scholarly journals On the dimensions of a family of overlapping self-affine carpets

2015 ◽  
Vol 36 (8) ◽  
pp. 2463-2481 ◽  
Author(s):  
JONATHAN M. FRASER ◽  
PABLO SHMERKIN
Keyword(s):  
Recent Work ◽  
Column Structure ◽  
Small Set ◽  
Self Similar ◽  
Key Features ◽  
Set Up ◽  
Partial Extension ◽  
Box Dimensions

We consider the dimensions of a family of self-affine sets related to the Bedford–McMullen carpets. In particular, we fix a Bedford–McMullen system and then randomize the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford–McMullen set-up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, Hochman’s recent work on the dimensions of self-similar sets and measures.

Dimensions of an overlapping generalization of Barański carpets

2017 ◽  
Vol 39 (3) ◽  
pp. 733-763 ◽  
Author(s):  
LETICIA PARDO-SIMÓN
Keyword(s):  
Hausdorff Dimension ◽  
Recent Work ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Small Set ◽  
Self Similar

We determine the Hausdorff, the packing and the box-counting dimensions of a family of self-affine sets generalizing Barański carpets. More specifically, we fix a Barański system and allow both vertical and horizontal random translations, while preserving the structure of the rows and columns. The alignment kept in the construction allows us to give expressions for these fractal dimensions outside of a small set of exceptional translations. Such formulae will coincide with those for the non-overlapping case, and thus provide examples where the box-counting and the Hausdorff dimension do not necessarily agree. These results rely on Hochman’s recent work on the dimensions of self-similar sets and measures, and can be seen as an extension of Fraser and Shmerkin [On the dimensions of a family of overlapping self-affine carpets. Ergod. Th. & Dynam. Sys.doi: 10.1017/etds.2015.21. Published online: 21 July 2015] results for Bedford–McMullen carpets with columns overlapping.

Falconer's formula for the Hausdorff dimension of a self-affine set in R2

1995 ◽  
Vol 15 (1) ◽  
pp. 77-97 ◽  
Author(s):  
Irene Hueter ◽  
Steven P. Lalley
Keyword(s):  
Hausdorff Dimension ◽  
Dimensional Hausdorff Measure ◽  
Similarity Transformations ◽  
Affine Mappings ◽  
Finite Set ◽  
Self Similar ◽  
Image Position ◽  
Affine Set ◽  
Small Overlap ◽  
Box Dimensions

Let A1, A2,…,Ak be a finite set of contractive, affine, invertible self-mappings of R2. A compact subset Λ of R2 is said to be self-affine with affinitiesA1, A2,…,Ak ifIt is known [8] that for any such set of contractive affine mappings there is a unique (compact) SA set with these affinities. When the affine mappings A1, A2,…,Ak are similarity transformations, the set Λ is said to be self-similar. Self-similar sets are well understood, at least when the images Ai(Λ) have ‘small’ overlap: there is a simple and explicit formula for the Hausdorff and box dimensions [12, 10]; these are always equal; and the δ-dimensional Hausdorff measure of such a set (where δ is the Hausdorff dimension) is always positive and finite.

On-Line Industrial 3D Measurement Techniques for Large Volume Objects

2005 ◽  
Vol 295-296 ◽  
pp. 423-430 ◽  
Author(s):  
Ji Gui Zhu ◽  
S.H. Ye ◽  
Xue You Yang ◽  
Xing Hua Qu ◽  
C.J. Liu ◽  
...  
Keyword(s):  
Large Volume ◽  
Measurement Techniques ◽  
Integrated System ◽  
3D Measurement ◽  
Digital Cameras ◽  
Combined Use ◽  
Small Set ◽  
Close Range ◽  
On Line ◽  
Set Up

Rapid progress in modern manufacturing demands for better measurement technique with on-line characteristics. This paper presents a systematic visual solution for on-line industrial 3D measurement. The solution comprises two parts, a multi-sensor visual inspecting station (MSVIS) and a digital close-range visual inspecting station (DCVIS). MSVIS is an integrated system with many sensors. It can meet the requirement of application with sparse measuring points distributed within a large volume. DCVIS only contains two digital cameras with one or more projectors. It has high relative accuracy and a small set up volume and is suitable for applications with dense measuring points. The combined use of MSVIS and DCVIS can provide a general solution for on-line industrial 3D measurement.

