scholarly journals Fiberwise convexity of Hill’s lunar problem

2017 ◽  
Vol 09 (04) ◽  
pp. 571-630 ◽  
Author(s):  
Junyoung Lee
Keyword(s):  
Energy Level ◽  
Contact Structure ◽  
Finsler Geometry ◽  
Critical Energy ◽  
Critical Value ◽  
Finsler Metrics ◽  
Tight Contact ◽  
Systolic Inequality ◽  
Geodesic Problem ◽  
Hill's Lunar Problem

In this paper, we prove the fiberwise convexity of the regularized Hill’s lunar problem below the critical energy level. This allows us to see Hill’s lunar problem of any energy level below the critical value as the Legendre transformation of a geodesic problem on [Formula: see text] with a family of Finsler metrics. Therefore the compactified energy hypersurfaces below the critical energy level have the unique tight contact structure on [Formula: see text]. Also one can apply the systolic inequality of Finsler geometry to the regularized Hill’s lunar problem.

scholarly journals The Legendrian knot complement problem

2018 ◽  
Vol 27 (14) ◽  
pp. 1850067 ◽  
Author(s):  
Marc Kegel
Keyword(s):  
Contact Structure ◽  
Legendrian Knot ◽  
Tight Contact ◽  
Legendrian Links ◽  
User Friendly ◽  
The Way

We prove that every Legendrian knot in the tight contact structure of the [Formula: see text]-sphere is determined by the contactomorphism type of its exterior. Moreover, by giving counterexamples we show this to be not true for Legendrian links in the tight [Formula: see text]-sphere. On the way a new user-friendly formula for computing the Thurston–Bennequin invariant of a Legendrian knot in a surgery diagram is given.

The Mechanics of Ozone Cracking

1962 ◽  
Vol 35 (1) ◽  
pp. 200-209 ◽  
Author(s):  
M. Braden ◽  
A. N. Gent
Keyword(s):  
Tensile Stress ◽  
Crack Growth ◽  
Energy Requirement ◽  
Critical Energy ◽  
Critical Value ◽  
Experimental Measurements ◽  
Rubber Sheet ◽  
Polymer Molecules ◽  
Two Factors ◽  
Applied Tensile Stress

Abstract Experimental measurements are described of the growth of a cut in a stretched rubber sheet under the action of an atmosphere containing ozone. A well-defined rate of crack growth is obtained, substantially independent of the applied tensile stress when this exceeds a critical value necessary for growth to occur at all. The rate of growth is found to be similar for a number of polymers and principally determined by the ozone concentration when the mobility of the polymer molecules is sufficiently high. When the molecular mobility is inadequate, crack growth is retarded. The critical condition is found to be similar for all the polymers examined, and largely independent of the conditions of exposure; it appears to reflect an energy requirement for growth of about 40 ergs/cm2 of newly-formed surface. The effect of the degree of vulcanization and the presence of additives, including antiozonants, on these two factors has also been examined. The dialkyl-p-phenylene diamines are found to confer protection by raising the critical energy required for growth to occur, in contrast to other protective agents which affect only the rate of crack propagation.

scholarly journals Reducing Packet Losses in Mobile Ad Hoc Network Using the Warning Message Generated from a Routing Node

2015 ◽  
Vol 62 (2) ◽  
pp. 141-145 ◽  
Author(s):  
Rezvi Shahariar ◽  
Abu Naser
Keyword(s):  
Energy Level ◽  
Total Energy ◽  
Packet Loss ◽  
Ad Hoc Network ◽  
Ad Hoc ◽  
Mobile Ad Hoc Network ◽  
Critical Energy ◽  
Packet Losses ◽  
Warning Message ◽  
Mobile Ad Hoc

In mobile ad hoc network communication is performed usually by using only send and receive messages and every node is powered by limited energy from low capacity battery. Every send or receive message takes particular amount of energy from the node. So node’s total energy level gradually decreases each time while it is sending or receiving something. In this way node will die out and packets coming from the source will be dropped since one of the routing node on the current route is no longer functioning. These packet loss events are observed and minimized in this paper. In the proposed approach, when source receives Warning Message from any routing node on the ongoing route then it will stop sending packets on the ongoing route. Critical energy level of routing node has been defined to generate a Warning Message when routing node’s energy level reduces to critical energy level. DOI: http://dx.doi.org/10.3329/dujs.v62i2.21979 Dhaka Univ. J. Sci. 62(2): 141-145, 2014 (July)

scholarly journals Periodic orbits in virtually contact structures

2018 ◽  
Vol 12 (02) ◽  
pp. 371-418
Author(s):  
Youngjin Bae ◽  
Kevin Wiegand ◽  
Kai Zehmisch
Keyword(s):  
Periodic Solutions ◽  
Potential Function ◽  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Contact Structure ◽  
Critical Value ◽  
Holomorphic Curves ◽  
Contact Structures ◽  
Contact Form ◽  
Contact Manifolds

