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1.
A geometric permutation induced by a transversal line of a finite family of disjoint convex sets in ℝd is the order in which the transversal meets the members of the family. It is known that the maximal number of geometric permutations
in families of n disjoint translates of a convex set in ℝ3 is 3. We prove that for d ≥ 3 the maximal number of geometric permutations for such families in ℝd is Ω(n). 相似文献
2.
We study both theoretically and numerically the Lyapunov families which bifurcate in the vertical direction from a horizontal
relative equilibrium in ℝ3. As explained in [1], very symmetric relative equilibria thus give rise to some recently studied classes of periodic solutions.
We discuss the possibility of continuing these families globally as action minimizers in a rotating frame where they become
periodic solutions with particular symmetries. A first step is to give estimates on intervals of the frame rotation frequency
over which the relative equilibrium is the sole absolute action minimizer: this is done by generalizing to an arbitrary relative
equilibrium the method used in [2] by V. Batutello and S. Terracini.
In the second part, we focus on the relative equilibrium of the equal-mass regular N-gon. The proof of the local existence of the vertical Lyapunov families relies on the fact that the restriction to the corresponding
directions of the quadratic part of the energy is positive definite. We compute the symmetry groups G
r/s
(N, k, η) of the vertical Lyapunov families observed in appropriate rotating frames, and use them for continuing the families globally.
The paradigmatic examples are the “Eight” families for an odd number of bodies and the “Hip- Hop” families for an even number.
The first ones generalize Marchal’s P
12 family for 3 bodies, which starts with the equilateral triangle and ends with the Eight [1, 3–6]; the second ones generalize
the Hip-Hop family for 4 bodies, which starts from the square and ends with the Hip-Hop [1, 7, 8].
We argue that it is precisely for these two families that global minimization may be used. In the other cases, obstructions
to the method come from isomorphisms between the symmetries of different families; this is the case for the so-called “chain”
choreographies (see [6]), where only a local minimization property is true (except for N = 3). Another interesting feature of these chains is the deciding role played by the parity, in particular through the value
of the angular momentum. For the Lyapunov families bifurcating from the regular N-gon whith N ≤ 6 we check in an appendix that locally the torsion is not zero, which justifies taking the rotation of the frame as a parameter.
To the memory of J. Moser, with admiration 相似文献
3.
J. H. Rieger 《manuscripta mathematica》1999,99(1):73-91
We study the recognition of -classes of multi-germs in families of corank-1 maps from n-space into n-space. From these recognition conditions we deduce certain geometric properties of bifurcation sets of such families of maps.
As applications we give a formula for the number of -codimension-1 classes of corank-1 multi-germs from ℂ
n
to ℂ
n
and an upper bound for the number of stable projections of algebraic hypersurfaces in ℝ
n
+1 into hyperplanes.
Received: 23 July 1998 相似文献
4.
A Helly Type Conjecture 总被引:2,自引:0,他引:2
A family of sets is Π
n
, or n -pierceable, if there exists a set of n points such that each member of the family contains at least one of them. It is Π
k
n
if every subfamily of size k or less is Π
n
. Helly's theorem is one of the fundamental results in Combinatorial Geometry. It asserts, in the special case of finite
families of convex sets in the plane, that Π
3
1
implies Π
1
. However, there is no k such that Π
k
2
implies 2 -pierceability for all finite families of convex sets in the plane. It is therefore natural to propose the following:
Conjecture.
There exists a
k
0
such that, for all planar finite families of convex sets , Π
k0
2
implies
Π
3
.
Proofs of this conjecture for restricted families of convex sets are discussed.
Received October 8, 1996, and in revised form August 12, 1997. 相似文献
5.
We establish the equicontinuity and normality of the families R
Φ of ring Q(x)-homeomorphisms with integral-type restrictions ∫Φ(Q(x))dm(x) < ∞ on a domain D ⊂ R
n
with n ≥ 2. The resulting conditions on Φ are not only sufficient but also necessary for the equicontinuity and normality of these
families of mappings. We give some applications of these results to the Sobolev classes W
loc1,n
. 相似文献
6.
Christian Okonek 《manuscripta mathematica》1994,84(1):421-442
In this article I describe construction methods for smooth subvarieties of codimension 3 in projective spaces or other ambient
spaces.
The methods include liaison of 3-folds in ℙ6, sections in smooth reflexive sheaves, and Pfaffians of twisted skew-symmetric vector bundle morphisms.
