共查询到20条相似文献,搜索用时 125 毫秒
1.
G. van der Laan A. J. J. Talman Z. Yang 《Journal of Optimization Theory and Applications》2010,144(2):391-407
Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set
{±1,±2,…,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits
a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite
set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1,±2,…,±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some
mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0,1}
n
+q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations
under certain natural conditions. An economic application is provided. 相似文献
2.
Pseudo-differential and Fourier series operators on the torus
\mathbbTn=(\BbbR/2p\BbbZ)n{{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}
are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal
symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is
established. Periodization of operators and hyperbolic partial differential equations is discussed. Fourier series operators,
which are analogues of Fourier integral operators on the torus, are introduced, and formulae for their compositions with pseudo-differential
operators are derived. It is shown that pseudo-differential and Fourier series operators are bounded on L
2 under certain conditions on their phases and amplitudes. 相似文献
3.
Reiner Wolff 《TOP》2009,17(2):433-439
Rabbi Moshe ben Maimon (1135–1204), known as Moses Maimonides, ranks among the most distinguished philosophers of the Middle
Ages. He is the renowned author of the Mishneh Torah, a comprehensive code of Jewish law. Book 12 (“Book of Acquisition”),
Treatise 4 (“Agents and Partners”), of the Code of Maimonides is devoted in Chapter 4 to the allocation of the surplus from
funds which a partnership invests in an indivisible input. The Rabbi’s case translates into a cooperative game where all intermediate
coalitions are inessential. Standard axioms for cooperative-game solutions then suggest that the surplus be shared equally
by the players, which is precisely the Maimonidean ruling. We show that this outcome can be preserved in spirit under much
weaker assumptions on the worth of a game’s intermediate coalitions. We present results both for the nucleolus and the Shapley
value of the underlying class of games. 相似文献
4.
For a finite triangulation of the plane with faces properly coloured white and black, let
AW\mathcal{A}_{W}
be the abelian group constructed by labelling the vertices with commuting indeterminates and adding relations which say that
the labels around each white triangle add to the identity. We show that
AW\mathcal{A}_{W}
has free rank exactly two. Let
AW*\mathcal{A}_{W}^{*}
be the torsion subgroup of
AW\mathcal{A}_{W}
, and
AB*\mathcal{A}_{B}^{*}
the corresponding group for the black triangles. We show that
AW*\mathcal{A}_{W}^{*}
and
AB*\mathcal{A}_{B}^{*}
have the same order, and conjecture that they are isomorphic.
For each spherical latin trade W, we show there is a unique disjoint mate B such that (W,B) is a connected and separated bitrade. The bitrade (W,B) is associated with a two-colourable planar triangulation and we show that W can be embedded in
AW*\mathcal{A}_{W}^{*}
, thereby proving a conjecture due to Cavenagh and Drápal. The proof involves constructing a (0,1) presentation matrix whose
permanent and determinant agree up to sign. The Smith normal form of this matrix determines
AW*\mathcal{A}_{W}^{*}
, so there is an efficient algorithm to construct the embedding. Contrasting with the spherical case, for each genus g≥1 we construct a latin trade which is not embeddable in any group and another that is embeddable in a cyclic group. 相似文献
5.
In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation
of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence
relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation
allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed
orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed.
Finally, a Markov’s type theorem is presented. 相似文献
6.
Zhaoxiang Li Erling Wei Jie Xu Yanpei Liu 《Journal of Applied Mathematics and Computing》2010,34(1-2):71-80
This paper provides the chromatic sum function equations of rooted 2-edge-connected maps on the projective plane. The enumerating function equations of rooted 2-edge-connected loopless maps and rooted 2-edge-connected bipartite maps on the projective plane are derived by the chromatic sum function equation of rooted 2-edge-connected maps on the projective plane. 相似文献
7.
Alex Shenfield Peter J. Fleming Visakan Kadirkamanathan Jeff Allan 《Annals of Operations Research》2010,180(1):213-231
The emerging paradigm of Grid Computing provides a powerful platform for the optimisation of complex computer models, such
as those used to simulate real-world logistics and supply chain operations. This paper introduces a Grid-based optimisation
framework that provides a powerful tool for the optimisation of such computationally intensive objective functions. This framework
is then used in the optimisation of maintenance scheduling strategies for fleets of aero-engines, a computationally intensive
problem with a high-degree of stochastic noise, achieving substantial improvements in the execution time of the algorithm. 相似文献
8.
In this article we establish a local parabolic almost monotonicity formula for two-phase free boundary problems on Riemannian
manifolds. 相似文献
9.
