Mobility of Li+, Na+, and Cs+ cations in Nafion membrane,as studied by NMR techniques

The local mobility and diffusion of Li⁺, Na⁺, and Cs⁺ cations in Nafion 117 membrane were explored by ⁷Li, ²³Na, and ¹³³Cs spin relaxation and pulsed field gradient NMR techniques. It was shown that the macroscopic mass transfer of cations is controlled by ion motion near sulfonate groups. Lithium and sodium cations, whose hydrated energy is higher than the water hydrogen bond energy, are moving together with water molecules, but cesium cations possessing a low hydrated energy are jumping directly between the neighboring sulfonate groups.     

More efficient estimators for marginal additive hazards model in case-cohort studies with multiple outcomes

Case-cohort study designs are widely used to reduce the cost of large cohort studies. When several diseases are of interest, we can use the same subcohort. In this paper, we will study the casecohort design of marginal additive hazards model for multiple outcomes by a more efficient version. Instead of analyzing each disease separately, ignoring the additional exposure measurements collected on subjects with other diseases, we propose a new weighted estimating equation approach to improve the efficiency by utilizing as much information collected as possible. The consistency and asymptotic normality of the resulting estimator are established. Simulation studies are conducted to examine the finite sample performance of the proposed estimator, which confirm the efficiency gains.     

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Brownian motion and normal distribution have been widely used in Cox-Ingersoll-Ross interest rate framework to model the instantaneous interest rate dynamics. However, empirical studies have also shown that the return distribution of interest rate has a higher peak and two fatter tails than those of the normal distribution. Meanwhile, when the rare catastrophic shocks occur or the regime shifts in the economy and finance, the money market may have jumps. In this paper, we will consider a class of reflected Cox-Ingersoll-Ross interest rate models with noise. Furthermore, we shall continue to supply the Laplace transform of the stationary distribution about this reflected diffusion process with jumps.     

Existence and uniqueness results for a fractional two‐times evolution problem with constraints of purely integral type

This paper deals with a fractional two‐times evolution equation associated with initial and purely boundary integral conditions. The existence and uniqueness of generalized solution are proved. The classical functional method based on a priori estimates and density used by many authors in the case of nonfractional differential equations is applied for the time fractional case. Copyright © 2015 John Wiley & Sons, Ltd.     

重复测量次数的讨论

本从三个观点出发,综合讨论了重复测量的次数。     

Coupling of the Polymer Threading a Membrane Transition to the Membrane Adsorption Transition

A polymer molecule threading through a pore in a plane membrane is allowed to adsorb on either or both sides of the membrane. Further, it is confined to the vicinity of the membrane by two plane barriers lying on either side of the membrane. A lattice model of this problem is exactly solvable by matrix techniques. The equilibrium translocation behavior is described as a function of the polymer MW, the membrane adsorption energies, the solution properties, the barrier separations, applied force, and the temperature. The transition is first-order, meaning that small changes in any of these 9 quantities can in the limit of infinite MW, completely translocate the polymer. The work of Park and Sung who used Smoluchowski-like equations to calculate translocation transit times can be generalized by use of the sea-snake model which is relevant to isolated polymer chains in solution. The physics behind the sea-snake model is that if one monomer is pulled into the membrane, the distance the center of mass of the untranslocated portion of the chain moves is MW^−1/2 of the distance between monomer units. This reduces the effective friction coefficient by MW^1/2. It is found for the sea-snake model that the MW dependence of transit times varies as MW^3/2 or MW depending on whether we use a free draining or a non-free draining picture for the polymer.     

暂留对称扩散过程全占据时的大偏差

本文讨论暂留对称扩散过程的全占据时的大偏差．我们证明在一致椭圆条件下,暂留对称扩散过程的全占据时满足大偏差原理．     

一类奇异抛物方程的超过程解法

对于如下一类奇异非线性抛物型方程：ｔｕ（ｔ,ｘ）＝Δｕ（ｔ,ｘ）－ｕβ（ｔ,ｘ）,ｘ∈Ｂ（０,ａ）,ｕ（０,ｘ）＝０,ｕ（ｔ,ｘ）｜ｘ｜→ａ－→∞,ｔ＞０,这里,１≤β≤２,Ｂ（ｏ,ａ）表示以ｏ为中心,以ａ为半径的Ｒｄ中的闭球,利用超过程的理论,给出了它的概率解法,从而推广了文［１］相应的结论     

Closed‐form formulas for Kirchhoff index

We find closed‐form expressions for the resistance, or Kirchhoff index, of certain connected graphs using Foster's theorems, random walks, and the superposition principle. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 135–140, 2001