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The asymptotic numbers of certain kinds of regular toroidal maps

J.M. Szucs
2000 Discrete Mathematics  
a toroidal map of type (3; 6) = the greatest common divisor of the numbers of the three kinds of normal cycles.) c  ...  The asymptotic number (of isomorphism classes) of toroidal maps of type (3; 6) with at most n vertices is found, together with the fraction of those with multiplicity 1.  ...  Acknowledgements The author thanks the referees for their valuable comments and for pointing out Kurth's paper.  ... 
doi:10.1016/s0012-365x(99)00236-8 fatcat:maiwq64nyrashcp2btsjygo4pq

Page 770 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
M. (1-TXAM2; Galveston, TX) The asymptotic numbers of certain kinds of regular toroidal maps. (English summary) Discrete Math. 215 (2000), no. 1-3, 225-244.  ...  These maps, of type (p,q), are cellular em- beddings of g-regular graphs, with multipie edges and loops, in the torus such that each face is a p-gon.  ... 

Index

2000 Discrete Mathematics  
Plummer (1}3) 171}179 Surowski, D.B., Liftings of automorphisms of hypermaps (1}3) 213}224 Szucs, J.M., The asymptotic numbers of certain kinds of regular toroidal maps (1}3) 225}244 Takahara, G., see  ...  Bogart (1}3) 13} 20 0012-365X/00/$ -see front matter 2000 Elsevier Science B.V. , X., The game coloring number of pseudo partial k-trees (1}3) 245}262 Bogart, K.P. and A.N.  ... 
doi:10.1016/s0012-365x(00)00038-8 fatcat:y7nkgmuj7jdelkiexh2ythrobm

Mappings of stochastic field lines in poloidal divertor tokamaks

S.S Abdullaev, K.H Finken, M Jakubowski, M Lehnen
2006 Nuclear Fusion  
The mappings are applied to study the properties of open stochastic field lines near the separatrix for the wire model of the plasma.  ...  Two mapping methods to study magnetic field lines near the separatrix of poloidal divertor tokamaks in the presence of external non-axisymmetric magnetic perturbations are proposed.  ...  Acknowledgments This work has been partially supported by the project SFB 591 of the Deutsche Forschungsgemeinschaft (DFG).  ... 
doi:10.1088/0029-5515/46/4/s02 fatcat:cctpne2wojdyvkqnmo7hqccu5e

Page 6491 of Mathematical Reviews Vol. , Issue 93m [page]

1993 Mathematical Reviews  
Pereverzev, Com- plexity of the Fredholm problem of second kind (255-272); V. M.  ...  Zhensykbaev], Generalized Gaussian quadrature formulas for weak Tchebyshev systems (115-140); Guan Rong Chen, Optimal recovery of certain nonlinear analytic mappings (141-144); Franz-J.  ... 

On description of magnetic stochasticity in poloidal divertor tokamaks

S. S. Abdullaev, M. Jakubowski, M. Lehnen, O. Schmitz, B. Unterberg
2008 Physics of Plasmas  
This integral allows us to obtain the analytical estimations for the characteristics of chaotic field lines near the magnetic separatrix, like the Chirikov parameter, the widths of the stochastic layer  ...  The method is based on the determination of the so-called Poincaré integral ͓S. S. Abdullaev, Phys. Rev.  ...  These field lines are not confined anymore in the plasma region, and they leave the plasma region hitting the divertor plates after a certain number of toroidal ͑or poloidal͒ turns.  ... 
doi:10.1063/1.2907163 fatcat:angwdfqzqrfoxifeatk6p4xdlu

Newton polyhedra and toroidal varieties

A. G. Khovanskii
1978 Functional analysis and its applications  
The inverse mapping in the coordinates of region Um coincides with rational mapping ~m : ~-+ (~ ~ 0) ~.  ...  Therefore, all the invariants of this kind depend on the Newton polyhedra ~, . . ., A k and do not depend on the specific choice of a nonsingular system of polynomials f~, ., fk. 4.  ... 
doi:10.1007/bf01077143 fatcat:iuipk25k7rcdflzvnniwydj6hi