I use these methods to construct new families of 3-folds in ℙ6, and new codimension 3 submanifolds in ℙ8 and ℙ9.
This article was processed using the LATEX macro package with LMAMULT style 相似文献
7.
A. M. Romanov 《Journal of Applied and Industrial Mathematics》2012,6(3):355-359
In this paper, the properties of the i-components of Hamming codes are described. We suggest constructions of the admissible families of components of Hamming codes. Each q-ary code of length m and minimum distance 5 (for q = 3, the minimum distance is 3) is shown to embed in a q-ary 1-perfect code of length n = (q m − 1)/(q − 1). Moreover, each binary code of length m+k and minimum distance 3k + 3 embeds in a binary 1-perfect code of length n = 2 m − 1. 相似文献
8.
Recent investigations of discretization schemes for the efficient numerical solution of boundary value ordinary differential
equations (BVODEs) have focused on a subclass of the well‐known implicit Runge–Kutta (RK) schemes, called mono‐implicit RK
(MIRK) schemes, which have been employed in two software packages for the numerical solution of BVODEs, called TWPBVP and
MIRKDC. The latter package also employs continuous MIRK (CMIRK) schemes to provide C
1 continuous approximate solutions. The particular schemes implemented in these codes come, in general, from multi‐parameter
families and, in some cases, do not represent optimal choices from these families. In this paper, several optimization criteria
are identified and applied in the derivation of optimal MIRK and CMIRK schemes for orders 1–6. In some cases the schemes obtained
result from the analysis of existent multi‐parameter families; in other cases new families are derived from which specific
optimal schemes are then obtained. New MIRK and CMIRK schemes are presented which are superior to those currently available.
Numerical examples are provided to demonstrate the practical improvements that can be obtained by employing the optimal schemes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
Families of nonlattice tilings of ℝ
n
by unit cubes are constructed. These tilings are specializations of certain families of nonlinear codes overGF(2). These cube-tilings provide building blocks for the construction of cube-tilings such that no two cubes have a high-dimensional
face in common. We construct cube-tilings of ℝ
n
such that no two cubes have a common face of dimension exceeding
. 相似文献
10.
The notion of m-regular system on the Hermitian variety ℋ(n,q
2) was introduced by B. Segre (Ann. Math. Pura Appl. 70:1–201, 1965). Here, three infinite families of hemisystems on ℋ(5,q
2), q odd, are constructed. 相似文献
11.
We determine shape-preserving regions and we describe a general setting to generate shape-preserving families for the 2-points
Hermite subdivision scheme introduced by Merrien (Numer. Algorithms 2:187–200, [1992]). This general construction includes the shape-preserving families presented in Merrien and Sablonníere (Constr. Approx.
19:279–298, [2003]) and Pelosi and Sablonníere (C
1 GP Hermite Interpolants Generated by a Subdivision Scheme, Prépublication IRMAR 06–23, Rennes, [2006]). New special families are presented as particular examples. Nonstationary and nonuniform versions of such schemes, which
produce smoother limits, are discussed.
相似文献
12.
V. B. Lazareva 《Journal of Mathematical Sciences》2011,177(4):579-588
A curvilinear three-web formed by three pencils of circles is called a circle web. Generally speaking, the circle three-web
is not regular, i.e., it is not locally diffeomorphic to a web formed by three families of parallel straight lines. In this
paper, all regular circle three-webs are classified up to circular transformations. The main result is as follows: There exist
48 nonequivalent (with respect to circular transformations) types of regular three-webs. Five of them contain ∞3 nonequivalent webs each, 11 types contain ∞2 nonequivalent webs each, and 12 types contain ∞1 nonequivalent webs each; 5 webs admit a one-parameter group of automorphisms. 相似文献
13.
We characterize Lp norms of functions onR
n for 1<p<∞ in terms of their Gabor coefficients. Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions
of Lp functions converge to the functions almost everywhere and in Lp for 1<p<∞. In L1 we prove an analogous result: the Gabor expansions converge to the functions almost everywhere and in L1 in a certain Cesàro sense. Consequently, we are able to establish that a large class of Gabor families generate Banach frames
for Lp (R
n) when 1≤p<∞. 相似文献
14.
