Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

关于负超几何分布期望与方差算法的注记

研究了非还原取样模型中负超几何随机变量的联合分布,得到了若干有用的推论.据此给出了负超几何分布的期望和方差的一种分解算法.     

Mechanical property and deformation mechanism of gold nanowire with non-uniform distribution of twinned boundaries:A molecular dynamics simulation study

The mechanical property and deformation mechanism of twinned gold nanowire with non-uniform distribution of twinned boundaries(TBs) are studied by the molecular dynamics(MD) method. It is found that the twin boundary spacing(TBS) has a great effect on the strength and plasticity of the nanowires with uniform distribution of TBs. And the strength enhances with the decrease of TBS, while its plasticity declines. For the nanowires with non-uniform distribution of TBs, the differences in distribution among different TBSs have little effect on the Young's modulus or strength, and the compromise in strength appears. But the differences have a remarkable effect on the plasticity of twinned gold nanowire. The twinned gold nanowire with higher local symmetry ratio has better plasticity. The initial dislocations always form in the largest TBS and the fracture always appears at or near the twin boundaries adjacent to the smallest TBS. Some simulation results are consistent with the experimental results.     

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.     

Modifying the physicochemical properties,solubility and foaming capacity of milk proteins by ultrasound-assisted alkaline pH-shifting treatment

This study investigated the effects of different treatment of alkaline pH-shifting on milk protein concentrate (MPC), micellar casein concentrate (MCC) and whey protein isolate (WPI) assisted by the same ultrasound conditions, including changes in the physicochemical properties, solubility and foaming capacity. The solubility of milk proteins had a significant increase with gradual enhancement of ultrasound-assisted alkaline pH-shifting (p < 0.05), especially for MCC up to 99.50 %. Also, treatment made a significant decline in the particle size of MPC and MCC, as well as the turbidity of the proteins (p < 0.05). The foaming capacity of MPC, MCC, and WPI was all improved, especially at pH 11, and at this pH, the milk protein also showed the highest surface hydrophobicity. The best foaming capacity at pH 11 was the result of the combined effect of particle size, potential, protein conformation, solubility, and surface hydrophobicity. In conclusion, ultrasound-assisted pH-shifting treatment was found to be effective in improving the physicochemical properties and solubility and foaming capacity of milk proteins, especially MCC, with promising application prospect in food industry.     

Coupling characteristics of laterally coupled gratings with slots

Laterally-coupled ridge-waveguide distributed feedback lasers fabricated without epitaxial regrowth steps have the advantages of process simplification and low cost. We present a laterally coupled grating with slots. The slots etched between the ridge and grating area are designed to suppress the lateral diffusion of carriers and to reduce the influence of the aspect-ratio-dependent-etching effect on the grating morphology in the etching process. Moreover, the grating height in this structure can be decreased to lower the aspect ratio significantly, which is advantageous over the conventional laterally coupled ridge waveguide gratings. The effects of five main structural parameters on the coupling characteristics of gratings are studied by MODE Solutions. It is found that varying the lateral width of the grating can be used as an effective way to tune the coupling strength; narrow slots (100 nm and 300 nm) and wide ridge (2 μm-4 μm) promote the stability of grating coupling coefficient and device performance. It is important to note that the grating bottom should be fabricated precisely. The comparative study of carrier distribution and mode field distribution shows that the introduction of narrow slots can strengthen the competitive advantage and stability of the fundamental mode.     

Synthesis,Crystal Structure,and Selected Properties of [Au(S2CNH2)2]SCN: A Precursor for Gold Macro-Needles Consisting of Gold Nanoparticles Glued by Graphitic Carbon Nitride

A new preparation route is developed for the synthesis of needle-like crystals of [Au(S₂CNH₂)₂]SCN, which avoids disproportionation of the Au^I salt used as a starting material. In the crystal structure, the two crystallographically independent Au^III centers are in a square-planar environment of two S₂CNH₂ ligands. The Hirshfeld surface analysis reveals the presence of noncovalent intermolecular S⋅⋅⋅S interactions, which are essential for the spatial arrangement of the molecules. Density functional theory (DFT) calculations including dispersion and damping corrections result in a unit cell volume very close to the value determined experimentally. Thermal decomposition in an inert atmosphere generates black needles with lengths of up to 500 μm. X-ray powder diffraction and pair distribution function analyses demonstrate that the needles are composed of nanosized crystals with a volume-weighted average domain size of 20(1) nm. According to results of X-ray photoemission experiments, the black needles are covered by a nitrogen-rich carbon nitride with composition near (CN)₂N. ¹³C solid-state NMR investigations indicate that two different carbon species are present, with signals corresponding well to heptazine units as in melon and triazine units as in poly(triazin imide) type compounds. Scanning transmission electron microscopy tomography evidences that the needles are composed of slightly elongated nanoparticles.     

Experimental determination of interfacial energy for solid Al in the Al-Sn-Mg eutectic system with Bridgman-type apparatus

The equilibrated grain boundary groove shape of solid Al in equilibrium with Al-Sn-Mg eutectic liquid was observed by using a Bridgman type directional solidification apparatus. The ratio of the thermal conductivity of the equilibrated liquid to the thermal conductivity of solid Al has been obtained as 0.91. In addition, the average Gibbs-Thomson coefficient, $\bar{\mathrm{\Gamma }}=(4.20\pm 0.35)\times {10}^{-8}\mathrm{Km}$, the solid-liquid interfacial energy, ${\sigma }_{SL}=180.68\pm 23.48\text{mJ}/{\text{m}}^2$ and the grain boundary energy, ${\sigma }_{GB}=309.30\pm 29.47\text{mJ}/{\text{m}}^2$, in the Al/Al-Sn-Mg system have been calculated from the measured grain boundary shapes.