共查询到20条相似文献,搜索用时 10 毫秒
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The Euclidean dimension of a graph G is the smallest integer p such that the vertices of G can be represented by points in the Euclidean space Rp with two points being 1 unit distance apart if and only if they represent adjacent vertices. We show that dim(Cm+Cn)=5 except that dim(C4+C4)=4, dim(C5+C5)=4, and dim(C6+C6)=6. 相似文献
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We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we obtain the intersections via equivariant localization with respect to a natural torus action. 相似文献
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T. Radul 《Topology and its Applications》2012,159(3):664-668
We investigate topology of the space of B-convex compacta of finite-dimensional Banach space (the notion of B-convexity space was introduced by M. Lassak). An answer to the question of M. van de Vel about a characterization of continuity of the closed B-convex hull is given. We prove that the space of B-convex compacta is a Q-manifold iff the map of the closed B-convex hull is continuous. 相似文献
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We obtain upper bounds for the Steklov eigenvalues of a smooth, compact, n-dimensional submanifold M of Euclidean space with boundary Σ that involve the intersection indices of M and of Σ. One of our main results is an explicit upper bound in terms of the intersection index of Σ, the volume of Σ and the volume of M as well as dimensional constants. By also taking the injectivity radius of Σ into account, we obtain an upper bound that has the optimal exponent of k with respect to the asymptotics of the Steklov eigenvalues as . 相似文献
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Theoretical and Mathematical Physics - We discuss the properties of second-order Killing tensors in three-dimensional Euclidean space that guarantee the existence of a third integral of motion... 相似文献
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《Topology and its Applications》1986,23(2):145-148
The algebraic functor K1 of the ring of continuous functions of three variables is computed. 相似文献
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Ishay Weissman 《Probability Theory and Related Fields》1976,37(1):35-41
Let be an Euclidean space; Y
n
, Z, U random vectors in ; h
n
, g
n
affine transformations and let þ be a subgroup of the group G of all the in vertible affine transformations, closed relative to G. Suppose that gn
and
where Z is nonsingular. The behaviour of
n
= h
n
g
n
–1
as n is discussed first. The results are used then to prove that if
for all t(0, ), where h
n
þ and Z
1 is nonsingular and nonsymmetric with respect to þ then
H,
for all t(0,) and is a continuous homomorphism of the multiplicative group of (0, ) into þ. The explicit forms of the possible are shown. 相似文献
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F. B��nger 《Advances in Computational Mathematics》2011,35(2-4):193-215
We consider the problem of minimizing or maximizing the quotient $$f_{m,n}(p,q):=\frac{\|{pq}\|}{\|{p}\|\|{q}\|} \ ,$$ where $p=p_0+p_1x+\dots+p_mx^m$ , $q=q_0+q_1x+\dots+q_nx^n\in{\mathbb K}[x]$ , ${\mathbb K}\in\{{\mathbb R},{\mathbb C}\}$ , are non-zero real or complex polynomials of maximum degree $m,n\in{\mathbb N}$ respectively and $\|{p}\|:=(|p_0|^2+\dots+|p_m|^2)^{\frac{1}{2}}$ is simply the Euclidean norm of the polynomial coefficients. Clearly f m,n is bounded and assumes its maximum and minimum values min f m,n ?=?f m,n (p min, q min) and max f m,n ?=?f(p max, q max). We prove that minimizers p min, q min for ${\mathbb K}={\mathbb C}$ and maximizers p max, q max for arbitrary ${\mathbb K}$ fulfill $\deg(p_{\min})=m=\deg(p_{\max})$ , $\deg(q_{\min})=n=\deg(q_{\max})$ and all roots of p min, q min, p max, q max have modulus one and are simple. For ${\mathbb K}={\mathbb R}$ we can only prove the existence of minimizers p min, q min of full degree m and n respectively having roots of modulus one. These results are obtained by transferring the optimization problem to that of determining extremal eigenvalues and corresponding eigenvectors of autocorrelation Toeplitz matrices. By the way we give lower bounds for min f m,n for real polynomials which are slightly better than the known ones and inclusions for max f m,n . 相似文献
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Marcos Salvai 《manuscripta mathematica》2005,118(2):181-189
We prove that the space of all oriented lines of the n-dimensional Euclidean space admits a pseudo-Riemannian metric which is invariant by the induced transitive action of a connected closed subgroup of the group of Euclidean motions, exactly when n=3 or n=7 (as usual, we consider Riemannian metrics as a particular case of pseudo-Riemannian ones). Up to equivalence, there are two such metrics for each dimension, and they are of split type and complete. Besides, we prove that the given metrics are Kähler or nearly Kähler if n=3 or n=7, respectively. 相似文献
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César Rosales Antonio Cañete Vincent Bayle Frank Morgan 《Calculus of Variations and Partial Differential Equations》2008,31(1):27-46
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize
isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions,
which lead to the conjecture that for a radial log-convex density, balls about the origin are isoperimetric regions. Finally,
we prove this conjecture and the uniqueness of minimizers for the density exp by using symmetrization techniques.
First and second authors are partially supported by MCyT-Feder research project MTM2004-01387, fourth author by the National
Science Foundation. 相似文献
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E. Kh. Gimadi A. V. Pyatkin I. A. Rykov 《Journal of Applied and Industrial Mathematics》2010,4(1):48-53
The problems under study are connected with the choice of a vector subset from a given finite set of vectors in the Euclidean
space ℝ
k
. The sum norm and averaged square of the sumnorm are considered as the target functions (to be maximized). The optimal combinatorial
algorithms with time complexity O(k
2
n
2k
) are developed for these problems. Thus, the polynomial solvability of these problems is proved for k fixed. 相似文献
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一般欧氏空间上的广义规范算子与广义规范矩阵 总被引:2,自引:0,他引:2
詹仕林 《纯粹数学与应用数学》2002,18(1):74-78
研究了一般欧氏空间上的广义规范算子与广义规范矩阵的性质。 相似文献
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Magnitude is a canonical invariant of finite metric spaces which has its origins in category theory; it is analogous to cardinality of finite sets. Here, by approximating certain compact subsets of Euclidean space with finite subsets, the magnitudes of line segments, circles and Cantor sets are defined and calculated. It is observed that asymptotically these satisfy the inclusion-exclusion principle, relating them to intrinsic volumes of polyconvex sets. 相似文献