共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider a formally integrable, strictly pseudoconvex CR manifold M of hypersurface type, of dimension 2n?1≥7. Local CR, i.e., holomorphic, embeddings of M are known to exist from the works of Kuranishi and Akahori. We address the problem of regularity of the embedding in standard Hölder spaces C a (M), a∈R. If the structure of M is of class C m , m∈Z, 4≤m≤∞, we construct a local CR embedding near each point of M. This embedding is of class C a , for every a, 0≤a<m+(1/2). Our method is based on Henkin’s local homotopy formula for the embedded case, some very precise estimates for the solution operators in it, and a substantial modification of a previous Nash–Moser argument due to the second author. 相似文献
2.
A. A. Yakovleva 《Journal of Mathematical Sciences》2002,112(4):4414-4418
The following theorem is proved. Let n be an odd integer; if all primes that occur in the canonical decomposition of the integer
with odd multiplicities have the form
, and
, then the splitting field of the polynomial
is embeddable in a nonsplit extension of degree 48. Bibliography: 2 titles. 相似文献
3.
The problem of embedding a quadratic extension of a number field into an extension with a cyclic 2-group is studied. We prove a reduction theorem showing that, under the compatibility condition, an additional embedding condition consists of the solvability of a problem with cyclic kernel of order 16 (of course, if the degree of the required field is no less than 16). An additional condition of embedding into a field of degree 16 is found; namely, the number generating the given quadratic extension must be a norm in a cyclotomic field containing the primitive eighth roots of unity. For Q, the embedding condition is simpler: all the odd prime divisors of the generating element must be congruent with 1 modulo the order of the extension group. In addition, the quadratic extension must be real. Bibliography: 7 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 144–152. 相似文献
4.
Richard Moeckel 《Regular and Chaotic Dynamics》2018,23(6):695-703
Solutions of the planar Kepler problem with fixed energy h determine geodesics of the corresponding Jacobi–Maupertuis metric. This is a Riemannian metric on ?2 if h ? 0 or on a disk D ? ?2 if h < 0. The metric is singular at the origin (the collision singularity) and also on the boundary of the disk when h < 0. The Kepler problem and the corresponding metric are invariant under rotations of the plane and it is natural to wonder whether the metric can be realized as a surface of revolution in ?3 or some other simple space. In this note, we use elementary methods to study the geometry of the Kepler metric and the embedding problem. Embeddings of the metrics with h ? 0 as surfaces of revolution in ?3 are constructed explicitly but no such embedding exists for h < 0 due to a problem near the boundary of the disk. We prove a theorem showing that the same problem occurs for every analytic central force potential. Returning to the Kepler metric, we rule out embeddings in the three-sphere or hyperbolic space, but succeed in constructing an embedding in four-dimensional Minkowski spacetime. Indeed, there are many such embeddings. 相似文献
5.
本文提出并解决了初等图形在球面型空间实现的问题: 预给两两之间度量的几何元素e1,e2…,el-1,el+1,…,eN(ei为点或超平面),初等图形{e1,…,el-1,el+1,…,eN}在球面型空间实现的充分必要条件是什么? 相似文献
6.
Thomas Andreae 《Results in Mathematics》2002,41(1-2):18-25
Recent results on the immersion relation for graphs are applied to show that there exist (uncountable) graphs A and G such that G contains n disjoint copies of A for each positive integer n, but the graph N0A consisting of infinitely many disjoint copies of A does not embed in G, where by ‘embedding’ we mean ‘immersion in the weak sense’. 相似文献
7.
A criticism sometimes made of dynamic programming is that in deterministic problems, optimal decisions are calculated which are never needed, as the decisions relate to states which never arise. In this paper we describe how some of these "redundant" calculations have been used, in a certain problem, to derive a working rule of general validity.The problem concerns the installation and replacement of an item of electrical equipment at a large number of sites, to meet a known load at each site which increases exponentially at a known rate. 相似文献
8.
9.
