NORMAL SURFACES IN THE FIGURE-8 KNOT COMPLEMENT

2003 ◽  
Vol 12 (02) ◽  
pp. 269-279 ◽  
Author(s):  
ENSIL KANG
Keyword(s):  
Seifert Surface ◽  
Normal Surface ◽  
Surface Theory ◽  
Normal Surfaces ◽  
Geometric Sums

An approach to normal surface theory for non-compact 3-manifolds with respect to ideal pseudo-triangulations is described in [12]. The figure-8 knot complement with a given ideal pseudo-triangulation with two ideal tetrahedra is fully worked out. We construct all Q-fundamental surfaces and the remaining normal surfaces are obtained by linear geometric sums of these. We also construct all almost normal surfaces in the figure-8 knot complement. As a result we obtain an example which does not contain any normal or almost normal surface representing a minimal Seifert surface of the knot. This leads that the figure-8 knot is fibered.

SEIFERT SURFACES IN KNOT COMPLEMENTS

2007 ◽  
Vol 16 (08) ◽  
pp. 1053-1066 ◽  
Author(s):  
ENSIL KANG
Keyword(s):  
Compact Surface ◽  
Seifert Surface ◽  
Normal Surface ◽  
Incompressible Surface ◽  
Ideal Triangulation ◽  
Seifert Surfaces ◽  
Knot Complements

In the ordinary normal surface for a compact 3-manifold, any incompressible, ∂-incompressible, compact surface can be moved by an isotopy to a normal surface [9]. But in a non-compact 3-manifold with an ideal triangulation, the existence of a normal surface representing an incompressible surface cannot be guaranteed. The figure-8 knot complement is presented in a counterexample in [12]. In this paper, we show the existence of normal Seifert surface under some restriction for a given ideal triangulation of the knot complement.

KAWACHI'S INVARIANT FOR NORMAL SURFACE SINGULARITIES

1998 ◽  
Vol 09 (05) ◽  
pp. 623-640 ◽  
Author(s):  
VLADIMIR MAŞEK
Keyword(s):  
Linear Systems ◽  
A Priori ◽  
Normal Surface ◽  
Numerical Invariant ◽  
Normal Surfaces ◽  
Log Canonical ◽  
Surface Singularities ◽  
Canonical Surface ◽  
Quick Proof ◽  
Canonical Singularities

We study a useful numerical invariant of normal surface singularities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic Gorenstein or rational (without assuming a priori that they are ℚ-Gorenstein). In Sec. 2 we prove effective results (stated in terms of Kawachi's invariant) regarding global generation of adjoint linear systems on normal surfaces with boundary. Such results can be used in proving effective estimates for global generation on singular threefolds. The theorem of Ein–Lazarsfeld and Kawamata, which says that the minimal center of log-canonical singularities is always normal, explains why the results proved here are relevant in that situation.

scholarly journals Normal surfaces in non-compact 3-manifolds

2005 ◽  
Vol 78 (3) ◽  
pp. 305-321 ◽  
Author(s):  
Ensil Kang
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Boundary Component ◽  
Unique Feature ◽  
Admissible Solution ◽  
Compact Surface ◽  
Normal Surface ◽  
Ideal Triangulation ◽  
Normal Surfaces ◽  
Ideal Triangulations

AbstractWe extend the normal surface Q-theory to non-compact 3-manifolds with respect to ideal triangulations. An ideal triangulation of a 3-manifold often has a small number of tetrahedra resulting in a system of Q-matching equations with a small number of variables. A unique feature of our approach is that a compact surface F with boundary properly embedded in a non-compact 3-manifold M with an ideal triangulation with torus cusps can be represented by a normal surface in M as follows. A half-open annulus made up of an infinite number of triangular disks is attached to each boundary component of F. The resulting surface , when normalized, will contain only a finite number of Q-disks and thus correspond to an admissible solution to the system of Q-matching equations. The correspondence is bijective.

The Effect of Benzene on Bluegill Olfactory Lamellae

1985 ◽  
Vol 43 ◽  
pp. 574-575
Author(s):  
D.R. Mattie ◽  
J.W. Fisher
Keyword(s):  
Surface Morphology ◽  
Soluble Fraction ◽  
Lepomis Macrochirus ◽  
Sublethal Concentration ◽  
Water Soluble ◽  
Major Constituent ◽  
Jet Fuels ◽  
Aquatic Biota ◽  
Normal Surface ◽  
Cacodylate Buffer

Jet fuels such as JP-4 can be introduced into the environment and come in contact with aquatic biota in several ways. Studies in this laboratory have demonstrated JP-4 toxicity to fish. Benzene is the major constituent of the water soluble fraction of JP-4. The normal surface morphology of bluegill olfactory lamellae was examined in conjunction with electrophysiology experiments. There was no information regarding the ultrastructural and physiological responses of the olfactory epithelium of bluegills to acute benzene exposure.The purpose of this investigation was to determine the effects of benzene on the surface morphology of the nasal rosettes of the bluegill sunfish (Lepomis macrochirus). Bluegills were exposed to a sublethal concentration of 7.7±0.2ppm (+S.E.M.) benzene for five, ten or fourteen days. Nasal rosettes were fixed in 2.5% glutaraldehyde and 2.0% paraformaldehyde in 0.1M cacodylate buffer (pH 7.4) containing 1.25mM calcium chloride. Specimens were processed for scanning electron microscopy.

Modeling Vibration-Induced Tire-Pavement Interaction Noise in the Mid-frequency Range

2020 ◽  
Author(s):  
Sterling McBride ◽  
Ricardo Burdisso ◽  
Corina Sandu
Keyword(s):  
Sound Intensity ◽  
Element Model ◽  
Dominant Frequency ◽  
Contact Forces ◽  
Surface Velocity ◽  
New Wave ◽  
Normal Surface ◽  
Radiated Noise ◽  
Physical Effects ◽  
Effects Of Rotation

ABSTRACT Tire-pavement interaction noise (TPIN) is one of the main sources of exterior noise produced by vehicles traveling at greater than 50 kph. The dominant frequency content is typically within 500–1500 Hz. Structural tire vibrations are among the principal TPIN mechanisms. In this work, the structure of the tire is modeled and a new wave propagation solution to find its response is proposed. Multiple physical effects are accounted for in the formulation. In an effort to analyze the effects of curvature, a flat plate and a cylindrical shell model are presented. Orthotropic and nonuniform structural properties along the tire's transversal direction are included to account for differences between its sidewalls and belt. Finally, the effects of rotation and inflation pressure are also included in the formulation. Modeled frequency response functions are analyzed and validated. In addition, a new frequency-domain formulation is presented for the computation of input tread pattern contact forces. Finally, the rolling tire's normal surface velocity response is coupled with a boundary element model to demonstrate the radiated noise at the leading and trailing edge locations. These results are then compared with experimental data measured with an on-board sound intensity system.

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