On the speed of a cookie random walk

We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just three cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.      

用多色菲涅耳全息滤波器作彩色图像特征识别

本文在用多色匹配滤波器(MSF)作彩色图像相关检测和用菲涅耳全息滤波器(FHF)作无透镜强度相关的基础上,提出一种把两者结合起来的技术,即用多色菲涅耳全息滤波器实现彩色图像的相关检测.     

The LIL for <Emphasis Type="Italic">U</Emphasis>-Statistics in Hilbert Spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest. R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30. R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29.     

A parallel-multipoint fiber-optic temperature sensor based on Fresnel reflection

A parallel-multipoint fiber-optic temperature sensor for monitoring ambient temperature with a measured temperature resolution of approximately 0.03 °C is presented. The sensor relies on the temperature-dependent Fresnel reflection from each interface between a sensing fiber tip and a thermo-optic medium. An arrayed waveguide grating is used to achieve wavelength-division multiplexed-multipoint sensing. Applying the relative-intensity technique, the errors resulting from fluctuation of the light source and other influences of the environment are eliminated, and the stability for long time measurement can be improved.     

A non-dimensional approach to diffraction phenomena in the Fresnel approximation

The paper presents a theoretical and numerical study of the diffraction problem approached in the Fresnel approximation. The problem was formulated by a non-dimensional approach, which implies the definition of two non-dimensional quantities: F and ζ. In particular the parameter F is the well-known Fresnel number, whose value was usually used to classify diffraction regime. In analyzing the numerical approach some limitations imposed by the discretization arise; in particular these limitations constrain the level of sampling to be used for the diffracting field by requiring more and more elements when the diffraction conditions become more severe — i.e. increasing the dimension of the diffracting aperture and/or decreasing the distance of the plane where the diffracted field is observed.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation

Based on the displacement-squeezing related squeezed coherent state representation ≤ft\vert z\right\rangle _{g} and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens--Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz-rz^{\ast } in the % ≤ft\vert z\right\rangle _{g} representation, while ≤ft\vert z\right\rangle _{g} in phase space is graphically denoted by an ellipse.     

Imaging Magnetic Domain Structures with Soft X-Ray Microscopy

The current achievements in magnetic transmission soft X-ray microscopy will be reviewed. The magnetic contrast is given by X-ray magnetic circular dichroism (X-MCD), i.e., the dependence of the absorption coefficient of circularly polarized X rays on the projection of the magnetization in a ferromagnetic system onto the photon propagation direction. X-MCD contrast can reach, e.g., at L_2,3 edges in transition metals, large values up to 50%. Combined with a soft X-ray microscope where Fresnel zone plates acting as optical elements provide a lateral resolution down at 25 nm, it allows for imaging magnetic microstructures. Specific features of this photon-based technique are the recording of images in varying external magnetic fields, an inherent chemical specificity, a high sensitivity to thin magnetic layers, due to the large contrast, and the possibility to distinguish between in-plane and out-of plane contributions. In this report, recent results obtained with the XM-1 microscope at the ALS (Berkeley/CA) demonstrate the broad applicability of this novel experimental technique to both fundamental and technological relevant issues in nanomagnetism. The future potential will be briefly outlined.