Ning Zhu 《偏微分方程(英文版)》1996,9(2):129-138
In this paper, we consider the Cauchy problem \frac{∂u}{∂t} = Δφ(u) in R^N × (0, T] u(x,0} = u_0(x) in R^N where φ ∈ C[0,∞) ∩ C¹(0,∞), φ(0 ) = 0 and (1 - \frac{2}{N})^+ < a ≤ \frac{φ'(s)s}{φ(s)} ≤ m for some a ∈ ((1 - \frac{2}{n})^+, 1), s > 0. The initial value u_0 (z) satisfies u_0(x) ≥ 0 and u_0(x) ∈ L¹_{loc}(R^N). We prove that, under some further conditions, there exists a weak solution u for the above problem, and moreover u ∈ C^{α, \frac{α}{2}}_{x,t_{loc}} (R^N × (0, T]) for some α > 0. 相似文献
10.
本文讨论非线性奇异抛物方程第一边值问题解的存在性、唯一性、稳定性以及当t充分大时解的渐近性态.利用先验估计的方法得到:存在唯一的光滑正解,解在L^1范数意义下连续依赖于初值.t充分大时,||u-u↑-||L^2收敛于一个常数. 相似文献
11.
It is proved that the universally solvable embedding problem with cyclic kernel of odd order is semidirect. Bibliography: 4 titles. 相似文献
12.
In this paper we solve the embedding problem for partial transitivetriple systems of order n and index , partial TTS(n, ) s, showingthat any partial TTS(n, ) can be embedded in a TTS(v, ) forall -admissible v 2n + 1. This lower bound on v is the bestpossible. A simple proof is also given of a result of Colbournand Harms which shows that every partial triple system of ordern and index 2 is the underlying triple system of a partial TTS(n,). 1991 Mathematics Subject Classification 05B07. 相似文献
13.
Let H : Lp ( R ) → Lp( R ), 1 < p < ∞ be the real HILBERT transform. A bounded, linear operator u:E → F (E, F BANACH spaces) is a HT-operator, if the mapping u ? H : E ? L2( R , E) → L2( R , F) has a bounded, linear extension to L2( R ) → L2( R , F). For E = F and u = idE BOURGAIN [3] and BURKHOLDER [5] have shown that this holds if and only if E ? UMD. We study these HT-operators and, in particular, we construct a HT-operator which is not UMD-factorable. Furthermore, we show that a UMD-space E is a HILBERT space if and only if |idE ? H| = 1. 相似文献
14.
Seongchan Kim 《Regular and Chaotic Dynamics》2018,23(3):304-324
In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body. 相似文献
15.
Chan-Gyun Kim 《Acta Appl Math》2010,112(1):79-90
In this study, using a fixed point index theorem on a cone, we present some existence results for one or multiple positive
solutions to the m-point boundary value problem with a nonlinear term which does not satisfy the L
1-Carathéodory condition. 相似文献
16.
Some properties of extremal functions in the inequality
are studied. Bibliography: 10 titles. 相似文献
17.
18.
It is proved that the universally solvable embedding problem with cyclic kernel of order 8 is semidirect. Bibliography: 4 titles. 相似文献
19.
Let n1 and let p be a prime. Expand j[0,p
n
–1]\(p) p-adically as j=
s0
a
s
p
s
with a
s
[0,p–1]. The #([0,j]\(p))th Z
(p)[
p
n
]-linear elementary divisor of the cyclotomic Dedekind embedding
has valuation
at 1–
p
n
. There is a similar result for the related cyclic Wedderburn embedding. 相似文献
20.
In this paper, we consider a q-difference equation $$\sum_{j=0}^{k}\sum_{t=1}^{\infty}C_{t,j}(z)(y(q^jz))^{t}=G(z)$$ in the complex field ${\mathbb C,}$ where C t,j (z) and G(z) have a h 1 order pole and a h 2 order pole at z = 0, respectively. Under the case 0 < |q| < 1 or |q| = 1, we give the existence of local analytic solutions for the above equation by using small divisor theory in dynamical systems. 相似文献