Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

新型多孔材料用作色谱手性固定相

手性固定相是色谱法分离分析手性化合物的关键。近年来,随着材料科学的迅速发展,越来越多的新型手性材料被作为色谱固定相用于手性分离分析。本文综述了近5年来液相色谱、气相色谱和毛细管电色谱领域的新型手性固定相的研究进展,重点总结了基于手性多孔材料的新型手性固定相研究,最后对手性固定相的研究进行了总结与展望。     

Characterization of diterpene metabolism in rats with ingestion of seed products from Euphorbia lathyris L. (Semen Euphorbiae and Semen Euphorbiae Pulveratum) using UHPLC-Q-Exactive MS

Previous pharmacological studies have indicated that diterpenoids are the primary effective chemical cluster in the seeds of Euphorbia lathyris L. The seed products are used in traditional Chinese medicine in the forms of Semen Euphorbiae (SE) and Semen Euphorbiae Pulveratum (SEP). However, the metabolism of the plant's diterpenoids has not been well elucidated, which means that the in vivo metabolite products have not been identified. The current study screened the physiological metabolites of six diterpenes [Euphorbia factor L₁ (L1), L₂ (L2), L₃ (L3), L_7a (L7a), L_7b (L7b), and L₈ (L8)] in feces and urine of rats after oral administration of SE and SEP using UHPLC-Q-Exactive MS. A total of 22 metabolites were detected in feces and 8 in urine, indicating that the major elimination route of diterpenoids is via the colon. Hydrolysis, methylation, and glucuronidation served as the primary metabolic pathways of these diterpenoids. In sum, this study contributed to the elucidation of new metabolites and metabolic pathways of SE and SEP, and the new chemical identities can be used to guide further pharmacokinetic studies.     

Visible light-driven acridone catalysis for atom transfer radical polymerization

Acridone as a new kind of visible light photocatalyst has been developed to catalyze metal free atom transfer radical polymerization (ATRP). The photocatalyst possess low excited state potential as can undergo an oxidative quenching pathway to initiate ATRP of vinyl monomers. Kinetic study and light on/off reaction demonstrate the “living”/controlled nature of the polymerization by light. Block copolymers can be achieved by using PMMA as macroinitiator to reinitiate polymerization of other vinyl monomers, which shows highly preserved Br chain-end functionality in the synthesized polymers. Moreover, the polymerization can be conducted under air atmosphere as most photocatalysts need anaerobic condition, which may give inspiration of further application of this kind of photocatalyst.     

Surface Engineering of Conjugated Polybenzothiadiazoles and Integration with Cobalt Oxides for Photocatalytic Water Oxidation

Conjugated polymers feature promising structure and properties for photocatalytic water splitting. Herein, a hydrolysis strategy was demonstrated to rationally modulate the surface hydrophilicity and band structures of conjugated poly-benzothiadiazoles. High hydrophilicity not only enhances the dispersions of polymeric solids in an aqueous solution but also reduces the absorption energy of water molecules. Besides, both theoretical and experimental results reveal that a more positive valence band potential is generated, which contributes to enhancing the photocatalytic water oxidation performance. Accordingly, the surface-modified conjugated polymers show largely promoted photocatalytic water oxidation activities by deposition of cobalt oxides as cocatalysts.     

Design of Functional Carbon Composite Materials for Energy Conversion and Storage

The carbon composite materials have been a research hotspot in the fields of catalysis, energy conversion and so on, because of their features of large structure and morphology variety, good chemical and electrochemical stability, and high electronic conductivity, large specific surface area and rich active sites. This paper summarizes some research progress of carbon composite materials, including assembly methodologies, their structure regulation, properties, and related applications. Moreover, the current challenges and the prospects of these materials are also discussed.     

基于抛光基材的热蒸镀铜箔生长高平整单层石墨烯薄膜

在石墨烯的化学气相沉积工艺中,铜箔是决定石墨烯薄膜质量的重要因素。传统铜箔由于制备工艺的限制,存在大量的缺陷,导致石墨烯薄膜的成核密度较高。本工作选用抛光铝板、抛光不锈钢板、微晶玻璃和SiO₂/Si作为基材,用热蒸镀法制备了不同粗糙度的铜箔,并详细讨论了以该系列铜箔生长高平整度石墨烯薄膜的条件及铜箔对石墨烯薄膜品质的影响。实验结果表明,铜箔以(111)取向为主,与基材分离后,表面具有纳米级平整度。在生长石墨烯后,从SiO₂/Si剥离的铜箔成核密度是4种基材中最小的。同时,从SiO₂/Si剥离的铜箔晶体结构变化最不明显,具有良好的结晶性,表面几乎不存在铜晶界缺陷。当压强为3 000 Pa,氢气和甲烷流速分别为300 mL/min和0.5 mL/min时,可以获得约1 mm横向尺寸的石墨烯单晶晶畴。     

配合参数对单晶炉驱动系统的影响分析

光伏产业的发展使得对硅材料的需求日益增加,同时硅单晶生产行业竞争也日趋激烈。作为生产硅单晶的重要装备,单晶炉的稳定性和可靠性关系到硅单晶生产效率的提升和成本的下降,因此其驱动系统的设计和优化成为装备制造的关键环节。本文以NVT-HG2000-V1型硅单晶生长炉的驱动系统为研究对象,用SolidWorks三维建模实现虚拟装配,采用ADAMS建立其动力学仿真模型,并对驱动系统的运动过程进行仿真模拟。采用控制变量法定量分析了铜套与升降轴的配合间隙及丝杠参数对驱动力和驱动力矩的影响规律,进而在提高硅单晶生长炉装备稳定性和可靠性方面给出合理的技术建议。结果表明,铜套与升降轴的配合间隙达到0.071 mm后能有效降低驱动系统运行所需驱动力矩,丝杠倾斜度、螺纹螺距与螺纹间摩擦系数的增大均会导致驱动系统运行所需力矩大幅增加。     

A quantum circuit design of AES requiring fewer quantum qubits and gate operations

Advanced Encryption Standard (AES) is one of the most widely used block ciphers nowadays, and has been established as an encryption standard in 2001. Here we design AES-128 and the sample-AES (S-AES) quantum circuits for deciphering. In the quantum circuit of AES-128, we perform an affine transformation for the SubBytes part to solve the problem that the initial state of the output qubits in SubBytes is not the |0>^⊗8 state. After that, we are able to encode the new round sub-key on the qubits encoding the previous round sub-key, and this improvement reduces the number of qubits used by 224 compared with Langenberg et al.’s implementation. For S-AES, a complete quantum circuit is presented with only 48 qubits, which is already within the reach of existing noisy intermediate-scale quantum computers.