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1.
In this paper,we explore two conjectures about Rademacher sequences.Let(εi)be a Rademacher sequence,i.e.,a sequence of independent{-1,1}-valued symmetric random variables.Set Sn=aiε1+…+anεn for a=(a1,…,an)∈Rn.The first con.jecture says that P(|Sn|≤‖a‖)>1/2 for all a∈Rn and n∈N.The second conjecture says that P(|Sn|>‖a‖)≥7/32 for all a∈Rn and n∈N.Regarding the first conjecture,we present several new equivalent formulations.These include a topological view,a combinatorial version and a strengthened version of the conjecture.Regarding the second conjecture,we prove that it holds true when n<7.  相似文献   
2.
张月荣  袁晓 《物理学报》2021,(4):349-359
标度拓展经典负半阶分抗逼近电路,可实现具有任意分数阶微积算子运算功能的分抗逼近电路,但牺牲了运算恒定性.从电路网络的角度分析具有恒定运算性能的负半阶Carlson分形格分抗逼近电路.根据标度分形格分抗逼近电路的等效无源双口网络,探讨该双口网络右侧端口的运算有效性,设计具有高运算恒定性的任意阶标度分形格分抗逼近电路.结合负实零极点对基元系统的零极点分布及其局域化特性,阐述具有任意实数阶微积算子运算功能的标度分形格分抗逼近电路运算振荡现象的物理本质,并从理论上分析有效抑制频域运算振荡现象的方法.结合对称阻容T型节电路优化理论及方法,对任意阶对称格型级联双口网络的频域逼近性能进行优化,获得具有高逼近效益的任意阶标度分形格分抗逼近电路.具有低振荡幅度的任意阶对称格型级联双口网络为高运算恒定性的分抗逼近电路设计及应用提供了一种新方法及思路.  相似文献   
3.
The molecular geometries and dissociation energies of AnO (An = Bk–Lr) molecules were first obtained at thecoupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] level of theory. Four hybrid functionals,B3LYP, M06-2X, TPSSh, and PBE0, were also employed in the calculations for the sake of comparison. In comparison ofthe CCSD(T) results, B3LYP, TPSSh, and PBE0 functionals can obtain more appropriate results than M06-2X and MP2.The analyses on molecular orbitals show that the 7s, 6d, and 5f atomic orbitals of actinide (An) atoms participate in thebonding of An–O bonds. The partial covalent nature between An and O atoms is revealed by QTAIM analyses.  相似文献   
4.
提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换(F2)法以及空间和频谱成像(S2)法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F2法和S2法。  相似文献   
5.
周磊  姜亚成  朱哲明  董玉清  牛草原  王蒙 《爆炸与冲击》2021,41(5):053102-1-053102-11
为深层次了解裂隙岩体在动载荷作用下的动态断裂特性及止裂机理,采用TWSRC(tunnel with single radial crack)构型进行中低速冲击实验,选择砂岩作为原材料制作裂隙岩体试样,以落锤冲击试验装置与裂纹扩展计实验系统对裂纹的动态起裂、扩展及止裂过程进行全过程监测,重点研究动态破裂过程的破裂行为及止裂现象。使用有限差分法程序进行数值模拟,验证冲击实验结果的科学性与准确性。研究发现:裂隙岩体的动态断裂过程是由起裂加速-高速扩展-缓慢减速-止裂-再次起裂加速-再次高速扩展等多次循环的过程构成,且止裂区间尺寸为微秒量级;裂隙岩体止裂位置的穿晶断裂比例远小于初始起裂点,青砂岩动态断裂过程的穿晶断裂比例稍大于黑砂岩;裂隙岩体中止裂点再次起裂所需的能量,远小于预制裂纹初始起裂所需要的能量。  相似文献   
6.
