Synthesis of a model cyclic triblock terpolymer of styrene,isoprene, and methyl methacrylate

The synthesis of a model cyclic triblock terpolymer [cyclic(S‐b‐I‐b‐MMA] of styrene (S), isoprene (I), and methyl methacrylate (MMA) was achieved by the end‐to‐end intramolecular amidation reaction of the corresponding linear α,ω‐amino acid precursor [S‐b‐I‐b‐MMA] under high‐dilution conditions. The linear precursor was synthesized by the sequential anionic polymerization of S, I, and MMA with 2,2,5,5‐tetramethyl‐1‐(3‐lithiopropyl)‐1‐aza‐2,5‐disilacyclopentane as an initiator and amine generator and 4‐bromo‐1,1,1‐trimethoxybutane as a terminator and carboxylic acid generator. The separation of the unreacted linear polymer from the cyclic terpolymer was facilitated by the transformation of the unreacted species into high molecular weight polymers by the evaporation of the reaction solvent and the continuation of the reaction under high‐concentration conditions. The intermediate materials and the final cyclic terpolymer, characterized by size exclusion chromatography, vapor pressure osmometry, thin‐layer chromatography, IR and NMR spectroscopy, exhibited high molecular weight and compositional homogeneity. Dilute‐solution viscosity measurements were used as an additional proof of the cyclic structure. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1476–1483, 2002     

Representations of unbounded optimization problems as integer programs

Any optimization problem in a finite structure can be represented as an integer or mixed-integer program in integral quantities.We show that, when an optimization problem on an unbounded structure has such a representation, it is very close to a linear programming problem, in the specific sense described in the following results. We also show that, if an optimization problem has such a representation, no more thann+2 equality constraints need be used, wheren is the number of variables of the problem.We obtain a necessary and sufficient condition for a functionf:SZ, withS Z ⁿ , to have a rational model in Meyer's sense, and show that Ibaraki models are a proper subset of Meyer models.This research was supported by NSF Grant No. GP-37510X1 and ONR Contract No. N00014-75-C0621, NR047-048.     

The alternating basis algorithm for assignment problems

The purpose of this paper is to present a new primal extreme point algorithm for solving assignment problems which both circumvents and exploits degeneracy. The algorithm is based on the observation that the degeneracy difficulties of the simplex method result from the unnecessary inspection of alternative basis representations of the extreme points. This paper characterizes a subsetQ of all bases that are capable of leading to an optimal solution to the problem if one exists. Using this characterization, an extreme point algorithm is developed which considers only those bases inQ. Computational results disclose that the new algorithm is substantially more efficient than previously developed primal and primal-dual extreme point (simplex) methods for assignment problems.     

STUDY ON POLYSULFONE-POLYESTER BLOCK COPOLYMERS

Synthesis and characterization of a series of Polysulfone (PSF)-Polyester (PEs) block copolymers were studied.The degree of randomness (B) of these block eopolymers was calculated from the intensities of their proton signals in ~1H NMR spectra and lies in the region of 0相似文献   

Faster GC analyses performed by flow programming in short capillary columns

The technique of programming the carrier gas flow rate in gas chromatography, especially in connection with the use of capillary columns shorter than 10 m can significantly accelerate GC analyses. Equations for calculation of the parameters of the exponential flow function and retention data are described. The effects of flow programming in a short capillary column are shown in a few chromatograms. Different programming rates are tested and compared with temperature programming.     

A model for quantitatively describing linear velocity programming in capillary SFC

Summary Linear velocity in capillary SFC is commonly controlled by restricting capillaries. In this paper, a model is described that quantitatively predicts the linear velocity of a supercritical fluid in SFC using tapered or ceramic frittype restrictors. In this model, the flow from the restricting capillary is assumed to be an isentropic expansion. The variation of the linear velocity as a function of pressure, temperature and cross-sectional area of the restricting aperture was predicted by this model. This predictive capability is important to the use of gradient programming in capillary SFC. Finally, the ideal variable restrictor for gradient programming was found to be one that could reversibly increase or decrease the linear velocity independent of the pressure, temperature, and/or density conditions used to create the gradient.     

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.     

Efficient algorithms for solving rank two and rank three bilinear programming problems

Finitely convergent algorithms for solving rank two and three bilinear programming problems are proposed. A rank k bilinear programming problem is a nonconvex quadratic programming problem with the following structure: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaacaWFTbGaa8% xAaiaa-5gacaWFPbGaa8xBaiaa-LgacaWF6bGaa8xzaiaa-bcacaWF% 7bacbiGaa43yamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+Hhaca% GFRaGaa4hzamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+LhacaGF% RaWaaabuaeaacaGFJbWaa0baaSqaaiaa+PgaaeaacaGF0baaaOGaam% iEaiabl+y6NjaadsgadaqhaaWcbaGaamOAaaqaaiaadshaaaGccaWG% 5bGaaiiFaaWcbaGaa8NAaiaa-1dacaWFXaaabeqdcqGHris5aOGaa4% hEaiabgIGiolaa+HfacaGFSaGaa4xEaiabgIGiolaa+LfacaWF9bGa% a8hlaaaa!5D2E!\[minimize \{ c_0^t x + d_0^t y + \sum\limits_{j = 1} {c_j^t xd_j^t y|} x \in X,y \in Y\} ,\]where X Rⁿ¹ and Y R ⁿ² are non-empty and bounded polytopes. We show that a variant of parametric simplex algorithm can solve large scale rank two bilinear programming problems efficiently. Also, we show that a cutting-cake algorithm, a more elaborate variant of parametric simplex algorithm can solve medium scale rank three problems.This research was supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. 63490010.     

On solving a D.C. programming problem by a sequence of linear programs

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ⁿ . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.