We consider continuous functions given on the boundary of a bounded domain D in ℂ
n
, n > 1, with the one-dimensional holomorphic extension property along families of complex lines. We study the existence of holomorphic
extensions of these functions to D depending on the dimension and location of the families of complex lines. 相似文献
15.
Eckhard Steffen 《Graphs and Combinatorics》1999,15(4):473-480
Snarks are cubic graphs with chromatic index χ′=4. A snark G is called critical if χ′ (G−{v,w})=3 for any two adjacent vertices v and w, and it is called bicritical if χ′ (G−{v,w})=3 for any two vertices v and w. We construct infinite families of critical snarks which are not bicritical. This solves a problem stated by Nedela and Škoviera.
Revised: January 11, 1999 相似文献
16.
Jawher El Goul 《manuscripta mathematica》1996,90(1):521-532
We reprove (after a paper of Y.T. Siu appeared in 1987) a simple vanishing theorem for the Wronskian of Brody curves under
a suitable assumption on the existence of global meromorphic connections. Next we give a slight improvement of a result due
to Y.T, Siu and A.M. Nadel (Duke Math. J., 1989) on the algebraic degeneracy of entire holomorphic curves contained in certain
hypersurfaces of ℙ
ℂ
n
. Especially, their result is generalized to a larger class of hypersurfaces. Our method produces algebraic families of smooth
hyperbolic surfaces in ℙ
ℂ
3
for all degreesd≥14; this brings us somewhat nearer than previously known from the expected ranged≥5. 相似文献
17.
Carlo Madonna 《Central European Journal of Mathematics》2005,3(3):404-411
By the results of the author and Chiantini in [3], on a general quintic threefold X⊂P
4 the minimum integer p for which there exists a positive dimensional family of irreducible rank p vector bundles on X without intermediate cohomology is at least three. In this paper we show that p≤4, by constructing series of positive dimensional families of rank 4 vector bundles on X without intermediate cohomology. The general member of such family is an indecomposable bundle from the extension class Ext
1 (E, F), for a suitable choice of the rank 2 ACM bundles E and F on X. The existence of such bundles of rank p=3 remains under question. 相似文献
18.
A sufficient condition is given under which an infinite computable family of Σ-1
a
-sets has computable positive but undecidable numberings, where a is a notation for a nonzero computable ordinal. This extends a theorem proved for finite levels of the Ershov hierarchy in
[1]. As a consequence, it is stated that the family of all Σ-1
a
-sets has a computable positive undecidable numbering. In addition, for every ordinal notation a > 1, an infinite family of Σ-1
a
-sets is constructed which possesses a computable positive numbering but has no computable Friedberg numberings. This answers
the question of whether such families exist at any—finite or infinite—level of the Ershov hierarchy, which was originally
raised by Badaev and Goncharov only for the finite levels bigger than 1. 相似文献
19.
Saâd Benbachir 《Numerical Algorithms》1999,21(1-4):57-77
The main aim of this work is to look for the periodic solutions of the nonintegrable Hamiltonian system of Ollongren in the
neighborhood of the origin. We apply a functional algorithm derived from the method of Lindstedt-Poincaré. We first show that
the system admits six main periodic families and then, by means of the computer algebra system “Mathematica”, compute the
series corresponding to these families up to O(ε14A29) as well as to their periods up to O(ε15A30), where A is the zeroth-order amplitude and έ is a perturbative parameter. Reducing the system to one degree of freedom we
also prove that the period of the two “oblique” periodic families is rigorously equal to a Gauss hypergeometric series. Moreover,
we study numerically the convergence of the L-P series and test the validity of these series using a numerical integration
technique. Finally, we compare our results with those of a geometrical method and a Lie series method.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
Andrew S. Raich 《Journal of Geometric Analysis》2006,16(2):353-374
We introduce classes of one-parameter families (OPF) of operators on C
c
t8
(ℂ) which characterize the behavior of operators associated to the
problem in the weighted space L2 (ℂ, e−2p) where p is a subharmonic, nonharmonic polynomial. We prove that an order 0 OPF operator extends to a bounded operator from
Lq (ℂ) to itself, 1 < q < ∞, with a bound that depends on q and the degree of p but not on the parameter τ or the coefficients
of p. Last, we show that there is a one-to-one correspondence given by the partial Fourier transform in τ between OPF operators
of order m ≤ 2 and nonisotropic smoothing (NIS) operators of order m ≤ 2 on polynomial models in ℂ2. 相似文献