Chemical inequivalence behavior of the protons attached to the same carbon in ethylene-propylene copolymer(EPC)

Six ethylene-propylene copolymer samples with different structural parameters were analyzed by ^1H NMR,^13C NMR and ^1H-^13C COSY in this paper.With the aid of the ^1H-^13C COSY spectra of ethylene-propylene copolymer,the chemical inequivalence behavior of the protons attached to the same carbon in the ethylene-propylene copolymer could be observed. Four basic types of chemical bonds were divided,and two kinds of main conformations were proposed to explain this phenomenon. Based on the calculation of conformation distribution,it can be proved that the explanation of this phenomenon was reasonable.

Frequency Dependence of Resonance Field of One-Dimensional Heisenberg Antiferromagnet KCuF3

The frequency dependence of the in-plane angular change of the antiferromagnetic resonance （AFMR） field of KCuF3 is systematically measured at frequencies ranging from 3.8 to 10.6 GHz at 4.2K. The effect of inequivalent g-tensors is found to gradually diminish with decreasing the frequency, and completely vanish when the frequency is decreased to the lower-frequency branch of C-band, while the effect of the effective anisotropy field is significantly enhanced with decreasing the frequency. The calculated AFMR field Hres based on the eight-sublattice model proposed by Yamada and Kato [J. Phys. Soc. Jpn. 63 （1994）289] is in good agreement with the experimental data.

Study on Photoluminescence Spectra of SiC

C SiC, 4H SiC and 6H SiC are the three kinds of silicon carbide (SiC) applied most extensively in semiconductor device fabrications. This work is engaged in analyzing their photoluminescence (PL) spectra and then summarizing the characteristics of the spectra. Special attention was paid to the inequiva lent sites existing in SiC and their effects on the PL spectra of SiC.

Macroscopic inequivalent entanglement witness in Heisenberg spin chain

Motivated by the wise idea of entanglement witness （EW）, we present an inequivalent entanglement witness （IEEW） that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication （SLOCC） in the Heisenberg spin chain. Since the IEEW is the absolute value of magnetization （M） that is a macroscopically measurable quantity, our conclusions provide a macroscopic method to detect inequivalent entanglement between microscopic spins, on the one hand, and clearly show that inequivalent entanglement can yield different macroscopic effects, on the other hand.

Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure

In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure. Therefore, it resolves a long-standing question.