Statistical Inference with Fractional Brownian Motion

We give a test between two complex hypothesis; namely we test whether a fractional Brownian motion (fBm) has a linear trend against a certain non-linear trend. We study some related questions, like goodness-of-fit test and volatility estimation in these models.     

Joint detection of a given number of reference fragments in a quasi-periodic sequence and its partition into segments containing series of identical fragments

The problem of joint a posteriori detection of reference fragments in a quasi-periodic sequence and its partition into segments containing series of recurring fragments from the reference tuple is solved. It is assumed that (i) an ordered reference tuple of sequences to be detected is given, (ii) the number of desired fragments is known, (iii) the index of the sequence term corresponding to the beginning of a fragment is a deterministic (not random) value, and (iv) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is established that the problem consists in testing a set of hypotheses about the mean of a random Gaussian vector. The cardinality of the set grows exponentially as the vector dimension (i.e., the sequence length) increases. An efficient a posteriori algorithm producing a maximum-likelihood optimal solution to the problem is substantiated. Time and space complexity bounds related to the parameters of the problem are derived. The results of numerical simulation are presented.     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

H andH NMR Relaxation in Hydrogen-Bonded Solids Due to a Complex Motion: Classical Jumps over a Barrier and Incoherent Tunneling

Equations for the temperature dependence of proton and deuteron spin–lattice relaxation rates and second moments due to a complex motion consisting of classical jumps over a potential barrier and quantum mechanical tunneling through the barrier have been derived. Asymmetric double and triple potential wells are considered. These equations have been employed to analyze proton spin–lattice relaxation data for solid naphthazarin in the laboratory and rotating frames as a function of temperature. It is shown that tunneling plays an important role in the proton transfer dynamics of this compound.     

在重力场和磁场影响下自旋刚性航天器的周期运动

考虑重力场和磁场对轴对称航天器本体的影响，研究其质心在圆形轨道上的运动,通过降低系统的运动方程数，并将它变成为一个带电粒子在电磁场作用下的平面运动．确认系统运动是稳定的，并通过Liapunov全纯积分定理，构建其近似的周期运动.     

A remark on the KAM theorem applied to a four-vortex system

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation number=(5—1)/2 and compare our result with numerical experiments.     

在“高聚物的结构与性能”课程中讲透高聚物的特点

通过对高分子链的柔性、聚合物独有的熵弹性、显著的粘弹性、特有的描述链段运动的WLF方程,可能实现的大尺寸取向和小尺寸解取向、银纹、单链凝聚态、折叠链片晶和伸直链晶体、分子量的多分散性、高分子溶液特性和高聚物熔体的弹性行为等的讨论,希望能突出“高聚物的结构与性能”课程中高聚物的特点。     

Proton magnetic relaxation study of water orientation around I− and Li+

Proton relaxation time measurements are performed for 6m aqueous solutions of⁷LiI and⁶LiI in D₂O containing small amounts of H₂O. The measurements are done at low temperatures and yield maxima of the relaxation rate plotted against 1/T. From the maxima of the relaxation rates, proteon-I^– and proton-Li⁺ distances in the first coordination sphere of the ions are determined, and from the knowledge of the ion-water oxygen distance it is shown that for iodide a somewhat broadened H-bonded configuration is valid and that for Li⁺ the electric dipole orientation deviates from the radial direction. In order to test the reliability of the method a proton-¹²⁷I interaction study is also performed in KI solution in glycerol. The I-H distance obtained is in satisfactory agreement with that found in the aqueous system.     

Rates of convergence of α-stable random motions

The rate-of-convergence problem in the central limit theorem is considered for -stable distributions on the noncommutative group of motions in ^d. The method used here is based on the theory of probability metrics.