A metric discrepancy result for the sequence of powers of minus two

The law of the iterated logarithm for discrepancies of _{(−2)kt}k${\left\{{(-2)}^{k}t\right\}}_k$ is proved. This result completes the concrete determination of the law of the iterated logarithm for discrepancies of the geometric progression with integer ratio, and reveals the fact that 2 is the only positive integer θ>1$\theta >1$ such that fractional parts of _{(−θ)kt}k${\left\{{(-\theta )}^{k}t\right\}}_k$ converge to uniform distribution faster than those of _{θkt}k${\left\{{\theta }^{k}t\right\}}_k$ a.e. t$t$.     

基于阿基米德定律的微小质量测量

基于阿基米德定律设计制作了一个可测量100~500 mg微小质量的测量仪,通过本仪器测量精度可达到2 mg。该测量仪原理简单,构思巧妙,全机械式结构,成本低廉,为质量测量提供了一种新方法。     

双Pearcey光束的构建及数学机理研究

通过推导椭圆线的菲涅耳衍射分布,得到了形如Pearcey函数的数学表达式.通过数值模拟和实验产生,发现椭圆光环经菲涅耳衍射后形成的Pearcey光束外形上很像两个经典Pearcey光束面对面组合而成,我们把它命名为双Pearcey光束,这是形式不变Pearcey光束家族的新成员.随后,利用数学突变理论,给出了双Pearcey光束所具有的光学拓扑结构的数学机理和相应表达式.     

Analytical atomic spectrometry and imaging: Looking backward from 2020 to 1975

Some general aspects of the evolution of atomic spectrometry for chemical analysis over the period 1975 to now are described. Performance parameters such as detection limits and spatial analytical potential (lateral and depth resolution) are compared with the evolution of integrated circuit technology as described in Moore's Law. A few general trends of future development for the coming decade are postulated. Attention will be focused on analysis and imaging with beam techniques, especially secondary ion mass spectrometry and X-ray techniques on the basis of excitation with synchrotron radiation.     

以实际算法为例评估MapReduce在石油勘探中的应用

石油勘探领域需要处理海量的地震数据,以获取地下构造用以发现和定位油藏。为评估云计算编程模型MapReduce对于石油勘探领域应用算法的适用性,设计并实现了基于MapReduce的三维Fresnel层析成像算法,实验发现MapReduce版本的性能比MPI版本慢3倍,而且对MapReduce作业调优的难度相当大。为了拓展MapReduce在石油勘探领域高性能计算领域的应用,需要在支持线程级并行、灵活性和提升I/O可扩展性3个方面进行改进,并提出了研究方法和技术路线。     

On the Separation and Order Law of Cancellation for Bounded Sets

In this paper we introduce the separation law for convex sets. Moreover, we prove that for a locally convex topological vector space the order cancellation law and separation law are equivalent.     

Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability

We give a unified treatment of the convergence of random series and the rate of convergence of the strong law of large numbers in the framework of game-theoretic probability of Shafer and Vovk (2001) [24]. We consider games with the quadratic hedge as well as more general weaker hedges. The latter corresponds to the existence of an absolute moment of order smaller than 2 in the measure-theoretic framework. We prove some precise relations between the convergence of centered random series and the convergence of the series of prices of the hedges. When interpreted in the measure-theoretic framework, these results characterize the convergence of a martingale in terms of the convergence of the series of conditional absolute moments. In order to prove these results we derive some fundamental results on deterministic strategies of Reality, who is a player in a protocol of game-theoretic probability. It is of particular interest, since Reality’s strategies do not have any counterparts in the measure-theoretic framework, ant yet they can be used to prove results which can be interpreted in the measure-theoretic framework.     

The Law of Iterated Logarithm of Rescaled Range Statistics for AR（1） Model

Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.     

Weberized Mumford-Shah Model with Bose-Einstein Photon Noise

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber's Law. The current paper develops a new segmentation model based on the integration of Weber's Law and the celebrated Mumford-Shah segmentation model (Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989). Explained in detail are issues concerning why the classical Mumford-Shah model lacks light adaptivity, and why its "weberized" version can more faithfully reflect human vision's superior segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein's distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford-Shah model with Bose-Einstein noise. In particular, Ambrosio-Tortorelli's Γ-convergence approximation theory is adapted (Boll. Un. Mat. Ital. B, vol. 6, pp. 105-123, 1992), and stable numerical algorithms are developed for the associated pair of nonlinear Euler-Lagrange PDEs.