共查询到20条相似文献,搜索用时 640 毫秒
1.
In the present paper, the already-known list of the rigid isotopy classes of nonsingular curves of degree 6 in
containing a symmetric curve is obtained in an elementary way. To prove that a curve in a given rigid isotopy class is not symmetric, we study the position of the curve with respect to auxiliary conics. Bibliography: 21 titles. 相似文献
2.
R. Penne 《Geometriae Dedicata》1993,45(1):49-82
We give a characterization of the planar layouts of configurations with at most five lines. From this we obtain a new proof of Viro's theorem that the isotopy type of such configurations is completely determined by chirality. We extend this result to labelled configurations. We also give an infinite family of non-realizable line diagrams, called alternatingC-angles, not containing non-realizable subdiagrams. 相似文献
3.
A rigid isotopy of nonsingular real algebraic curves on a quadric is a path in the space of such curves of a given bidegree.
We obtain the rigid isotopy classification of nonsingular real algebraic curves of bidegree (3, 3) on a hyperboloid and on
an ellipsoid. We also study of the space of real algebraic curves of bidegree (3, 3) with a single node or cusp.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 810–815, December, 1999. 相似文献
4.
A projective m-configuration is a collection of m nonoriented pairwise disjoint lines in ℝP
3. An isotopy consisting of projective m-configurations is called a rigid isotopy. In the paper, the rigid isotopy classification
of ordered projective m-configurations is obtained for m≤7. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 269–285.
Translated by V. F. Mazurovskii. 相似文献
5.
V. I. Zvonilov 《Journal of Mathematical Sciences》2003,113(6):804-809
The rigid isotopy classification of nonsingular real algebraic curves of bidegree
on the Hirzebruch surface
(the projective plane with a point blown up) is obtained. Consequences for the space of curves with a single node or a cusp on a hyperboloid and on
are given. Bibliography: 15 titles. 相似文献
6.
Mathematical Notes - The paper is devoted to finding the rigid isotopy classes of real projective surfaces that are obtained from nonsingular cubic sections of a chosen nonsingular real quadric.... 相似文献
7.
The work presents some results on the asymptotics of the number of real plane algebraic curves as the degree grows. In particular, we obtain the asymptotics of the number of curves considered up to the isotopy and rigid isotopy, as well as the number of isotopic classes of maximal curves realizable by T-curves. Some results are generalized to hypersurfaces in nonsingular algebraic varieties of arbitrary dimension. Bibliography: 18 titles. 相似文献
8.
Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots in ??3 which can be viewed as a first order Vassiliev invariant. In this paper we look at real algebraic knots of degree d with the maximal possible value of this invariant. We show that for a given d all such knots are topologically isotopic and explicitly identify their knot type. 相似文献
9.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献
10.
Elena Edi Giorgi 《Geometriae Dedicata》1999,78(1):49-62
The characteristic foliation of a sphere embedded in the standard tight contact structure (R3, 0) is unique up to isotopy. We show that any Morse-Smale foliation on the sphere with null Euler class, is, up to isotopy, the characteristic foliation of a sphere embedded in the standard overtwisted contact structure (R3, 1). We thus have a new way of looking at the two standard structures as opposites in the world of contact structures. 相似文献
11.
In this paper we consider configurations of straight lines in
general position in a plane with all intersection points marked to show
which of the two lines is above the other. We prove that there exist two
isotopic configurations such that one of them can be obtained as a
projection of a collection of straight lines in 3-space, and the other
not. We investigate some isotopism class of configurations of six lines
and find a necessary and sufficient condition for configurations from this
class to be a projection of a collection of lines in 3-space. Received: 13 May 2002 相似文献
12.
A semigroup with 15 generators and 84 relations is constructed. The center of the semigroup is in a one-to-one correspondence with the set of all isotopy classes of nonoriented singular knots (links with finitely many double intersections in general position) in 3. 相似文献
13.
Vincent Borrelli 《Annals of Global Analysis and Geometry》1999,17(4):371-384
Given a totally real embedding j of the 2-torus
into 2, one defines a 1-class 1 – its linking class – which is a tool to detect arcwise connected components of the space of totally real embeddings EmbTr(
, 2). We generalize the construction of the linking class to any totally real embedding j of a connected, oriented, compact manifold without boundary M
n
into n. We obtain an (n – 1)-class
n– 1 which is still an invariant for isotopy classes of totally real embeddings. We show that this class is nontrivial by computing it for some families of totally real embeddings. We then study the relationship between isotopy classes of ordinary embeddings and the linking class. With additional assumptions on M
n
(n 4 and M
n
parallelizable) we obtain the following: two totally real embeddings of M
n
into
n
which belong to the same isotopy class of totally real immersion, belong to the same isotopy class of ordinary embedding if and only if (1) their linking classes are the same (if n odd); (2) the images of their linking classes by the coefficient homomorphism : H
n– 1 (M
n
, ) H
n– 1 (M
n
, 2) are the same (if n even). 相似文献
14.
