线型高聚物分子量分布函数的另一种推导方法

针对自由基聚合歧化终止和偶合终止两类机理生成的线型高聚物,应用统计物理的基本原理,对其分子量分布重新进行了理论推导,其方法简洁清晰,无须任何附加假定,导出FlorySchulz分布.结果有助于从另一方面理解FlorySchulz分布的物理学基础.     

Extensions of the Borel–Cantelli lemma in general measure spaces

In this paper, an important bilateral inequality for a sequence of nonnegative measurable functions on a measure space \((S,\mathcal {B}_S,\mu )\) is obtained, and some sufficient conditions for \(\mu \left( \limsup \limits _{n\rightarrow \infty }A_n\right) =\mu (S)\) are given. In addition, a weighted version of the Borel–Cantelli Lemma on the measure space is obtained. Our results generalize the corresponding ones for bounded random sequences to the case of unbounded measurable functions.     

Photoinduced Mo−CN Bond Breakage in Octacyanomolybdate Leading to Spin Triplet Trapping

The photoinduced properties of the octacoordinated complex K₄Mo^IV(CN)₈⋅2 H₂O were studied by theoretical calculations, crystallography, and optical and magnetic measurements. The crystal structure recorded at 10 K after blue light irradiation reveals an heptacoordinated Mo(CN)₇ species originating from the light-induced cleavage of one Mo−CN bond, concomitant with the photoinduced formation of a paramagnetic signal. When this complex is heated to 70 K, it returns to its original diamagnetic ground state, demonstrating full reversibility. The photomagnetic properties show a partial conversion into a triplet state possessing significant magnetic anisotropy, which is in agreement with theoretical studies. Inspired by these results, we isolated the new compound [K(crypt-222)]₃[Mo^IV(CN)₇]⋅3 CH₃CN using a photochemical pathway, confirming that photodissociation leads to a stable heptacyanomolybdate(IV) species in solution.     

NONLINEAR VIBRATION RESPONSE AND BIFURCATION OF CIRCULAR CYLINDRICAL SHELLS UNDER TRAVELING CONCENTRATED HARMONIC EXCITATION

The nonlinear vibration of a cantilever cylindrical shell under a concentrated harmonic excitation moving in a concentric circular path is proposed. Nonlinearities due to large-amplitude shell motion are considered, with account taken of the effect of viscous structure damping. The system is discretized by Galerkin's method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifurcation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations.     

轴向运动复合材料圆柱壳的非线性振动研究

采用Runge–Kutta法和多尺度法对轴向运动分层复合材料薄壁圆柱壳的非线性振动特性进行了研究。首先根据层合壳理论建立轴向运动分层复合材料薄壁圆柱壳的波动方程,利用Galerkin法对方程进行离散,得到相互耦合模态方程组。然后应用Runge –Kutta法分析了不同参数条件下的幅频特性曲线,得到了系统由于固有频率接近所导致的内共振现象,以及系统呈现软特性等非线性特性。最后采用多尺度法进行了系统1:1内共振时的近似解析分析,对系统在不同参数下的振动研究表明,激振力幅值、阻尼、速度等参数对位移响应幅值、共振区间、模态间的耦合度及系统软特性程度均有影响,其结论与数值计算结果一致,并同时对解的稳定性进行了研究。     

轴向移动局部浸液单向板的1:3内共振分析

考虑单向板的轴向速度、轴向张力、流固耦合作用以及阻尼等因素, 基于由 von Kármán薄板大挠度方程得到的轴向移动局部浸液单向板的非线性振动方程, 研究了外激励作用下单向板在1:3内共振情况时的非线性振动特性. 首先利用Galerkin法对非线性振动方程离散化, 然后分别应用数值法和近似解析法对离散后模态方程组进行求解, 获得了系统内共振情况下复杂的幅频特性曲线, 并讨论了周期解的稳定性. 最后研究了1:3内共振系统平均方程组的运动分岔现象.     

Large-scale fabrication of polymer/Ag core–shell nanorod array as flexible SERS substrate by combining direct nanoimprint and electroless deposition

We demonstrate a highly sensitive surface-enhanced Raman scattering (SERS) substrate, which consists of Ag nanoparticles (NPs) assembled on the surface of a nanopatterned polymer film. The fabrication route of a polymer/Ag core–shell nanorod (PACSN) array employed a direct nanoimprint technique to create a high-resolution polymer nanorod array. The obtained nanopatterned polymer film was subjected to electroless deposition to form a sea-cucumber-like Ag shell over the surface of the polymer nanorod. The morphology and structures of PACSNs were analyzed by using scanning electron microscopy and X-ray diffraction. The as-synthesized PACSNs exhibited a remarkable SERS activity and Raman signal reproducibility to rhodamine 6G, and a concentration down to 10^?12 M can be identified. The effect of electroless deposition time of Ag NPs onto the polymer nanorod surface was investigated. It was found that the electroless deposition time played an important role in SERS activity. Our results revealed that the combination of direct nanoimprint and electroless deposition provided a convenient and cost-effective way for large-scale fabrication of reliable SERS substrates without the requirement of expensive instruments.     

旋转薄壁圆柱壳振型进动的非线性振动特性

选取在工程上常用的悬臂旋转薄壁圆柱壳为研究模型,首先推导出考虑阻尼的振型进动因子,然后根据Donnell's简化壳理论建立考虑科氏力,阻尼与几何大变形的非线性波动方程,采用Galerkin方法对波动方程进行离散化,得到模态坐标中相互耦合的三阶非线性微分方程组.应用Runge-Kutta法求解获得非线性幅频特性曲线,分析了不同模态组合下系统主模态(m=1,n=6,k=1)的共振响应.应用谐波平衡法对系统三阶非线性微分方程组解析分析,与数值解比较验证了解析解的正确性和有效性.最后分析了动力系统的运动稳定性.结果表明,节径数n和频率倍数k对于主模态共振响应的影响很小,而轴向半波数m对主共振的影响则相对较大,因此只需选取相邻的两个轴向模态(M=2)即可较为简洁,准确的描述主共振响应;谐波平衡法可以很好的解决三阶微分方程组的非线性问题,并且能够达到较为满意的精度.     

Glucose and pH Dual‐Responsive Nanogels for Efficient Protein Delivery

Direct delivery of protein suffers from their in vitro and in vivo instability, immunogenicity, and a relatively short half‐life within the body. To overcome these challenges, pH and glucose dual‐responsive biodegradable nanogels comprised of dextran and poly(L‐glutamic acid)‐g‐methoxy poly‐(ethylene glycol)/phenyl boronic acid (PLG‐g‐mPEG/PBA) are designed. The cross‐linked network imparted drug‐loading efficacy of α‐amylase up to 55.6% and hyaluronidase up to 29.1%. In vitro protein release profiles reveal that the release of protein is highly dependent on the pH or glucose concentrations, that is, less amount of protein is released at pH 7.4 or healthy blood glucose level (1 mg mL^?1 glucose), while quicker release of protein occurs at pH 5.5 or diabetic blood glucose level (above 3 mg mL^?1 glucose). Circular dichroism spectra show that the secondary structure of released protein is maintained compared to naive protein. Overall, the nanogels have provided a simple and effective strategy to deliver protein.     

两两NQD序列部分和的强大数定律

By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding result of pairwise NQD random variables.