通过宽线固体核磁共振氢谱研究半晶高分子的相结构

宽线固体核磁共振氢谱（¹H NMR）是一种研究半晶高分子相结构的经典方法.本文以半晶聚乙烯的宽线固体¹H NMR谱为例，探讨了通过Gaussian/Sinc、Gaussian和Lorentzian函数组合对宽线固体¹H NMR谱图进行拟合的方案，并根据半晶聚乙烯的相结构成分对拟合得到的各信号成分进行归属.并在此基础上探讨了各个相结构中分子链运动与信号线型的相关性，以及利用宽线固体¹H NMR谱测量半晶高分子结晶度存在的困难.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

Solid-State 17O NMR studies of organic and biological molecules: Recent advances and future directions

This Trends article highlights the recent advances published between 2012 and 2015 in solid-state ¹⁷O NMR for organic and biological molecules. New developments in the following areas are described: (1) new oxygen-containing functional groups, (2) metal organic frameworks, (3) pharmaceuticals, (4) probing molecular motion in organic solids, (5) dynamic nuclear polarization, and (6) paramagnetic coordination compounds. For each of these areas, the author offers his personal views on important problems to be solved and possible future directions.     

DETERMINATION OF QUADRICEPS FORCES IN SQUAT AND ITS APPLICATION IN CONTACT PRESSURE ANALYSIS OF KNEE JOINT

While the quadriceps muscles of human body are quite important to the daily activities of knee joints,the determination of quadriceps forces poses significant challenges since it cannot be measured in ...     

Extinction Effects of Multiplicative Non-Gaussian L′evy Noise in a Tumor Growth System with Immunization

The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.     

Arithmetic Brownian motion and real options

We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.     

On asymptotic elastodynamic homogenization approaches for periodic media

A fairly large family of asymptotic elastodynamic homogenization methods is shown to be derivable from Willis exact elastodynamic homogenization theory for periodic media under appropriate approximation assumptions about, for example, frequencies, wavelengths and phase contrast. In light of this result, two long-wavelength and low-frequency asymptotic elastodynamic approaches are carefully analyzed and compared in connection with higher-order strain-gradient media. In particular, these approaches are proved to be unable to capture, at least in the one-dimensional setting, the optical branches of the dispersion curve. As an example, a two-phase string is thoroughly studied so as to illustrate the main results of the present work.