On the application of a single-crystal κ-diffractometer and a CCD area detector for studies of thin films

2013 ◽  
Vol 20 (4) ◽  
pp. 644-647 ◽  
Author(s):  
Henrik Hovde Sønsteby ◽  
Dmitry Chernyshov ◽  
Michael Getz ◽  
Ola Nilsen ◽  
Helmer Fjellvåg
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Crystal Orientation ◽  
Atomic Layer ◽  
Area Detector ◽  
Layer Deposition ◽  
Crucial Information ◽  
Key Features ◽  
Set Up

A multipurpose six-axis κ-diffractometer, together with the brilliance of the ESRF light source and a CCD area detector, has been explored for studying epitaxial relations and crystallinity in thin film systems. The geometrical flexibility of the six-axis goniometer allows measurement of a large volume in reciprocal space, providing an in-depth understanding of sample crystal relationships. By a set of examples of LaAlO3thin films deposited by the atomic layer deposition technique, the possibilities of the set-up are presented. A fast panoramic scan provides determination of the crystal orientation matrices, prior to more thorough inspection of single Bragg nodes. Such information, in addition to a broadening analysis of families of single reflections, is shown to correlate well with the crystallinity, crystallite size, strain and epitaxial relationships in the thin films. The proposed set-up offers fast and easy sample mounting and alignment, along with crucial information on key features of the thin film structures.

scholarly journals REINVENTING THE NATIONAL TOPOGRAPHIC DATABASE

2016 ◽  
Vol XLI-B4 ◽  
pp. 733-736 ◽  
Author(s):  
A. Jakobsson ◽  
R. Ilves
Keyword(s):  
Technical Architecture ◽  
Land Survey ◽  
Key Features ◽  
Set Up

The National Land Survey (NLS) has had a digital topographic database (TDB) since 1992. Many of its features are based on the Basic Map created by M. Kajamaa in 1947, mapping first completed in 1977. The basis for the renewal of the TDB begun by investigating the value of the TDB, a study made by the Aalto University in 2014 and a study on the new TDB system 2030 published by the Ministry of Agriculture in 2015. As a result of these studies the NLS set up a programme for creating a new National Topographic Database (NTDB) in beginning of 2015. First new version should be available in 2019. The new NTDB has following key features: 1) it is based on processes where data is naturally maintained, 2) it is quality managed, 3) it has persistent Ids, 4) it supports 3D, 4D, 5) it is based on standards. <br><br> The technical architecture is based on interoperable modules. A website for following the development of the NTDB can be accessed for more information: <a href="http://kmtk.maanmittauslaitos.fi/"target="_blank">http://kmtk.maanmittauslaitos.fi/</a>.

scholarly journals Pathways and Obstacles to eParticipation at the European level

2010 ◽  
Vol 2 (2) ◽  
pp. 99-110 ◽  
Author(s):  
Romain Badouard
Keyword(s):  
European Union ◽  
The European Union ◽  
European Level ◽  
European Context ◽  
Online Consultation ◽  
European Institutions ◽  
Collateral Effects ◽  
Key Features ◽  
Institutional Strategies ◽  
Set Up

Since the early 2000's, the European Institutions have set up several eParticipation projects. These projects are embedded in different political strategies and are managed by different actors within the institutions. This leads to a wide variety of projects and prevents the European Union to develop a single and concerted strategy in terms of online participation.This paper intends to compare two different models of online consultation : the Commission consultations hosted on the site Your Voice in Europe, and the European Citizens' Consultation 2009. The paper tackles three main subjects : the institutional strategies which frame these sites; the actors that they mobilize; their main and collateral effects. The goal of this synthesis is to identify some key features that fit to the european context, in order to assess the possibilities of sustainability of such political experiments.

