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1.
For a smooth irreducible complete algebraic curveC the “gaps” are the integersn such that every linear series of degreen has at least a base point. The Lüroth semigroup SC of a curveC is the subsemigroup ofN whose elements are not gaps. In this paper we deal with irreducible smooth curves of type (a, b) on a smooth quadricQ. The main result is an algorithm by which we can say if some integer λ∈N is a gap or is in SC. In the general case there are integers λ which are undecidable. For curves such as complete intersection, arithmetically
Cohen-Macaulay or Buchsbaum, we are able to describe explicitly “intervals” of gaps and “intervals” of integers which belong
to SC. For particular cases we can completely determine SC, by giving just the type of the curve (in particular the degree and the genus).
Work done with financial support of M.U.R.S.T. while the authors were members of G.N.S.A.G.A. of C.N.R. 相似文献
2.
We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers
of
\mathbbP1{{\mathbb{P}_1}} with given ramification over ∞ and sufficiently many fixed ramification points elsewhere. Degeneration of the target and
judicious localization expresses such classes in terms of localization trees weighted by “top intersections” of tautological
classes and genus 0 double Hurwitz numbers. This identity of generating series can be inverted, yielding a “combinatorialization”
of top intersections of Y{\Psi} -classes. As genus 0 double Hurwitz numbers with at most 3 parts over ∞ are well understood, we obtain Faber’s Intersection
Number Conjecture for up to 3 parts, and an approach to the Conjecture in general (bypassing the Virasoro Conjecture). We
also recover other geometric results in a unified manner, including Looijenga’s theorem, the socle theorem for curves with
rational tails, and the hyperelliptic locus in terms of κ
g–2. 相似文献
3.
Jacob Feldman 《Israel Journal of Mathematics》1980,36(3-4):321-345
A new approach is given to the entropy of a probability-preserving group action (in the context ofZ and ofR
n
), by defining an approximate “r-entropy”, 0<r<1, and lettingr → 0. If the usual entropy may be described as the growth rate of the number of essential names, then ther-entropy is the growth rate of the number of essential “groups of names” of width≦r, in an appropriate sense. The approach is especially useful for actions of continuous groups. We apply these techniques to
state and prove a “second order” equipartition theorem forZ
m
×R
n
and to give a “natural” proof of Ornstein’s isomorphism theorem for Bernoulli actions ofZ
m
×R
n
, as well as a characterization of such actions which seems to be the appropriate generalization of “finitely determined”. 相似文献
4.
In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low regularity, where
the nonlinear term depends on u and ∂
t
u. We prove a ill-posedness result for the “defocusing” case, and give an alternative proof for the supercritical “focusing”
case, which improves the result in Fang and Wang (Chin. Ann. Math. Ser. B 26(3), 361–378, 2005).
Supported by NSF of China 10571158. 相似文献
5.
6.
O. D. Frolkina 《Moscow University Mathematics Bulletin》2009,64(6):253-258
In 1998, Y. Benyamini published interesting results concerning interpolation of sequences using continuous functions ℝ → ℝ.
In particular, he proved that there exists a continuous function ℝ → ℝ which in some sense “interpolates” all sequences (x
n
)
n∈ℤ ∈ [0, 1]ℤ “simultaneously.” In 2005, M.R. Naulin and C. Uzcátegui unified and generalized Benyamini’s results. In this paper, the case
of topological spaces X and Y with an Abelian group acting on X is considered. A similar problem of “simultaneous interpolation” of all “generalized sequences” using continuous mappings
X → Y is posed. Further generalizations of Naulin-Uncátegui theorems, in particular, multidimensional analogues of Benyamini’s
results are obtained. 相似文献
7.
We prove, outside the influence region of a ball of radius R
0 centred in the origin of the initial data hypersurface, Σ0, the existence of global solutions near to Kerr spacetime, provided that the initial data are sufficiently near to those
of Kerr. This external region is the “far” part of the outer region of the perturbed Kerr spacetime. Moreover, if we assume
that the corrections to the Kerr metric decay sufficiently fast, o(r
−3), we prove that the various null components of the Riemann tensor decay in agreement with the “Peeling theorem”. 相似文献
8.
Summary Let Lεu and L
0
v be the elliptic and “backward” heat operators defined by(1.1) and(1.2), respectively. The following question is considered for a pair of “non-well posed” initial-boundary value problems for Lε and L
0
: if u and v are the respective solutions, under what restrictions on the classes of admissible solutions and in what sense,
if any, does u converge to v as ɛ →0?
This research was supported in part by the National Science Foundation Grant No. GP 5882 with Cornell University. 相似文献
9.
