scholarly journals Subdividing three-dimensional Riemannian disks

2016 ◽  
Vol 09 (03) ◽  
pp. 533-550
Author(s):  
Parker Glynn-Adey ◽  
Zhifei Zhu
Keyword(s):  
Three Dimensional ◽  
Area Formula ◽  
Homotopy Formula ◽  
Boundary Area ◽  
Volume Formula

Papasoglu asked whether for any Riemannian 3-disk [Formula: see text] with diameter [Formula: see text], boundary area [Formula: see text] and volume [Formula: see text], there exists a homotopy [Formula: see text] contracting the boundary to a point so that the area of [Formula: see text] is bounded by [Formula: see text] for some function [Formula: see text]. He further asks whether it is possible to subdivide [Formula: see text] by a disk [Formula: see text] into two regions of volume [Formula: see text] so that the area of [Formula: see text] is bounded by some function [Formula: see text]. In this paper, we answer the questions above in the negative: We prove that given [Formula: see text] and [Formula: see text], one can construct a metric [Formula: see text] so that any 2-disk [Formula: see text] subdividing [Formula: see text] into two regions of volume at least [Formula: see text], the area of [Formula: see text] is greater than [Formula: see text]. We further prove that for any Riemannian 3-sphere [Formula: see text], there is a surface that subdivides the disk into two regions of volume no less than [Formula: see text], and the area of this surface is bounded by [Formula: see text], where [Formula: see text] is the homological filling function of [Formula: see text].

scholarly journals UPAYA PENINGKATKAN PEMAHAMAN RUMUS PADA LUAS PERMUKAAN BANGUN RUANG SISI DATAR DENGAN METODE PENGAJARAN INQUIRY DISCOVERY LEARNING DAN PEMANFAATAN MEDIA TIGA DIMENSI DI SMP NEGERI 4 SIBABANGUN

PeTeKa ◽  
2018 ◽  
Vol 1 (2) ◽  
pp. 115
Author(s):  
Samson Panggabean
Keyword(s):  
Action Research ◽  
Three Dimensional ◽  
Class Action ◽  
Discovery Learning ◽  
Male Students ◽  
Area Formula ◽  
Flat Side ◽  
Research Procedure ◽  
Research Grade ◽  
Waking Up

See the low understanding of student learning outcomes and on subjects of mathematics focused on, whether the application of the Learning Metode of inquiry – discovery learning with three-dimensional media graphics can enhance the understanding of the students against the formula on the widespread the surface of the flat-sided room wake up on subjects of mathematics grade VIII SMP Negeri 4 even semester Sibabangun. The purpose of this class action research is to find out whether there is an increased understanding of the students against the surface area formula woke up flat-side space in the subject of mathematics the lesson using the learning metode of inquiry-discovery learning media with three-dimensional graphics. This research procedure includes twocycles where each cycle comprising planning, implementation, observation, and reflection. Class action research was conducted in the State JUNIOR 4 Sibabangun, with the object of research grade VIII totaling 42 students, consisting of 17 female students and 25 male students. The results showed that Math learning by using learning metode of inquiry-discovery learning can improve the understanding of the students against the formation of extensive formula is found waking up flat-side room with the results of the cycle I 59.04% and the cycle II 70.02%, and (2) an increase in the diprosentasekan cycle 1 to cycle 2 = 10.98%.Keywords: improve understanding of learning Media, three-dimensional graphics, metodes of inquiry-discovery learning. 

scholarly journals IDENTIFIKASI KEBERADAAN BENDA ASING PADA AREA PENGUKURAN TOMOGRAFI DENGAN MENGGUNAKAN METODA ELECTRICAL IMPEDANCE TOMOGRAPHY (EIT) BERBASIS LABVIEW

2018 ◽  
Vol 17 (2) ◽  
Author(s):  
Endang Wijaya ◽  
Sastra Kusuma Wijaya
Keyword(s):  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Three Dimensional ◽  
Test Sample ◽  
Test Results ◽  
Impedance Tomography ◽  
Boundary Area ◽  
3D Images ◽  
Foreign Objects ◽  
3D Image Reconstruction

ABSTRACTEIT (Electrical Impedance Tomography) is one of several tomographic methods to estimate impedance distribution in a domain based on the measurement of a boundary area in a certain area. This method is widely used to observe the presence and growth of foreign matter in the area observed, such as cancer in the breast.In this study an instrument was designed to identify the presence and geometry of foreign objects, which were placed in the area of tomography measurement (phantom) in the form of three-dimensional (3D) images, Data acquisition instrument uses NI USB 6351 and LabVIEW (hard & software), with l testing and analysis of 3D image reconstruction using a modeling algorithm "n3r2",The test results can be concluded that the EIT instrument model is able to detect the presence and location of test samples placed in the tomography measurement area (phantom), although 3D images that appear to be unrepresentative illustrate the geometry of the test sample. This is due to an error in the data generated by three (3), namely S0-S1, S1-S2, and S31-S.Keysword : Method, EIT, LabView, 3D, algoritm”n3r2”ABSTRAKEIT (Electrical Impedance Tomography) adalah satu diantara beberapa metode tomografi untuk memperkirakan distribusi impedansi dalam suatu domain berdasarkan pengukuran daerah batas di tertentu. Metode ini banyak digunakan untuk mengamati keberadaan dan pertumbuhan benda asing pada daerah yang diamati, seperti kanker pada payudara.Dalam penelitian ini dirancang instrumen untuk mengidentifikasi keberadaan dan bentuk geometri benda asing, yang diletakkan pada daerah pengukuran tomografi (phantom) dalam bentuk gambar tiga dimensi (3D), Instrument akuisisi data menggunakan NI USB 6351 dan LabVIEW (hard & software),dengan l pengujian dan analisis rekonstruksi gambar 3D menggunakan dengan pemodelan algoritma “n3r2”,Hasil pengujian dapat disimpulkan bahwa model instrumen EIT mampu mendeteksi keberadaan dan lokasi sampel uji yang diletakkan`di dalam area pengukuran tomografi (phantom), meskipun gambar 3D yang nampak belum representatif menggambarkan bentuk geometri dari sampel uji. Hal ini disebabkan adanya kesalahan data yang dihasilkan oleh tiga (3) yaitu S0-S1, S1-S2, dan S31-S0.Kata kunci: Metode, EIT, LabView, 3D, algoritma”n3r2”

