Strict isomorphism between butylene succinate and butylene fumarate in poly(butylene succinate-co-butylene fumarate) (PBSF) was revealed by DSC and wide-angle X-ray diffraction results. They adopt the same crystal modification, with only a little difference in crystal lattice parameters. The melting point of the copolymer increases linearly with increasing molar ratio of butylene fumarate and the melting enthalpy hardly changes, which meet the requirement of strict isomorphism. The introduction of unsaturated comonomer, fumaric acid, into PBS can enhance the total crystallization rate and the radial growth rate of spherulites. Consequently, PBF and PBSF are highly efficient polymeric nucleating agents for PBS and its copolymers. In this work, strict isomorphism provides us a new method to find polymeric nucleating agent.

Abstract. Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.

This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.

We study the numerical radius of Lipschitz operators on Banach spaces via the Lipschitz numerical index, which is an analogue of the numerical index in Banach space theory. We give a characterization of the numerical radius and obtain a necessary and sufficient condition for Banach spaces to have Lipschitz numerical index 1. As an application, we show that real lush spaces and C-rich subspaces have Lipschitz numerical index 1. Moreover, using the Gâteaux differentiability of Lipschitz operators, we characterize the Lipschitz numerical index of separable Banach spaces with the RNP. Finally, we prove that the Lipschitz numerical index has the stability properties for the c0-, l1-, and l∞-sums of spaces and vector-valued function spaces. From this, we show that the C(K) spaces, L1(µ)-spaces and L∞(ν) spaces have Lipschitz numerical index 1.

Four similar Mn­(II) metal–organic frameworks (MOFs), {[Mn2(nbtc)­(H2O)2(S)]­·S­·0.5H2O} n [S = DMF (1), DMA (2), NMP (3), DEF (4)] (DMF = N,N′-dimethylformamide, DMA = N,N′-dimethylacetamide, NMP = N-methyl-2-pyrrolidinone, DEF = N,N′-diethylformamide), have been assembled solvothermally from the nitro and carboxyl doubly functionalized ligand 6,6′-dinitro-2,2′,4,4′-biphenyl tetracarboxylic acid (H4nbtc) and characterized by single-crystal X-ray diffraction, elemental analyses, infrared spectroscopy, thermogravimetric analyses, and powder X-ray diffraction. All MOFs exhibit unique three-dimensional double-walled open-frameworks with one-dimensional parallelogram channels and have guest/coordinated water and carbonyl solvent molecules, reasonably providing a good example of the competitive behavior of water and carbonyl solvent molecules and an excellent candidate for studying the single crystal coordinated solvent exchange transformations. Interestingly, because of the different steric hindrance of the series of coordinated carbonyl solvent molecules, the MOFs’ structural differences primarily display on the coordination mode of O1W and coordination sphere of Mn1/Mn2 between MOFs 1(4) and 2(3). And it is also found that a small variation of the lattice parameters, unit cell volume, and density occurs. Furthermore, MOFs 1–3 show solvent-induced single-crystal-to-single-crystal (SCSC) transformations, which only exchange coordinated and guest carbonyl solvent molecules (DMF, DMA, NMP). And fortunately, the available single crystal data of 2′ and 2″ have been collected, which were obtained by soaking 1 and 3 in DMA solution for 5 days and 7 days respectively, and they have the same molecular formula as 2 but slightly different structures from 2. In such transformations, the complete solvent exchanging time discrimination of 2 to 3 (10 days), 3 to 2 (7 days), 3 to 1 (5 days), 1 to 2 (5 days), and 2 to 1 (3 days) is susceptible to the size of carbonyl solvent molecules (NMP > DMA > DMF), and the metal coordination sphere of SCSC regenerated samples is influenced not only by the character of coordinated carbonyl solvents but also the nature of mother crystals. In addition, MOFs 1–4 exhibit antiferromagnetic coupling, confirmed through magnetic susceptibility measurements.