Lower bounds are obtained for thegl constants and hence also for the unconditional basis constants of subspaces of finite dimensional Banach spaces. Sharp results
are obtained for subspaces ofl
∞
n
, while in the general case thegl constants of “random large” subspaces are related to the distance of “random large” subspaces to Euclidean spaces. In addition,
a new isometric characterization ofl
∞
n
is given, some new information is obtained concerningp-absolutely summing operators, and it is proved that every Banach space of dimensionn contains a subspace whose projection constant is of ordern
1/2.
The research for this paper was begun while both authors were guests of the Mittag-Leffler Institute.
Supported in part by NSF-MCS 79-03042. 相似文献
10.
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
11.
We describe a tower of spaces whose inverse limit is a “fiberwise completion” of a fibrationE →B, and study the resulting spectral sequence converging to the homotopy groups of the space of lifts of a mapX →B. This is used to give a proof of the “generalized Sullivan conjecture”.
All three authors were supported in part by the National Science Foundation. 相似文献
12.
S. V. Talalov 《Theoretical and Mathematical Physics》2010,165(2):1517-1526
We construct an infinite-dimensional dynamical Hamiltonian system that can be interpreted as a localized structure (“quasiparticle”)
on the plane E
2. The model is based on the theory of an infinite string in the Minkowski space E
1,3
formulated in terms of the second fundamental forms of the worldsheet. The model phase space H is parameterized by the coordinates,
which are interpreted as “internal” (E(2)-invariant) and “external” (elements of T*E
2) degrees of freedom. The construction is nontrivial because H contains a finite number of constraints entangling these two
groups of coordinates. We obtain the expressions for the energy and for the effective mass of the constructed system and the
formula relating the proper angular momentum and the energy. We consider a possible interpretation of the proposed construction
as an anyon model. 相似文献
13.
The purpose of this paper is to study the L
2 boundedness of operators of the form f ↦ ψ(x) ∫ f (γ
t
(x))K(t)dt, where γ
t
(x) is a C
∞ function defined on a neighborhood of the origin in (t, x) ∈ ℝ
N
× ℝ
n
, satisfying γ
0(x) ≡ x, ψ is a C
∞ cut-off function supported on a small neighborhood of 0 ∈ ℝ
n
, and K is a “multi-parameter singular kernel” supported on a small neighborhood of 0 ∈ ℝ
N
. The goal is, given an appropriate class of kernels K, to give conditions on γ such that every operator of the above form is bounded on L
2. The case when K is a Calderón-Zygmund kernel was studied by Christ, Nagel, Stein, and Wainger; we generalize their conditions to the case
when K has a “multi-parameter” structure. For example, when K is given by a “product kernel.” Even when K is a Calderón- Zygmund kernel, our methods yield some new results. This is the first paper in a three part series, the later
two of which are joint with E. M. Stein. The second paper deals with the related question of L
p
boundedness, while the third paper deals with the special case when γ is real analytic. 相似文献
14.
This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS(e) - CS(e) = degA, where e and e are two (global) frames of M, and A : M → SO(3) is the "difference" map. An interesting phenomenon is that the "jumps" of the Chern-Simons integrals for various frames of many 3-manifolds are at least two, instead of one. The second purpose is to give an explicit representation of CS(e+) and CS(e_), where e+ and e_ are the "left" and "right" quaternionic frames on M3 induced from an immersion M^3 → E^4, respectively. Consequently we find many metrics on S^3 (Berger spheres) so that they can not be conformally embedded in E^4. 相似文献
15.
Chafik Samir P.-A. Absil Anuj Srivastava Eric Klassen 《Foundations of Computational Mathematics》2012,12(1):49-73
Given data points p
0,…,p
N
on a closed submanifold M of ℝ
n
and time instants 0=t
0<t
1<⋅⋅⋅<t
N
=1, we consider the problem of finding a curve γ on M that best approximates the data points at the given instants while being as “regular” as possible. Specifically, γ is expressed as the curve that minimizes the weighted sum of a sum-of-squares term penalizing the lack of fitting to the
data points and a regularity term defined, in the first case as the mean squared velocity of the curve, and in the second
case as the mean squared acceleration of the curve. In both cases, the optimization task is carried out by means of a steepest-descent
algorithm on a set of curves on M. The steepest-descent direction, defined in the sense of the first-order and second-order Palais metric, respectively, is
shown to admit analytical expressions involving parallel transport and covariant integral along curves. Illustrations are
given in ℝ
n
and on the unit sphere. 相似文献
16.