M. M. H. Pang 《Semigroup Forum》2009,78(2):238-252
We adapt a method originally developed by E.B. Davies for second order elliptic operators to obtain an upper heat kernel bound
for the Laplacian defined on a uniform grid on the plane. 相似文献
10.
Let Π n d denote the space of all spherical polynomials of degree at most n on the unit sphere $\mathbb{S}^{d}Let Π
n
d
denote the space of all spherical polynomials of degree at most n on the unit sphere
\mathbbSd\mathbb{S}^{d}
of ℝ
d+1, and let d(x,y) denote the geodesic distance arccos x⋅y between
x,y ? \mathbbSdx,y\in\mathbb{S}^{d}
. Given a spherical cap
B(e,a)={x ? \mathbbSd:d(x,e) £ a} (e ? \mathbbSd, a ? (0,p) is bounded awayfrom p),B(e,\alpha)=\big\{x\in\mathbb{S}^{d}:d(x,e)\leq\alpha\big\}\quad \bigl(e\in\mathbb{S}^{d},\ \alpha\in(0,\pi)\ \mbox{is bounded awayfrom}\ \pi\bigr), 相似文献
11.
A new generalized Radon transform R
α, β
on the plane for functions even in each variable is defined which has natural connections with the bivariate Hankel transform,
the generalized biaxially symmetric potential operator Δ
α, β
, and the Jacobi polynomials Pk(b, a)(t)P_{k}^{(\beta,\,\alpha)}(t). The transform R
α, β
and its dual Ra, b*R_{\alpha,\,\beta}^{\ast} are studied in a systematic way, and in particular, the generalized Fuglede formula and some inversion formulas for R
α, β
for functions in
La, bp(\mathbbR2+)L_{\alpha,\,\beta}^{p}(\mathbb{R}^{2}_{+}) are obtained in terms of the bivariate Hankel–Riesz potential. Moreover, the transform R
α, β
is used to represent the solutions of the partial differential equations Lu:=?j=1majDa, bju=fLu:=\sum_{j=1}^{m}a_{j}\Delta_{\alpha,\,\beta}^{j}u=f with constant coefficients a
j
and the Cauchy problem for the generalized wave equation associated with the operator Δ
α, β
. Another application is that, by an invariant property of R
α, β
, a new product formula for the Jacobi polynomials of the type Pk(b, a)(s)C2ka+b+1(t)=còòPk(b, a)P_{k}^{(\beta,\,\alpha)}(s)C_{2k}^{\alpha+\beta+1}(t)=c\int\!\!\int P_{k}^{(\beta,\,\alpha)} is obtained. 相似文献
12.
A k-dimensional box is a Cartesian product R
1 × · · · × R
k
where each R
i
is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. That is, two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc
graph is a graph that can be represented as the intersection graph of arcs on a circle. We show that if G is a circular arc graph which admits a circular arc representation in which no arc has length at least
p(\fraca-1a){\pi(\frac{\alpha-1}{\alpha})} for some
a ? \mathbbN 3 2{\alpha\in\mathbb{N}_{\geq 2}}, then box(G) ≤ α (Here the arcs are considered with respect to a unit circle). From this result we show that if G has maximum degree
D < ?\fracn(a-1)2a?{\Delta < \lfloor{\frac{n(\alpha-1)}{2\alpha}}\rfloor} for some
a ? \mathbbN 3 2{\alpha \in \mathbb{N}_{\geq 2}}, then box(G) ≤ α. We also demonstrate a graph having box(G) > α but with
D = n\frac(a-1)2a+ \fracn2a(a+1)+(a+2){\Delta=n\frac{(\alpha-1)}{2\alpha}+ \frac{n}{2\alpha(\alpha+1)}+(\alpha+2)}. For a proper circular arc graph G, we show that if
D < ?\fracn(a-1)a?{\Delta < \lfloor{\frac{n(\alpha-1)}{\alpha}}\rfloor} for some
a ? \mathbbN 3 2{\alpha\in \mathbb{N}_{\geq 2}}, then box(G) ≤ α. Let r be the cardinality of the minimum overlap set, i.e. the minimum number of arcs passing through any point on the circle, with
respect to some circular arc representation of G. We show that for any circular arc graph G, box(G) ≤ r + 1 and this bound is tight. We show that if G admits a circular arc representation in which no family of k ≤ 3 arcs covers the circle, then box(G) ≤ 3 and if G admits a circular arc representation in which no family of k ≤ 4 arcs covers the circle, then box(G) ≤ 2. We also show that both these bounds are tight. 相似文献
13.
Alessio Martini 《Mathematische Zeitschrift》2010,265(4):831-848
The Heisenberg–Pauli–Weyl (HPW) uncertainty inequality on
\mathbbRn{\mathbb{R}^n} says that
|