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1.
Valentino Magnani 《Central European Journal of Mathematics》2006,4(1):82-109
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence
of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple
examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence
of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg
group. 相似文献
2.
We study the conditional sojourn time distributions of processor sharing (PS), foreground background processor sharing (FBPS)
and shortest remaining processing time first (SRPT) scheduling disciplines on an event where the job size of a customer arriving
in stationarity is smaller than exactly k≥0 out of the preceding m≥k arrivals. Then, conditioning on the preceding event, the sojourn time distribution of this newly arriving customer behaves
asymptotically the same as if the customer were served in isolation with a server of rate (1−ρ)/(k+1) for PS/FBPS, and (1−ρ) for SRPT, respectively, where ρ is the traffic intensity. Hence, the introduced notion of conditional limits allows us to distinguish the asymptotic performance
of the studied schedulers by showing that SRPT exhibits considerably better asymptotic behavior for relatively smaller jobs
than PS/FBPS.
Inspired by the preceding results, we propose an approximation to the SRPT discipline based on a novel adaptive job grouping
mechanism that uses relative size comparison of a newly arriving job to the preceding m arrivals. Specifically, if the newly arriving job is smaller than k and larger than m−k of the previous m jobs, it is routed into class k. Then, the classes of smaller jobs are served with higher priorities using the static priority scheduling. The good performance
of this mechanism, even for a small number of classes m+1, is demonstrated using the asymptotic queueing analysis under the heavy-tailed job requirements. We also discuss refinements
of the comparison grouping mechanism that improve the accuracy of job classification at the expense of a small additional
complexity.
This work is supported by NSF Grant 0615126. 相似文献
3.
Bang-Yen Chen 《Israel Journal of Mathematics》1995,91(1-3):373-391
In [3] the author initiated the study of submanifolds whose mean curvature vectorH is an eigenvector of the Laplacian Δ and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type.
The classification of surfaces with ΔH=λH in a Euclidean 3-space was done by the author in 1988. Moreover, in [4] the author classified such submanifolds in hyperbolic
spaces. In this article we study this problem for space-like submanifolds of the Minkowski space-timeE
1
m
when the submanifolds lie in a de Sitter space-time. As a result, we characterize and classify such submanifolds in de Sitter
space-times. 相似文献
4.
Yong Seung CHO Myung Im LIM 《数学学报(英文版)》2006,22(1):115-122
Let (M, ω) be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds (V^2m,ω) of (M,ω), 1 ≤m ≤ n - 1, with (m - 1)-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 (M) on π2(M) is trivial and there exists a retraction r : M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds. 相似文献
5.
Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space 总被引:1,自引:0,他引:1
We treat m-dimensional real submanifolds M of complex space forms ̿M when the maximal holomorphic tangent subspace is (m−1)-dimensional. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX,Y)−h(X,FY) = g(FX,Y)η, η∊ T⊥(M), on the structure F and on the second fundamental form h of these submanifolds. Especially when the ambient space ̿M is a complex Euclidean space, we obtain a complete classification of submanifolds M which satisfy these conditions.Mathematics Subject Classifications (2000): 53C15, 53C40, 53B20. 相似文献
6.
Avik De 《Ukrainian Mathematical Journal》2011,62(11):1803-1809
The object of the present paper is to study invariant submanifolds of a (k, μ)-contact manifold and to find the necessary and sufficient conditions for an invariant submanifold of a (k, μ)-contact manifold to be totally geodesic. 相似文献
7.
Let f(2m,k) be the Maximum k-diameter of k-regular k-connected graphs on 2m vertices. In this paper we give an algorithm and prove that we can construct k-regular k-connected graphs on 2m vertices with the maximum k-diameter using it. We also prove some known results about f(2m,k) and verify that we can get some unknown values of f(2m,k) by our algorithm.
Received: December 1, 2000 Final version received: March 12, 2002
Acknowledgments. We thank the referee for many useful suggestions. 相似文献
8.
We obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds of constant sectional curvature of space forms, which we call the L-transformation. It allows to construct a family of such submanifolds starting with a given one and a vector-valued solution of a system of linear partial differential equations. We prove a decomposition theorem for the L-transformation, which is a far-reaching generalization of the classical permutability formula for the Ribaucour transformation of surfaces of constant curvature in Euclidean three space. As a consequence, we derive a Bianchi-cube theorem, which allows to produce, from k initial scalar L-transforms of a given submanifold of constant curvature, a whole k-dimensional cube all of whose remaining \(2^k-(k+1)\) vertices are submanifolds with the same constant sectional curvature given by explicit algebraic formulae. We also obtain further reductions, as well as corresponding decomposition and Bianchi-cube theorems, for the classes of n-dimensional flat Lagrangian submanifolds of \({\mathbb {C}}^n\) and n-dimensional Lagrangian submanifolds with constant curvature c of the complex projective space \({\mathbb {C}}{\mathbb {P}}^n(4c)\) or the complex hyperbolic space \({\mathbb {C}}{\mathbb {H}}^n(4c)\) of complex dimension n and constant holomorphic curvature 4c. 相似文献
9.
10.
We study m-dimensional real submanifolds M with (m − 1)-dimensional maximal holomorphic tangent subspace in complex projective space. On these manifolds there exists an almost
contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX, Y) − h(X, FY) = g(FX, Y)η, η ∈ T
⊥(M), on the almost contact structure F and on the second fundamental form h of these submanifolds and we characterize certain model spaces in complex projective space. 相似文献
11.
We introduce a family of scalar non-conforming finite elements of arbitrary order k≥1 with respect to the H1-norm on triangles. Their vector-valued version generates together with a discontinuous pressure approximation of order k−1 an inf-sup stable finite element pair of order k for the Stokes problem in the energy norm. For k=1 the well-known Crouzeix-Raviart element is recovered. 相似文献
12.
Plamen Iliev 《Selecta Mathematica, New Series》2007,13(3):497-530
We consider the heat equation u
t
= Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients α
k
(n, m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schr?dinger operator.
We derive an explicit formula for α
k
in terms of the wave and the adjoint wave functions of the Toda lattice hierarchy. As a first application of this result,
we prove that the values of these coefficients on the diagonals n = m and n = m + 1 define a hierarchy of differential-difference equations which is equivalent to the Toda lattice hierarchy. Using this
fact and the correspondence between commutative rings of difference operators and algebraic curves we show that the fundamental
solution can be summed up, giving a finite formula involving only two Bessel functions with polynomial coefficients in the
time variable t, if and only if the operator L belongs to the family of bispectral operators constructed in [18].
相似文献
13.
We prove that each 3-connected plane graph G without triangular or quadrangular faces either contains a k-path P
k
, a path on k vertices, such that each of its k vertices has degree ≤5/3k in G or does not contain any k-path. We also prove that each 3-connected pentagonal plane graph G which has a k-cycle, a cycle on k vertices, k∈ {5,8,11,14}, contains a k-cycle such that all its vertices have, in G, bounded degrees. Moreover, for all integers k and m, k≥ 3, k∉ {5,8,11,14} and m≥ 3, we present a graph in which every k-cycle contains a vertex of degree at least m.
Received: June 29, 1998 Final version received: April 11, 2000 相似文献
14.
Plamen Iliev 《Selecta Mathematica, New Series》2008,13(3):497-530
We consider the heat equation u
t
= Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients α
k
(n, m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schr?dinger operator.
We derive an explicit formula for α
k
in terms of the wave and the adjoint wave functions of the Toda lattice hierarchy. As a first application of this result,
we prove that the values of these coefficients on the diagonals n = m and n = m + 1 define a hierarchy of differential-difference equations which is equivalent to the Toda lattice hierarchy. Using this
fact and the correspondence between commutative rings of difference operators and algebraic curves we show that the fundamental
solution can be summed up, giving a finite formula involving only two Bessel functions with polynomial coefficients in the
time variable t, if and only if the operator L belongs to the family of bispectral operators constructed in [18]. 相似文献
15.
本文研究了容有半对称度量联络的广义复空间中的子流形上的Chen-Ricci不等式.利用代数技巧,建立了子流形上的Chen-Ricci不等式.这些不等式给出了子流形的外在几何量-关于半对称联络的平均曲率与内在几何量-Ricci曲率及k-Ricci曲率之间的关系,推广了Mihai和Özgür的一些结果. 相似文献
16.
