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.

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。

3D打印技术下空心螺钉微创固定对Tile B型骨盆骨折的近期疗效及并发症的影响

目的 探究3D打印技术下空心螺钉微创固定对Tile B型骨盆骨折的近期疗效及并发症的影响。方法 选取四川省广元市中心医院2019年6月至2022年10月收治的80例Tile B型骨盆骨折患者作为研究对象,按照Excel软件随机分组方法分为对照组(40例)与观察组(40例),对照组采用空心螺钉微创固定治疗方法,观察组采用3D打印技术下空心螺钉微创固定治疗方法。比较两组患者治疗指标(手术时间、术中透视次数、伤口愈合时间、功能恢复时间)、治疗效果、并发症发生率及治疗满意度。结果 观察组患者手术时间、伤口愈合时间、功能恢复时间均短于对照组,术中透视次数少于对照组(均P<0.001);观察组治疗有效率高于对照组(90.0%vs. 67.5%,P=0.014);观察组并发症发生率较对照组低(7.5%vs. 27.5%,P=0.019);观察组治疗满意度高于对照组(95.0%vs. 75.0%,P=0.012)。结论 3D打印技术下空心螺钉微创固定治疗Tile B型骨盆骨折可取得良好的治疗效果,能缩短手术时间,促进患者伤口愈合,加快骨盆功能恢复,减少术中透视次数,并能降低患者并发症发生率,使患者获得较高的治疗满意度。

INFIX技术与外固定支架分别联合骶髂关节螺钉治疗Tile B型骨折的效果观察

目的:探讨前环皮下内置外固定架(INFIX)技术与外固定支架分别联合骶髂关节螺钉治疗Tile B型骨折的效果。方法:回顾性分析2019年3月至2022年3月就诊于本院骨科的88例Tile B型骨折患者,其中47例给予INFIX技术+骶髂关节螺钉治疗(INFIX组),41例给予外固定支架+骶髂关节螺钉治疗(外固定支架组),比较两组手术时间、术中出血量、住院时间、术后负重时间、愈合时间、并发症发生率、Matta评分、Majeed评分以及术后1、3、6个月EQ-5D评分及VAS评分。结果:INFIX组住院时间及愈合时间均短于外固定支架组,并发症发生率低于外固定支架组(P<0.05);术后6个月,INFIX组Matta评分优良率(95.74%)高于外固定支架组(80.49%)(P<0.05);INFIX组性生活评分高于外固定支架组(P<0.05);EQ-5D评分及VAS评分组间、时间点及交互差异均有统计学意义(P<0.0001),术后1个月及术后3个月INFIX组EQ-5D评分均大于外固定支架组,术后1个月及术后3个月INFIX组VAS评分均小于外固定支架组(P<0.05)。结论:INFIX技术联合骶髂关节螺钉治疗Tile B型骨折临床疗效更好,恢复期短,更有利于患者进行早期功能性锻炼,且并发症发生率较低。

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.

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.

Implementation of a 3D WebGIS for Dynamic Geo-Referencing of 3D Tiles on the Virtual Globe

Needs for real-time interactive visualization of 3D Tiles for massive 3D content on the web-based virtual globe is rapidly increasing, and to achieve this goal, 3D Tiles needs to be correctly geo-referenced to other geospatial data on a web-based virtual globe. It is possible to generate 3D Tiles from different kinds of spatial data through various software tools. However, due to various factors the 3D Tile datasets are often poorly or not at all geo-referenced. To tackle this issue, we propose a new 3D WebGIS framework that facilitates dynamic geo-referencing 3D Tiles on the CesiumJS virtual globe.

A Sketch-Based Generation Model for Diverse Ceramic Tile Images Using Generative Adversarial Network

