Weak solutions for stochastic differential equations with additive fractional noise

In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter , and a discontinuous drift. The proof of this result is based on the Girsanov theorem for the fractional Brownian motion.     

Theoretical predictions of diffusion from Brownian motion in superstrong polymers

This paper presents a summary of unique highly nonlinear static and dynamic theories for chain molecules (actually, for almost any kind of organic molecule), including the first superstrong polymers. These theories have been used to predict and explain (1) the physical self-assembly (self-ordering) of specific kinds of molecules into liquid crystalline (LC) phases (i.e., partially ordered phases) and (2) the diffusion of these molecules in various LC phases and the isotropic (I) liquid phase.By acceptance of this article, the publisher recognizes that the U. S. Government retains a nonexclusive, royality-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.     

Study on vacancy motion in Y2O3-doped CeO2 by 17O NMR technique

The ¹⁷O NMR measurement was made to elucidate the microscopic nature of vacancy motion in Y₂O₃-doped CeO₂. Spin-lattice relaxation rate, T^?1₁, spin-spin relaxation rate, T^?1₂, and resonance intensity were measured at v₀ = 8.13 MHz as a function of temperature [385 < T (K) < 1110] and composition [$\text{0.06 <}\text{Y}{}_2\text{O}{}_3\text{(}\text{m}\text{o}\text{) < 6}$]. The static electric field gradient associated with lattice defects resulted in the composition dependences of the line width and the intensity. In low dopant concentrations, doubly peaked temperature dependence of T^?1₁ was found, while a single and asymmetric peak was observed in high concentrations. T^?1₁ of 4.0 and 6.0 $\text{m}\text{o}$ doped samples were analyzed using a barrier height distribution model for the oxygen vacancy jump. The mean value of the activation energy was found to increase with the Y₂O₃ concentration.     

Activated drift motion of a classical particle with a dynamical pinning effect

A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of “ageing” effects. The depth of each trap increases with the time elapsed since the particle has fallen into it. The consequences of this dynamical pinning are studied, and velocity-force characteristics are numerically obtained. A special attention is paid to the situation where the particle is pulled with a spring to ensure a finite average velocity. In the low velocity regime, the presence of a broad distribution of trapping times leads to suppression of linear response, replaced by a threshold or by sublinear dynamics. A regime of strong fluctuations is obtained when the particle is driven at intermediate velocities. Received: 12 December 1997 / Accepted: 25 February 1998     

Restoration of images degraded by extreme mechanical vibrations

A method of numerically calculating the optical transfer function appropriate to any type of image motion and vibration, including random, has been recently developed. This method has been verified experimentally with real vibrations, and the close agreement justifies implementation in image restoration from blur deriving from any type of image motion, including random displacement. Here, image restorations of actual physically degraded images are presented, based on a constrained least squares improvement of the original Wiener filter. Even for extreme vibrations where the blur extent is much larger than the blurred detail, restoration is quite complete. The key to restoration is the determination of the optical transfer function unique to the particular image motion and vibration causing the blur. Results are also presented for low vibration frequency motion of random blur extent, as well as for high vibration frequencies.     

Confinement model for quarks

A confinement model of hadron with its constituent quarks bound in a strong gravitational field is presented. The gravitational field plays the role of a medium having, as if, space dependent permeabilities from a fixed centre. The massless Dirac equation modified by the gravitational field is solved. The solution for the wavefunction of the quarks obtained shows the characteristic features of confinement, i.e., (i) wavefunction with higher energy states lying closer to the centre, (ii) equispaced energy levels without continuum, (iii) the quark orbits lying within a distance ∼ 10⁻¹⁴ cm, the characteristic radius of a typical hadron.     

欧式向下敲出看涨幂期权的Esscher变换定价

首先根据障碍期权的不同类型,对普通欧式向下敲出看涨幂期权、部分时间开始、部分时间结束、一般部分时间欧式向下敲出看涨幂期权给出定义.通过E sscher变换分别给出定价公式.另外,对两资产欧式向下敲出幂期权也给出了定价公式,为实践者提供了理论上的参考价格.最后,阐述了此方法的优点.     

薄膜生长初期多原子移动影响的模拟

模拟了在低温底上沉积单层薄膜初期的表面形貌．提出了新的算法，实现了多个原子同时在沉积基底上移动的过程，克服了以往只能模拟基底上仅有一个运动原于的缺点，同时引入了沉积流量，并在此基础上讨论了移动步数、沉积流量等因素对生长的影响作用．模拟结果与实验相近，获得的花样具有分形特征．     

Weak convergence to the fractional Brownian sheet in Besov spaces

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent fractional brownian motions.     

A Wiener-Wintner theorem for 1/f power spectra

Wiener's generalized harmonic analysis (GHA) provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the L¹,L², and Fourier series theories; and it does it in a way that is usually more quantitative than that provided by the theory of distributions. On the other hand, GHA does not yield an adequate spectral analysis of large classes of functions, including nonstationary processes and, in particular, 1/f noise. In this paper we adapt GHA to deal with 1/f noise by extending the Wiener-Wintner theorem to the case of 1/f power spectra.