A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures
of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that quasirandomness
can often be measured by means of certain easily described norms, known as uniformity norms. However, determining which uniformity
norms work for which structures turns out to be a surprisingly hard question. In [GW10a] and [GW10b], [GW10c], we gave a complete answer to this question for groups of the form G = F
p
n
, provided p is not too small. In ℤ
N
, substantial extra difficulties arise, of which the most important is that an “inverse theorem” even for the uniformity norm
|| ·||U3{\left\| \cdot \right\|_{{U^3}}} requires a more sophisticated “local” formulation. When N is prime, ℤ
N
is not rich in subgroups, so one must use regular Bohr neighbourhoods instead. In this paper, we prove the first non-trivial
case of the main conjecture from [GW10a]. Moreover, we obtain a doubly exponential bound. 相似文献
17.
The main goal of the article is to show that Paley-Wiener functions ƒ ∈ L
2(M) of a fixed band width to on a Riemannian manifold of bounded geometry M completely determined and can be reconstructed
from a set of numbers Φi (ƒ), i ∈ ℕwhere Φi
is a countable sequence of weighted integrals over a collection of “small” and “densely” distributed compact subsets. In particular, Φi, i ∈ ℕ,can be a sequence of weighted Dirac measures δxi, xi ∈M.
It is shown that Paley-Wiener functions on M can be reconstructed as uniform limits of certain variational average spline
functions.
To obtain these results we establish certain inequalities which are generalizations of the Poincaré-Wirtingen and Plancherel-Polya
inequalities.
Our approach to the problem and most of our results are new even in the one-dimensional case. 相似文献
18.
Andrew Putman 《Geometric And Functional Analysis》2009,19(2):591-643
In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose
generators consist of the set of all “separating twists”, all “bounding pair maps”, and all “commutators of simply intersecting
pairs” and whose relations all come from a short list of topological configurations of these generators on the surface. Aside
from a few obvious ones, all of these relations come from a set of embeddings of groups derived from surface groups into the
Torelli group. In the process of analyzing these embeddings, we derive a novel presentation for the fundamental group of a
closed surface whose generating set is the set of all simple closed curves. 相似文献
19.
D. A. Korotkin 《Journal of Mathematical Sciences》1997,85(1):1684-1697
It is shown that the general local solution of the self-duality equation with SU(1,1) and SU(2) gauge groups is associated with some algebraic curve with moving branch points if the related “monodromy matrix” is rational.
The “multisoliton” solutions including monopoles and instantons, correspond to degenerate curves when the branch cuts collapse
to double points. Bibliography:18 titles.
Dedicated to L. D. Faddeev on the occasion of his 60th birthday
Published inZapiski Nauchnykh Seminarov POMI, Vol. 215, 1994, pp. 197–216.
Translated by D. A. Korotkin. 相似文献
20.
Rubber rolling over a sphere 总被引:2,自引:2,他引:0
“Rubber” coated bodies rolling over a surface satisfy a no-twist condition in addition to the no slip condition satisfied
by “marble” coated bodies [1]. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures
of the curves on the surfaces at corresponding points are equal. The associated distribution in the 5 dimensional configuration
space has 2–3–5 growth (these distributions were first studied by Cartan; he showed that the maximal symmetries occurs for
rubber rolling of spheres with 3:1 diameters ratio and materialize the exceptional group G
2). The 2–3–5 nonholonomic geometries are classified in a companion paper [2] via Cartan’s equivalence method [3]. Rubber rolling
of a convex body over a sphere defines a generalized Chaplygin system [4–8] with SO(3) symmetry group, total space Q = SO(3) × S
2 and base S
2, that can be reduced to an almost Hamiltonian system in T*S
2 with a non-closed 2-form ωNH. In this paper we present some basic results on the sphere-sphere problem: a dynamically asymmetric but balanced sphere of
radius b (unequal moments of inertia I
j but with center of gravity at the geometric center), rubber rolling over another sphere of radius a. In this example ωNH is conformally symplectic [9]: the reduced system becomes Hamiltonian after a coordinate dependent change of time. In particular
there is an invariant measure, whose density is the determinant of the reduced Legendre transform, to the power p = 1/2(b/a − 1). Using sphero-conical coordinates we verify the result by Borisov and Mamaev [10] that the system is integrable for
p = −1/2 (ball over a plane). They have found another integrable case [11] corresponding to p = −3/2 (rolling ball with twice the radius of a fixed internal ball). Strikingly, a different set of sphero-conical coordinates
separates the Hamiltonian in this case. No other integrable cases with different I
j are known.
相似文献