Three-dimensional hyperbolic manifolds of small volume with three hyperelliptic involutions

1999 ◽  
Vol 40 (5) ◽  
pp. 873-886 ◽  
Author(s):  
A. Yu. Vesnin ◽  
A. D. Mednykh
Keyword(s):  
Small Volume ◽  
Three Dimensional ◽  
Hyperbolic Manifolds

scholarly journals MEMS-Based Integrated Triaxial Electrochemical Seismometer

Micromachines ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1156
Author(s):  
Wenjie Qi ◽  
Bowen Liu ◽  
Tian Liang ◽  
Jian Chen ◽  
Deyong Chen ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Ground Motion ◽  
Small Volume ◽  
Three Dimensional ◽  
Experimental Results ◽  
Good Prospect ◽  
High Symmetry ◽  
Noise Levels ◽  
Sensitivity Curves ◽  
Simulation Results

This paper presents a micro-electromechanical systems (MEMS)-based integrated triaxial electrochemical seismometer, which can detect three-dimensional vibration. By integrating three axes, the integrated triaxial electrochemical seismometer is characterized by small volume and high symmetry. The numerical simulation results inferred that the integrated triaxial electrochemical seismometer had excellent independence among three axes. Based on the experimental results, the integrated triaxial electrochemical seismometer had the advantage of small axial crosstalk and could detect vibration in arbitrary directions. Furthermore, compared with the uniaxial electrochemical seismometer, the integrated triaxial electrochemical seismometer had similar sensitivity curves ranging from 0.01 to 100 Hz. In terms of random ground motion response, high consistencies between the developed integrated triaxial electrochemical seismometer and the uniaxial electrochemical seismometer could be easily observed, which indicated that the developed integrated triaxial electrochemical seismometer produced comparable noise levels to those of the uniaxial electrochemical seismometer. These results validated the performance of the integrated triaxial electrochemical seismometer, which has a good prospect in the field of deep geophysical exploration and submarine seismic monitoring.

scholarly journals A comparative study between currently used methods and Small Volume-Cone Beam Tomography for surgical placement of mini implants

2014 ◽  
Vol 85 (3) ◽  
pp. 446-453 ◽  
Author(s):  
Melissa Landin ◽  
Aniket Jadhav ◽  
Sumit Yadav ◽  
Aditya Tadinada
Keyword(s):  
Small Volume ◽  
Preoperative Evaluation ◽  
Three Dimensional ◽  
Panoramic Radiograph ◽  
Imaging Modalities ◽  
Cone Beam ◽  
Root Structure ◽  
Mini Implants ◽  
Area Of Interest ◽  
Human Skulls

ABSTRACT Objective:  To compare the outcome of mini implant placement by four different methods: blind placement, a single periapical radiograph (PA), a single panoramic radiograph, and a small-volume cone-beam computed tomography (SV-CBCT). Our hypothesis was that SV-CBCT, with its high resolution, low radiation dose, and three-dimensional depiction of area of interest would yield superior diagnostic information in assessing the potential anchorage site compared to currently used methods that often result in undesired root perforations. Materials and Methods:  Potential mini implant sites of 20 dentate or partially dentate human skulls were imaged using three different imaging modalities: PA, panoramic radiograph, and SV-CBCT. Mini implants were placed in 10 maxillary and 10 mandibular randomized sites blindly and using each of the three imaging modalities. Large-volume CBCT scans done postoperatively were used to detect root perforation. Two oral radiologists analyzed the images for perforation of root structures at each site. Results:  There was significantly (P < .05) less root perforation with SV-CBCT when compared with other imaging modalities. Fifty-five percent of mini implants placed blindly, 60% of mini implants placed using PA, and 50% of mini implants placed using a panoramic radiograph perforated a root structure, whereas only 5% of mini implants placed using SV-CBCT perforated a root structure. Conclusions:  Preoperative evaluation of potential mini implant insertion sites using SV-CBCT aids in predictable placement and results in the least amount of root perforation.

On the complexity of three-dimensional cusped hyperbolic manifolds

2014 ◽  
Vol 89 (3) ◽  
pp. 267-270 ◽  
Author(s):  
A. Yu. Vesnin ◽  
V. V. Tarkaev ◽  
E. A. Fominykh
Keyword(s):  
Three Dimensional ◽  
Hyperbolic Manifolds

Three-dimensional Rayleigh-Taylor instability Part 2. Experiment

1988 ◽  
Vol 187 ◽  
pp. 353-371 ◽  
Author(s):  
J. W. Jacobs ◽  
I. Catton
Keyword(s):  
High Speed ◽  
Small Volume ◽  
Circular Tube ◽  
Three Dimensional ◽  
Vertical Tube ◽  
Taylor Instability ◽  
Gravitational Acceleration ◽  
Lateral Direction ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

Three-dimensional Rayleigh-Taylor instability, induced by accelerating a small volume of water down a vertical tube using air pressure, is investigated. Two geometries are studied: a 15.875 cm circular tube and a 12.7 cm square tube. Runs were made with initial disturbances in the form of standing waves forced by shaking the test section in a lateral direction. Accelerations ranging from 5 to 10 times gravitational acceleration and wavenumbers from 1 cm−1 to 8 cm−1 are studied. The resulting instability was recorded and later analysed using high-speed motion picture photography. Measurements of the growth rate are found to agree well with linear theory. In addition, good qualitative agreement between photographs and three-dimensional surface plots of the weakly nonlinear solution of Part 1 of this series (Jacobs & Catton 1988) is obtained.

scholarly journals Borel and Volume Classes for Dense Representations of Discrete Groups

2021 ◽  
Author(s):  
James Farre
Keyword(s):  
Three Dimensional ◽  
Hyperbolic Manifolds ◽  
Discrete Groups ◽  
Bounded Cohomology ◽  
Hyperbolic Volume ◽  
Uniformly Separated ◽  
Point Line ◽  
Borel Class ◽  
Dense Representation ◽  
The Continuum

Abstract We show that the bounded Borel class of any dense representation $\rho : G\to{\operatorname{PSL}}_n{\mathbb{C}}$ is non-zero in degree three bounded cohomology and has maximal semi-norm, for any discrete group $G$. When $n=2$, the Borel class is equal to the three-dimensional hyperbolic volume class. Using tools from the theory of Kleinian groups, we show that the volume class of a dense representation $\rho : G\to{\operatorname{PSL}}_2{\mathbb{C}}$ is uniformly separated in semi-norm from any other representation $\rho ^{\prime}: G\to{\operatorname{PSL}}_2 {\mathbb{C}}$ for which there is a subgroup $H\le G$ on which $\rho $ is still dense but $\rho ^{\prime}$ is discrete or indiscrete but stabilizes a point, line, or plane in ${\mathbb{H}}^3\cup \partial{\mathbb{H}}^3$. We exhibit a family of dense representations of a non-abelian free group on two letters and a family of discontinuous dense representations of ${\operatorname{PSL}}_2{\mathbb{R}}$, whose volume classes are linearly independent and satisfy some additional properties; the cardinality of these families is that of the continuum. We explain how the strategy employed may be used to produce non-trivial volume classes in higher dimensions, contingent on the existence of a family of hyperbolic manifolds with certain topological and geometric properties.

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