We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Mañé critical value. For that we develop a theory of holomorphic curves in symplectizations of non-compact contact manifolds that arise as the covering space of a virtually contact structure whose contact form is bounded with all derivatives up to order three.

scholarly journals Legendrian torus knots in S1 × S2

2015 ◽  
Vol 24 (12) ◽  
pp. 1550064 ◽  
Author(s):  
Feifei Chen ◽  
Fan Ding ◽  
Youlin Li
Keyword(s):  
Contact Structure ◽  
Torus Knots ◽  
Tight Contact

We classify Legendrian torus knots in S1 × S2 with its standard tight contact structure up to Legendrian isotopy.

scholarly journals CONTACT STRUCTURES, σ-CONFOLIATIONS AND CONTAMINATIONS IN 3-MANIFOLDS

2009 ◽  
Vol 11 (02) ◽  
pp. 201-264 ◽  
Author(s):  
ULRICH OERTEL ◽  
JACEK ŚWIATKOWSKI
Keyword(s):  
Contact Structure ◽  
Contact Structures ◽  
Tight Contact ◽  
Branched Surface ◽  
Definition Of ◽  
Branched Surfaces ◽  
Natural Way

We propose in this paper a method for studying contact structures in 3-manifolds by means of branched surfaces. We explain what it means for a contact structure to be carried by a branched surface embedded in a 3-manifold. To make the transition from contact structures to branched surfaces, we first define auxiliary objects called σ-confoliations and pure contaminations, both generalizing contact structures. We study various deformations of these objects and show that the σ-confoliations and pure contaminations obtained by suitably modifying a contact structure remember the contact structure up to isotopy. After defining tightness for all pure contaminations in a natural way, generalizing the definition of tightness for contact structures, we obtain some conditions on (the embedding of) a branched surface in a 3-manifold sufficient to guarantee that any pure contamination carried by the branched surface is tight. We also find conditions sufficient to prove that a branched surface carries only overtwisted (non-tight) contact structures. Our long-term goal in developing these methods is twofold: Not only do we want to study tight contact structures and pure contaminations, but we also wish to use them as tools for studying 3-manifold topology.

scholarly journals EXPLICIT HORIZONTAL OPEN BOOKS ON SOME PLUMBINGS

2006 ◽  
Vol 17 (09) ◽  
pp. 1013-1031 ◽  
Author(s):  
TOLGA ETGÜ ◽  
BURAK OZBAGCI
Keyword(s):  
Contact Structure ◽  
Complex Surface ◽  
Contact Structures ◽  
Open Book ◽  
Open Books ◽  
Tight Contact ◽  
Weinstein Conjecture ◽  
Circle Bundles ◽  
Surface Singularities

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, on some Seifert fibered 3-manifolds we describe open books which are horizontal with respect to their plumbing description. As another application we describe horizontal open books isomorphic to Milnor open books for some complex surface singularities. Moreover we give examples of tight contact 3-manifolds supported by planar open books. As a consequence, the Weinstein conjecture holds for these tight contact structures [1].

scholarly journals A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY

2012 ◽  
Vol 54 (3) ◽  
pp. 637-645 ◽  
Author(s):  
XIAOHUAN MO ◽  
ZHONGMIN SHEN ◽  
HUAIFU LIU
Keyword(s):  
Scalar Curvature ◽  
Simple Proof ◽  
Finsler Geometry ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Riemannian Curvature

AbstractIn this note, we study a new Finslerian quantity Ĉ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that the Ĉ-curvature is closely related to the flag curvature and the H-curvature. We show that Ĉ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.

On general (α,β)-metrics of Landsberg type

2016 ◽  
Vol 13 (06) ◽  
pp. 1650085 ◽  
Author(s):  
M. Zohrehvand ◽  
H. Maleki
Keyword(s):  
General Formula ◽  
Open Problem ◽  
Finsler Geometry ◽  
Riemannian Metric ◽  
Finsler Metrics

In this paper, we study a class of Finsler metrics, which are defined by a Riemannian metric [Formula: see text] and a one-form [Formula: see text]. They are called general [Formula: see text]-metrics. We have proven that, every Landsberg general [Formula: see text]-metric is a Berwald metric, under a certain condition. This shows that the hunting for an unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful in the class of general [Formula: see text]-metrics.

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