LaRC TPI 1500 series polymers

The crystallization behavior and the melt flow properties of two batches of 1500 series LaRC-TPI polymers from Mitsui Toatsu Chemicals (MTC) were investigated. The characterization methods include Differential Scanning Calorimetry, the x ray diffractography and the melt rheology. The as-received materials possess initial crystalline melting peak temperatures of 295 and 305 C, respectively. These materials are less readily recrystallizable at elevated temperatures when compared to other semicrystalline thermoplastics. For the samples annealed at temperatures below 330 C, a semicrystalline polymer can be obtained. On the other hand, a purely amorphous structure is realized in the samples annealed at temperatures above 330 C. Isothermal crystallization kinetics were studied by means of the simple Avrami equation. The viscoelastic properties at elevated temperatures below and above glass transition temperature of the polymers were measured. Information with regard to the molecule sizes and distributions in these polymers were also extracted from melt rheology

The Happer's puzzle degeneracies and Yangian

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for condensed vapor of $^{87}$Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of $Y(sl(2))$.Comment: 8 pages, Latex fil