Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Sharper uncertainty principles associated with Lp-norm

Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the L^p-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.     

Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

Strain induced strengthening of soft thermoplastic polyurethanes under cyclic deformation

We investigate the cyclic mechanical behavior in uniaxial tension of three different commercial thermoplastic polyurethane elastomers (TPU) often considered as a sustainable replacement for common filled elastomers. All TPU have similar hard segment contents and linear moduli but sensibly different large strain properties as shown by X-ray analysis. Despite these differences, we found a stiffening effect after conditioning in step cyclic loading which greatly differs from the common softening (also referred as Mullins effect) observed in chemically crosslinked filled rubbers. We propose that this self-reinforcement is related to the fragmentation of hard domains, naturally present in TPU, in smaller but more numerous sub-units that may act as new physical crosslinking points. The proposed stiffening mechanism is not dissimilar to the strain-induced crystallization observed in stretched natural rubber, but it presents a persistent nature. In particular, it may cause a local reinforcement where an inhomogeneous strain field is present, as is the case of a crack propagating in cyclic fatigue, providing a potential explanation for the well-known toughness and wear resistance of TPU.     

单斜氧化锆表面水合和脱水的动态模拟

常用的氧化物负载金属催化剂通常在水相中制备，且在使用前常常需要经过煅烧. 因此，氧化物载体表面的水合和脱水过程对于负载型金属催化剂的真实建模至关重要. 通过第一性原理分子动力学模拟，本文考察了温和温度下无水单斜氧化锆(111)表面在显式溶剂水中的演化. 在模拟过程中，所有的双重配位桥位氧位点很快被溶剂水质子化，形成酸性羟基(HO_L)，并在锆原子上留下碱性羟基(HO^*). 这些碱性羟基(HO^*)可以与表面未解离的吸附水分子(H₂O^*$)进行活跃的质子交换，进而在表面自由扩散. 在273 K到373 K的温度范围下，第一性原理分子动力学水相模拟可以得到一种较为确定的、有代表性的平衡水合单斜氧化锆(111)表面，其表面锆原子上覆盖度(θ)为0.75. 随后，为了模拟低于800 K的温和煅烧温度下的表面脱水过程，本文使用密度泛函理论计算了表面水分子的逐步脱附自由能. 通过获得表面的脱水相图，总结了不同煅烧温度下有代表性的、部分水合的单斜氧化锆(111)表面(0.25≤θ<0.75). 这些水合单斜氧化锆(111)表面具有重要的理论意义，可以方便快捷地被应用于氧化锆催化剂及氧化锆负载金属催化剂的真实建模与模拟.