On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

烯烃对噻吩在介孔分子筛Al-MCM-41活性位物种上吸附脱硫机制的影响

采用后嫁接法制备了不同铝负载量的Al-MCM-41分子筛。运用XRD、N₂吸附-脱附、NH₃-TPD、Py-FTIR等方法对分子筛进行物性表征，利用固定床评价其对噻吩的吸附性能。通过将分子筛吸附噻吩能力与分子筛的酸性质及织构性质进行关联，考察烯烃存在对Al-MCM-41活性位物种吸附脱硫机制的影响。结果表明，铝物种的引入即产生了B酸中心，也同时产生了两种类型的L酸中心L₁和L₂。引入低含量铝物种利于形成B酸中心和L₁型酸中心，引入高含量铝物种利于形成L₂型酸中心。其中，L₂型酸中心对噻吩的吸附效果最佳。烯烃和噻吩在B酸中心发生竞争吸附和催化转化反应，且催化转化反应占主导地位。L₂酸中心的存在促进了B酸中心上的催化转化反应，其所生成的大分子硫化物取代噻吩吸附在分子筛酸活性中心上提高了Al-MCM-41分子筛的饱和吸附硫容量。     

Nanoscale detection of faint machinery vibration using the NV center in diamond

We propose a novel method for detection of the faint machinery vibration at the nanometer resolution based on the spin magnetic resonant effect. A suspension magnet acts as a vibration sensor to transfer the vibration signals as the magnetic field fluctuation to excite the spin magnetic resonance. Due to the high sensitivity of the magnetic field of the nitrogen-vacancy center in diamond, the theoretical detection limit of mechanical vibration is as high as 5.7 nm, and the actual measurement resolution reached 12.8 nm, and proved the potential for further improvement to ∼pm resolution. The feasibility of this method is verified by dynamic tests. This method provides a novel approach for the detection of micro-mechanical vibrations.     

多片导模法蓝宝石晶体的缺陷研究

使用导模法(EFG)生长了多片a面蓝宝石晶体。显微拉曼光谱结合电感耦合等离子体发射光谱(ICP-AES)测试得出晶体的气泡中可能存在含S化合物。晶体表面明显的生长条纹主要与温度、生长速度的波动以及模具的加工精度有关。化学腐蚀分析表明晶体位错密度在4.2×10⁴ cm^-2,未存在小角度晶界缺陷,双晶摇摆曲线半峰宽(FWHM)为70.63″。由于采用石墨保温材料,晶体中存在F心与F⁺色心。晶体在400~3 000 nm波段透过率高于80%,空气中退火后可减弱色心吸收。本文研究结果可为蓝宝石晶体缺陷形成理论研究提供参考,也可为导模法蓝宝石工业生产技术改进提供借鉴。     

Not All Fluorescent Nanodiamonds Are Created Equal: A Comparative Study

Fluorescent nanodiamonds (FNDs) are vital to many emerging nanotechnological applications, from bioimaging and sensing to quantum nanophotonics. Yet, understanding and engineering the properties of fluorescent defects in nanodiamonds remain challenging. The most comprehensive study to date is presented, of the optical and physical properties of five different nanodiamond samples, in which fluorescent nitrogen‐vacancy (NV) centers are created using different fabrication techniques. The FNDs' fluorescence spectra, lifetime, and spin relaxation time (T₁) are investigated via single‐particle confocal fluorescence microscopy and in ensemble measurements in solution (T₁ excepted). Particle sizes and shapes are determined using scanning electron microscopy and correlated with the optical results. Statistical tests are used to explore correlations between the properties of individual particles and also analyze average results to directly compare different fabrication techniques. Spectral unmixing is used to quantify the relative NV charge‐state (NV^? and NV⁰) contributions to the overall fluorescence. A strong variation is found and quantified in the properties of individual particles within all analyzed samples and significant differences between the different particle types. This study is an important contribution toward understanding the properties of NV centers in nanodiamonds. It motivates new approaches to the improved engineering of NV‐containing nanodiamonds for future applications.     

Nonlinear Measures to Evaluate Upright Postural Stability: A Systematic Review

Conventional biomechanical analyses of human movement have been generally derived from linear mathematics. While these methods can be useful in many situations, they fail to describe the behavior of the human body systems that are predominately nonlinear. For this reason, nonlinear analyses have become more prevalent in recent literature. These analytical techniques are typically investigated using concepts related to variability, stability, complexity, and adaptability. This review aims to investigate the application of nonlinear metrics to assess postural stability. A systematic review was conducted of papers published from 2009 to 2019. Databases searched were PubMed, Google Scholar, Science-Direct and EBSCO. The main inclusion consisted of: Sample entropy, fractal dimension, Lyapunov exponent used as nonlinear measures, and assessment of the variability of the center of pressure during standing using force plate. Following screening, 43 articles out of the initial 1100 were reviewed including 33 articles on sample entropy, 10 articles on fractal dimension, and 4 papers on the Lyapunov exponent. This systematic study shows the reductions in postural regularity related to aging and the disease or injures in the adaptive capabilities of the movement system and how the predictability changes with different task constraints.     

On categories associated to a Quasi-Hopf algebra

A quasi-Hopf algebra H can be seen as a commutative algebra A in the center 𝒵(H-Mod) of H-Mod. We show that the category of A-modules in 𝒵(H-Mod) is equivalent (as a monoidal category) to H-Mod. This can be regarded as a generalization of the structure theorem of Hopf bimodules of a Hopf algebra to the quasi-Hopf setting.     

Stability,periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory

By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation where A ,B ,D > 0,u _?1,u ₀>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence of multiplicity harmonic and subharmonic solutions for second‐order quasilinear equation via Poincaré‐Birkhoff twist theorem

In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second‐order quasilinear equation where , g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase‐plane analysis methods and a generalized version of the Poincaré‐Birkhoff twist theorem.     

Brauer代数的中心维数问题

Brauer代数B_n(t)是一种在表示论,数学物理中重要的带一个参数t的有限维代数.当t取普通值时它们的结构已经了解得比较清楚,例如,不可约表示分类.当t取某些特殊值时有关它们还仍有些问题未探明.本文讨论任意参数时Brauer代数的中心的维数问题.主要结论是当t取某些特殊值时,Brauer代数中心的维数必定大于或等于t取普通值时它们的维数.