REFINABLE DISTRIBUTIONS SUPPORTED ON SELF-AFFINE TILES

In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-Stieltjes measures are given.

On self-affine tiles that are homeomorphic to a ball

Let M be a 3×3 integer matrix which is expanding in the sense that each of its eigenvalues is greater than 1 in modulus and let D?Z^(3)be a digit set containing|det M|elements.Then the unique nonempty compact set T=T(M,D)defined by the set equation MT=T+D is called an integral self-affine tile if its interior is nonempty.If D is of the form D={0,v,...,(|det M|-1)v},we say that T has a collinear digit set.The present paper is devoted to the topology of integral self-affine tiles with collinear digit sets.In particular,we prove that a large class of these tiles is homeomorphic to a closed 3-dimensional ball.Moreover,we show that in this case,T carries a natural CW complex structure that is defined in terms of the intersections of T with its neighbors in the lattice tiling{T+z:z∈Z^(3)}induced by T.This CW complex structure is isomorphic to the CW complex defined by the truncated octahedron.

Boundary parametrization of planar self-affine tiles with collinear digit set

We consider a class of planar self-affine tiles T = M-1 a∈D(T + a) generated by an expanding integral matrix M and a collinear digit set D as follows:M =(0-B 1-A),D = {(00),...,(|B|0-1)}.We give a parametrization S1 →T of the boundary of T with the following standard properties.It is H¨older continuous and associated with a sequence of simple closed polygonal approximations whose vertices lie on T and have algebraic preimages.We derive a new proof that T is homeomorphic to a disk if and only if 2|A| |B + 2|.

Integral Self-affine Tiles of Bandt's Model

Integral self-affine tiling of Bandt＇s model is a generalization of the integral self-affine tiling. Using ergodic theory, we show that the Lebesgue measure of the tile is a rational number where the denominator equals to the order of the associate symmetry group. We apply the result to the study of the Levy Dragon.

可编辑三维场景的动态3D Tiles构建方法

可编辑的大型三维WebGIS具有一定的应用场景需求,常见的3DTiles数据格式局限于静态场景渲染,在编辑的三维场景中,需要构建动态的3D Tile文件格式和多细节层次(level of detail,Lo D)渲染方法。本文从动态空间索引和多细节层次技术两方面研究Web在线编辑大型三维场景的构建方法,将动态松散八叉树和半边折叠LoD构建算法应用于3D Tiles构建流程中,实现支持可编辑场景的3D Tiles构建与更新。结果表明:(1)松散八叉树索引在计算量上能够实现动态更新的目标,且在视锥体剔除上有着良好的精度;(2)基于半边折叠法进行准实时LoD的构建,能够满足动态场景下实时计算LoD的需求;(3)所构建的3D Tiles场景,配合Three.js等成熟框架并应用WebWorker等技术,能够顺利完成3DTiles的高效调度和渲染。研究成果对城市三维模型在线编辑、动态地理三维场景的加载渲染等相关研究和应用具有一定的参考价值。

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

THE UPPER BOUND OF BOX DIMENSION OF THE WEYL-MARCHAUD DERIVATIVE OF SELF-AFFINE CURVES

A certain type of self-affine curves can be transferred into fractal functions. The upper bound of fractal dimensions of the Weyl-Marchaud derivative of these functions has been investigated, and further questions have been put forwarded.

HAUSDORFF DIMENSION OF GENERALIZED STATISTICALLY SELF-AFFINE FRACTALS

The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.

Study on Properties of Intensity Profiles Scattered from the Self-Affine Fractal Random Surfaces: an Approximate Theory and Simulations

We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering,by letting them have the same maximum value and half-width,and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained.The previous results in the two extreme cases are included in the results of this paper.In the simulational verification,we propose a method for the generation of self-affine fractal random surfaces,using the square-root of Fourier transform of the correlation function of the surface height.The simulated results conform well with the theory.