Ceramic tiles are one of the most indispensable materials for interior decoration.The ceramic patterns can’t match the design requirements in terms of diversity and interactivity due to their natural textures.In this paper,we propose a sketch-based generation method for generating diverse ceramic tile images based on a hand-drawn sketches using Generative Adversarial Network(GAN).The generated tile images can be tailored to meet the specific needs of the user for the tile textures.The proposed method consists of four steps.Firstly,a dataset of ceramic tile images with diverse distributions is created and then pre-trained based on GAN.Secondly,for each ceramic tile image in the dataset,the corresponding sketch image is generated and then the mapping relationship between the images is trained based on a sketch extraction network using ResNet Block and jump connection to improve the quality of the generated sketches.Thirdly,the sketch style is redefined according to the characteristics of the ceramic tile images and then double cross-domain adversarial loss functions are employed to guide the ceramic tile generation network for fitting in the direction of the sketch style and to improve the training speed.Finally,we apply hidden space perturbation and interpolation for further enriching the output textures style and satisfying the concept of“one style with multiple faces”.We conduct the training process of the proposed generation network on 2583 ceramic tile images dataset.To measure the generative diversity and quality,we use Frechet Inception Distance(FID)and Blind/Referenceless Image Spatial Quality Evaluator(BRISQUE)metrics.The experimental results prove that the proposed model greatly enhances the generation results of the ceramic tile images,with FID of 32.47 and BRISQUE of 28.44.

Synthesis of Ceramic Tiles Reinforced with Addition of Aluminum Particulate Waste

Research conducted on ceramic materials has been investigating the incorporation of solid waste into their formulations,driven by the proper disposal of such waste and the reduction of negative environmental impacts.This study analyzed the effects of adding aluminum powder residue to the physical properties of ceramic masses with the aim of obtaining new formulations for ceramic tiles.The aluminum residue and the standard mass for ceramic tile production were chemically characterized and homogenized to obtain new formulations with the incorporation of 4%,6%,8%,and 10%aluminum powder in the ceramic mass.The specimens were uniaxially pressed and sintered at a temperature of 1,200°C for 2 h,undergoing three different temperatures(100°C,400°C,and 650°C)for 30 min each.They were evaluated for WA(water absorption),RLq(linear shrinkage),SEM(scanning electron microscopy),and TRF(flexural strength)modulus.The results demonstrate that the addition of aluminum powder residue is feasible in the proposed formulations(4%,6%,8%,and 10%),as they enhance the mechanical properties of the ceramics compared to the formulation with 0%residue,at a sintering temperature of 1,200°C.

修复缺陷嫌疑区域的无监督磁瓦表面缺陷检测

磁瓦表面缺陷样本数量少,异常视觉特征分布发散,现有依赖目标特征的有监督检测方法不能有效检测未定义缺陷;磁瓦表面正常纹理呈非均匀且非周期性分布,使得经典重构网络难以准确地重构磁瓦表面正常特征,导致相关无监督检测方法性能低下.为此,采用多头注意力增强的掩码图像修复网络(MIINet),长距离提取图像特征,捕捉全局信息,增强图像修复的能力;引入视觉显著性算法抑制磁瓦表面纹理信息和突显缺陷区域,以便二值化算法精准分割缺陷嫌疑区域;利用MIINet修复待检测图像缺陷嫌疑区域,选用修复前后图像的残差图像和结构相似性实现缺陷检测与缺陷判定.与经典无监督方法相比,修复缺陷嫌疑区域的表面缺陷检测方法的准确率提升了2.36%,F1值提升了1.62%.

基于要素稠度的电子海图矢量瓦片组合构建方法

为进一步提升基于WebGIS技术的电子海图在前端的加载效率,对海图矢量瓦片的划分方法进行深入研究。在考虑要素空间分布稠度的基础上,提出一种海图瓦片的组合格网划分方法。在四叉树划分过程中引入矢量瓦片数据阈值将其改造成非平衡四叉树,作为瓦片划分的第1阶段,在瓦片划分至单瓦片最大数据量小于数据阈值后,通过融合变异系数的二叉树对瓦片进行第2阶段的划分。将组合格网法、原始均匀格网法和改进均匀格网法生成的矢量瓦片数据与试验结果进行对比。研究结果表明,在瓦片第3~第9层级范围内,相对于2种均匀格网法,基于要素稠度的组合格网法生成的矢量瓦片在同一层级的标准差更小,矢量要素在瓦片上的分布更加均衡,在同一视窗范围内,组合格网法生成的瓦片加载时间更短。

莆田地震台铟瓦棒伸缩仪故障分析及维修技术研究

该文论述莆田地震台形变观测仪器SS-Y型铟瓦棒伸缩仪近几年来的故障,从电源、主机、传感器、线路故障等几个方面对故障进行整理、分类、统计。通过故障的表现形式分析故障原因,整理出不同故障曲线形态产生的原因。总结莆田地震台维修经验,结合其他台站经验,针对不同故障给出维修方案,可为其他相关地震台站提供借鉴。