Antibiotics, once being released into the environment, become recalcitrant organic pollutants, which pose a potential risk to ecological balance and human health. In this study, a Z-scheme heterojunction of bismuth oxyiodide (BiOI)/exfoliated g-C3N4 (BiOI/ECN hereafter) was synthesized by the combination of thermal exfoliation of g-C3N4 and chemical precipitation of BiOI for efficient photocatalytic degradation of tetracycline in aqueous solutions under visible light irradiation. The optimized BiOI/ECN delivered an outstanding degradation rate at circa 0.0705 min?1, which was 10 times higher than that of the bulk g-C3N4. The photocatalytic degradation efficiency of tetracycline remained almost unchanged in a pH range of 3–11, and the BiOI/ECN displayed an excellent photostability upon recycled usage. The photocatalytic mechanism of tetracycline was ascribed to the main reactive oxidation species of photogenerated holes and superoxide radicals. In addition, the possible degradation pathways of tetracycline were investigated by HPLC-MS to identify intermediates. The toxicity of photocatalytic-generated intermediates of tetracycline was found significantly alleviated according to the calculation of quantitative structure–activity relationship prediction. This work not only provides an attractive photocatalyst for the removal of tetracycline but also opens a new avenue for rational design of Z-scheme heterojunction composites for tetracycline degradation.  相似文献   
7.
Addressing arsenite pollution in groundwater has drawn great attention. It is attractive to pre-oxidize highly mobile As(III) to relatively low-toxic As(V) with a subsequent adsorption separation process. Herein, BiOI anchoring on γ-Fe2O3 is performed to synthesize BiOI/γ-Fe2O3 core–shell nanoparticles for efficient removal of As(III) via a simultaneous photocatalytic oxidization–adsorption process. The physical and chemical structures of BiOI/γ-Fe2O3 are investigated by transmission electron microscopy, Fourier transform infrared spectroscopy, and X-ray diffraction measurements. The photoluminescence and electron spin resonance (ESR) characterization were employed to ascertain the possible reaction mechanism of visible-light-driven photocatalytic oxidation of As(III). Such BiOI/γ-Fe2O3 delivers a superior As(III) removal capability under visible light irradiation with an arsenic removal efficiency of 99.8% within 180 min, higher than those of BiOCl/γ-Fe2O3 (81.7%) and BiOBr/γ-Fe2O3 (98.9%). The optimal BiOI/γ-Fe2O3 (molar ratio of 2:1) is obtained by rationally adjusting the molar ratio of BiOI to γ-Fe2O3. The as-synthesized BiOI/γ-Fe2O3 performs well in a wide pH range of 2–8. Only coexisting PO43? anions have a significant effect on the As(III) removal. The free radical trapping experiment and ESR results demonstrate that the ?O2? and h+ are the main active substances for the photocatalytic oxidation of As(III) on BiOI/γ-Fe2O3. This work not only gives a novel magnetic core–shell nanoparticle photocatalyst for efficient photocatalytic oxidation and adsorption of As(III) but also offers a new strategy to rationally design BiOX for its related practical applications.  相似文献   
8.
曾彦  梁浩  管诗雪  王俊普  梁文嘉  黄梦阳  彭放 《中国物理 B》2022,31(1):16104-016104
Structural stability in terms of the decomposition temperature in LiMn2O4 was systematically investigated by a series of high-temperature and high-pressure experiments.LiMn2O4 was found to have structural stability up to 5 GPa at room temperature.Under ambient pressure,the compound decomposed at 1300℃.The decomposition temperature decreased with increasing pressure,yielding more complex decomposed products.Below the decomposition temperature,the crystal structure of LiMn2O4 varied with pressure.The presented results in this study offer new insights into the thermal and pressure stability of LiMn2O4 materials as a cathode for lithium-ion batteries that can operate under extreme conditions.Therefore,these findings may serve as a useful guide for future work for improving lithium-ion batteries.  相似文献   
9.
Yukai Zhuang 《中国物理 B》2022,31(8):89101-089101
Iron oxides are widely found as ores in Earth's crust and are also important constituents of its interiors. Their polymorphism, composition changes, and electronic structures play essential roles in controlling the structure and geodynamic properties of the solid Earth. While all-natural occurring iron oxides are semiconductors or insulators at ambient pressure, they start to metalize under pressure. Here in this work, we review the electronic conductivity and metallization of iron oxides under high-pressure conditions found in Earth's lower mantle. We summarize that the metallization of iron oxides is generally controlled by the pressure-induced bandgap closure near the Fermi level. After metallization, they possess much higher electrical and thermal conductivity, which will facilitate the thermal convection, support a more stable and thicker D$\prime\prime$ layer, and formulate Earth's magnetic field, all of which will constrain the large-scale dynamos of the mantle and core.  相似文献   
10.
Luo  Hao  Chen  Long 《Mathematical Programming》2022,195(1-2):735-781
Mathematical Programming - Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A...  相似文献   
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