Improved Flexible Triboelectric Nanogenerator Based on Tile-Nanostructure for Wireless Human Health Monitor

Triboelectric nanogenerators(TENGs)have emerged as promising candidates for integrating with flexible electronics as self-powered systems owing to their intrinsic flexibility,biocompatibility,and miniaturization.In this study,an improved flexible TENG with a tile-nanostructured MXene/polymethyl methacrylate(PMMA)composite electrode(MP-TENG)is proposed for use in wireless human health monitor.The multifunctional tile-nanostructured MXene/PMMA film,which is self-assembled through vacuum filtration,exhibits good conductivity,excellent charge capacity,and high flexibility.Thus,the MXene/PMMA composite electrode can simultaneously function as a charge-generating,charge-trapping,and charge-collecting layer.Furthermore,the charge-trapping capacity of a tile nanostructure can be optimized on the basis of the PMMA concentration.At a mass fraction of 4%PMMA,the MP-TENG achieves the optimal output performance,with an output voltage of 37.8 V,an output current of 1.8μA,and transferred charge of 14.1 nC.The output power is enhanced over twofold compared with the pure MXene-based TENG.Moreover,the MP-TENG has sufficient power capacity and durability to power small electronic devices.Finally,a wireless human motion monitor based on the MP-TENG is utilized to detect physiological signals in various kinematic motions.Consequently,the proposed performance-enhanced MP-TENG proves a considerable potential for use in health monitoring,telemedicine,and self-powered systems.

Self-Affine Fractals and the Fractal Dimension of Fractured Rock Profiles

The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same

Non-Spectral Problem of Self-Affine Measures in R³

The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on μM,D is to estimate the number of orthogonal exponentials in L2(μM,D). In the present paper, we establish some relations inside the zero set by the Fourier transform of the self-affine measure μM,D. Based on these facts, we show that μM,D is a non-spectral measure and there exist at most 4 mutually orthogonal exponential functions in L2(μM,D), where the number 4 is the best possible. This extends several known conclusions.

基于3D Tiles的大规模三维地质模型共享技术研究

针对三维地质模型的网络共享与发布研究较少,基于3D Tiles提出了一种大规模三维地质模型共享发布方案:首先采用基于二次误差测度(QEM)的半边折叠算法,对模型进行简化,建立分层LOD模型;再利用平面四叉树+纵向固定距离切分的方法对各级模型进行分块,建立瓦片分层结构树;最后计算出所需的几何误差、变换矩阵等参数,并生成3D Tiles瓦片内容及瓦片集描述文件。基于此方案选取了某区域约1000 km^(2)的三维地质体模型进行了实验,实验表明该方案在保障模型的几何特征和细节表现的同时,可对大规模三维地质模型进行高效、流畅的加载与显示。

经皮骶髂置钉内固定联合前环外固定架手术治疗Tile B、C型骨盆骨折患者的疗效观察

目的观察经皮骶髂置钉内固定联合前环外固定架手术治疗Tile B、C型骨盆骨折患者疗效及并发症。方法以2020年1月至2022年12月山东省聊城市中医医院收治的Tile B、C型骨盆骨折患者为研究对象,选择其中接受前路切开复位骨板内固定传统手术的87例患者为传统组,另选择接受经皮骶髂置钉内固定联合前环外固定架手术的89例患者为联合组。比较两组患者手术相关指标,术后3 d、7 d、14 d疼痛视觉模拟评分法(VAS)评分,术后3个月与6个月Majeed功能评分、Matta评分及并发症发生率。结果联合组患者手术时间短于传统组,出血量少于传统组,差异均有统计学意义(P<0.05);两组住院时间、负重行走时间、骨折愈合时间比较,差异均无统计学意义(P>0.05)。两组患者术后3 d、7 d、14 d时VAS评分差异均无统计学意义(P>0.05)。联合组患者术后3个月Majeed功能评分、Matta评分优良率高于传统组,差异具有统计学意义(P<0.05)。两组患者术后6个月Majeed功能评分、优良率差异无统计学意义(P>0.05)。联合组患者并发症发生率低于传统组,差异具有统计学意义(P<0.05)。结论与传统手术治疗Tile B、C型骨盆骨折相比,经皮骶髂置钉内固定联合前环外固定架手术可缩短手术时间,减少术中出血量,降低术后并发症风险。

基于Vector 3D Tiles格式的三维矢量数据可视化研究

为了探究Vector 3D Tiles格式在三维矢量地物表达方面的效果和性能,研究了一套Vector 3D Tiles格式生产和表达工具,用于在Cesium平台上对矢量数据进行可视化展示。主要工作包括两部分:一是将数据从传统的矢量格式转换为Vector 3D Tiles格式,二是在Cesium平台上展示转换后的Vector 3D Tiles数据。为了验证方法可行性,采用广州市地下管线数据开展了实验,对Shapefile、GeoJSON二维矢量格式进行处理,生成Vector 3D Tiles格式后,在Cesium平台上进行三维可视化展示。通过不同格式数据的加载效率和呈现效果比较,证明了矢量切片数据比原始矢量格式加载更快、渲染更平滑。在此基础上,对矢量切片数据基于自定义三维样式的渲染能力进行了验证。