Motivated by the construction of confidence intervals in statistics, we study optimal configurations of 2 d ? 1 lines in real projective space ?? d?1. For small d, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of 2 d ? 1 lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature. 相似文献
15.
A. Albrecht S.K. Cheung K.S. Leung C.K. Wong 《Computational Optimization and Applications》2001,19(2):179-208
This paper deals with the minimization of local forces in two-dimensional placements of flexible objects within rigid boundaries. The objects are disks of the same size but, in general, of different materials. Potential applications include the design of new amorphous polymeric and related granular materials as well as the design of package cushioning systems. The problem is considered on a grid structure with a fixed step size w and for a fixed diameter of the discs, i.e., the number of placed disks may increase as the size of the placement region increases. The near-equilibrium configurations have to be calculated from uniformly distributed random initial placements. The final arrangements of disks must ensure that any particular object is deformed only within the limits of elasticity of the material. The main result concerns -approximations of the probability distribution on the set of equilibrium placements. Under a natural assumption about the configuration space, we prove that a run-time of n+logO(1)(1/} is sufficient to approach with probability 1 – the minimum value of the objective function, where depends on the maximum of the escape depth of local minima within the underlying energy landscape. The result is derived from a careful analysis of the interaction among probabilities assigned to configurations from adjacent distance levels to minimum placements. The overall approach for estimating the convergence rate is relatively independent of the particular placement problem and can be applied to various optimization problems with similar properties of the associated landscape of the objective function. 相似文献
16.
Swarup Kumar Panda 《Czechoslovak Mathematical Journal》2017,67(4):1133-1143
A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)?1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in H which possess unicyclic inverses. We present a characterization of unicyclic graphs in H which possess bicyclic inverses. 相似文献
17.
A linear astral (nk) configuration is a collection of points and straight lines, so that each point lies on k lines and each line passes through k points, with symmetry (transitivity) classes of points and lines under rotations and reflections mapping the configuration to itself. We discuss the possible structures of astral (n5) configurations with dihedral symmetry group Dm in the Euclidean plane, and we provide methods to investigate the existence of such configurations. In doing so, we introduce a new class of astral (n3) configurations. 相似文献
18.
S. S. Podkorytov 《Journal of Mathematical Sciences》1998,91(6):3526-3531
We prove that mirror nonsingular configurations of m points and n lines in ℝP
3 exist only for m≤3, n≡0 or 1 (mod 4) and for m=0 or 1 (mod 4), n≡0 (mod 2). In addition, we give an elementary proof of V. M. Kharlamov’s well-known result saying that if a nonsingular surface of
degree four in ℝP
3 is noncontractible and has M≥5 components, then it is nonmirror. For the cases M=5, 6, 7 and 8, Kharlamov suggested an elementary
proof using an analogy between such surfaces and configurations of M−1 points and a line. Our proof covers the remaining cases
M=9, 10. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 299–308.
Translated by N. Yu. Netsvetaev. 相似文献
19.
We give an affirmative answer to a problem of Liao and Mañé which asks whether, for a nonsingular flow to loose the Ω-stability, it must go through a critical-element-bifurcation. More precisely, a vector field S on a compact boundaryless manifold is called a star system if S has a C 1 neighborhood $\mathcal{U}We give an affirmative answer to a problem of Liao and Ma?é which asks whether, for a nonsingular flow to loose the Ω-stability,
it must go through a critical-element-bifurcation. More precisely, a vector field S on a compact boundaryless manifold is called a star system if S has a C1 neighborhood
in the set of C1 vector fields such that every singularity and every periodic orbit of every
is hyperbolic. We prove that any nonsingular star flow satisfies Axiom A and the no cycle condition.
Dedicated to Shaotao Liao and Ricardo Ma?é
Mathematics Subject Classification (2000) 37D30 相似文献
20.
Albert Fathi 《Inventiones Mathematicae》1987,87(1):129-151
Summary We show that it is possible to obtain many pseudo-Anosov diffeomorphisms from Dehn twists. In particular, we generalize a theorem of Long and Morton to obtain that iff is a pseudo-Anosov diffeomorphism of an oriented surface andT
is the Dehn twist around the simple closed curve , then the isotopy class ofT
n
f contains a pseudo-Anosov diffeomorphism except for at most 7 consecutive values ofn. 相似文献