Canonical symbolic dynamics for one-dimensional generalized solenoids

We define canonical subshift of finite type covers for Williams' one-dimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.

     

Prime T-Ideals in Polynomial and Power Series Rings Over a Pseudo-Valuation Domain

Let R be an m-dimensional pseudo-valuation domain with residue field k, let V be the associated valuation domain with residue field K, and let k ₀ be the maximal separable extension of k in K. We compute the t-dimension of polynomial and power series rings over R. It is easy to see that t-dim R[x ₁,…, x _n ] = 2 if m = 1 and K is transcendental over k, but equals m otherwise, and that t-dim R[[x ₁,…, x _n ]] = ∞ if R is a nonSFT-ring. When R is an SFT-ring, we also show that: (1) t-dim R[[x]] = m; (2) t-dim R[[x ₁,…, x _n ]] = 2m ? 1, if n ≥ 2, K has finite exponent over k ₀, and [k ₀: k] < ∞; (3) t-dim R[[x ₁,…, x _n ]] = 2m, otherwise.     

Effect of Slow and Fast Moving Liquid Zones on Solute Transport in Porous Media

A conceptual model is developed in this article that accounts for the effect of slow and fast moving liquid zones on solute transport in porous media. The liquid phase within the porous media is divided into three zones—immobile, slow moving, and fast moving. Slow moving liquids surround the solid particles in thin layers and have lower velocity in flow. Fast moving liquids have higher velocity and are not in contact with the solid particles. Solute mass transfer occurs between the slow and fast liquids, and the slow and immobile liquids. The immobile and slow moving liquids interact with the solid matrix in the media through the mechanism of sorption and desorption. Implicit finite-difference methods are used to solve the partial differential equations that describe the slow and fast movement of solute in the porous medium. The model was validated for a laboratory column experimental data. Sensitivity analyses were conducted to ascertain the effects of the model parameters on solute movement. The effect of each parameter on retardation of the solute movement was analyzed. It was observed that the maximum retardation of solute occurs when there is high adsorption coefficient, high mass transfer rates, and high volume of slow moving liquid in the porous media.     

Arnold's Theorem on the Strongly Finite Type (SFT) Property and the Dimension of Power Series Rings

We present a simplified proof of Arnold's Theorem on the SFT property and the dimension of power series rings.     

Dynamic equations for curved submerged floating tunnel

In virtue of reference Cartesian coordinates,geometrical relations of spatial curved structure are presented in orthogonal curvilinear coordinates.Dynamic equations for helical girder are derived by Hamilton principle.These equations indicate that four generalized displacements are coupled with each other.When spatial structure degener- ates into planar curvilinear structure,two generalized displacements in two perpendicular planes are coupled with each other.Dynamic equations for arbitrary curvilinear structure may be obtained by the method used in this paper.     

水中悬浮隧道的空间曲线结构运动方程

借助参考直线坐标系,求解空间曲线结构在曲线坐标系中的几何方程．运用Hamilton原理推导空间螺旋曲线梁结构的运动方程．方程表明空间曲线结构4个自由度相互耦合,当结构退化为平面曲线结构时,两个相互垂直平面内的各自由度相互耦合．空间任意曲线梁结构的动力方程均可按照该文推导思路得出．对于水中悬浮隧道结构,可以忽略转动动能对振动的影响．