Boundary-Reducing and Toroidal Dehn Fillings at the Maximal Distance

2015 ◽  
Vol 2016 (15) ◽  
pp. 4487-4543
Author(s):  
Sangyop Lee
Keyword(s):  
Maximal Distance ◽  
Dehn Fillings

scholarly journals On hyperbolic knots in S3 with exceptional surgeries at maximal distance

2018 ◽  
Vol 18 (4) ◽  
pp. 2371-2417
Author(s):  
Benjamin Audoux ◽  
Ana Lecuona ◽  
Fionntan Roukema
Keyword(s):  
Maximal Distance

scholarly journals Jumping in frogs: assessing the design of the skeletal system by anatomically realistic modeling and forward dynamic simulation

2002 ◽  
Vol 205 (12) ◽  
pp. 1683-1702 ◽  
Author(s):  
William J. Kargo ◽  
Frank Nelson ◽  
Lawrence C. Rome
Keyword(s):  
Degrees Of Freedom ◽  
The Body ◽  
Joint Torque ◽  
Rotational Degree ◽  
Skeletal System ◽  
Dynamic Simulations ◽  
Inverse Dynamic ◽  
Maximal Distance ◽  
Out Of Plane ◽  
Rotational Degrees Of Freedom

SUMMARY Comparative musculoskeletal modeling represents a tool to understand better how motor system parameters are fine-tuned for specific behaviors. Frog jumping is a behavior in which the physical properties of the body and musculotendon actuators may have evolved specifically to extend the limits of performance. Little is known about how the joints of the frog contribute to and limit jumping performance. To address these issues, we developed a skeletal model of the frog Rana pipiens that contained realistic bones, joints and body-segment properties. We performed forward dynamic simulations of jumping to determine the minimal number of joint degrees of freedom required to produce maximal-distance jumps and to produce jumps of varied take-off angles. The forward dynamics of the models was driven with joint torque patterns determined from inverse dynamic analysis of jumping in experimental frogs. When the joints were constrained to rotate in the extension—flexion plane, the simulations produced short jumps with a fixed angle of take-off. We found that, to produce maximal-distance jumping,the skeletal system of the frog must minimally include a gimbal joint at the hip (three rotational degrees of freedom), a universal Hooke's joint at the knee (two rotational degrees of freedom) and pin joints at the ankle,tarsometatarsal, metatarsophalangeal and iliosacral joints (one rotational degree of freedom). One of the knee degrees of freedom represented a unique kinematic mechanism (internal rotation about the long axis of the tibiofibula)and played a crucial role in bringing the feet under the body so that maximal jump distances could be attained. Finally, the out-of-plane degrees of freedom were found to be essential to enable the frog to alter the angle of take-off and thereby permit flexible neuromotor control. The results of this study form a foundation upon which additional model subsystems (e.g. musculotendon and neural) can be added to test the integrative action of the neuromusculoskeletal system during frog jumping.

Reducing Spheres and Klein Bottles after Dehn Fillings

2003 ◽  
Vol 46 (2) ◽  
pp. 265-267 ◽  
Author(s):  
Seungsang Oh
Keyword(s):  
Short Proof ◽  
Klein Bottle ◽  
Dehn Fillings

AbstractLet M be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on M along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.

scholarly journals Boundaries of Dehn fillings

2019 ◽  
Vol 23 (6) ◽  
pp. 2929-3002 ◽  
Author(s):  
Daniel Groves ◽  
Jason Fox Manning ◽  
Alessandro Sisto
Keyword(s):  
Dehn Fillings

scholarly journals A note on distance spectral radius of trees

2017 ◽  
Vol 5 (1) ◽  
pp. 296-300
Author(s):  
Yanna Wang ◽  
Rundan Xing ◽  
Bo Zhou ◽  
Fengming Dong
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Distance Matrix ◽  
Largest Eigenvalue ◽  
Maximal Distance ◽  
The Largest Eigenvalue

Abstract The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. We determine the unique non-starlike non-caterpillar tree with maximal distance spectral radius.

The Generalized Pair Chart for Right­Censored Observations

1982 ◽  
Vol 31 (1-2) ◽  
pp. 13-26 ◽  
Author(s):  
Igusti Ngurah Agung ◽  
Pranab Kumar Sen
Keyword(s):  
Partial Observations ◽  
Maximal Distance ◽  
Two Samples ◽  
Alternative Pair

The pair chart is known to be a convenient descriptive tool in comparing two samples and in calculating and interpreting various nonparametric procedures for the two­sample problem (see Quade (1973)). To incorporate rightcensored data in the two­sample problem, a generalized pair chart is considered and the same is utilized in the schematic computation of Gehan's W­statistic (Gehan (1965)) and a triplet statistic (see Crouse and Steffens (1969)) among others. An alternative pair chart based on partial observations is also considered. A maximal distance statistic, based on the generalized pair chart, has been considered for testing the hypothesis of equality of the two distributions.

A Note on Finite Dehn Fillings

1999 ◽  
Vol 42 (2) ◽  
pp. 149-154
Author(s):  
S. Boyer ◽  
X. Zhang
Keyword(s):  
Finite Volume ◽  
Hyperbolic Metric ◽  
Fundamental Groups ◽  
Dehn Fillings ◽  
Zero Class

AbstractLet M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in H1(∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.

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