Kristallstruktur und Konformation eines linearen Pentapyrrols

The crystal structure of the pentapyrrin1 was determined by X-ray diffraction methodes at two temperatures (298K and 97K). It is the first structure determination of a linear polypyrrole with more than four pyrrole rings. In the crystal, the molecule is located on a crystallographic two-fold axis, which passes through the central pyrrole ring. It assumes a helical overall-conformation, which is stabilized by intramolecular hydrogen bonding. The acidic proton at the nitrogen atom of the central pyrrolic ring is disordered, being observed with half occupancy at two symmetry-equivalent positions off the crystallographic diad. Attempts to remove the disorder by cooling to 97K were unsuccessful, since no indication for a phase transition was detected.

     

Rheological investigation of the influence of molecular structure on natural and accelerated UV degradation of linear low density polyethylene

Metallocene and Ziegler-Natta (ZN) linear low density polyethylenes (LLDPEs) of different branch types and contents as well as linear high density polyethylene (HDPE) were exposed to natural and accelerated weather conditions. The degree of UV degradation of exposed samples was measured by rheological techniques and results were compared with unexposed polymers. Dynamic shear measurements were performed in an ARES rheometer in the linear viscoelastic range. The degree of enhancement or reduction in viscosity and elasticity was used as a measure of the degree of cross-linking or chain scission, respectively. The degradation results of LLDPE suggest that both cross-linking and chain scission are taking place. Chain scission dominated the degradation at high levels of short chain branching (SCB) and long exposure times. The degradation mechanism of m-LLDPE and ZN-LLDPE is similar; however, m-LLDPE showed a higher degradation rate than ZN-LLDPE of similar M_w and average SCB. ZN-LLDPE was found to be more stable than a similar m-LLDPE. Comonomer type had little influence on degradation. Dynamic shear rheology was very useful in revealing the influence of different molecular parameters and it exposed the degradation mechanism.     

Isotachophoretic separation of alkylsulfonates and determination of methanesulfonic acid as main component and as trace component in pharmaceutical drug substances

Alkylsulfonates from methanesulfonic acid to decanesulfonic acid were separated by isotachophoresis with conductivity detection in a common electrolyte system at pH 4.8. The electrolyte system consisted of 10 mM HCl buffered with epsilon-aminocaproic acid (pH 4.8) and 0.1% methylhydroxyethylcellulose (MHEC) acting as the leading electrolyte. The terminating electrolyte was 20 mM caproic acid also containing 0.05% MHEC. Current settings of 250 microA for the first and 50 microA for the second capillary were applied. On one hand, the method was applied to the determination of the content of methanesulfonate as the salt forming agent (mesilate) in a recently registered drug substance. The results obtained by ITP were compared with an orthogonal titration method. On the other hand, due to the column-coupling configuration of the electrophoretic instrument, the method could be extended to the trace determination in the ppm range in order to monitor methanesulfonic acid as an impurity in a drug substance. The validation confirmed the linearity of the method between 1 and 10 mg/l, limits of detection and quantification below 1 mg/l, recovery rates from 92.4 to 95.4%, and repeatability with a R.S.D. of 3.8% (six runs with a 4 mg/l spiked sample). Finally, three batches of a newly produced drug substance could be checked for methanesulfonic acid giving results of below 0.0014% (concentration related to the drug substance).     

General analysis of the measurements of the lateral crystal lattice moduli of semicrystalline polymers by x-ray diffraction and the application to nylon 6

A mathematical representation based on a linear elastic theory is proposed by which one may investigate the dependences of molecular orientation and crystallinity on the crystal lattice moduli and linear thermal expansion coefficients in the direction perpendicular to the chain axis as commonly measured by x-ray diffraction. In the theoretical calculation, a previously introduced model was employed in which oriented crystalline phase is surrounded by oriented amorphous phase and the strains of the two phases at the boundary are identical. The mathematical analysis indicated that the lateral crystal lattice moduli and linear thermal coefficients as measured by x-ray diffraction may be different from the intrinsic crystal moduli and linear thermal coefficients of a crystal unit cell, depending on the structure of the polymer solid. The numerical calculation was applied to nylon 6. As a result, it may be confirmed that the lateral crystal lattice moduli measured by x-ray diffraction are sensitive to the morphology of the bulk speciments and close to the intrinsic crystal moduli if the morphology of the test specimen can be represented by a parallel model with respect to the original stretching longitudinal direction.     