骨盆骨折Tile分类与患者早期输血量之间的关系

目的 :研究骨盆骨折Tile分类与患者输血量之间的关系 ,便于对骨折患者的输血量进行预测 ,指导临床早期对血流动力学不稳患者的救治 ,减少死亡率。方法 :回顾性研究 5年间我院收治的 97例骨盆骨折患者 (平均年龄 40 .7岁 )输血量、ISS评分、伴发损伤、住院时间、死亡率等与骨折不同分类之间的关系。结果 :3型骨折患者骨折的严重程度与输血量、ISS、死亡率等 ,各组之间具统计学显著性差异。患者平均输血量为 912ml ,其中C组平均输血 2 2 0 0ml。ISS评分平均为 18.4,其中C组为 2 8.7。死亡率平均为 5 .2 % ,C组平均为 19.0 %。并且骨折的 3组分类的伴发损伤之间也有统计学上差别。结论 :Tile骨折分类方法能对骨盆骨折患者输血量有一定的预测价值。骨折类型越严重 ,患者早期复苏时的输血量就越多 。

基于TileStache的多源投影矢量数据瓦片生成技术研究

瓦片技术的出现改变了传统Web GIS的服务架构,提高了地图数据请求响应的效率。针对多种地图投影类型或地理坐标的矢量数据在瓦片划分过程中遇到的问题,本文基于OGR地理数据模型,设计了多投影数据转换Python模块,扩展至开源应用程序Tile Stache,得到适用于多源投影矢量地理数据的瓦片生成工具OTile Tool;从而实现矢量地理数据瓦片的快速生成,为网络地理信息系统提供了表达地理信息的Geo JSON格式瓦片数据。

Tile C 型骨盆骨折患者死亡相关危险因素分析

目的：回顾性分析 Tile C 型骨盆骨折患者死亡相关的危险因素。方法2010年1月至2014年12月我院收治的 Tile C 型骨盆骨折患者139例,收集资料包括术前一般情况、伤后就诊时间、休克指数、各类创伤评分、最低氧合指数、伤后6 h 乳酸清除率等,采用多因素 Logistic 回归分析死亡相关危险因素。结果入院后死亡41例（29.5%）,其中入院后48 h 内死亡36例（25.9%）。多因素回归分析显示,休克指数＆gt;2（OR=2.591,95%CI 1.041~4.216）、损伤严重程度评分（ISS）≥25分（OR=47.96,95%CI 15.89~147.23）、改良创伤评分（RTS）≤8分（OR=6.917,95%CI 1.147-13.862）、格拉斯哥昏迷评分（GCS）〈9分（OR=4.172,95%CI 2.962~6.268）、最低氧合指数〈200（OR=117.016,95%CI 51.011~176.032）、伤后6 h 乳酸清除率〈10%（OR=2.785,95%CI 1.191~4.892）,以及合并头部损伤（OR=6.302,95%CI 2.270~13.175）或胸部损伤（OR=12.233,95%CI 5.193~33.985）是骨盆骨折患者死亡相关危险因素（P 〈0.01）。早期行血管栓塞治疗有助于降低死亡风险（OR=0.887,95%CI 0.875~0.899）。结论创伤评分高,出现严重休克、昏迷、氧合指数下降和6 h 乳酸清除率降低,合并头部和胸部损伤是导致 Tile C 型骨盆骨折患者死亡的危险因素。

基于PSO的Wang Tiles纹理合成

如何在纹理样图中选择组成Wang Tiles的图像块决定着纹理的合成质量。基于PSO的Wang Tiles纹理合成通过粒子群优化算法在纹理样图中快速搜索边界差异最小的图像块,并用选取的图像块构建Wang Tiles,最后用Wang Tiles纹理合成算法合成纹理。实验表明,该算法合成的纹理具有较少的接缝,比随机选择图像块具有更好的合成效果。

基于Tile自组装模型的最大匹配问题算法研究

Tile自组装模型作为一种重要的DNA计算模型,在解决NP问题时展现出了巨大优势.文中针对现有最大匹配问题DNA计算算法实验操作复杂,错误率高的缺点,提出了一种基于Tile自组装模型的最大匹配问题新算法.算法所需的Tile分子种类为O(mn),所需生物操作数为O(1),计算时间为O(m),计算空间复杂度为O(mn)(其中m为边数,n为顶点数,且O(m)=O(n2)).与现有的最大匹配问题DNA计算算法相比,本算法不仅可靠性更好,而且更具可操作性.