In this paper, we prove that an m-connected graph G on n vertices has a spanning tree with at most k leaves (for k ≥ 2 and m ≥ 1) if every independent set of G with cardinality m + k contains at least one pair of vertices with degree sum at least n − k + 1. This is a common generalization of results due to Broersma and Tuinstra and to Win. 相似文献
17.
Oscar Blasco 《Arkiv f?r Matematik》2000,38(1):21-36
Inequalities of the form
for allf∈H
1, where {m
k
} are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy's inequality
and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms ff atoms and that they
actually characterizeB-convexity. It is also shown that for 1<q<∞ and 0<α<∞ the spaceX=H(1,q,γa) consisting of analytic functions on the unit disc such that
satisfies the previous inequality for vector valued functions inH
1 (X), defined as the space ofX-valued Bochner integrable functions on the torus whose negative Fourier coefficients vanish, for the case {m
k
}={2k} but not for {m
k
}={k
a
} for any α ∈ N.
The author has been partially supported by the Spanish DGICYT, Proyecto PB95-0291. 相似文献
18.
The following results are proved. In Theorem 1, it is stated that there exist both finitely presented and not finitely presented
2-generated nonfree groups which are k-free-like for any k ⩾ 2. In Theorem 2, it is claimed that every nonvirtually cyclic (resp., noncyclic and torsion-free) hyperbolic m-generated group is k-free-like for every k ⩾ m + 1 (resp., k ⩾ m). Finally, Theorem 3 asserts that there exists a 2-generated periodic group G which is k-free-like for every k ⩾ 3.
Supported by NSF (grant Nos. DMS 0455881 and DMS-0700811). (A. Yu. Olshanskii, M. V. Sapir)
Supported by RFBR project No. 08-01-00573. (A. Yu. Olshanskii)
Supported by BSF grant (USA–Israel). (M. V. Sapir)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 245–257, March–April, 2009. 相似文献
19.
Goran Mui? 《The Ramanujan Journal》2012,27(2):181-208
Let Γ⊂SL
2(ℝ) be a Fuchsian group of the first kind. For a character χ of Γ→ℂ× of finite order, we define the usual space S
m
(Γ,χ) of cuspidal modular forms of weight m≥0. For each ξ in the upper half–plane and m≥3, we construct cuspidal modular forms Δ
k,m,ξ,χ
∈S
m
(Γ,χ) (k≥0) which represent the linear functionals
f?\fracdkfdzk|z=xf\mapsto\frac{d^{k}f}{dz^{k}}|_{z=\xi} in terms of the Petersson inner product. We write their Fourier expansion and use it to write an expression for the Ramanujan
Δ-function. Also, with the aid of the geometry of the Riemann surface attached to Γ, for each non-elliptic point ξ and integer m≥3, we construct a basis of S
m
(Γ,χ) out of the modular forms Δ
k,m,ξ
,χ (k≥0). For Γ=Γ
0(N), we use this to write a matrix realization of the usual Hecke operators T
p
for S
m
(N,χ). 相似文献
20.
Hom(G, H) is a polyhedral complex defined for any two undirected graphsG andH. This construction was introduced by Lovász to give lower bounds for chromatic numbers of graphs. In this paper we initiate
the study of the topological properties of this class of complexes.
We prove that Hom(K
m, Kn) is homotopy equivalent to a wedge of (n−m)-dimensional spheres, and provide an enumeration formula for the number of the spheres. As a corollary we prove that if for
some graphG, and integersm≥2 andk≥−1, we have ϖ
1
k
(Hom(K
m, G))≠0, thenχ(G)≥k+m; here ℤ2-action is induced by the swapping of two vertices inK
m, and ϖ1 is the first Stiefel-Whitney class corresponding to this action.
Furthermore, we prove that a fold in the first argument of Hom(G, H) induces a homotopy equivalence. It then follows that Hom(F, K
n) is homotopy equivalent to a direct product of (n−2)-dimensional spheres, while Hom(F, K
n) is homotopy equivalent to a wedge of spheres, whereF is an arbitrary forest andF is its complement.
The second author acknowledges support by the University of Washington, Seattle, the Swiss National Science Foundation Grant
PP002-102738/1, the University of Bern, and the Royal Institute of Technology, Stockholm. 相似文献