrature. For a scheme involving numerical integration, bounds similar to those obtained for the catalyst problem are shown to hold. Received May 25, 1993 / Revised version received July 5, 1994     

Optimal Control of an <Emphasis Type="Italic">M/E</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>/1 Queueing System with a Removable Service Station

This paper studies the optimal operation of an M/E _k /1 queueing system with a removable service station under steady-state conditions. Analytic closed-form solutions of the controllable M/E _k /1 queueing system are derived. This is a generalization of the controllable M/M/1, the ordinary M/E _k /1, and the ordinary M/M/1 queueing systems in the literature. We prove that the probability that the service station is busy in the steady-state is equal to the traffic intensity. Following the construction of the expected cost function per unit time, we determine the optimal operating policy at minimum cost.     

An Algorithm for the Economic Design of <Emphasis Type="Italic">np</Emphasis> Charts for a Multiplicity of Assignable Causes

Chiu, in 1976, studied the economic design of np charts for processes subject to a multiplicity of assignable causes. Chiu developed a two-step minimization procedure to obtain the three control variables, namely, the sampling interval, the sample size and the acceptance number. Although Chiu's two-step minimization procedure is simple, applicable and down to earth, it is rather inefficient and has some drawbacks. This paper presents an algorithm to overcome these drawbacks. The results and the execution times of all numerical examples show that the accuracy and the efficiency of the algorithm is reasonably good.     

A Heuristic Decomposition Algorithm for Scheduling Problems on Mixed Graphs

We consider a scheduling problem where a set of n jobs has to be processed on a set of m machines and arbitrary precedence constraints between operations are given. Moreover, for any two operations i and j values a _ij >0 and a _ji >0 may be given where a _ij is the minimal difference between the starting times of operations i and j when operation i is processed first. Often, the objective is to minimize the makespan but we consider also arbitrary regular criteria. Even the special cases of the classical job shop problem J//C_max belong to the set of NP-hard problems. Therefore, approximation or heuristic algorithms are necessary to handle large-dimension problems. Based on the mixed graph model we give a heuristic decomposition algorithm for such a problem, i.e. the initial problem is partitioned into subproblems that can be solved exactly or approximately with a small error bound. These subproblems are obtained by a relaxation of a subset of the set of undirected edges of the mixed graph. The subproblems are successively solved and a proportion of the results obtained for one subproblem is kept for further subproblem definitions. Numerical results of the algorithm presented here are given.     

Chaos in thermal pulse combustion

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not yet been reproduced experimentally, but similarities are demonstrated between the dynamic features of pressure fluctuations in the model and experiment. Correlation dimension, Kolmogorov entropy, and projections of reconstructed attractors using chaotic time series analysis are demonstrated to be useful in classifying dynamical behavior of the experimental combustor and for comparison of test data to the model results. Ways to improve the model are suggested. (c) 1995 American Institute of Physics.