Optimizing control of simulated moving beds--linear isotherm

A new optimization based adaptive control strategy for simulated moving beds (SMBs) is proposed. A linearized reduced order model, which accounts for the periodic nature of the SMB process, is used for online optimization and control. The manipulated variables are the four inlet flow rates, the outputs are the raffinate and extract concentrations. Concentration measurements at the raffinate and extract outlets are used as the feedback information. The state estimate from the periodic Kalman filter is used for the prediction of the outlet concentrations over a chosen horizon. Predicted outlet concentrations are the basis for the calculation of the optimal input adjustments, which maximize the productivity and minimize the desorbent consumption subject to constraints on product purities. The realization of this concept is discussed and the implementation on a virtual eight column SMB platform is assessed, in the case of binary linear systems. For a whole series of typical plant disturbances it is shown that the proposed approach is effective in minimizing off-spec products and in achieving optimal SMB operation, also in the case where there are significant model uncertainties.     

Comparative analysis of affine scaling algorithms based on simplifying assumptions

We analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions. We show that, under a strong probabilistic assumption regarding the distribution of the data in an iteration, the decrease in the primal potential function will be with high probability, compared to the guaranteed(1). ( 2n is a parameter in the potential function andn is the number of variables.) Under the same assumption, we further show that the objective reduction rate of Dikin's affine scaling algorithm is with high probability, compared to no guaranteed convergence rate.Research supported in part by NSF Grant DDM-8922636.     

Improving the rate of convergence of interior point methods for linear programming

This paper proposes a procedure for improving the rate of convergence of interior point methods for linear programming. If (x ^k ) is the sequence generated by an interior point method, the procedure derives an auxiliary sequence ( ). Under the suitable assumptions it is shown that the sequence ( ) converges superlinearly faster to the solution than (x ^k ). Application of the procedure to the projective and afflne scaling algorithms is discussed and some computational illustration is provided.     

Partially and totally asynchronous algorithms for linear complementarity problems

A unified treatment is given for partially and totally asynchronous parallel successive overrelaxation (SOR) algorithms for the linear complementarity problem. Convergence conditions are established and compared to previous results. Convergence of the partially asynchronous method for the symmetric linear complementarity problem can be guaranteed if the relaxation factor is sufficiently small. Unlike previous results, this relaxation factor interval does not depend explicitly on problem size.This material is based on research supported by the Air Force Office of Scientific Research Grant No. AFOSR-89-0410.The author wishes to thank the referee for pointing out how to improve the bound (12). The same technique can be used to reduce the factorn in Ref. 5, p. 553, to .     

A note on a characterization of P-matrices

In this note we show that the characterization results for P-matrices due to K.G. Murty and A. Tamir which state that a given square matrixM of ordern is a P-matrix if and only if the linear complementarity problem (q, M) has a unique solution for allq in a specified finite subset of ⁿ depending onM are incorrect whenn > 3.Research supported by Dr. K.S. Krishnan (DAE) fellowship for research in Mathematics and Computer Science, Bombay, India.     

On the convergence of the affine-scaling algorithm

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm concerns its convergence in the presence of degeneracy. In this paper, we give new convergence results for this algorithm that do not require any non-degeneracy assumption on the problem. In particular, we show that if the stepsize choice of either Dikin or Barnes or Vanderbei, et al. is used, then the algorithm generates iterates that converge at least linearly with a convergence ratio of , wheren is the number of variables and (0,1] is a certain stepsize ratio. For one particular stepsize choice which is an extension of that of Barnes, we show that the cost of the limit point is within O(/(1–)) of the optimal cost and, for sufficiently small (roughly, proportional to how close the cost of the nonoptimal vertices are to the optimal cost), is exactly optimal. We prove the latter result by using an unusual proof technique, that of analyzing the ergodic convergence of the corresponding dual vectors. For the special case of network flow problems with integer data, we show that it suffices to take = 1/(6mC), wherem is the number of constraints andC is the sum of the cost coefficients, to attain exact optimality.This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 (Center for Intelligent Control Systems), by the National Science Foundation, grant NSF-ECS-8519058, and by the Science and Engineering Research Board of McMaster University.