Wide‐angle X‐ray diffraction and differential scanning calorimetry study of the crystallization of poly(ethylene naphthalate), poly(butylene naphthalate), and their copolymers

The crystallization behavior of a series of poly(ethylene‐co‐butylene naphthalate) (PEBN) random copolymers was studied. Wide‐angle X‐ray diffraction (WAXD) patterns showed that the crystallization of these copolymers could occur over the entire range of compositions. This resulted in the formation of poly(ethylene naphthalate) or poly(butylene naphthalate) crystals, depending on the composition of the copolymers. Sharp diffraction peaks were observed, except for 50/50 PEBN. Eutectic behavior was also observed. This showed isodimorphic cocrystallization of the PEBN copolymers. The variation of the enthalpy of fusion of the copolymers with the composition was estimated. The isothermal and nonisothermal crystallization kinetics were studied. The crystallization rates were found to decrease as the comonomer unit content increased. The tensile properties were also measured and were found to decrease as the butylene naphthalate content of the copolymers increased. For initially amorphous specimens, orientation was proved by WAXD patterns after drawing, but no crystalline reflections were observed. However, the fast crystallization of drawn specimens occurred when they were heated above the glass‐transition temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 843–860, 2004     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

Nontrivial Solutions for Resonant Hemivariational Inequalities

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants no. 2 P03A 003 25 and no. 4 T07A 027 26.     

A Family of Fifth-Order Runge-Kutta Pairs

The construction of a Runge-Kutta pair of order with the minimal number of stages requires the solution of a nonlinear system of order conditions in unknowns. We define a new family of pairs which includes pairs using function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of Kutta's simplifying assumption on the original system of the order conditions, i.e., that all the internal nodes of a method contributing to the estimation of the endpoint solution provide, at these nodes, cost-free second-order approximations to the true solution of any differential equation. In both cases the solution of the resulting system of nonlinear equations is completely classified and described in terms of five free parameters. Optimal Runge-Kutta pairs with respect to minimized truncation error coefficients, maximal phase-lag order and various stability characteristics are presented. These pairs were selected under the assumption that they are used in Local Extrapolation Mode (the propagated solution of a problem is the one provided by the fifth-order formula of the pair). Numerical results obtained by testing the new pairs over a standard set of test problems suggest a significant improvement in efficiency when using a specific pair of the new family with minimized truncation error coefficients, instead of some other existing pairs.

     

On the formation of estrone lactam esters of N,N-bis(2-chloroethyl)aminocinnamic acid isomers,p-N,N-bis(2-chloroethyl)aminophenylbutyric acid and their antitumor activity

New estrone-lactam esters, 17α-aza-D-homo-Δ^1,3,5(10)-estratrien-3-ol-17-one-N,N-bis(2-chloroethyl)-aminocinnamic isomers and p-N,N-bis(2-chloroethyl)aminophenylbutyrate have been synthesized and tested in P388 leukemia in vivo and P388 and L1210 leukemias in vitro. The effect of these compounds on SCE rates and on cell kinetics in cultured human lymphocytes was studied also.     

Nucleosides and nucleotides. Part 25.. Synthesis of a protected 1-(2′-deoxy-β-D-ribofuranosyl)-1 H-benzimidazole 3′-phosphate

1-(2′-Deoxy-5′-O-dimethoxytrityl-′-D -ribofuranosyl)-1 H-benzimidazole 3′-[(p-chlorophenyl)(2-cyanoethyl) phosphate] ( 6 ) has been synthesized from 1-(β-D -ribofuranosyl)-1H-benzimidazole ( 3b ) using regiospecific 2′-deoxygenation. The latter compound was obtained by glycosylation of benzimidazole with the D -ribose derivative 2 leading exclusively of the β-D -anomer.     

A convergence result for a sequence of distributed-parameter optimal control problems

In this paper, we consider a sequence of abstract optimal control problems by allowing the cost integrand, the partial differential operator, and the control constraint set all to vary simultaneously. Using the notions of -convergence of functions,G-convergence of operators, and Kuratowski-Mosco convergence of sets, we show that the values of the approximating problems converge to that of the limit problem. Also we show that a convergent sequence of optimal pairs for the approximating problems has a limit which is optimal for the limit problem. A concrete example of parabolic optimal control problems is worked out in detail.This research was supported by NSF Grant No. DMS-88-02688.     

Radon—Nikodym theorems for multimeasures and transition multimeasures

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Research supported by N. S. F. Grant DMS-8802688.     

A facile method to synthesize high‐molecular‐weight biobased polyesters from 2,5‐furandicarboxylic acid and long‐chain diols

In this study, biobased furan dicarboxylate polyesters have been prepared using 2,5‐furandicarboxylic acid (FDCA) and diols with high number of methylene groups (long‐chain diols), namely, 8, 9, 10, and 12. Because of the high boiling points of these diols, a modified procedure of the well‐known melt polycondensation was applied in this work. According to this, the dimethyl ester of FDCA (DMFD) reacted in the first transesterification stage with the corresponding diols forming bis‐hydroxy‐alkylene furan dicarboxylates (BHFD). In the second stage, the BHFD reacted with DMFD again at temperatures of 150–170 °C (for 4–5 h), and in the final stage, the temperature was raised to 210–230 °C (vacuum was applied for 2–3 h). The molecular weight of the polyesters and the content of oligomers, as was verified by gel permeation chromatography analysis, depend on the polycondensation time and temperature. The chemical structure of the polyesters was verified from ¹H NMR spectroscopy. All the polymers were found to be semicrystalline, with melting temperatures from 69 to 140 °C depending on the diol used. In addition, the mechanical properties also varied with the type of diol. The higher values were observed for poly(octylene 2,5‐furanoate), whereas the lowest values were observed for poly(dodecylene 2,5‐furanoate) with the higher number of methylene groups in its repeating unit. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2617–2632