scholarly journals Three-Dimensional Stefan Equation for Thermokarst Lake and Talik Geometry Characterization

2021 ◽  
Author(s):  
Noriaki Ohara ◽  
Benjamin M. Jones ◽  
Andrew D. Parsekian ◽  
Kenneth M. Hinkel ◽  
Katsu Yamatani ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Ground Subsidence ◽  
The Arctic ◽  
Permafrost Region ◽  
Boundary Area ◽  
Near Surface ◽  
Thermokarst Lakes ◽  
Thermokarst Lake ◽  
Permafrost Thaw ◽  
Transient Electromagnetic

Abstract. Thermokarst lake dynamics, which plays an essential role in carbon release due to permafrost thaw, is affected by various geomorphological processes. In this study, we derive a three-dimensional (3D) Stefan equation to characterize talik geometry under a hypothetical thermokarst lake in the continuous permafrost region. Using the Euler equation in the calculus of variations, the lower bounds of the talik were determined as an extremum of the functional describing the phase boundary area with a fixed total talik volume. We demonstrate that the semi-ellipsoid geometry of the talik is optimal for minimizing the total permafrost thaw under the lake for a given annual heat supply. The model predicting ellipsoidal talik geometry was verified by talik thickness observations using transient electromagnetic (TEM) soundings in Peatball Lake on the Arctic Coastal Plain (ACP) of Alaska. The lake width-depth ratio of the elliptic talik can characterize the energy flux anisotropy in the permafrost although the lake bathymetry cross section may not be elliptic due to the presence of near-surface ice-rich permafrost. This theory suggests that talik development stabilizes thermokarst lakes by ground subsidence due to permafrost thaw while wind-induced waves and currents are likely responsible for the elongation and orientation of thermokarst lakes in certain regions such as the ACP of northern Alaska.

scholarly journals Three-Dimensional Morphological Characteristics of Lower Lumbar Intervertebral Foramen with Age

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Shuaifeng Yan ◽  
Yunfan Zhang ◽  
Kai Wang ◽  
Yingchao Han ◽  
Kai Zhu ◽  
...  
Keyword(s):  
Spinous Process ◽  
Age Groups ◽  
Three Dimensional ◽  
Morphological Characteristics ◽  
Intervertebral Foramen ◽  
Boundary Area ◽  
Articular Process ◽  
Significant Difference ◽  
Lower Lumbar

Intervertebral foramen is the doorway of nerve root and it plays an important role of radiculopathy and surgical treatment of intervertebral foramen diseases. The purpose of the study is to obtain three-dimensional (3D) morphological characteristics of lumbar intervertebral foramen and their relationship with age. Pedicle-superior articular process (P-SAP), disc height between adjacent vertebra (DH), pedicle-inferior vertebrae (P-IV), inferior posterior vertebrae-superior articular process (IPV-SAP), and bony boundary area (BBA) were measured in entrance, middle slice, and exit of lumbar intervertebral foramen for 25 males of different age groups. Spinous process to intervertebral foramen entrance (SP-IFE) was measured for 25 males of different age groups. Overall, P-SAP and P-IV decreased and IPV-SAP increased from the entrance to the exit of intervertebral foramen for L3/4-L5S1. DH decreased at entrance slice, middle slice, and exit slice for L3/4-L5S1 with age. Significant difference with aging was found only at the middle slice of L3/4 and L4/5 for P-SAP. And the significant decrease of IPV-SAP was observed at middle slice of L3/4, entrance slice of L4/5 and L5S1, and exit slice of L5S1. SP-IFE is not consistent for all subjects. In addition, the decrease of BBA at L3/4 and L4/5 was observed earlier than at L5S1. The present study described detailed information of intervertebral foramen, which may be of benefit for better understanding of the pathology and surgical planning for intervertebral foramen diseases.

Contracting thin disks

2019 ◽  
Vol 11 (04) ◽  
pp. 965-970
Author(s):  
Panos Papasoglu
Keyword(s):  
Area Formula ◽  
Homotopy Formula ◽  
Boundary Length ◽  
Thin Disks

We answer a question of Liokumovich–Nabutovsky–Rotman showing that if [Formula: see text] is a Riemannian 2-disk with boundary length [Formula: see text], diameter [Formula: see text] and area [Formula: see text] then [Formula: see text] can be filled by a homotopy [Formula: see text] with [Formula: see text] bounded by [Formula: see text].

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Sign in / Sign up

Export Citation Format

Share Document