2 Highlights

2018 ◽  
Author(s):  
Lichtenstein Natalie
Keyword(s):  
World Bank ◽  
The Other ◽  
Multilateral Development Banks ◽  
The World Bank ◽  
The World ◽  
Key Features ◽  
Similarities And Differences ◽  
Development Banks ◽  
Set Up

Chapter 2, Highlights, offers a survey of the key features of the AIIB Charter that define AIIB, in close comparison with the Charters of other multilateral development banks (AfDB, AsDB, EBRD, IADB and the World Bank). The highlights of the coming Chapters are summarized, offering answers to the basic questions about AIIB: Why establish AIIB? (Mandate, Chapter 3) What will AIIB do? (Investment Operations, Chapter 4) Who will join AIIB? (Membership, Chapter 5) How will AIIB be funded? (Capital and Finance, Chapter 6) How will AIIB be run? (Governance, Chapter 7) How was AIIB first set up? (Transitions, Chapter 8) How will the organization work? (Institutional Matters, Chapter 9). The Chapter concludes with some observations about heritage and innovation in the AIIB Charter, outlining principal similarities and differences with the other Charters.

scholarly journals Adequate target volume in total-body irradiation by intensity-modulated radiation therapy using helical tomotherapy: a simulation study

2016 ◽  
Vol 58 (2) ◽  
pp. 210-216 ◽  
Author(s):  
Ryosuke Takenaka ◽  
Akihiro Haga ◽  
Hideomi Yamashita ◽  
Keiichi Nakagawa
Keyword(s):  
Radiation Therapy ◽  
Total Body Irradiation ◽  
Intensity Modulated Radiation Therapy ◽  
Target Volume ◽  
The Body ◽  
High Fluence ◽  
Intensity Modulated ◽  
Small Set ◽  
Total Body ◽  
Set Up

Abstract Recently, intensity-modulated radiation therapy (IMRT) has been used for total-body irradiation (TBI). Since the planning target volume (PTV) for TBI includes the surrounding air, a dose prescription to the PTV provides high fluence to the body surface. Thus with just a small set-up error, the body might be exposed to a high-fluence beam. This study aims to assess which target volume should be prescribed the dose, such as a clinical target volume (CTV) with a margin, or a CTV that excludes the surface area of the skin. Three treatment plans were created for each patient: the 5-mm clipped plan (Plan A), the 0-mm margin plan (Plan B) and the 5-mm margin plan (Plan C). The CTV was the whole body. PTVs were the CTV with the exception of 5 mm from the skin surface in Plan A, equal to the CTV in Plan B, and the CTV with a 5 mm margin in Plan C. The prescribed dose was 12 Gy in six fractions. To assess the influence of the set-up error, dose distributions were simulated on computed tomography (CT) images shifted 2 pixels (= 4.296 mm), 5 pixels (= 10.74 mm) and 10 pixels (= 21.48 mm) in the lateral direction from the original CT. With a set-up error of 10.74 mm, V110% was 8.8%, 11.1% and 23.3% in Plans A, B and C, respectively. The prescription to the PTV containing the surrounding air can be paradoxically vulnerable to a high-dose as a consequence of a small set-up error.

Grading Fish for Quality. 2. Statistical Analysis of the Results of Experiments Regarding Grades and Trimethylamine values

1958 ◽  
Vol 15 (4) ◽  
pp. 717-728 ◽  
Author(s):  
P. L. Hoogland
Keyword(s):  
Statistical Analysis ◽  
Linear Regression ◽  
Recent Work ◽  
Statistical Treatment ◽  
Regression Equation ◽  
Linear Regression Equation ◽  
Grade Ii ◽  
Set Up ◽  
Grade Iii

The results of recent work at this station regarding the organoleptic grade of cod and haddock and the trimethylamine content of these fish were subjected to statistical treatment. It was established that there is a relation between grade and trimethylamine content which may be represented by a linear regression equation, if the trimethylamine content is expressed as log (1 + TMA value). The confidence with which this TMA index may be used to estimate grade was also determined. Based on these findings, a scale of TMA values for use in practical grading was set up; the suggested values are grade I: TMA value 0.00 to 1.00; grade II: TMA value 1.01 to 7.00 and grade III: TMA value 7.01 and higher. Finally, a method is suggested by means of which the ability of a grader to judge the quality of fish may be assessed.

scholarly journals Inhomogeneous self-similar sets and box dimensions

2012 ◽  
Vol 213 (2) ◽  
pp. 133-156 ◽  
Author(s):  
Jonathan M. Fraser
Keyword(s):  
Self Similar ◽  
Box Dimensions
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