Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Classification problems for shifts on modules over a principal ideal domain

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.

     

Clifford分析中无界域上正则函数的边值问题

在引入修正Cauchy核的基础上,讨论了无界域上正则函数的带共轭值的边值问题：a(t)Φ (t) b(t)Φ (t) c(t)Φ-(t) d(t)Φ=g(t)．首先给出了无界域上正则函数的Plemelj公式,然后利用积分方程方法和压缩不动点原理证明了问题解的存在唯一性．     

从 ${\cal B}^0$ 到 $E(p,q)$ 和 $E_0(p,q)$ 空间的复合算子

设 $\varphi$ 是单位园盘 $D$ 到自身的解析映射, $X$ 是 $D$ 上解析函数的 Banach 空间, 对 $f\in X$, 定义复合算子$C_\varphi $ : $C_\varphi (f)=f\circ \varphi$. 我们利用从 ${\cal B}^0$到 $E(p,q)$ 和 $E_0(p,q)$ 空间的复合算子研究了空间 $E(p,q)$ 和 $E_0(p,q)$, 给出了一个新的特征.     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in C~n

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain of D'Angelo finite type in Cn (n > 1) is an automorphism.     

Carbon-13 NMR evidence for cocrystallization of cellulose as a mechanism for hornification of bleached kraft pulp

Solid-state ¹³C NMR spectroscopy was used to characterize a bleached softwood kraft pulp in the never-dried state and after cycles of drying and remoistening. Changes in NMR signal strengths indicated that growth of crystalline domains involved cocrystallization rather than accretion of cellulose from noncrystalline domains. A cluster of C-4 signals at 89.4 ppm, assigned to the interiors of crystalline domains, grew at the expense of C-4 signals at 84.0 and 84.9 ppm, assigned to the well-ordered surfaces of crystalline domains. Irreversible changes were not detected until the moisture content dropped below 18%. They were enhanced by a second drying/remoistening cycle, but showed little further change on subsequent cycles. The necessary conditions resembled those reported for hornification, suggesting that cocrystallization might provide a mechanism for hornification.     

ΓD‐convergence for a class of quasilinear elliptic equations in thin structures

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε) of asymptotically degenerating measure, i.e. meas Ω^(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.     

Total energy decay for the wave equation in exterior domains with a dissipation near infinity

We show that the energy of solutions to the initial boundary value problem for the wave equation in exterior domains with a dissipation which is localized only near infinity tends to zero as the time goes to infinity. We do not make any geometrical condition like star-shapedness on the boundary.     

良序套张量积的代数中的强不可约算子

设Ｈ为复的可分无限维Ｈｉｌｂｅｒｔ空间，称有界线性算子Ｔ为强不可约的，如果与Ｔ可交换的幂等算子只有０和Ｉ．王宗尧、蒋春澜、纪有清等人证明了在任何一个套的套代数中都存在大量的强不可约算子，并且找到了它们的酉轨道闭包．本文考虑有限个套的张量积的代数中强不可约算子的存在性问题。证明了：对复平面上任何一个连通完备集σ、总存在一个对角算子Ｎ和它的一个范数可以任意小的紧摄动Ｔ＝Ｘ＋Ｋ，使得Ｔ是一个强不可约算子、Ｔ在有限个良序套的张量积的代数中，并且σ（Ｔ）＝σｌｒｅ（Ｔ）＝σ（Ｎ）＝σｌｒｅ（Ｎ）＝σ进一步，文章还对具有单点谱的算子和良序套与正交补为良序套的张量积的代数进行了讨论，得到了一些结果．