On mapping models of field lines in a stochastic magnetic field

S.S Abdullaev
2004 Nuclear Fusion  
The generating function of the symmetric mapping depends only on the perturbation field while the one for the nonsymmetric map depends also on the safety factor (or winding number).  ...  They are usually constructed in a certain symplectic form by imposing several constraints that make them compatible with a toroidal geometry.  ...  This work has been done in the frame of the project SFB 591 of the Deutsche Forschungsgemeinschaft (DFG).  ... 
doi:10.1088/0029-5515/44/6/s02 fatcat:pzfi4kmx5vf4lar3j4guygyx3q

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

D. Borgogno, D. Grasso, F. Pegoraro, T. J. Schep
2011 Physics of Plasmas  
Regions where the magnetic field is stochastic exist next to regions where the field is more regular.  ...  The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated.  ...  The views and opinions expressed herein do not necessarily reflect those of the European Commission.  ... 
doi:10.1063/1.3647339 fatcat:26gahzp7anh2vc2xelypyfj6fa

Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum [article]

M. Rieutord, B. Georgeot, L. Valdettaro
2000 arXiv   pre-print
We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero.  ...  We first consider the mapping made by the characteristics of the hyperbolic equation (Poincaré's equation) satisfied by inviscid solutions.  ...  Using the properties of the mapping (2.11), we have been able to prove under certain hypotheses (see appendix C), that the number of attractors is bounded by the number of points of discontinuity (which  ... 
arXiv:physics/0007007v1 fatcat:oirjegx3evdlfigf5atfxxmdwq

Stationary Black Holes: Uniqueness and Beyond

Piotr T. Chruściel, João Lopes Costa, Markus Heusler
2012 Living Reviews in Relativity  
This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.  ...  The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways.  ...  of a compact set and of a finite number of asymptotically-flat ends.  ... 
doi:10.12942/lrr-2012-7 pmid:28179837 pmcid:PMC5255892 fatcat:difnulsqvrgvreg5fmg2e6uctq

Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum

M. RIEUTORD, B. GEORGEOT, L. VALDETTARO
2001 Journal of Fluid Mechanics  
We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero.  ...  We show that these attractors exist in bands of frequencies the size of which decreases with the number of reflection points of the attractor.  ...  Using the properties of the mapping (2.11), we have been able to prove under certain hypotheses (see appendix C), that the number of attractors is bounded by the number of points of discontinuity (which  ... 
doi:10.1017/s0022112001003718 fatcat:2bmeecbyfnfsjcj4y6fw3ykl2e

4-Regular Maps on the Klein Bottle

Han Ren, Yanpei Liu
2001 Journal of combinatorial theory. Series B (Print)  
Also the number of rooted near-4-regular maps with exactly k nonroot-vertex loops on this surface is provided.  ...  In this paper the number of rooted near-4-regular maps on the Klein bottle is investigated and formulae with up to four parameters are given.  ...  examples such as those determined by the maps in Fig. 2 as one of the initial steps of the numerical verification of Theorem 2.  ... 
doi:10.1006/jctb.2000.2030 fatcat:hurpgfx4xjczhpif5ispcajoaa

Overview of magnetic structure induced by the TEXTOR-DED and the related transport

S.S Abdullaev, K.H Finken, M.W Jakubowski, S.V Kasilov, M Kobayashi, D Reiser, D Reiter, A.M Runov, R Wolf
2003 Nuclear Fusion  
New methods to study the magnetic field, in particular, the field line mapping have been developed.  ...  The presentation gives the overview of the studies on the structure of magnetic field in the DED, the formation of the ergodic and laminar zones of field lines at the plasma edge.  ...  .), where s (s 1) is an integer number which stands for a number of map steps per one toroidal rotation along the torus.  ... 
doi:10.1088/0029-5515/43/5/302 fatcat:3hij4ia2abfhfgpxjutoreuiry

Asymptotic stability and quasi-periodicity in form and evolution of model socio-spatial structures

Dimitrios S. Dendrinos
1991 Computers and Mathematics with Applications  
Cyclicd asymptotic stability, toroidal flow and their transition to ch8os 8re only some of the nmny events contained in the uuiversel map.  ...  The cases document the univers8lity of the deterministic map. For example, the Curry-Yorke toroidal flow of a quasi-periodic attmctor in absolute dynamics is shown to be present here.  ...  Beyond the novelty of the menu of chae and toroidal flows uncovered, core properties found in the time-one maps, their Poincard sections and corresponding circle maps are revealed.  ... 
doi:10.1016/0898-1221(91)90003-m fatcat:g6oy5hwv25elnkvjhf56hfbkjm
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